diff --git a/books/bookvol10.3.pamphlet b/books/bookvol10.3.pamphlet index 3beba17..6bf7891 100644 --- a/books/bookvol10.3.pamphlet +++ b/books/bookvol10.3.pamphlet @@ -258,26 +258,27 @@ in the bootstrap set. Thus, --S 1 of 1 )show AffinePlane ---R AffinePlane K: Field is a domain constructor +--R +--R AffinePlane(K: Field) is a domain constructor --R Abbreviation for AffinePlane is AFFPL --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for AFFPL --R --R------------------------------- Operations -------------------------------- ---R ?=? : (%,%) -> Boolean affinePoint : List K -> % ---R coerce : List K -> % coerce : % -> List K +--R ?=? : (%,%) -> Boolean affinePoint : List(K) -> % +--R coerce : List(K) -> % coerce : % -> List(K) --R coerce : % -> OutputForm conjugate : % -> % --R definingField : % -> K degree : % -> PositiveInteger --R ?.? : (%,Integer) -> K hash : % -> SingleInteger ---R latex : % -> String list : % -> List K ---R orbit : % -> List % origin : () -> % ---R pointValue : % -> List K rational? : % -> Boolean +--R latex : % -> String list : % -> List(K) +--R orbit : % -> List(%) origin : () -> % +--R pointValue : % -> List(K) rational? : % -> Boolean --R setelt : (%,Integer,K) -> K ?~=? : (%,%) -> Boolean --R conjugate : (%,NonNegativeInteger) -> % ---R orbit : (%,NonNegativeInteger) -> List % +--R orbit : (%,NonNegativeInteger) -> List(%) --R rational? : (%,NonNegativeInteger) -> Boolean ---R removeConjugate : List % -> List % ---R removeConjugate : (List %,NonNegativeInteger) -> List % +--R removeConjugate : List(%) -> List(%) +--R removeConjugate : (List(%),NonNegativeInteger) -> List(%) --R --E 1 @@ -336,7 +337,8 @@ AffinePlane(K):Exports == Implementation where --S 1 of 1 )show AffinePlaneOverPseudoAlgebraicClosureOfFiniteField ---R AffinePlaneOverPseudoAlgebraicClosureOfFiniteField K: FiniteFieldCategory is a domain constructor +--R +--R AffinePlaneOverPseudoAlgebraicClosureOfFiniteField(K: FiniteFieldCategory) is a domain constructor --R Abbreviation for AffinePlaneOverPseudoAlgebraicClosureOfFiniteField is AFFPLPS --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for AFFPLPS @@ -345,21 +347,21 @@ AffinePlane(K):Exports == Implementation where --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R conjugate : % -> % degree : % -> PositiveInteger --R hash : % -> SingleInteger latex : % -> String ---R orbit : % -> List % origin : () -> % +--R orbit : % -> List(%) origin : () -> % --R rational? : % -> Boolean ?~=? : (%,%) -> Boolean ---R affinePoint : List PseudoAlgebraicClosureOfFiniteField K -> % ---R coerce : List PseudoAlgebraicClosureOfFiniteField K -> % ---R coerce : % -> List PseudoAlgebraicClosureOfFiniteField K +--R affinePoint : List(PseudoAlgebraicClosureOfFiniteField(K)) -> % +--R coerce : List(PseudoAlgebraicClosureOfFiniteField(K)) -> % +--R coerce : % -> List(PseudoAlgebraicClosureOfFiniteField(K)) --R conjugate : (%,NonNegativeInteger) -> % ---R definingField : % -> PseudoAlgebraicClosureOfFiniteField K ---R ?.? : (%,Integer) -> PseudoAlgebraicClosureOfFiniteField K ---R list : % -> List PseudoAlgebraicClosureOfFiniteField K ---R orbit : (%,NonNegativeInteger) -> List % ---R pointValue : % -> List PseudoAlgebraicClosureOfFiniteField K +--R definingField : % -> PseudoAlgebraicClosureOfFiniteField(K) +--R ?.? : (%,Integer) -> PseudoAlgebraicClosureOfFiniteField(K) +--R list : % -> List(PseudoAlgebraicClosureOfFiniteField(K)) +--R orbit : (%,NonNegativeInteger) -> List(%) +--R pointValue : % -> List(PseudoAlgebraicClosureOfFiniteField(K)) --R rational? : (%,NonNegativeInteger) -> Boolean ---R removeConjugate : List % -> List % ---R removeConjugate : (List %,NonNegativeInteger) -> List % ---R setelt : (%,Integer,PseudoAlgebraicClosureOfFiniteField K) -> PseudoAlgebraicClosureOfFiniteField K +--R removeConjugate : List(%) -> List(%) +--R removeConjugate : (List(%),NonNegativeInteger) -> List(%) +--R setelt : (%,Integer,PseudoAlgebraicClosureOfFiniteField(K)) -> PseudoAlgebraicClosureOfFiniteField(K) --R --E 1 @@ -436,26 +438,27 @@ AffinePlaneOverPseudoAlgebraicClosureOfFiniteField(K):Exports == Impl where --S 1 of 1 )show AffineSpace +--R --R AffineSpace(dim: NonNegativeInteger,K: Field) is a domain constructor --R Abbreviation for AffineSpace is AFFSP --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for AFFSP --R --R------------------------------- Operations -------------------------------- ---R ?=? : (%,%) -> Boolean affinePoint : List K -> % ---R coerce : List K -> % coerce : % -> List K +--R ?=? : (%,%) -> Boolean affinePoint : List(K) -> % +--R coerce : List(K) -> % coerce : % -> List(K) --R coerce : % -> OutputForm conjugate : % -> % --R definingField : % -> K degree : % -> PositiveInteger --R ?.? : (%,Integer) -> K hash : % -> SingleInteger ---R latex : % -> String list : % -> List K ---R orbit : % -> List % origin : () -> % ---R pointValue : % -> List K rational? : % -> Boolean +--R latex : % -> String list : % -> List(K) +--R orbit : % -> List(%) origin : () -> % +--R pointValue : % -> List(K) rational? : % -> Boolean --R setelt : (%,Integer,K) -> K ?~=? : (%,%) -> Boolean --R conjugate : (%,NonNegativeInteger) -> % ---R orbit : (%,NonNegativeInteger) -> List % +--R orbit : (%,NonNegativeInteger) -> List(%) --R rational? : (%,NonNegativeInteger) -> Boolean ---R removeConjugate : List % -> List % ---R removeConjugate : (List %,NonNegativeInteger) -> List % +--R removeConjugate : List(%) -> List(%) +--R removeConjugate : (List(%),NonNegativeInteger) -> List(%) --R --E 1 @@ -618,7 +621,8 @@ AffineSpace(dim,K):Exports == Implementation where --S 1 of 1 )show AlgebraGivenByStructuralConstants ---R AlgebraGivenByStructuralConstants(R: Field,n: PositiveInteger,ls: List Symbol,gamma: Vector Matrix R) is a domain constructor +--R +--R AlgebraGivenByStructuralConstants(R: Field,n: PositiveInteger,ls: List(Symbol),gamma: Vector(Matrix(R))) is a domain constructor --R Abbreviation for AlgebraGivenByStructuralConstants is ALGSC --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ALGSC @@ -632,59 +636,59 @@ AffineSpace(dim,K):Exports == Implementation where --R ?=? : (%,%) -> Boolean 0 : () -> % --R alternative? : () -> Boolean antiAssociative? : () -> Boolean --R antiCommutative? : () -> Boolean antiCommutator : (%,%) -> % ---R apply : (Matrix R,%) -> % associative? : () -> Boolean ---R associator : (%,%,%) -> % basis : () -> Vector % ---R coerce : Vector R -> % coerce : % -> OutputForm +--R apply : (Matrix(R),%) -> % associative? : () -> Boolean +--R associator : (%,%,%) -> % basis : () -> Vector(%) +--R coerce : Vector(R) -> % coerce : % -> OutputForm --R commutative? : () -> Boolean commutator : (%,%) -> % ---R convert : Vector R -> % convert : % -> Vector R ---R coordinates : % -> Vector R ?.? : (%,Integer) -> R +--R convert : Vector(R) -> % convert : % -> Vector(R) +--R coordinates : % -> Vector(R) ?.? : (%,Integer) -> R --R flexible? : () -> Boolean hash : % -> SingleInteger --R jacobiIdentity? : () -> Boolean jordanAdmissible? : () -> Boolean --R jordanAlgebra? : () -> Boolean latex : % -> String --R leftAlternative? : () -> Boolean leftDiscriminant : () -> R ---R leftDiscriminant : Vector % -> R leftNorm : % -> R ---R leftTrace : % -> R leftTraceMatrix : () -> Matrix R +--R leftDiscriminant : Vector(%) -> R leftNorm : % -> R +--R leftTrace : % -> R leftTraceMatrix : () -> Matrix(R) --R lieAdmissible? : () -> Boolean lieAlgebra? : () -> Boolean --R powerAssociative? : () -> Boolean rank : () -> PositiveInteger ---R represents : Vector R -> % rightAlternative? : () -> Boolean ---R rightDiscriminant : () -> R rightDiscriminant : Vector % -> R ---R rightNorm : % -> R rightTrace : % -> R ---R rightTraceMatrix : () -> Matrix R sample : () -> % ---R someBasis : () -> Vector % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean +--R represents : Vector(R) -> % rightAlternative? : () -> Boolean +--R rightDiscriminant : () -> R rightNorm : % -> R +--R rightTrace : % -> R rightTraceMatrix : () -> Matrix(R) +--R sample : () -> % someBasis : () -> Vector(%) +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (NonNegativeInteger,%) -> % ---R associatorDependence : () -> List Vector R if R has INTDOM ---R conditionsForIdempotents : () -> List Polynomial R ---R conditionsForIdempotents : Vector % -> List Polynomial R ---R coordinates : Vector % -> Matrix R ---R coordinates : (Vector %,Vector %) -> Matrix R ---R coordinates : (%,Vector %) -> Vector R ---R leftCharacteristicPolynomial : % -> SparseUnivariatePolynomial R ---R leftMinimalPolynomial : % -> SparseUnivariatePolynomial R if R has INTDOM +--R associatorDependence : () -> List(Vector(R)) if R has INTDOM +--R conditionsForIdempotents : () -> List(Polynomial(R)) +--R conditionsForIdempotents : Vector(%) -> List(Polynomial(R)) +--R coordinates : Vector(%) -> Matrix(R) +--R coordinates : (Vector(%),Vector(%)) -> Matrix(R) +--R coordinates : (%,Vector(%)) -> Vector(R) +--R leftCharacteristicPolynomial : % -> SparseUnivariatePolynomial(R) +--R leftMinimalPolynomial : % -> SparseUnivariatePolynomial(R) if R has INTDOM --R leftPower : (%,PositiveInteger) -> % ---R leftRankPolynomial : () -> SparseUnivariatePolynomial Polynomial R if R has FIELD +--R leftRankPolynomial : () -> SparseUnivariatePolynomial(Polynomial(R)) if R has FIELD --R leftRecip : % -> Union(%,"failed") if R has INTDOM ---R leftRegularRepresentation : % -> Matrix R ---R leftRegularRepresentation : (%,Vector %) -> Matrix R ---R leftTraceMatrix : Vector % -> Matrix R +--R leftRegularRepresentation : % -> Matrix(R) +--R leftRegularRepresentation : (%,Vector(%)) -> Matrix(R) +--R leftTraceMatrix : Vector(%) -> Matrix(R) --R leftUnit : () -> Union(%,"failed") if R has INTDOM ---R leftUnits : () -> Union(Record(particular: %,basis: List %),"failed") if R has INTDOM +--R leftUnits : () -> Union(Record(particular: %,basis: List(%)),"failed") if R has INTDOM --R noncommutativeJordanAlgebra? : () -> Boolean --R plenaryPower : (%,PositiveInteger) -> % --R recip : % -> Union(%,"failed") if R has INTDOM ---R represents : (Vector R,Vector %) -> % ---R rightCharacteristicPolynomial : % -> SparseUnivariatePolynomial R ---R rightMinimalPolynomial : % -> SparseUnivariatePolynomial R if R has INTDOM +--R represents : (Vector(R),Vector(%)) -> % +--R rightCharacteristicPolynomial : % -> SparseUnivariatePolynomial(R) +--R rightDiscriminant : Vector(%) -> R +--R rightMinimalPolynomial : % -> SparseUnivariatePolynomial(R) if R has INTDOM --R rightPower : (%,PositiveInteger) -> % ---R rightRankPolynomial : () -> SparseUnivariatePolynomial Polynomial R if R has FIELD +--R rightRankPolynomial : () -> SparseUnivariatePolynomial(Polynomial(R)) if R has FIELD --R rightRecip : % -> Union(%,"failed") if R has INTDOM ---R rightRegularRepresentation : % -> Matrix R ---R rightRegularRepresentation : (%,Vector %) -> Matrix R ---R rightTraceMatrix : Vector % -> Matrix R +--R rightRegularRepresentation : % -> Matrix(R) +--R rightRegularRepresentation : (%,Vector(%)) -> Matrix(R) +--R rightTraceMatrix : Vector(%) -> Matrix(R) --R rightUnit : () -> Union(%,"failed") if R has INTDOM ---R rightUnits : () -> Union(Record(particular: %,basis: List %),"failed") if R has INTDOM ---R structuralConstants : () -> Vector Matrix R ---R structuralConstants : Vector % -> Vector Matrix R +--R rightUnits : () -> Union(Record(particular: %,basis: List(%)),"failed") if R has INTDOM +--R structuralConstants : () -> Vector(Matrix(R)) +--R structuralConstants : Vector(%) -> Vector(Matrix(R)) --R subtractIfCan : (%,%) -> Union(%,"failed") --R unit : () -> Union(%,"failed") if R has INTDOM --R @@ -1190,161 +1194,163 @@ AlgebraGivenByStructuralConstants(R:Field, n : PositiveInteger,_ --S 1 of 1 )show AlgebraicFunctionField ---R AlgebraicFunctionField(F: Field,UP: UnivariatePolynomialCategory F,UPUP: UnivariatePolynomialCategory Fraction UP,modulus: UPUP) is a domain constructor +--R +--R AlgebraicFunctionField(F: Field,UP: UnivariatePolynomialCategory(F),UPUP: UnivariatePolynomialCategory(Fraction(UP)),modulus: UPUP) is a domain constructor --R Abbreviation for AlgebraicFunctionField is ALGFF --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ALGFF --R --R------------------------------- Operations -------------------------------- ---R ?*? : (Fraction UP,%) -> % ?*? : (%,Fraction UP) -> % +--R ?*? : (Fraction(UP),%) -> % ?*? : (%,Fraction(UP)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % --R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % basis : () -> Vector % +--R ?^? : (%,PositiveInteger) -> % basis : () -> Vector(%) --R branchPoint? : UP -> Boolean branchPoint? : F -> Boolean ---R coerce : Fraction UP -> % coerce : Integer -> % +--R coerce : Fraction(UP) -> % coerce : Integer -> % --R coerce : % -> OutputForm convert : UPUP -> % ---R convert : % -> UPUP convert : Vector Fraction UP -> % ---R convert : % -> Vector Fraction UP definingPolynomial : () -> UPUP ---R discriminant : () -> Fraction UP elt : (%,F,F) -> F +--R convert : % -> UPUP definingPolynomial : () -> UPUP +--R discriminant : () -> Fraction(UP) elt : (%,F,F) -> F --R generator : () -> % genus : () -> NonNegativeInteger --R hash : % -> SingleInteger integral? : (%,UP) -> Boolean --R integral? : (%,F) -> Boolean integral? : % -> Boolean ---R integralBasis : () -> Vector % latex : % -> String ---R lift : % -> UPUP norm : % -> Fraction UP +--R integralBasis : () -> Vector(%) latex : % -> String +--R lift : % -> UPUP norm : % -> Fraction(UP) --R one? : % -> Boolean primitivePart : % -> % --R ramified? : UP -> Boolean ramified? : F -> Boolean --R rank : () -> PositiveInteger rationalPoint? : (F,F) -> Boolean --R recip : % -> Union(%,"failed") reduce : UPUP -> % ---R represents : (Vector UP,UP) -> % retract : % -> Fraction UP +--R represents : (Vector(UP),UP) -> % retract : % -> Fraction(UP) --R sample : () -> % singular? : UP -> Boolean ---R singular? : F -> Boolean trace : % -> Fraction UP +--R singular? : F -> Boolean trace : % -> Fraction(UP) --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (%,Fraction Integer) -> % if Fraction UP has FIELD ---R ?*? : (Fraction Integer,%) -> % if Fraction UP has FIELD +--R ?*? : (%,Fraction(Integer)) -> % if Fraction(UP) has FIELD +--R ?*? : (Fraction(Integer),%) -> % if Fraction(UP) has FIELD --R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,Integer) -> % if Fraction UP has FIELD +--R ?**? : (%,Integer) -> % if Fraction(UP) has FIELD --R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (%,%) -> % if Fraction UP has FIELD ---R D : % -> % if Fraction UP has DIFRING and Fraction UP has FIELD or Fraction UP has FFIELDC ---R D : (%,NonNegativeInteger) -> % if Fraction UP has DIFRING and Fraction UP has FIELD or Fraction UP has FFIELDC ---R D : (%,Symbol) -> % if Fraction UP has FIELD and Fraction UP has PDRING SYMBOL ---R D : (%,List Symbol) -> % if Fraction UP has FIELD and Fraction UP has PDRING SYMBOL ---R D : (%,Symbol,NonNegativeInteger) -> % if Fraction UP has FIELD and Fraction UP has PDRING SYMBOL ---R D : (%,List Symbol,List NonNegativeInteger) -> % if Fraction UP has FIELD and Fraction UP has PDRING SYMBOL ---R D : (%,(Fraction UP -> Fraction UP)) -> % if Fraction UP has FIELD ---R D : (%,(Fraction UP -> Fraction UP),NonNegativeInteger) -> % if Fraction UP has FIELD ---R ?^? : (%,Integer) -> % if Fraction UP has FIELD +--R ?/? : (%,%) -> % if Fraction(UP) has FIELD +--R D : % -> % if Fraction(UP) has DIFRING and Fraction(UP) has FIELD or Fraction(UP) has FFIELDC +--R D : (%,NonNegativeInteger) -> % if Fraction(UP) has DIFRING and Fraction(UP) has FIELD or Fraction(UP) has FFIELDC +--R D : (%,Symbol) -> % if Fraction(UP) has FIELD and Fraction(UP) has PDRING(SYMBOL) +--R D : (%,List(Symbol)) -> % if Fraction(UP) has FIELD and Fraction(UP) has PDRING(SYMBOL) +--R D : (%,Symbol,NonNegativeInteger) -> % if Fraction(UP) has FIELD and Fraction(UP) has PDRING(SYMBOL) +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if Fraction(UP) has FIELD and Fraction(UP) has PDRING(SYMBOL) +--R D : (%,(Fraction(UP) -> Fraction(UP))) -> % if Fraction(UP) has FIELD +--R D : (%,(Fraction(UP) -> Fraction(UP)),NonNegativeInteger) -> % if Fraction(UP) has FIELD +--R ?^? : (%,Integer) -> % if Fraction(UP) has FIELD --R ?^? : (%,NonNegativeInteger) -> % --R absolutelyIrreducible? : () -> Boolean --R algSplitSimple : (%,(UP -> UP)) -> Record(num: %,den: UP,derivden: UP,gd: UP) ---R associates? : (%,%) -> Boolean if Fraction UP has FIELD +--R associates? : (%,%) -> Boolean if Fraction(UP) has FIELD --R branchPointAtInfinity? : () -> Boolean --R characteristic : () -> NonNegativeInteger --R characteristicPolynomial : % -> UPUP ---R charthRoot : % -> Union(%,"failed") if Fraction UP has CHARNZ ---R charthRoot : % -> % if Fraction UP has FFIELDC ---R coerce : % -> % if Fraction UP has FIELD ---R coerce : Fraction Integer -> % if Fraction UP has FIELD or Fraction UP has RETRACT FRAC INT ---R complementaryBasis : Vector % -> Vector % ---R conditionP : Matrix % -> Union(Vector %,"failed") if Fraction UP has FFIELDC ---R coordinates : Vector % -> Matrix Fraction UP ---R coordinates : % -> Vector Fraction UP ---R coordinates : (Vector %,Vector %) -> Matrix Fraction UP ---R coordinates : (%,Vector %) -> Vector Fraction UP ---R createPrimitiveElement : () -> % if Fraction UP has FFIELDC ---R derivationCoordinates : (Vector %,(Fraction UP -> Fraction UP)) -> Matrix Fraction UP if Fraction UP has FIELD ---R differentiate : % -> % if Fraction UP has DIFRING and Fraction UP has FIELD or Fraction UP has FFIELDC ---R differentiate : (%,NonNegativeInteger) -> % if Fraction UP has DIFRING and Fraction UP has FIELD or Fraction UP has FFIELDC ---R differentiate : (%,Symbol) -> % if Fraction UP has FIELD and Fraction UP has PDRING SYMBOL ---R differentiate : (%,List Symbol) -> % if Fraction UP has FIELD and Fraction UP has PDRING SYMBOL ---R differentiate : (%,Symbol,NonNegativeInteger) -> % if Fraction UP has FIELD and Fraction UP has PDRING SYMBOL ---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if Fraction UP has FIELD and Fraction UP has PDRING SYMBOL +--R charthRoot : % -> Union(%,"failed") if Fraction(UP) has CHARNZ +--R charthRoot : % -> % if Fraction(UP) has FFIELDC +--R coerce : % -> % if Fraction(UP) has FIELD +--R coerce : Fraction(Integer) -> % if Fraction(UP) has FIELD or Fraction(UP) has RETRACT(FRAC(INT)) +--R complementaryBasis : Vector(%) -> Vector(%) +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if Fraction(UP) has FFIELDC +--R convert : Vector(Fraction(UP)) -> % +--R convert : % -> Vector(Fraction(UP)) +--R coordinates : Vector(%) -> Matrix(Fraction(UP)) +--R coordinates : % -> Vector(Fraction(UP)) +--R coordinates : (Vector(%),Vector(%)) -> Matrix(Fraction(UP)) +--R coordinates : (%,Vector(%)) -> Vector(Fraction(UP)) +--R createPrimitiveElement : () -> % if Fraction(UP) has FFIELDC +--R derivationCoordinates : (Vector(%),(Fraction(UP) -> Fraction(UP))) -> Matrix(Fraction(UP)) if Fraction(UP) has FIELD +--R differentiate : % -> % if Fraction(UP) has DIFRING and Fraction(UP) has FIELD or Fraction(UP) has FFIELDC +--R differentiate : (%,NonNegativeInteger) -> % if Fraction(UP) has DIFRING and Fraction(UP) has FIELD or Fraction(UP) has FFIELDC +--R differentiate : (%,Symbol) -> % if Fraction(UP) has FIELD and Fraction(UP) has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol)) -> % if Fraction(UP) has FIELD and Fraction(UP) has PDRING(SYMBOL) +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if Fraction(UP) has FIELD and Fraction(UP) has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if Fraction(UP) has FIELD and Fraction(UP) has PDRING(SYMBOL) --R differentiate : (%,(UP -> UP)) -> % ---R differentiate : (%,(Fraction UP -> Fraction UP)) -> % if Fraction UP has FIELD ---R differentiate : (%,(Fraction UP -> Fraction UP),NonNegativeInteger) -> % if Fraction UP has FIELD ---R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if Fraction UP has FFIELDC ---R discreteLog : % -> NonNegativeInteger if Fraction UP has FFIELDC ---R discriminant : Vector % -> Fraction UP ---R divide : (%,%) -> Record(quotient: %,remainder: %) if Fraction UP has FIELD +--R differentiate : (%,(Fraction(UP) -> Fraction(UP))) -> % if Fraction(UP) has FIELD +--R differentiate : (%,(Fraction(UP) -> Fraction(UP)),NonNegativeInteger) -> % if Fraction(UP) has FIELD +--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if Fraction(UP) has FFIELDC +--R discreteLog : % -> NonNegativeInteger if Fraction(UP) has FFIELDC +--R discriminant : Vector(%) -> Fraction(UP) +--R divide : (%,%) -> Record(quotient: %,remainder: %) if Fraction(UP) has FIELD --R elliptic : () -> Union(UP,"failed") ---R euclideanSize : % -> NonNegativeInteger if Fraction UP has FIELD ---R expressIdealMember : (List %,%) -> Union(List %,"failed") if Fraction UP has FIELD ---R exquo : (%,%) -> Union(%,"failed") if Fraction UP has FIELD ---R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if Fraction UP has FIELD ---R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if Fraction UP has FIELD ---R factor : % -> Factored % if Fraction UP has FIELD ---R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if Fraction UP has FFIELDC ---R gcd : (%,%) -> % if Fraction UP has FIELD ---R gcd : List % -> % if Fraction UP has FIELD ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if Fraction UP has FIELD +--R euclideanSize : % -> NonNegativeInteger if Fraction(UP) has FIELD +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if Fraction(UP) has FIELD +--R exquo : (%,%) -> Union(%,"failed") if Fraction(UP) has FIELD +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if Fraction(UP) has FIELD +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if Fraction(UP) has FIELD +--R factor : % -> Factored(%) if Fraction(UP) has FIELD +--R factorsOfCyclicGroupSize : () -> List(Record(factor: Integer,exponent: Integer)) if Fraction(UP) has FFIELDC +--R gcd : (%,%) -> % if Fraction(UP) has FIELD +--R gcd : List(%) -> % if Fraction(UP) has FIELD +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if Fraction(UP) has FIELD --R hyperelliptic : () -> Union(UP,"failed") ---R index : PositiveInteger -> % if Fraction UP has FINITE ---R init : () -> % if Fraction UP has FFIELDC +--R index : PositiveInteger -> % if Fraction(UP) has FINITE +--R init : () -> % if Fraction(UP) has FFIELDC --R integralAtInfinity? : % -> Boolean ---R integralBasisAtInfinity : () -> Vector % ---R integralCoordinates : % -> Record(num: Vector UP,den: UP) ---R integralDerivationMatrix : (UP -> UP) -> Record(num: Matrix UP,den: UP) ---R integralMatrix : () -> Matrix Fraction UP ---R integralMatrixAtInfinity : () -> Matrix Fraction UP ---R integralRepresents : (Vector UP,UP) -> % ---R inv : % -> % if Fraction UP has FIELD ---R inverseIntegralMatrix : () -> Matrix Fraction UP ---R inverseIntegralMatrixAtInfinity : () -> Matrix Fraction UP +--R integralBasisAtInfinity : () -> Vector(%) +--R integralCoordinates : % -> Record(num: Vector(UP),den: UP) +--R integralDerivationMatrix : (UP -> UP) -> Record(num: Matrix(UP),den: UP) +--R integralMatrix : () -> Matrix(Fraction(UP)) +--R integralMatrixAtInfinity : () -> Matrix(Fraction(UP)) +--R integralRepresents : (Vector(UP),UP) -> % +--R inv : % -> % if Fraction(UP) has FIELD +--R inverseIntegralMatrix : () -> Matrix(Fraction(UP)) +--R inverseIntegralMatrixAtInfinity : () -> Matrix(Fraction(UP)) --R knownInfBasis : NonNegativeInteger -> Void ---R lcm : (%,%) -> % if Fraction UP has FIELD ---R lcm : List % -> % if Fraction UP has FIELD ---R lookup : % -> PositiveInteger if Fraction UP has FINITE ---R minimalPolynomial : % -> UPUP if Fraction UP has FIELD ---R multiEuclidean : (List %,%) -> Union(List %,"failed") if Fraction UP has FIELD ---R nextItem : % -> Union(%,"failed") if Fraction UP has FFIELDC ---R nonSingularModel : Symbol -> List Polynomial F if F has FIELD ---R normalizeAtInfinity : Vector % -> Vector % +--R lcm : (%,%) -> % if Fraction(UP) has FIELD +--R lcm : List(%) -> % if Fraction(UP) has FIELD +--R lookup : % -> PositiveInteger if Fraction(UP) has FINITE +--R minimalPolynomial : % -> UPUP if Fraction(UP) has FIELD +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") if Fraction(UP) has FIELD +--R nextItem : % -> Union(%,"failed") if Fraction(UP) has FFIELDC +--R nonSingularModel : Symbol -> List(Polynomial(F)) if F has FIELD +--R normalizeAtInfinity : Vector(%) -> Vector(%) --R numberOfComponents : () -> NonNegativeInteger ---R order : % -> OnePointCompletion PositiveInteger if Fraction UP has FFIELDC ---R order : % -> PositiveInteger if Fraction UP has FFIELDC ---R prime? : % -> Boolean if Fraction UP has FIELD ---R primeFrobenius : % -> % if Fraction UP has FFIELDC ---R primeFrobenius : (%,NonNegativeInteger) -> % if Fraction UP has FFIELDC ---R primitive? : % -> Boolean if Fraction UP has FFIELDC ---R primitiveElement : () -> % if Fraction UP has FFIELDC ---R principalIdeal : List % -> Record(coef: List %,generator: %) if Fraction UP has FIELD ---R ?quo? : (%,%) -> % if Fraction UP has FIELD +--R order : % -> OnePointCompletion(PositiveInteger) if Fraction(UP) has FFIELDC +--R order : % -> PositiveInteger if Fraction(UP) has FFIELDC +--R prime? : % -> Boolean if Fraction(UP) has FIELD +--R primeFrobenius : % -> % if Fraction(UP) has FFIELDC +--R primeFrobenius : (%,NonNegativeInteger) -> % if Fraction(UP) has FFIELDC +--R primitive? : % -> Boolean if Fraction(UP) has FFIELDC +--R primitiveElement : () -> % if Fraction(UP) has FFIELDC +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if Fraction(UP) has FIELD +--R ?quo? : (%,%) -> % if Fraction(UP) has FIELD --R ramifiedAtInfinity? : () -> Boolean ---R random : () -> % if Fraction UP has FINITE ---R rationalPoints : () -> List List F if F has FINITE ---R reduce : Fraction UPUP -> Union(%,"failed") if Fraction UP has FIELD ---R reduceBasisAtInfinity : Vector % -> Vector % ---R reducedSystem : Matrix % -> Matrix Fraction UP ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Fraction UP,vec: Vector Fraction UP) ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if Fraction UP has LINEXP INT ---R reducedSystem : Matrix % -> Matrix Integer if Fraction UP has LINEXP INT ---R regularRepresentation : % -> Matrix Fraction UP ---R regularRepresentation : (%,Vector %) -> Matrix Fraction UP ---R ?rem? : (%,%) -> % if Fraction UP has FIELD ---R representationType : () -> Union("prime",polynomial,normal,cyclic) if Fraction UP has FFIELDC ---R represents : Vector Fraction UP -> % ---R represents : (Vector Fraction UP,Vector %) -> % ---R retract : % -> Fraction Integer if Fraction UP has RETRACT FRAC INT ---R retract : % -> Integer if Fraction UP has RETRACT INT ---R retractIfCan : % -> Union(Fraction UP,"failed") ---R retractIfCan : % -> Union(Fraction Integer,"failed") if Fraction UP has RETRACT FRAC INT ---R retractIfCan : % -> Union(Integer,"failed") if Fraction UP has RETRACT INT +--R random : () -> % if Fraction(UP) has FINITE +--R rationalPoints : () -> List(List(F)) if F has FINITE +--R reduce : Fraction(UPUP) -> Union(%,"failed") if Fraction(UP) has FIELD +--R reduceBasisAtInfinity : Vector(%) -> Vector(%) +--R reducedSystem : Matrix(%) -> Matrix(Fraction(UP)) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Fraction(UP)),vec: Vector(Fraction(UP))) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if Fraction(UP) has LINEXP(INT) +--R reducedSystem : Matrix(%) -> Matrix(Integer) if Fraction(UP) has LINEXP(INT) +--R regularRepresentation : % -> Matrix(Fraction(UP)) +--R regularRepresentation : (%,Vector(%)) -> Matrix(Fraction(UP)) +--R ?rem? : (%,%) -> % if Fraction(UP) has FIELD +--R representationType : () -> Union("prime",polynomial,normal,cyclic) if Fraction(UP) has FFIELDC +--R represents : Vector(Fraction(UP)) -> % +--R represents : (Vector(Fraction(UP)),Vector(%)) -> % +--R retract : % -> Fraction(Integer) if Fraction(UP) has RETRACT(FRAC(INT)) +--R retract : % -> Integer if Fraction(UP) has RETRACT(INT) +--R retractIfCan : % -> Union(Fraction(UP),"failed") +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if Fraction(UP) has RETRACT(FRAC(INT)) +--R retractIfCan : % -> Union(Integer,"failed") if Fraction(UP) has RETRACT(INT) --R singularAtInfinity? : () -> Boolean ---R size : () -> NonNegativeInteger if Fraction UP has FINITE ---R sizeLess? : (%,%) -> Boolean if Fraction UP has FIELD ---R squareFree : % -> Factored % if Fraction UP has FIELD ---R squareFreePart : % -> % if Fraction UP has FIELD +--R size : () -> NonNegativeInteger if Fraction(UP) has FINITE +--R sizeLess? : (%,%) -> Boolean if Fraction(UP) has FIELD +--R squareFree : % -> Factored(%) if Fraction(UP) has FIELD +--R squareFreePart : % -> % if Fraction(UP) has FIELD --R subtractIfCan : (%,%) -> Union(%,"failed") ---R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if Fraction UP has FFIELDC ---R traceMatrix : () -> Matrix Fraction UP ---R traceMatrix : Vector % -> Matrix Fraction UP ---R unit? : % -> Boolean if Fraction UP has FIELD ---R unitCanonical : % -> % if Fraction UP has FIELD ---R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Fraction UP has FIELD ---R yCoordinates : % -> Record(num: Vector UP,den: UP) +--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if Fraction(UP) has FFIELDC +--R traceMatrix : () -> Matrix(Fraction(UP)) +--R traceMatrix : Vector(%) -> Matrix(Fraction(UP)) +--R unit? : % -> Boolean if Fraction(UP) has FIELD +--R unitCanonical : % -> % if Fraction(UP) has FIELD +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Fraction(UP) has FIELD +--R yCoordinates : % -> Record(num: Vector(UP),den: UP) --R --E 1 @@ -1642,6 +1648,7 @@ AlgebraicFunctionField(F, UP, UPUP, modulus): Exports == Impl where --S 1 of 1 )show AlgebraicNumber +--R --R AlgebraicNumber is a domain constructor --R Abbreviation for AlgebraicNumber is AN --R This constructor is exposed in this frame. @@ -1649,110 +1656,113 @@ AlgebraicFunctionField(F, UP, UPUP, modulus): Exports == Impl where --R --R------------------------------- Operations -------------------------------- --R ?*? : (PositiveInteger,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (%,%) -> % ?*? : (%,Fraction Integer) -> % ---R ?*? : (Fraction Integer,%) -> % ?**? : (%,PositiveInteger) -> % ---R ?**? : (%,Integer) -> % ?**? : (%,Fraction Integer) -> % ---R ?+? : (%,%) -> % -? : % -> % ---R ?-? : (%,%) -> % ?/? : (%,%) -> % ---R ? Boolean ?<=? : (%,%) -> Boolean ---R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean ---R ?>=? : (%,%) -> Boolean D : % -> % ---R D : (%,NonNegativeInteger) -> % 1 : () -> % ---R 0 : () -> % ?^? : (%,PositiveInteger) -> % ---R ?^? : (%,Integer) -> % associates? : (%,%) -> Boolean ---R belong? : BasicOperator -> Boolean box : List % -> % ---R box : % -> % coerce : Integer -> % ---R coerce : % -> % coerce : Fraction Integer -> % ---R coerce : Kernel % -> % coerce : % -> OutputForm ---R convert : % -> Complex Float convert : % -> DoubleFloat ---R convert : % -> Float differentiate : % -> % ---R distribute : (%,%) -> % distribute : % -> % ---R elt : (BasicOperator,%,%) -> % elt : (BasicOperator,%) -> % ---R eval : (%,List %,List %) -> % eval : (%,%,%) -> % ---R eval : (%,Equation %) -> % eval : (%,List Equation %) -> % ---R eval : (%,Kernel %,%) -> % factor : % -> Factored % ---R freeOf? : (%,Symbol) -> Boolean freeOf? : (%,%) -> Boolean ---R gcd : (%,%) -> % gcd : List % -> % ---R hash : % -> SingleInteger height : % -> NonNegativeInteger ---R inv : % -> % is? : (%,Symbol) -> Boolean ---R kernel : (BasicOperator,%) -> % kernels : % -> List Kernel % ---R latex : % -> String lcm : (%,%) -> % ---R lcm : List % -> % map : ((% -> %),Kernel %) -> % +--R ?*? : (%,%) -> % ?*? : (%,Fraction(Integer)) -> % +--R ?*? : (Fraction(Integer),%) -> % ?**? : (%,PositiveInteger) -> % +--R ?**? : (%,Integer) -> % ?+? : (%,%) -> % +--R -? : % -> % ?-? : (%,%) -> % +--R ?/? : (%,%) -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R D : % -> % D : (%,NonNegativeInteger) -> % +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % ?^? : (%,Integer) -> % +--R associates? : (%,%) -> Boolean belong? : BasicOperator -> Boolean +--R box : List(%) -> % box : % -> % +--R coerce : Integer -> % coerce : % -> % +--R coerce : Fraction(Integer) -> % coerce : Kernel(%) -> % +--R coerce : % -> OutputForm convert : % -> Complex(Float) +--R convert : % -> DoubleFloat convert : % -> Float +--R differentiate : % -> % distribute : (%,%) -> % +--R distribute : % -> % elt : (BasicOperator,%,%) -> % +--R elt : (BasicOperator,%) -> % eval : (%,%,%) -> % +--R eval : (%,Equation(%)) -> % eval : (%,Kernel(%),%) -> % +--R factor : % -> Factored(%) freeOf? : (%,Symbol) -> Boolean +--R freeOf? : (%,%) -> Boolean gcd : (%,%) -> % +--R gcd : List(%) -> % hash : % -> SingleInteger +--R height : % -> NonNegativeInteger inv : % -> % +--R is? : (%,Symbol) -> Boolean kernel : (BasicOperator,%) -> % +--R kernels : % -> List(Kernel(%)) latex : % -> String +--R lcm : (%,%) -> % lcm : List(%) -> % --R max : (%,%) -> % min : (%,%) -> % ---R norm : (%,List Kernel %) -> % norm : (%,Kernel %) -> % +--R norm : (%,List(Kernel(%))) -> % norm : (%,Kernel(%)) -> % --R nthRoot : (%,Integer) -> % one? : % -> Boolean ---R paren : List % -> % paren : % -> % +--R paren : List(%) -> % paren : % -> % --R prime? : % -> Boolean ?quo? : (%,%) -> % --R recip : % -> Union(%,"failed") reduce : % -> % ---R ?rem? : (%,%) -> % retract : % -> Fraction Integer ---R retract : % -> Integer retract : % -> Kernel % ---R rootOf : Polynomial % -> % rootsOf : Polynomial % -> List % ---R sample : () -> % sizeLess? : (%,%) -> Boolean ---R sqrt : % -> % squareFree : % -> Factored % ---R squareFreePart : % -> % subst : (%,Equation %) -> % ---R tower : % -> List Kernel % unit? : % -> Boolean ---R unitCanonical : % -> % zero? : % -> Boolean ---R zeroOf : Polynomial % -> % zerosOf : Polynomial % -> List % +--R ?rem? : (%,%) -> % retract : % -> Fraction(Integer) +--R retract : % -> Integer retract : % -> Kernel(%) +--R rootOf : Polynomial(%) -> % sample : () -> % +--R sizeLess? : (%,%) -> Boolean sqrt : % -> % +--R squareFree : % -> Factored(%) squareFreePart : % -> % +--R subst : (%,Equation(%)) -> % tower : % -> List(Kernel(%)) +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean zeroOf : Polynomial(%) -> % --R ?~=? : (%,%) -> Boolean --R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,NonNegativeInteger) -> % +--R ?**? : (%,Fraction(Integer)) -> % --R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger ---R coerce : SparseMultivariatePolynomial(Integer,Kernel %) -> % +--R coerce : SparseMultivariatePolynomial(Integer,Kernel(%)) -> % --R definingPolynomial : % -> % if $ has RING ---R denom : % -> SparseMultivariatePolynomial(Integer,Kernel %) +--R denom : % -> SparseMultivariatePolynomial(Integer,Kernel(%)) --R differentiate : (%,NonNegativeInteger) -> % --R divide : (%,%) -> Record(quotient: %,remainder: %) ---R elt : (BasicOperator,List %) -> % +--R elt : (BasicOperator,List(%)) -> % --R elt : (BasicOperator,%,%,%,%) -> % --R elt : (BasicOperator,%,%,%) -> % --R euclideanSize : % -> NonNegativeInteger --R eval : (%,BasicOperator,(% -> %)) -> % ---R eval : (%,BasicOperator,(List % -> %)) -> % ---R eval : (%,List BasicOperator,List (List % -> %)) -> % ---R eval : (%,List BasicOperator,List (% -> %)) -> % +--R eval : (%,BasicOperator,(List(%) -> %)) -> % +--R eval : (%,List(BasicOperator),List((List(%) -> %))) -> % +--R eval : (%,List(BasicOperator),List((% -> %))) -> % --R eval : (%,Symbol,(% -> %)) -> % ---R eval : (%,Symbol,(List % -> %)) -> % ---R eval : (%,List Symbol,List (List % -> %)) -> % ---R eval : (%,List Symbol,List (% -> %)) -> % ---R eval : (%,List Kernel %,List %) -> % ---R even? : % -> Boolean if $ has RETRACT INT ---R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R eval : (%,Symbol,(List(%) -> %)) -> % +--R eval : (%,List(Symbol),List((List(%) -> %))) -> % +--R eval : (%,List(Symbol),List((% -> %))) -> % +--R eval : (%,List(%),List(%)) -> % +--R eval : (%,List(Equation(%))) -> % +--R eval : (%,List(Kernel(%)),List(%)) -> % +--R even? : % -> Boolean if $ has RETRACT(INT) +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") --R exquo : (%,%) -> Union(%,"failed") --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) --R is? : (%,BasicOperator) -> Boolean ---R kernel : (BasicOperator,List %) -> % ---R mainKernel : % -> Union(Kernel %,"failed") ---R minPoly : Kernel % -> SparseUnivariatePolynomial % if $ has RING ---R multiEuclidean : (List %,%) -> Union(List %,"failed") ---R norm : (SparseUnivariatePolynomial %,List Kernel %) -> SparseUnivariatePolynomial % ---R norm : (SparseUnivariatePolynomial %,Kernel %) -> SparseUnivariatePolynomial % ---R numer : % -> SparseMultivariatePolynomial(Integer,Kernel %) ---R odd? : % -> Boolean if $ has RETRACT INT +--R kernel : (BasicOperator,List(%)) -> % +--R mainKernel : % -> Union(Kernel(%),"failed") +--R map : ((% -> %),Kernel(%)) -> % +--R minPoly : Kernel(%) -> SparseUnivariatePolynomial(%) if $ has RING +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") +--R norm : (SparseUnivariatePolynomial(%),List(Kernel(%))) -> SparseUnivariatePolynomial(%) +--R norm : (SparseUnivariatePolynomial(%),Kernel(%)) -> SparseUnivariatePolynomial(%) +--R numer : % -> SparseMultivariatePolynomial(Integer,Kernel(%)) +--R odd? : % -> Boolean if $ has RETRACT(INT) --R operator : BasicOperator -> BasicOperator ---R operators : % -> List BasicOperator ---R principalIdeal : List % -> Record(coef: List %,generator: %) ---R reducedSystem : Matrix % -> Matrix Fraction Integer ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Fraction Integer,vec: Vector Fraction Integer) ---R reducedSystem : Matrix % -> Matrix Integer ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) ---R retractIfCan : % -> Union(Fraction Integer,"failed") +--R operators : % -> List(BasicOperator) +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) +--R reducedSystem : Matrix(%) -> Matrix(Fraction(Integer)) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Fraction(Integer)),vec: Vector(Fraction(Integer))) +--R reducedSystem : Matrix(%) -> Matrix(Integer) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) +--R retractIfCan : % -> Union(Fraction(Integer),"failed") --R retractIfCan : % -> Union(Integer,"failed") ---R retractIfCan : % -> Union(Kernel %,"failed") ---R rootOf : SparseUnivariatePolynomial % -> % ---R rootOf : (SparseUnivariatePolynomial %,Symbol) -> % ---R rootsOf : SparseUnivariatePolynomial % -> List % ---R rootsOf : (SparseUnivariatePolynomial %,Symbol) -> List % ---R subst : (%,List Kernel %,List %) -> % ---R subst : (%,List Equation %) -> % +--R retractIfCan : % -> Union(Kernel(%),"failed") +--R rootOf : SparseUnivariatePolynomial(%) -> % +--R rootOf : (SparseUnivariatePolynomial(%),Symbol) -> % +--R rootsOf : Polynomial(%) -> List(%) +--R rootsOf : SparseUnivariatePolynomial(%) -> List(%) +--R rootsOf : (SparseUnivariatePolynomial(%),Symbol) -> List(%) +--R subst : (%,List(Kernel(%)),List(%)) -> % +--R subst : (%,List(Equation(%))) -> % --R subtractIfCan : (%,%) -> Union(%,"failed") --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) ---R zeroOf : SparseUnivariatePolynomial % -> % ---R zeroOf : (SparseUnivariatePolynomial %,Symbol) -> % ---R zerosOf : SparseUnivariatePolynomial % -> List % ---R zerosOf : (SparseUnivariatePolynomial %,Symbol) -> List % +--R zeroOf : SparseUnivariatePolynomial(%) -> % +--R zeroOf : (SparseUnivariatePolynomial(%),Symbol) -> % +--R zerosOf : Polynomial(%) -> List(%) +--R zerosOf : SparseUnivariatePolynomial(%) -> List(%) +--R zerosOf : (SparseUnivariatePolynomial(%),Symbol) -> List(%) --R --E 1 @@ -2001,7 +2011,8 @@ AnonymousFunction():SetCategory == add --S 1 of 1 )show AntiSymm ---R AntiSymm(R: Ring,lVar: List Symbol) is a domain constructor +--R +--R AntiSymm(R: Ring,lVar: List(Symbol)) is a domain constructor --R Abbreviation for AntiSymm is ANTISYM --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ANTISYM @@ -2015,7 +2026,7 @@ AnonymousFunction():SetCategory == add --R 0 : () -> % ?^? : (%,PositiveInteger) -> % --R coefficient : (%,%) -> R coerce : R -> % --R coerce : Integer -> % coerce : % -> OutputForm ---R degree : % -> NonNegativeInteger exp : List Integer -> % +--R degree : % -> NonNegativeInteger exp : List(Integer) -> % --R hash : % -> SingleInteger homogeneous? : % -> Boolean --R latex : % -> String leadingBasisTerm : % -> % --R leadingCoefficient : % -> R map : ((R -> R),%) -> % @@ -2304,7 +2315,7 @@ a:Any := [1,2] --R --R --R (1) [1,2] ---R Type: List PositiveInteger +--R Type: List(PositiveInteger) --E 1 --S 2 of 18 @@ -2312,7 +2323,7 @@ b:Any := [1,2] --R --R --R (2) [1,2] ---R Type: List PositiveInteger +--R Type: List(PositiveInteger) --E 2 --S 3 of 18 @@ -2328,7 +2339,7 @@ c := [1,2] --R --R --R (4) [1,2] ---R Type: List PositiveInteger +--R Type: List(PositiveInteger) --E 4 --S 5 of 18 @@ -2343,7 +2354,7 @@ typeOf a typeOf c --R --R ---R (6) List PositiveInteger +--R (6) List(PositiveInteger) --R Type: Domain --E 6 @@ -2360,7 +2371,7 @@ b := [1,3] --R --R --R (8) [1,3] ---R Type: List PositiveInteger +--R Type: List(PositiveInteger) --E 8 --S 9 of 18 @@ -2408,8 +2419,8 @@ Sae := SAE(FRAC INT, UP(x, FRAC INT), x^2-3) --R --R --R (14) ---R SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(x,Fraction Int ---R eger),x*x-3) +--R SimpleAlgebraicExtension(Fraction(Integer),UnivariatePolynomial(x,Fraction(In +--R teger)),x^2+-3) --R Type: Domain --E 14 @@ -2418,7 +2429,7 @@ a := generator()$Sae --R --R --R (15) x ---RType: SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),x*x-3) +--RType: SimpleAlgebraicExtension(Fraction(Integer),UnivariatePolynomial(x,Fraction(Integer)),x^2+-3) --E 15 --S 16 of 18 @@ -2426,7 +2437,7 @@ b := generator()$Sae --R --R --R (16) x ---RType: SimpleAlgebraicExtension(Fraction Integer,UnivariatePolynomial(x,Fraction Integer),x*x-3) +--RType: SimpleAlgebraicExtension(Fraction(Integer),UnivariatePolynomial(x,Fraction(Integer)),x^2+-3) --E 16 --S 17 of 18 @@ -2659,7 +2670,7 @@ a:ArrayStack INT:= arrayStack [1,2,3,4,5] --R --R --R (1) [1,2,3,4,5] ---R Type: ArrayStack Integer +--R Type: ArrayStack(Integer) --E 1 --S 2 of 44 @@ -2675,7 +2686,7 @@ a --R --R --R (3) [2,3,4,5] ---R Type: ArrayStack Integer +--R Type: ArrayStack(Integer) --E 3 --S 4 of 44 @@ -2691,7 +2702,7 @@ a --R --R --R (5) [3,4,5] ---R Type: ArrayStack Integer +--R Type: ArrayStack(Integer) --E 5 --S 6 of 44 @@ -2707,7 +2718,7 @@ a --R --R --R (7) [9,3,4,5] ---R Type: ArrayStack Integer +--R Type: ArrayStack(Integer) --E 7 --S 8 of 44 @@ -2715,7 +2726,7 @@ insert!(8,a) --R --R --R (8) [8,9,3,4,5] ---R Type: ArrayStack Integer +--R Type: ArrayStack(Integer) --E 8 --S 9 of 44 @@ -2723,7 +2734,7 @@ a --R --R --R (9) [8,9,3,4,5] ---R Type: ArrayStack Integer +--R Type: ArrayStack(Integer) --E 9 --S 10 of 44 @@ -2803,7 +2814,7 @@ parts a --R --R --R (19) [8,9,3,4,5] ---R Type: List Integer +--R Type: List(Integer) --E 19 --S 20 of 44 @@ -2811,7 +2822,7 @@ bag([1,2,3,4,5])$ArrayStack(INT) --R --R --R (20) [5,4,3,2,1] ---R Type: ArrayStack Integer +--R Type: ArrayStack(Integer) --E 20 --S 21 of 44 @@ -2819,7 +2830,7 @@ b:=empty()$(ArrayStack INT) --R --R --R (21) [] ---R Type: ArrayStack Integer +--R Type: ArrayStack(Integer) --E 21 --S 22 of 44 @@ -2835,7 +2846,7 @@ sample()$ArrayStack(INT) --R --R --R (23) [] ---R Type: ArrayStack Integer +--R Type: ArrayStack(Integer) --E 23 --S 24 of 44 @@ -2843,7 +2854,7 @@ c:=copy a --R --R --R (24) [8,9,3,4,5] ---R Type: ArrayStack Integer +--R Type: ArrayStack(Integer) --E 24 --S 25 of 44 @@ -2931,7 +2942,7 @@ map(x+->x+10,a) --R --R --R (35) [18,19,13,14,15] ---R Type: ArrayStack Integer +--R Type: ArrayStack(Integer) --E 35 --S 36 of 44 @@ -2939,7 +2950,7 @@ a --R --R --R (36) [8,9,3,4,5] ---R Type: ArrayStack Integer +--R Type: ArrayStack(Integer) --E 36 --S 37 of 44 @@ -2947,7 +2958,7 @@ map!(x+->x+10,a) --R --R --R (37) [18,19,13,14,15] ---R Type: ArrayStack Integer +--R Type: ArrayStack(Integer) --E 37 --S 38 of 44 @@ -2955,7 +2966,7 @@ a --R --R --R (38) [18,19,13,14,15] ---R Type: ArrayStack Integer +--R Type: ArrayStack(Integer) --E 38 --S 39 of 44 @@ -2963,7 +2974,7 @@ members a --R --R --R (39) [18,19,13,14,15] ---R Type: List Integer +--R Type: List(Integer) --E 39 --S 40 of 44 @@ -3001,13 +3012,13 @@ latex a --S 44 of 44 )show ArrayStack --R ---R ArrayStack S: SetCategory is a domain constructor +--R ArrayStack(S: SetCategory) is a domain constructor --R Abbreviation for ArrayStack is ASTACK --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASTACK --R --R------------------------------- Operations -------------------------------- ---R arrayStack : List S -> % bag : List S -> % +--R arrayStack : List(S) -> % bag : List(S) -> % --R copy : % -> % depth : % -> NonNegativeInteger --R empty : () -> % empty? : % -> Boolean --R eq? : (%,%) -> Boolean extract! : % -> S @@ -3021,19 +3032,19 @@ latex a --R coerce : % -> OutputForm if S has SETCAT --R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT --R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate ---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if S has SETCAT --R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT ---R members : % -> List S if $ has finiteAggregate +--R members : % -> List(S) if $ has finiteAggregate --R more? : (%,NonNegativeInteger) -> Boolean ---R parts : % -> List S if $ has finiteAggregate +--R parts : % -> List(S) if $ has finiteAggregate --R size? : (%,NonNegativeInteger) -> Boolean --R ?~=? : (%,%) -> Boolean if S has SETCAT --R @@ -3528,26 +3539,28 @@ ArrayStack(S:SetCategory): StackAggregate(S) with --S 1 of 1 )show Asp1 ---R Asp1 name: Symbol is a domain constructor +--R +--R Asp1(name: Symbol) is a domain constructor --R Abbreviation for Asp1 is ASP1 --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP1 --R --R------------------------------- Operations -------------------------------- ---R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : FortranCode -> % coerce : List(FortranCode) -> % --R coerce : % -> OutputForm outputAsFortran : % -> Void ---R retract : Polynomial Integer -> % retract : Polynomial Float -> % ---R retract : Expression Integer -> % retract : Expression Float -> % +--R retract : Polynomial(Float) -> % retract : Expression(Float) -> % --R coerce : FortranExpression([construct,QUOTEX],[construct],MachineFloat) -> % ---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % ---R retract : Fraction Polynomial Integer -> % ---R retract : Fraction Polynomial Float -> % ---R retractIfCan : Fraction Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Fraction Polynomial Float -> Union(%,"failed") ---R retractIfCan : Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Polynomial Float -> Union(%,"failed") ---R retractIfCan : Expression Integer -> Union(%,"failed") ---R retractIfCan : Expression Float -> Union(%,"failed") +--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % +--R retract : Fraction(Polynomial(Integer)) -> % +--R retract : Fraction(Polynomial(Float)) -> % +--R retract : Polynomial(Integer) -> % +--R retract : Expression(Integer) -> % +--R retractIfCan : Fraction(Polynomial(Integer)) -> Union(%,"failed") +--R retractIfCan : Fraction(Polynomial(Float)) -> Union(%,"failed") +--R retractIfCan : Polynomial(Integer) -> Union(%,"failed") +--R retractIfCan : Polynomial(Float) -> Union(%,"failed") +--R retractIfCan : Expression(Integer) -> Union(%,"failed") +--R retractIfCan : Expression(Float) -> Union(%,"failed") --R --E 1 @@ -3698,28 +3711,29 @@ Asp1(name): Exports == Implementation where --S 1 of 1 )show Asp10 ---R Asp10 name: Symbol is a domain constructor +--R +--R Asp10(name: Symbol) is a domain constructor --R Abbreviation for Asp10 is ASP10 --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP10 --R --R------------------------------- Operations -------------------------------- ---R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : FortranCode -> % coerce : List(FortranCode) -> % --R coerce : % -> OutputForm outputAsFortran : % -> Void ---R coerce : Vector FortranExpression([construct,QUOTEJINT,QUOTEX,QUOTEELAM],[construct],MachineFloat) -> % ---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % ---R retract : Vector Fraction Polynomial Integer -> % ---R retract : Vector Fraction Polynomial Float -> % ---R retract : Vector Polynomial Integer -> % ---R retract : Vector Polynomial Float -> % ---R retract : Vector Expression Integer -> % ---R retract : Vector Expression Float -> % ---R retractIfCan : Vector Fraction Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Vector Fraction Polynomial Float -> Union(%,"failed") ---R retractIfCan : Vector Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Vector Polynomial Float -> Union(%,"failed") ---R retractIfCan : Vector Expression Integer -> Union(%,"failed") ---R retractIfCan : Vector Expression Float -> Union(%,"failed") +--R coerce : Vector(FortranExpression([construct,QUOTEJINT,QUOTEX,QUOTEELAM],[construct],MachineFloat)) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % +--R retract : Vector(Fraction(Polynomial(Integer))) -> % +--R retract : Vector(Fraction(Polynomial(Float))) -> % +--R retract : Vector(Polynomial(Integer)) -> % +--R retract : Vector(Polynomial(Float)) -> % +--R retract : Vector(Expression(Integer)) -> % +--R retract : Vector(Expression(Float)) -> % +--R retractIfCan : Vector(Fraction(Polynomial(Integer))) -> Union(%,"failed") +--R retractIfCan : Vector(Fraction(Polynomial(Float))) -> Union(%,"failed") +--R retractIfCan : Vector(Polynomial(Integer)) -> Union(%,"failed") +--R retractIfCan : Vector(Polynomial(Float)) -> Union(%,"failed") +--R retractIfCan : Vector(Expression(Integer)) -> Union(%,"failed") +--R retractIfCan : Vector(Expression(Float)) -> Union(%,"failed") --R --E 1 @@ -3902,7 +3916,8 @@ Asp10(name): Exports == Implementation where --S 1 of 1 )show Asp12 ---R Asp12 name: Symbol is a domain constructor +--R +--R Asp12(name: Symbol) is a domain constructor --R Abbreviation for Asp12 is ASP12 --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP12 @@ -4020,28 +4035,29 @@ Asp12(name): Exports == Implementation where --S 1 of 1 )show Asp19 ---R Asp19 name: Symbol is a domain constructor +--R +--R Asp19(name: Symbol) is a domain constructor --R Abbreviation for Asp19 is ASP19 --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP19 --R --R------------------------------- Operations -------------------------------- ---R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : FortranCode -> % coerce : List(FortranCode) -> % --R coerce : % -> OutputForm outputAsFortran : % -> Void ---R coerce : Vector FortranExpression([construct],[construct,QUOTEXC],MachineFloat) -> % ---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % ---R retract : Vector Fraction Polynomial Integer -> % ---R retract : Vector Fraction Polynomial Float -> % ---R retract : Vector Polynomial Integer -> % ---R retract : Vector Polynomial Float -> % ---R retract : Vector Expression Integer -> % ---R retract : Vector Expression Float -> % ---R retractIfCan : Vector Fraction Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Vector Fraction Polynomial Float -> Union(%,"failed") ---R retractIfCan : Vector Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Vector Polynomial Float -> Union(%,"failed") ---R retractIfCan : Vector Expression Integer -> Union(%,"failed") ---R retractIfCan : Vector Expression Float -> Union(%,"failed") +--R coerce : Vector(FortranExpression([construct],[construct,QUOTEXC],MachineFloat)) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % +--R retract : Vector(Fraction(Polynomial(Integer))) -> % +--R retract : Vector(Fraction(Polynomial(Float))) -> % +--R retract : Vector(Polynomial(Integer)) -> % +--R retract : Vector(Polynomial(Float)) -> % +--R retract : Vector(Expression(Integer)) -> % +--R retract : Vector(Expression(Float)) -> % +--R retractIfCan : Vector(Fraction(Polynomial(Integer))) -> Union(%,"failed") +--R retractIfCan : Vector(Fraction(Polynomial(Float))) -> Union(%,"failed") +--R retractIfCan : Vector(Polynomial(Integer)) -> Union(%,"failed") +--R retractIfCan : Vector(Polynomial(Float)) -> Union(%,"failed") +--R retractIfCan : Vector(Expression(Integer)) -> Union(%,"failed") +--R retractIfCan : Vector(Expression(Float)) -> Union(%,"failed") --R --E 1 @@ -4358,28 +4374,29 @@ Asp19(name): Exports == Implementation where --S 1 of 1 )show Asp20 ---R Asp20 name: Symbol is a domain constructor +--R +--R Asp20(name: Symbol) is a domain constructor --R Abbreviation for Asp20 is ASP20 --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP20 --R --R------------------------------- Operations -------------------------------- ---R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : FortranCode -> % coerce : List(FortranCode) -> % --R coerce : % -> OutputForm outputAsFortran : % -> Void ---R coerce : Matrix FortranExpression([construct],[construct,QUOTEX,QUOTEHESS],MachineFloat) -> % ---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % ---R retract : Matrix Fraction Polynomial Integer -> % ---R retract : Matrix Fraction Polynomial Float -> % ---R retract : Matrix Polynomial Integer -> % ---R retract : Matrix Polynomial Float -> % ---R retract : Matrix Expression Integer -> % ---R retract : Matrix Expression Float -> % ---R retractIfCan : Matrix Fraction Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Matrix Fraction Polynomial Float -> Union(%,"failed") ---R retractIfCan : Matrix Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Matrix Polynomial Float -> Union(%,"failed") ---R retractIfCan : Matrix Expression Integer -> Union(%,"failed") ---R retractIfCan : Matrix Expression Float -> Union(%,"failed") +--R coerce : Matrix(FortranExpression([construct],[construct,QUOTEX,QUOTEHESS],MachineFloat)) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % +--R retract : Matrix(Fraction(Polynomial(Integer))) -> % +--R retract : Matrix(Fraction(Polynomial(Float))) -> % +--R retract : Matrix(Polynomial(Integer)) -> % +--R retract : Matrix(Polynomial(Float)) -> % +--R retract : Matrix(Expression(Integer)) -> % +--R retract : Matrix(Expression(Float)) -> % +--R retractIfCan : Matrix(Fraction(Polynomial(Integer))) -> Union(%,"failed") +--R retractIfCan : Matrix(Fraction(Polynomial(Float))) -> Union(%,"failed") +--R retractIfCan : Matrix(Polynomial(Integer)) -> Union(%,"failed") +--R retractIfCan : Matrix(Polynomial(Float)) -> Union(%,"failed") +--R retractIfCan : Matrix(Expression(Integer)) -> Union(%,"failed") +--R retractIfCan : Matrix(Expression(Float)) -> Union(%,"failed") --R --E 1 @@ -4588,26 +4605,28 @@ Asp20(name): Exports == Implementation where --S 1 of 1 )show Asp24 ---R Asp24 name: Symbol is a domain constructor +--R +--R Asp24(name: Symbol) is a domain constructor --R Abbreviation for Asp24 is ASP24 --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP24 --R --R------------------------------- Operations -------------------------------- ---R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : FortranCode -> % coerce : List(FortranCode) -> % --R coerce : % -> OutputForm outputAsFortran : % -> Void ---R retract : Polynomial Integer -> % retract : Polynomial Float -> % ---R retract : Expression Integer -> % retract : Expression Float -> % +--R retract : Polynomial(Float) -> % retract : Expression(Float) -> % --R coerce : FortranExpression([construct],[construct,QUOTEXC],MachineFloat) -> % ---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % ---R retract : Fraction Polynomial Integer -> % ---R retract : Fraction Polynomial Float -> % ---R retractIfCan : Fraction Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Fraction Polynomial Float -> Union(%,"failed") ---R retractIfCan : Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Polynomial Float -> Union(%,"failed") ---R retractIfCan : Expression Integer -> Union(%,"failed") ---R retractIfCan : Expression Float -> Union(%,"failed") +--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % +--R retract : Fraction(Polynomial(Integer)) -> % +--R retract : Fraction(Polynomial(Float)) -> % +--R retract : Polynomial(Integer) -> % +--R retract : Expression(Integer) -> % +--R retractIfCan : Fraction(Polynomial(Integer)) -> Union(%,"failed") +--R retractIfCan : Fraction(Polynomial(Float)) -> Union(%,"failed") +--R retractIfCan : Polynomial(Integer) -> Union(%,"failed") +--R retractIfCan : Polynomial(Float) -> Union(%,"failed") +--R retractIfCan : Expression(Integer) -> Union(%,"failed") +--R retractIfCan : Expression(Float) -> Union(%,"failed") --R --E 1 @@ -4768,16 +4787,17 @@ Asp24(name): Exports == Implementation where --S 1 of 1 )show Asp27 ---R Asp27 name: Symbol is a domain constructor +--R +--R Asp27(name: Symbol) is a domain constructor --R Abbreviation for Asp27 is ASP27 --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP27 --R --R------------------------------- Operations -------------------------------- ---R coerce : FortranCode -> % coerce : List FortranCode -> % ---R coerce : Matrix MachineFloat -> % coerce : % -> OutputForm ---R outputAsFortran : % -> Void ---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R coerce : FortranCode -> % coerce : List(FortranCode) -> % +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % +--R coerce : Matrix(MachineFloat) -> % --R --E 1 @@ -4917,16 +4937,17 @@ Asp27(name): Exports == Implementation where --S 1 of 1 )show Asp28 ---R Asp28 name: Symbol is a domain constructor +--R +--R Asp28(name: Symbol) is a domain constructor --R Abbreviation for Asp28 is ASP28 --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP28 --R --R------------------------------- Operations -------------------------------- ---R coerce : FortranCode -> % coerce : List FortranCode -> % ---R coerce : Matrix MachineFloat -> % coerce : % -> OutputForm ---R outputAsFortran : % -> Void ---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R coerce : FortranCode -> % coerce : List(FortranCode) -> % +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % +--R coerce : Matrix(MachineFloat) -> % --R --E 1 @@ -5177,7 +5198,8 @@ Asp28(name): Exports == Implementation where --S 1 of 1 )show Asp29 ---R Asp29 name: Symbol is a domain constructor +--R +--R Asp29(name: Symbol) is a domain constructor --R Abbreviation for Asp29 is ASP29 --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP29 @@ -5298,16 +5320,17 @@ Asp29(name): Exports == Implementation where --S 1 of 1 )show Asp30 ---R Asp30 name: Symbol is a domain constructor +--R +--R Asp30(name: Symbol) is a domain constructor --R Abbreviation for Asp30 is ASP30 --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP30 --R --R------------------------------- Operations -------------------------------- ---R coerce : FortranCode -> % coerce : List FortranCode -> % ---R coerce : Matrix MachineFloat -> % coerce : % -> OutputForm ---R outputAsFortran : % -> Void ---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R coerce : FortranCode -> % coerce : List(FortranCode) -> % +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % +--R coerce : Matrix(MachineFloat) -> % --R --E 1 @@ -5477,28 +5500,29 @@ Asp30(name): Exports == Implementation where --S 1 of 1 )show Asp31 ---R Asp31 name: Symbol is a domain constructor +--R +--R Asp31(name: Symbol) is a domain constructor --R Abbreviation for Asp31 is ASP31 --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP31 --R --R------------------------------- Operations -------------------------------- ---R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : FortranCode -> % coerce : List(FortranCode) -> % --R coerce : % -> OutputForm outputAsFortran : % -> Void ---R coerce : Vector FortranExpression([construct,QUOTEX],[construct,QUOTEY],MachineFloat) -> % ---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % ---R retract : Vector Fraction Polynomial Integer -> % ---R retract : Vector Fraction Polynomial Float -> % ---R retract : Vector Polynomial Integer -> % ---R retract : Vector Polynomial Float -> % ---R retract : Vector Expression Integer -> % ---R retract : Vector Expression Float -> % ---R retractIfCan : Vector Fraction Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Vector Fraction Polynomial Float -> Union(%,"failed") ---R retractIfCan : Vector Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Vector Polynomial Float -> Union(%,"failed") ---R retractIfCan : Vector Expression Integer -> Union(%,"failed") ---R retractIfCan : Vector Expression Float -> Union(%,"failed") +--R coerce : Vector(FortranExpression([construct,QUOTEX],[construct,QUOTEY],MachineFloat)) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % +--R retract : Vector(Fraction(Polynomial(Integer))) -> % +--R retract : Vector(Fraction(Polynomial(Float))) -> % +--R retract : Vector(Polynomial(Integer)) -> % +--R retract : Vector(Polynomial(Float)) -> % +--R retract : Vector(Expression(Integer)) -> % +--R retract : Vector(Expression(Float)) -> % +--R retractIfCan : Vector(Fraction(Polynomial(Integer))) -> Union(%,"failed") +--R retractIfCan : Vector(Fraction(Polynomial(Float))) -> Union(%,"failed") +--R retractIfCan : Vector(Polynomial(Integer)) -> Union(%,"failed") +--R retractIfCan : Vector(Polynomial(Float)) -> Union(%,"failed") +--R retractIfCan : Vector(Expression(Integer)) -> Union(%,"failed") +--R retractIfCan : Vector(Expression(Float)) -> Union(%,"failed") --R --E 1 @@ -5704,7 +5728,8 @@ Asp31(name): Exports == Implementation where --S 1 of 1 )show Asp33 ---R Asp33 name: Symbol is a domain constructor +--R +--R Asp33(name: Symbol) is a domain constructor --R Abbreviation for Asp33 is ASP33 --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP33 @@ -5805,16 +5830,17 @@ Asp33(name): Exports == Implementation where --S 1 of 1 )show Asp34 ---R Asp34 name: Symbol is a domain constructor +--R +--R Asp34(name: Symbol) is a domain constructor --R Abbreviation for Asp34 is ASP34 --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP34 --R --R------------------------------- Operations -------------------------------- ---R coerce : FortranCode -> % coerce : List FortranCode -> % ---R coerce : Matrix MachineFloat -> % coerce : % -> OutputForm ---R outputAsFortran : % -> Void ---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R coerce : FortranCode -> % coerce : List(FortranCode) -> % +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % +--R coerce : Matrix(MachineFloat) -> % --R --E 1 @@ -5956,28 +5982,29 @@ Asp34(name): Exports == Implementation where --S 1 of 1 )show Asp35 ---R Asp35 name: Symbol is a domain constructor +--R +--R Asp35(name: Symbol) is a domain constructor --R Abbreviation for Asp35 is ASP35 --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP35 --R --R------------------------------- Operations -------------------------------- ---R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : FortranCode -> % coerce : List(FortranCode) -> % --R coerce : % -> OutputForm outputAsFortran : % -> Void ---R coerce : Vector FortranExpression([construct],[construct,QUOTEX],MachineFloat) -> % ---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % ---R retract : Vector Fraction Polynomial Integer -> % ---R retract : Vector Fraction Polynomial Float -> % ---R retract : Vector Polynomial Integer -> % ---R retract : Vector Polynomial Float -> % ---R retract : Vector Expression Integer -> % ---R retract : Vector Expression Float -> % ---R retractIfCan : Vector Fraction Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Vector Fraction Polynomial Float -> Union(%,"failed") ---R retractIfCan : Vector Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Vector Polynomial Float -> Union(%,"failed") ---R retractIfCan : Vector Expression Integer -> Union(%,"failed") ---R retractIfCan : Vector Expression Float -> Union(%,"failed") +--R coerce : Vector(FortranExpression([construct],[construct,QUOTEX],MachineFloat)) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % +--R retract : Vector(Fraction(Polynomial(Integer))) -> % +--R retract : Vector(Fraction(Polynomial(Float))) -> % +--R retract : Vector(Polynomial(Integer)) -> % +--R retract : Vector(Polynomial(Float)) -> % +--R retract : Vector(Expression(Integer)) -> % +--R retract : Vector(Expression(Float)) -> % +--R retractIfCan : Vector(Fraction(Polynomial(Integer))) -> Union(%,"failed") +--R retractIfCan : Vector(Fraction(Polynomial(Float))) -> Union(%,"failed") +--R retractIfCan : Vector(Polynomial(Integer)) -> Union(%,"failed") +--R retractIfCan : Vector(Polynomial(Float)) -> Union(%,"failed") +--R retractIfCan : Vector(Expression(Integer)) -> Union(%,"failed") +--R retractIfCan : Vector(Expression(Float)) -> Union(%,"failed") --R --E 1 @@ -6193,26 +6220,28 @@ Asp35(name): Exports == Implementation where --S 1 of 1 )show Asp4 ---R Asp4 name: Symbol is a domain constructor +--R +--R Asp4(name: Symbol) is a domain constructor --R Abbreviation for Asp4 is ASP4 --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP4 --R --R------------------------------- Operations -------------------------------- ---R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : FortranCode -> % coerce : List(FortranCode) -> % --R coerce : % -> OutputForm outputAsFortran : % -> Void ---R retract : Polynomial Integer -> % retract : Polynomial Float -> % ---R retract : Expression Integer -> % retract : Expression Float -> % +--R retract : Polynomial(Float) -> % retract : Expression(Float) -> % --R coerce : FortranExpression([construct],[construct,QUOTEX],MachineFloat) -> % ---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % ---R retract : Fraction Polynomial Integer -> % ---R retract : Fraction Polynomial Float -> % ---R retractIfCan : Fraction Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Fraction Polynomial Float -> Union(%,"failed") ---R retractIfCan : Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Polynomial Float -> Union(%,"failed") ---R retractIfCan : Expression Integer -> Union(%,"failed") ---R retractIfCan : Expression Float -> Union(%,"failed") +--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % +--R retract : Fraction(Polynomial(Integer)) -> % +--R retract : Fraction(Polynomial(Float)) -> % +--R retract : Polynomial(Integer) -> % +--R retract : Expression(Integer) -> % +--R retractIfCan : Fraction(Polynomial(Integer)) -> Union(%,"failed") +--R retractIfCan : Fraction(Polynomial(Float)) -> Union(%,"failed") +--R retractIfCan : Polynomial(Integer) -> Union(%,"failed") +--R retractIfCan : Polynomial(Float) -> Union(%,"failed") +--R retractIfCan : Expression(Integer) -> Union(%,"failed") +--R retractIfCan : Expression(Float) -> Union(%,"failed") --R --E 1 @@ -6366,28 +6395,29 @@ Asp4(name): Exports == Implementation where --S 1 of 1 )show Asp41 +--R --R Asp41(nameOne: Symbol,nameTwo: Symbol,nameThree: Symbol) is a domain constructor --R Abbreviation for Asp41 is ASP41 --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP41 --R --R------------------------------- Operations -------------------------------- ---R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : FortranCode -> % coerce : List(FortranCode) -> % --R coerce : % -> OutputForm outputAsFortran : % -> Void ---R coerce : Vector FortranExpression([construct,QUOTEX,QUOTEEPS],[construct,QUOTEY],MachineFloat) -> % ---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % ---R retract : Vector Fraction Polynomial Integer -> % ---R retract : Vector Fraction Polynomial Float -> % ---R retract : Vector Polynomial Integer -> % ---R retract : Vector Polynomial Float -> % ---R retract : Vector Expression Integer -> % ---R retract : Vector Expression Float -> % ---R retractIfCan : Vector Fraction Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Vector Fraction Polynomial Float -> Union(%,"failed") ---R retractIfCan : Vector Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Vector Polynomial Float -> Union(%,"failed") ---R retractIfCan : Vector Expression Integer -> Union(%,"failed") ---R retractIfCan : Vector Expression Float -> Union(%,"failed") +--R coerce : Vector(FortranExpression([construct,QUOTEX,QUOTEEPS],[construct,QUOTEY],MachineFloat)) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % +--R retract : Vector(Fraction(Polynomial(Integer))) -> % +--R retract : Vector(Fraction(Polynomial(Float))) -> % +--R retract : Vector(Polynomial(Integer)) -> % +--R retract : Vector(Polynomial(Float)) -> % +--R retract : Vector(Expression(Integer)) -> % +--R retract : Vector(Expression(Float)) -> % +--R retractIfCan : Vector(Fraction(Polynomial(Integer))) -> Union(%,"failed") +--R retractIfCan : Vector(Fraction(Polynomial(Float))) -> Union(%,"failed") +--R retractIfCan : Vector(Polynomial(Integer)) -> Union(%,"failed") +--R retractIfCan : Vector(Polynomial(Float)) -> Union(%,"failed") +--R retractIfCan : Vector(Expression(Integer)) -> Union(%,"failed") +--R retractIfCan : Vector(Expression(Float)) -> Union(%,"failed") --R --E 1 @@ -6649,28 +6679,29 @@ Asp41(nameOne,nameTwo,nameThree): Exports == Implementation where --S 1 of 1 )show Asp42 +--R --R Asp42(nameOne: Symbol,nameTwo: Symbol,nameThree: Symbol) is a domain constructor --R Abbreviation for Asp42 is ASP42 --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP42 --R --R------------------------------- Operations -------------------------------- ---R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : FortranCode -> % coerce : List(FortranCode) -> % --R coerce : % -> OutputForm outputAsFortran : % -> Void ---R coerce : Vector FortranExpression([construct,QUOTEEPS],[construct,QUOTEYA,QUOTEYB],MachineFloat) -> % ---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % ---R retract : Vector Fraction Polynomial Integer -> % ---R retract : Vector Fraction Polynomial Float -> % ---R retract : Vector Polynomial Integer -> % ---R retract : Vector Polynomial Float -> % ---R retract : Vector Expression Integer -> % ---R retract : Vector Expression Float -> % ---R retractIfCan : Vector Fraction Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Vector Fraction Polynomial Float -> Union(%,"failed") ---R retractIfCan : Vector Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Vector Polynomial Float -> Union(%,"failed") ---R retractIfCan : Vector Expression Integer -> Union(%,"failed") ---R retractIfCan : Vector Expression Float -> Union(%,"failed") +--R coerce : Vector(FortranExpression([construct,QUOTEEPS],[construct,QUOTEYA,QUOTEYB],MachineFloat)) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % +--R retract : Vector(Fraction(Polynomial(Integer))) -> % +--R retract : Vector(Fraction(Polynomial(Float))) -> % +--R retract : Vector(Polynomial(Integer)) -> % +--R retract : Vector(Polynomial(Float)) -> % +--R retract : Vector(Expression(Integer)) -> % +--R retract : Vector(Expression(Float)) -> % +--R retractIfCan : Vector(Fraction(Polynomial(Integer))) -> Union(%,"failed") +--R retractIfCan : Vector(Fraction(Polynomial(Float))) -> Union(%,"failed") +--R retractIfCan : Vector(Polynomial(Integer)) -> Union(%,"failed") +--R retractIfCan : Vector(Polynomial(Float)) -> Union(%,"failed") +--R retractIfCan : Vector(Expression(Integer)) -> Union(%,"failed") +--R retractIfCan : Vector(Expression(Float)) -> Union(%,"failed") --R --E 1 @@ -6954,26 +6985,28 @@ Asp42(nameOne,nameTwo,nameThree): Exports == Implementation where --S 1 of 1 )show Asp49 ---R Asp49 name: Symbol is a domain constructor +--R +--R Asp49(name: Symbol) is a domain constructor --R Abbreviation for Asp49 is ASP49 --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP49 --R --R------------------------------- Operations -------------------------------- ---R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : FortranCode -> % coerce : List(FortranCode) -> % --R coerce : % -> OutputForm outputAsFortran : % -> Void ---R retract : Polynomial Integer -> % retract : Polynomial Float -> % ---R retract : Expression Integer -> % retract : Expression Float -> % +--R retract : Polynomial(Float) -> % retract : Expression(Float) -> % --R coerce : FortranExpression([construct],[construct,QUOTEX],MachineFloat) -> % ---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % ---R retract : Fraction Polynomial Integer -> % ---R retract : Fraction Polynomial Float -> % ---R retractIfCan : Fraction Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Fraction Polynomial Float -> Union(%,"failed") ---R retractIfCan : Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Polynomial Float -> Union(%,"failed") ---R retractIfCan : Expression Integer -> Union(%,"failed") ---R retractIfCan : Expression Float -> Union(%,"failed") +--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % +--R retract : Fraction(Polynomial(Integer)) -> % +--R retract : Fraction(Polynomial(Float)) -> % +--R retract : Polynomial(Integer) -> % +--R retract : Expression(Integer) -> % +--R retractIfCan : Fraction(Polynomial(Integer)) -> Union(%,"failed") +--R retractIfCan : Fraction(Polynomial(Float)) -> Union(%,"failed") +--R retractIfCan : Polynomial(Integer) -> Union(%,"failed") +--R retractIfCan : Polynomial(Float) -> Union(%,"failed") +--R retractIfCan : Expression(Integer) -> Union(%,"failed") +--R retractIfCan : Expression(Float) -> Union(%,"failed") --R --E 1 @@ -7163,28 +7196,29 @@ Asp49(name): Exports == Implementation where --S 1 of 1 )show Asp50 ---R Asp50 name: Symbol is a domain constructor +--R +--R Asp50(name: Symbol) is a domain constructor --R Abbreviation for Asp50 is ASP50 --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP50 --R --R------------------------------- Operations -------------------------------- ---R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : FortranCode -> % coerce : List(FortranCode) -> % --R coerce : % -> OutputForm outputAsFortran : % -> Void ---R coerce : Vector FortranExpression([construct],[construct,QUOTEXC],MachineFloat) -> % ---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % ---R retract : Vector Fraction Polynomial Integer -> % ---R retract : Vector Fraction Polynomial Float -> % ---R retract : Vector Polynomial Integer -> % ---R retract : Vector Polynomial Float -> % ---R retract : Vector Expression Integer -> % ---R retract : Vector Expression Float -> % ---R retractIfCan : Vector Fraction Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Vector Fraction Polynomial Float -> Union(%,"failed") ---R retractIfCan : Vector Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Vector Polynomial Float -> Union(%,"failed") ---R retractIfCan : Vector Expression Integer -> Union(%,"failed") ---R retractIfCan : Vector Expression Float -> Union(%,"failed") +--R coerce : Vector(FortranExpression([construct],[construct,QUOTEXC],MachineFloat)) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % +--R retract : Vector(Fraction(Polynomial(Integer))) -> % +--R retract : Vector(Fraction(Polynomial(Float))) -> % +--R retract : Vector(Polynomial(Integer)) -> % +--R retract : Vector(Polynomial(Float)) -> % +--R retract : Vector(Expression(Integer)) -> % +--R retract : Vector(Expression(Float)) -> % +--R retractIfCan : Vector(Fraction(Polynomial(Integer))) -> Union(%,"failed") +--R retractIfCan : Vector(Fraction(Polynomial(Float))) -> Union(%,"failed") +--R retractIfCan : Vector(Polynomial(Integer)) -> Union(%,"failed") +--R retractIfCan : Vector(Polynomial(Float)) -> Union(%,"failed") +--R retractIfCan : Vector(Expression(Integer)) -> Union(%,"failed") +--R retractIfCan : Vector(Expression(Float)) -> Union(%,"failed") --R --E 1 @@ -7390,28 +7424,29 @@ Asp50(name): Exports == Implementation where --S 1 of 1 )show Asp55 ---R Asp55 name: Symbol is a domain constructor +--R +--R Asp55(name: Symbol) is a domain constructor --R Abbreviation for Asp55 is ASP55 --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP55 --R --R------------------------------- Operations -------------------------------- ---R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : FortranCode -> % coerce : List(FortranCode) -> % --R coerce : % -> OutputForm outputAsFortran : % -> Void ---R coerce : Vector FortranExpression([construct],[construct,QUOTEX],MachineFloat) -> % ---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % ---R retract : Vector Fraction Polynomial Integer -> % ---R retract : Vector Fraction Polynomial Float -> % ---R retract : Vector Polynomial Integer -> % ---R retract : Vector Polynomial Float -> % ---R retract : Vector Expression Integer -> % ---R retract : Vector Expression Float -> % ---R retractIfCan : Vector Fraction Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Vector Fraction Polynomial Float -> Union(%,"failed") ---R retractIfCan : Vector Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Vector Polynomial Float -> Union(%,"failed") ---R retractIfCan : Vector Expression Integer -> Union(%,"failed") ---R retractIfCan : Vector Expression Float -> Union(%,"failed") +--R coerce : Vector(FortranExpression([construct],[construct,QUOTEX],MachineFloat)) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % +--R retract : Vector(Fraction(Polynomial(Integer))) -> % +--R retract : Vector(Fraction(Polynomial(Float))) -> % +--R retract : Vector(Polynomial(Integer)) -> % +--R retract : Vector(Polynomial(Float)) -> % +--R retract : Vector(Expression(Integer)) -> % +--R retract : Vector(Expression(Float)) -> % +--R retractIfCan : Vector(Fraction(Polynomial(Integer))) -> Union(%,"failed") +--R retractIfCan : Vector(Fraction(Polynomial(Float))) -> Union(%,"failed") +--R retractIfCan : Vector(Polynomial(Integer)) -> Union(%,"failed") +--R retractIfCan : Vector(Polynomial(Float)) -> Union(%,"failed") +--R retractIfCan : Vector(Expression(Integer)) -> Union(%,"failed") +--R retractIfCan : Vector(Expression(Float)) -> Union(%,"failed") --R --E 1 @@ -7660,28 +7695,29 @@ Asp55(name): Exports == Implementation where --S 1 of 1 )show Asp6 ---R Asp6 name: Symbol is a domain constructor +--R +--R Asp6(name: Symbol) is a domain constructor --R Abbreviation for Asp6 is ASP6 --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP6 --R --R------------------------------- Operations -------------------------------- ---R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : FortranCode -> % coerce : List(FortranCode) -> % --R coerce : % -> OutputForm outputAsFortran : % -> Void ---R coerce : Vector FortranExpression([construct],[construct,QUOTEX],MachineFloat) -> % ---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % ---R retract : Vector Fraction Polynomial Integer -> % ---R retract : Vector Fraction Polynomial Float -> % ---R retract : Vector Polynomial Integer -> % ---R retract : Vector Polynomial Float -> % ---R retract : Vector Expression Integer -> % ---R retract : Vector Expression Float -> % ---R retractIfCan : Vector Fraction Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Vector Fraction Polynomial Float -> Union(%,"failed") ---R retractIfCan : Vector Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Vector Polynomial Float -> Union(%,"failed") ---R retractIfCan : Vector Expression Integer -> Union(%,"failed") ---R retractIfCan : Vector Expression Float -> Union(%,"failed") +--R coerce : Vector(FortranExpression([construct],[construct,QUOTEX],MachineFloat)) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % +--R retract : Vector(Fraction(Polynomial(Integer))) -> % +--R retract : Vector(Fraction(Polynomial(Float))) -> % +--R retract : Vector(Polynomial(Integer)) -> % +--R retract : Vector(Polynomial(Float)) -> % +--R retract : Vector(Expression(Integer)) -> % +--R retract : Vector(Expression(Float)) -> % +--R retractIfCan : Vector(Fraction(Polynomial(Integer))) -> Union(%,"failed") +--R retractIfCan : Vector(Fraction(Polynomial(Float))) -> Union(%,"failed") +--R retractIfCan : Vector(Polynomial(Integer)) -> Union(%,"failed") +--R retractIfCan : Vector(Polynomial(Float)) -> Union(%,"failed") +--R retractIfCan : Vector(Expression(Integer)) -> Union(%,"failed") +--R retractIfCan : Vector(Expression(Float)) -> Union(%,"failed") --R --E 1 @@ -7873,28 +7909,29 @@ Asp6(name): Exports == Implementation where --S 1 of 1 )show Asp7 ---R Asp7 name: Symbol is a domain constructor +--R +--R Asp7(name: Symbol) is a domain constructor --R Abbreviation for Asp7 is ASP7 --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP7 --R --R------------------------------- Operations -------------------------------- ---R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : FortranCode -> % coerce : List(FortranCode) -> % --R coerce : % -> OutputForm outputAsFortran : % -> Void ---R coerce : Vector FortranExpression([construct,QUOTEX],[construct,QUOTEY],MachineFloat) -> % ---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % ---R retract : Vector Fraction Polynomial Integer -> % ---R retract : Vector Fraction Polynomial Float -> % ---R retract : Vector Polynomial Integer -> % ---R retract : Vector Polynomial Float -> % ---R retract : Vector Expression Integer -> % ---R retract : Vector Expression Float -> % ---R retractIfCan : Vector Fraction Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Vector Fraction Polynomial Float -> Union(%,"failed") ---R retractIfCan : Vector Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Vector Polynomial Float -> Union(%,"failed") ---R retractIfCan : Vector Expression Integer -> Union(%,"failed") ---R retractIfCan : Vector Expression Float -> Union(%,"failed") +--R coerce : Vector(FortranExpression([construct,QUOTEX],[construct,QUOTEY],MachineFloat)) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % +--R retract : Vector(Fraction(Polynomial(Integer))) -> % +--R retract : Vector(Fraction(Polynomial(Float))) -> % +--R retract : Vector(Polynomial(Integer)) -> % +--R retract : Vector(Polynomial(Float)) -> % +--R retract : Vector(Expression(Integer)) -> % +--R retract : Vector(Expression(Float)) -> % +--R retractIfCan : Vector(Fraction(Polynomial(Integer))) -> Union(%,"failed") +--R retractIfCan : Vector(Fraction(Polynomial(Float))) -> Union(%,"failed") +--R retractIfCan : Vector(Polynomial(Integer)) -> Union(%,"failed") +--R retractIfCan : Vector(Polynomial(Float)) -> Union(%,"failed") +--R retractIfCan : Vector(Expression(Integer)) -> Union(%,"failed") +--R retractIfCan : Vector(Expression(Float)) -> Union(%,"failed") --R --E 1 @@ -8071,28 +8108,29 @@ Asp7(name): Exports == Implementation where --S 1 of 1 )show Asp73 ---R Asp73 name: Symbol is a domain constructor +--R +--R Asp73(name: Symbol) is a domain constructor --R Abbreviation for Asp73 is ASP73 --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP73 --R --R------------------------------- Operations -------------------------------- ---R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : FortranCode -> % coerce : List(FortranCode) -> % --R coerce : % -> OutputForm outputAsFortran : % -> Void ---R coerce : Vector FortranExpression([construct,QUOTEX,QUOTEY],[construct],MachineFloat) -> % ---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % ---R retract : Vector Fraction Polynomial Integer -> % ---R retract : Vector Fraction Polynomial Float -> % ---R retract : Vector Polynomial Integer -> % ---R retract : Vector Polynomial Float -> % ---R retract : Vector Expression Integer -> % ---R retract : Vector Expression Float -> % ---R retractIfCan : Vector Fraction Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Vector Fraction Polynomial Float -> Union(%,"failed") ---R retractIfCan : Vector Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Vector Polynomial Float -> Union(%,"failed") ---R retractIfCan : Vector Expression Integer -> Union(%,"failed") ---R retractIfCan : Vector Expression Float -> Union(%,"failed") +--R coerce : Vector(FortranExpression([construct,QUOTEX,QUOTEY],[construct],MachineFloat)) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % +--R retract : Vector(Fraction(Polynomial(Integer))) -> % +--R retract : Vector(Fraction(Polynomial(Float))) -> % +--R retract : Vector(Polynomial(Integer)) -> % +--R retract : Vector(Polynomial(Float)) -> % +--R retract : Vector(Expression(Integer)) -> % +--R retract : Vector(Expression(Float)) -> % +--R retractIfCan : Vector(Fraction(Polynomial(Integer))) -> Union(%,"failed") +--R retractIfCan : Vector(Fraction(Polynomial(Float))) -> Union(%,"failed") +--R retractIfCan : Vector(Polynomial(Integer)) -> Union(%,"failed") +--R retractIfCan : Vector(Polynomial(Float)) -> Union(%,"failed") +--R retractIfCan : Vector(Expression(Integer)) -> Union(%,"failed") +--R retractIfCan : Vector(Expression(Float)) -> Union(%,"failed") --R --E 1 @@ -8281,28 +8319,29 @@ Asp73(name): Exports == Implementation where --S 1 of 1 )show Asp74 ---R Asp74 name: Symbol is a domain constructor +--R +--R Asp74(name: Symbol) is a domain constructor --R Abbreviation for Asp74 is ASP74 --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP74 --R --R------------------------------- Operations -------------------------------- ---R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : FortranCode -> % coerce : List(FortranCode) -> % --R coerce : % -> OutputForm outputAsFortran : % -> Void ---R coerce : Matrix FortranExpression([construct,QUOTEX,QUOTEY],[construct],MachineFloat) -> % ---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % ---R retract : Matrix Fraction Polynomial Integer -> % ---R retract : Matrix Fraction Polynomial Float -> % ---R retract : Matrix Polynomial Integer -> % ---R retract : Matrix Polynomial Float -> % ---R retract : Matrix Expression Integer -> % ---R retract : Matrix Expression Float -> % ---R retractIfCan : Matrix Fraction Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Matrix Fraction Polynomial Float -> Union(%,"failed") ---R retractIfCan : Matrix Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Matrix Polynomial Float -> Union(%,"failed") ---R retractIfCan : Matrix Expression Integer -> Union(%,"failed") ---R retractIfCan : Matrix Expression Float -> Union(%,"failed") +--R coerce : Matrix(FortranExpression([construct,QUOTEX,QUOTEY],[construct],MachineFloat)) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % +--R retract : Matrix(Fraction(Polynomial(Integer))) -> % +--R retract : Matrix(Fraction(Polynomial(Float))) -> % +--R retract : Matrix(Polynomial(Integer)) -> % +--R retract : Matrix(Polynomial(Float)) -> % +--R retract : Matrix(Expression(Integer)) -> % +--R retract : Matrix(Expression(Float)) -> % +--R retractIfCan : Matrix(Fraction(Polynomial(Integer))) -> Union(%,"failed") +--R retractIfCan : Matrix(Fraction(Polynomial(Float))) -> Union(%,"failed") +--R retractIfCan : Matrix(Polynomial(Integer)) -> Union(%,"failed") +--R retractIfCan : Matrix(Polynomial(Float)) -> Union(%,"failed") +--R retractIfCan : Matrix(Expression(Integer)) -> Union(%,"failed") +--R retractIfCan : Matrix(Expression(Float)) -> Union(%,"failed") --R --E 1 @@ -8533,28 +8572,29 @@ Asp74(name): Exports == Implementation where --S 1 of 1 )show Asp77 ---R Asp77 name: Symbol is a domain constructor +--R +--R Asp77(name: Symbol) is a domain constructor --R Abbreviation for Asp77 is ASP77 --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP77 --R --R------------------------------- Operations -------------------------------- ---R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : FortranCode -> % coerce : List(FortranCode) -> % --R coerce : % -> OutputForm outputAsFortran : % -> Void ---R coerce : Matrix FortranExpression([construct,QUOTEX],[construct],MachineFloat) -> % ---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % ---R retract : Matrix Fraction Polynomial Integer -> % ---R retract : Matrix Fraction Polynomial Float -> % ---R retract : Matrix Polynomial Integer -> % ---R retract : Matrix Polynomial Float -> % ---R retract : Matrix Expression Integer -> % ---R retract : Matrix Expression Float -> % ---R retractIfCan : Matrix Fraction Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Matrix Fraction Polynomial Float -> Union(%,"failed") ---R retractIfCan : Matrix Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Matrix Polynomial Float -> Union(%,"failed") ---R retractIfCan : Matrix Expression Integer -> Union(%,"failed") ---R retractIfCan : Matrix Expression Float -> Union(%,"failed") +--R coerce : Matrix(FortranExpression([construct,QUOTEX],[construct],MachineFloat)) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % +--R retract : Matrix(Fraction(Polynomial(Integer))) -> % +--R retract : Matrix(Fraction(Polynomial(Float))) -> % +--R retract : Matrix(Polynomial(Integer)) -> % +--R retract : Matrix(Polynomial(Float)) -> % +--R retract : Matrix(Expression(Integer)) -> % +--R retract : Matrix(Expression(Float)) -> % +--R retractIfCan : Matrix(Fraction(Polynomial(Integer))) -> Union(%,"failed") +--R retractIfCan : Matrix(Fraction(Polynomial(Float))) -> Union(%,"failed") +--R retractIfCan : Matrix(Polynomial(Integer)) -> Union(%,"failed") +--R retractIfCan : Matrix(Polynomial(Float)) -> Union(%,"failed") +--R retractIfCan : Matrix(Expression(Integer)) -> Union(%,"failed") +--R retractIfCan : Matrix(Expression(Float)) -> Union(%,"failed") --R --E 1 @@ -8750,28 +8790,29 @@ Asp77(name): Exports == Implementation where --S 1 of 1 )show Asp78 ---R Asp78 name: Symbol is a domain constructor +--R +--R Asp78(name: Symbol) is a domain constructor --R Abbreviation for Asp78 is ASP78 --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP78 --R --R------------------------------- Operations -------------------------------- ---R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : FortranCode -> % coerce : List(FortranCode) -> % --R coerce : % -> OutputForm outputAsFortran : % -> Void ---R coerce : Vector FortranExpression([construct,QUOTEX],[construct],MachineFloat) -> % ---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % ---R retract : Vector Fraction Polynomial Integer -> % ---R retract : Vector Fraction Polynomial Float -> % ---R retract : Vector Polynomial Integer -> % ---R retract : Vector Polynomial Float -> % ---R retract : Vector Expression Integer -> % ---R retract : Vector Expression Float -> % ---R retractIfCan : Vector Fraction Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Vector Fraction Polynomial Float -> Union(%,"failed") ---R retractIfCan : Vector Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Vector Polynomial Float -> Union(%,"failed") ---R retractIfCan : Vector Expression Integer -> Union(%,"failed") ---R retractIfCan : Vector Expression Float -> Union(%,"failed") +--R coerce : Vector(FortranExpression([construct,QUOTEX],[construct],MachineFloat)) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % +--R retract : Vector(Fraction(Polynomial(Integer))) -> % +--R retract : Vector(Fraction(Polynomial(Float))) -> % +--R retract : Vector(Polynomial(Integer)) -> % +--R retract : Vector(Polynomial(Float)) -> % +--R retract : Vector(Expression(Integer)) -> % +--R retract : Vector(Expression(Float)) -> % +--R retractIfCan : Vector(Fraction(Polynomial(Integer))) -> Union(%,"failed") +--R retractIfCan : Vector(Fraction(Polynomial(Float))) -> Union(%,"failed") +--R retractIfCan : Vector(Polynomial(Integer)) -> Union(%,"failed") +--R retractIfCan : Vector(Polynomial(Float)) -> Union(%,"failed") +--R retractIfCan : Vector(Expression(Integer)) -> Union(%,"failed") +--R retractIfCan : Vector(Expression(Float)) -> Union(%,"failed") --R --E 1 @@ -8942,16 +8983,17 @@ Asp78(name): Exports == Implementation where --S 1 of 1 )show Asp8 ---R Asp8 name: Symbol is a domain constructor +--R +--R Asp8(name: Symbol) is a domain constructor --R Abbreviation for Asp8 is ASP8 --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP8 --R --R------------------------------- Operations -------------------------------- ---R coerce : FortranCode -> % coerce : List FortranCode -> % ---R coerce : Vector MachineFloat -> % coerce : % -> OutputForm ---R outputAsFortran : % -> Void ---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R coerce : FortranCode -> % coerce : List(FortranCode) -> % +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % +--R coerce : Vector(MachineFloat) -> % --R --E 1 @@ -9122,28 +9164,29 @@ Asp8(name): Exports == Implementation where --S 1 of 1 )show Asp80 ---R Asp80 name: Symbol is a domain constructor +--R +--R Asp80(name: Symbol) is a domain constructor --R Abbreviation for Asp80 is ASP80 --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP80 --R --R------------------------------- Operations -------------------------------- ---R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : FortranCode -> % coerce : List(FortranCode) -> % --R coerce : % -> OutputForm outputAsFortran : % -> Void ---R coerce : Matrix FortranExpression([construct,QUOTEXL,QUOTEXR,QUOTEELAM],[construct],MachineFloat) -> % ---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % ---R retract : Matrix Fraction Polynomial Integer -> % ---R retract : Matrix Fraction Polynomial Float -> % ---R retract : Matrix Polynomial Integer -> % ---R retract : Matrix Polynomial Float -> % ---R retract : Matrix Expression Integer -> % ---R retract : Matrix Expression Float -> % ---R retractIfCan : Matrix Fraction Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Matrix Fraction Polynomial Float -> Union(%,"failed") ---R retractIfCan : Matrix Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Matrix Polynomial Float -> Union(%,"failed") ---R retractIfCan : Matrix Expression Integer -> Union(%,"failed") ---R retractIfCan : Matrix Expression Float -> Union(%,"failed") +--R coerce : Matrix(FortranExpression([construct,QUOTEXL,QUOTEXR,QUOTEELAM],[construct],MachineFloat)) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % +--R retract : Matrix(Fraction(Polynomial(Integer))) -> % +--R retract : Matrix(Fraction(Polynomial(Float))) -> % +--R retract : Matrix(Polynomial(Integer)) -> % +--R retract : Matrix(Polynomial(Float)) -> % +--R retract : Matrix(Expression(Integer)) -> % +--R retract : Matrix(Expression(Float)) -> % +--R retractIfCan : Matrix(Fraction(Polynomial(Integer))) -> Union(%,"failed") +--R retractIfCan : Matrix(Fraction(Polynomial(Float))) -> Union(%,"failed") +--R retractIfCan : Matrix(Polynomial(Integer)) -> Union(%,"failed") +--R retractIfCan : Matrix(Polynomial(Float)) -> Union(%,"failed") +--R retractIfCan : Matrix(Expression(Integer)) -> Union(%,"failed") +--R retractIfCan : Matrix(Expression(Float)) -> Union(%,"failed") --R --E 1 @@ -9337,26 +9380,28 @@ Asp80(name): Exports == Implementation where --S 1 of 1 )show Asp9 ---R Asp9 name: Symbol is a domain constructor +--R +--R Asp9(name: Symbol) is a domain constructor --R Abbreviation for Asp9 is ASP9 --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP9 --R --R------------------------------- Operations -------------------------------- ---R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : FortranCode -> % coerce : List(FortranCode) -> % --R coerce : % -> OutputForm outputAsFortran : % -> Void ---R retract : Polynomial Integer -> % retract : Polynomial Float -> % ---R retract : Expression Integer -> % retract : Expression Float -> % +--R retract : Polynomial(Float) -> % retract : Expression(Float) -> % --R coerce : FortranExpression([construct,QUOTEX],[construct,QUOTEY],MachineFloat) -> % ---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % ---R retract : Fraction Polynomial Integer -> % ---R retract : Fraction Polynomial Float -> % ---R retractIfCan : Fraction Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Fraction Polynomial Float -> Union(%,"failed") ---R retractIfCan : Polynomial Integer -> Union(%,"failed") ---R retractIfCan : Polynomial Float -> Union(%,"failed") ---R retractIfCan : Expression Integer -> Union(%,"failed") ---R retractIfCan : Expression Float -> Union(%,"failed") +--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % +--R retract : Fraction(Polynomial(Integer)) -> % +--R retract : Fraction(Polynomial(Float)) -> % +--R retract : Polynomial(Integer) -> % +--R retract : Expression(Integer) -> % +--R retractIfCan : Fraction(Polynomial(Integer)) -> Union(%,"failed") +--R retractIfCan : Fraction(Polynomial(Float)) -> Union(%,"failed") +--R retractIfCan : Polynomial(Integer) -> Union(%,"failed") +--R retractIfCan : Polynomial(Float) -> Union(%,"failed") +--R retractIfCan : Expression(Integer) -> Union(%,"failed") +--R retractIfCan : Expression(Float) -> Union(%,"failed") --R --E 1 @@ -9528,7 +9573,8 @@ Asp9(name): Exports == Implementation where --S 1 of 1 )show AssociatedJordanAlgebra ---R AssociatedJordanAlgebra(R: CommutativeRing,A: NonAssociativeAlgebra R) is a domain constructor +--R +--R AssociatedJordanAlgebra(R: CommutativeRing,A: NonAssociativeAlgebra(R)) is a domain constructor --R Abbreviation for AssociatedJordanAlgebra is JORDAN --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for JORDAN @@ -9546,73 +9592,73 @@ Asp9(name): Exports == Implementation where --R latex : % -> String sample : () -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (NonNegativeInteger,%) -> % ---R alternative? : () -> Boolean if A has FINAALG R ---R antiAssociative? : () -> Boolean if A has FINAALG R ---R antiCommutative? : () -> Boolean if A has FINAALG R ---R apply : (Matrix R,%) -> % if A has FRNAALG R ---R associative? : () -> Boolean if A has FINAALG R ---R associatorDependence : () -> List Vector R if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM ---R basis : () -> Vector % if A has FRNAALG R ---R commutative? : () -> Boolean if A has FINAALG R ---R conditionsForIdempotents : Vector % -> List Polynomial R if A has FINAALG R ---R conditionsForIdempotents : () -> List Polynomial R if A has FRNAALG R ---R convert : % -> Vector R if A has FRNAALG R ---R convert : Vector R -> % if A has FRNAALG R ---R coordinates : (%,Vector %) -> Vector R if A has FINAALG R ---R coordinates : (Vector %,Vector %) -> Matrix R if A has FINAALG R ---R coordinates : % -> Vector R if A has FRNAALG R ---R coordinates : Vector % -> Matrix R if A has FRNAALG R ---R ?.? : (%,Integer) -> R if A has FRNAALG R ---R flexible? : () -> Boolean if A has FINAALG R ---R jacobiIdentity? : () -> Boolean if A has FINAALG R ---R jordanAdmissible? : () -> Boolean if A has FINAALG R ---R jordanAlgebra? : () -> Boolean if A has FINAALG R ---R leftAlternative? : () -> Boolean if A has FINAALG R ---R leftCharacteristicPolynomial : % -> SparseUnivariatePolynomial R if A has FINAALG R ---R leftDiscriminant : Vector % -> R if A has FINAALG R ---R leftDiscriminant : () -> R if A has FRNAALG R ---R leftMinimalPolynomial : % -> SparseUnivariatePolynomial R if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM ---R leftNorm : % -> R if A has FINAALG R +--R alternative? : () -> Boolean if A has FINAALG(R) +--R antiAssociative? : () -> Boolean if A has FINAALG(R) +--R antiCommutative? : () -> Boolean if A has FINAALG(R) +--R apply : (Matrix(R),%) -> % if A has FRNAALG(R) +--R associative? : () -> Boolean if A has FINAALG(R) +--R associatorDependence : () -> List(Vector(R)) if A has FINAALG(R) and R has INTDOM or A has FRNAALG(R) and R has INTDOM +--R basis : () -> Vector(%) if A has FRNAALG(R) +--R commutative? : () -> Boolean if A has FINAALG(R) +--R conditionsForIdempotents : Vector(%) -> List(Polynomial(R)) if A has FINAALG(R) +--R conditionsForIdempotents : () -> List(Polynomial(R)) if A has FRNAALG(R) +--R convert : % -> Vector(R) if A has FRNAALG(R) +--R convert : Vector(R) -> % if A has FRNAALG(R) +--R coordinates : (%,Vector(%)) -> Vector(R) if A has FINAALG(R) +--R coordinates : (Vector(%),Vector(%)) -> Matrix(R) if A has FINAALG(R) +--R coordinates : % -> Vector(R) if A has FRNAALG(R) +--R coordinates : Vector(%) -> Matrix(R) if A has FRNAALG(R) +--R ?.? : (%,Integer) -> R if A has FRNAALG(R) +--R flexible? : () -> Boolean if A has FINAALG(R) +--R jacobiIdentity? : () -> Boolean if A has FINAALG(R) +--R jordanAdmissible? : () -> Boolean if A has FINAALG(R) +--R jordanAlgebra? : () -> Boolean if A has FINAALG(R) +--R leftAlternative? : () -> Boolean if A has FINAALG(R) +--R leftCharacteristicPolynomial : % -> SparseUnivariatePolynomial(R) if A has FINAALG(R) +--R leftDiscriminant : Vector(%) -> R if A has FINAALG(R) +--R leftDiscriminant : () -> R if A has FRNAALG(R) +--R leftMinimalPolynomial : % -> SparseUnivariatePolynomial(R) if A has FINAALG(R) and R has INTDOM or A has FRNAALG(R) and R has INTDOM +--R leftNorm : % -> R if A has FINAALG(R) --R leftPower : (%,PositiveInteger) -> % ---R leftRankPolynomial : () -> SparseUnivariatePolynomial Polynomial R if A has FRNAALG R and R has FIELD ---R leftRecip : % -> Union(%,"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM ---R leftRegularRepresentation : (%,Vector %) -> Matrix R if A has FINAALG R ---R leftRegularRepresentation : % -> Matrix R if A has FRNAALG R ---R leftTrace : % -> R if A has FINAALG R ---R leftTraceMatrix : Vector % -> Matrix R if A has FINAALG R ---R leftTraceMatrix : () -> Matrix R if A has FRNAALG R ---R leftUnit : () -> Union(%,"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM ---R leftUnits : () -> Union(Record(particular: %,basis: List %),"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM ---R lieAdmissible? : () -> Boolean if A has FINAALG R ---R lieAlgebra? : () -> Boolean if A has FINAALG R ---R noncommutativeJordanAlgebra? : () -> Boolean if A has FINAALG R +--R leftRankPolynomial : () -> SparseUnivariatePolynomial(Polynomial(R)) if A has FRNAALG(R) and R has FIELD +--R leftRecip : % -> Union(%,"failed") if A has FINAALG(R) and R has INTDOM or A has FRNAALG(R) and R has INTDOM +--R leftRegularRepresentation : (%,Vector(%)) -> Matrix(R) if A has FINAALG(R) +--R leftRegularRepresentation : % -> Matrix(R) if A has FRNAALG(R) +--R leftTrace : % -> R if A has FINAALG(R) +--R leftTraceMatrix : Vector(%) -> Matrix(R) if A has FINAALG(R) +--R leftTraceMatrix : () -> Matrix(R) if A has FRNAALG(R) +--R leftUnit : () -> Union(%,"failed") if A has FINAALG(R) and R has INTDOM or A has FRNAALG(R) and R has INTDOM +--R leftUnits : () -> Union(Record(particular: %,basis: List(%)),"failed") if A has FINAALG(R) and R has INTDOM or A has FRNAALG(R) and R has INTDOM +--R lieAdmissible? : () -> Boolean if A has FINAALG(R) +--R lieAlgebra? : () -> Boolean if A has FINAALG(R) +--R noncommutativeJordanAlgebra? : () -> Boolean if A has FINAALG(R) --R plenaryPower : (%,PositiveInteger) -> % ---R powerAssociative? : () -> Boolean if A has FINAALG R ---R rank : () -> PositiveInteger if A has FINAALG R ---R recip : % -> Union(%,"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM ---R represents : (Vector R,Vector %) -> % if A has FINAALG R ---R represents : Vector R -> % if A has FRNAALG R ---R rightAlternative? : () -> Boolean if A has FINAALG R ---R rightCharacteristicPolynomial : % -> SparseUnivariatePolynomial R if A has FINAALG R ---R rightDiscriminant : Vector % -> R if A has FINAALG R ---R rightDiscriminant : () -> R if A has FRNAALG R ---R rightMinimalPolynomial : % -> SparseUnivariatePolynomial R if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM ---R rightNorm : % -> R if A has FINAALG R +--R powerAssociative? : () -> Boolean if A has FINAALG(R) +--R rank : () -> PositiveInteger if A has FINAALG(R) +--R recip : % -> Union(%,"failed") if A has FINAALG(R) and R has INTDOM or A has FRNAALG(R) and R has INTDOM +--R represents : (Vector(R),Vector(%)) -> % if A has FINAALG(R) +--R represents : Vector(R) -> % if A has FRNAALG(R) +--R rightAlternative? : () -> Boolean if A has FINAALG(R) +--R rightCharacteristicPolynomial : % -> SparseUnivariatePolynomial(R) if A has FINAALG(R) +--R rightDiscriminant : Vector(%) -> R if A has FINAALG(R) +--R rightDiscriminant : () -> R if A has FRNAALG(R) +--R rightMinimalPolynomial : % -> SparseUnivariatePolynomial(R) if A has FINAALG(R) and R has INTDOM or A has FRNAALG(R) and R has INTDOM +--R rightNorm : % -> R if A has FINAALG(R) --R rightPower : (%,PositiveInteger) -> % ---R rightRankPolynomial : () -> SparseUnivariatePolynomial Polynomial R if A has FRNAALG R and R has FIELD ---R rightRecip : % -> Union(%,"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM ---R rightRegularRepresentation : (%,Vector %) -> Matrix R if A has FINAALG R ---R rightRegularRepresentation : % -> Matrix R if A has FRNAALG R ---R rightTrace : % -> R if A has FINAALG R ---R rightTraceMatrix : Vector % -> Matrix R if A has FINAALG R ---R rightTraceMatrix : () -> Matrix R if A has FRNAALG R ---R rightUnit : () -> Union(%,"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM ---R rightUnits : () -> Union(Record(particular: %,basis: List %),"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM ---R someBasis : () -> Vector % if A has FINAALG R ---R structuralConstants : Vector % -> Vector Matrix R if A has FINAALG R ---R structuralConstants : () -> Vector Matrix R if A has FRNAALG R +--R rightRankPolynomial : () -> SparseUnivariatePolynomial(Polynomial(R)) if A has FRNAALG(R) and R has FIELD +--R rightRecip : % -> Union(%,"failed") if A has FINAALG(R) and R has INTDOM or A has FRNAALG(R) and R has INTDOM +--R rightRegularRepresentation : (%,Vector(%)) -> Matrix(R) if A has FINAALG(R) +--R rightRegularRepresentation : % -> Matrix(R) if A has FRNAALG(R) +--R rightTrace : % -> R if A has FINAALG(R) +--R rightTraceMatrix : Vector(%) -> Matrix(R) if A has FINAALG(R) +--R rightTraceMatrix : () -> Matrix(R) if A has FRNAALG(R) +--R rightUnit : () -> Union(%,"failed") if A has FINAALG(R) and R has INTDOM or A has FRNAALG(R) and R has INTDOM +--R rightUnits : () -> Union(Record(particular: %,basis: List(%)),"failed") if A has FINAALG(R) and R has INTDOM or A has FRNAALG(R) and R has INTDOM +--R someBasis : () -> Vector(%) if A has FINAALG(R) +--R structuralConstants : Vector(%) -> Vector(Matrix(R)) if A has FINAALG(R) +--R structuralConstants : () -> Vector(Matrix(R)) if A has FRNAALG(R) --R subtractIfCan : (%,%) -> Union(%,"failed") ---R unit : () -> Union(%,"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM +--R unit : () -> Union(%,"failed") if A has FINAALG(R) and R has INTDOM or A has FRNAALG(R) and R has INTDOM --R --E 1 @@ -9787,7 +9833,8 @@ AssociatedJordanAlgebra(R:CommutativeRing,A:NonAssociativeAlgebra R): --S 1 of 1 )show AssociatedLieAlgebra ---R AssociatedLieAlgebra(R: CommutativeRing,A: NonAssociativeAlgebra R) is a domain constructor +--R +--R AssociatedLieAlgebra(R: CommutativeRing,A: NonAssociativeAlgebra(R)) is a domain constructor --R Abbreviation for AssociatedLieAlgebra is LIE --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for LIE @@ -9805,73 +9852,73 @@ AssociatedJordanAlgebra(R:CommutativeRing,A:NonAssociativeAlgebra R): --R latex : % -> String sample : () -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (NonNegativeInteger,%) -> % ---R alternative? : () -> Boolean if A has FINAALG R ---R antiAssociative? : () -> Boolean if A has FINAALG R ---R antiCommutative? : () -> Boolean if A has FINAALG R ---R apply : (Matrix R,%) -> % if A has FRNAALG R ---R associative? : () -> Boolean if A has FINAALG R ---R associatorDependence : () -> List Vector R if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM ---R basis : () -> Vector % if A has FRNAALG R ---R commutative? : () -> Boolean if A has FINAALG R ---R conditionsForIdempotents : Vector % -> List Polynomial R if A has FINAALG R ---R conditionsForIdempotents : () -> List Polynomial R if A has FRNAALG R ---R convert : % -> Vector R if A has FRNAALG R ---R convert : Vector R -> % if A has FRNAALG R ---R coordinates : (%,Vector %) -> Vector R if A has FINAALG R ---R coordinates : (Vector %,Vector %) -> Matrix R if A has FINAALG R ---R coordinates : % -> Vector R if A has FRNAALG R ---R coordinates : Vector % -> Matrix R if A has FRNAALG R ---R ?.? : (%,Integer) -> R if A has FRNAALG R ---R flexible? : () -> Boolean if A has FINAALG R ---R jacobiIdentity? : () -> Boolean if A has FINAALG R ---R jordanAdmissible? : () -> Boolean if A has FINAALG R ---R jordanAlgebra? : () -> Boolean if A has FINAALG R ---R leftAlternative? : () -> Boolean if A has FINAALG R ---R leftCharacteristicPolynomial : % -> SparseUnivariatePolynomial R if A has FINAALG R ---R leftDiscriminant : Vector % -> R if A has FINAALG R ---R leftDiscriminant : () -> R if A has FRNAALG R ---R leftMinimalPolynomial : % -> SparseUnivariatePolynomial R if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM ---R leftNorm : % -> R if A has FINAALG R +--R alternative? : () -> Boolean if A has FINAALG(R) +--R antiAssociative? : () -> Boolean if A has FINAALG(R) +--R antiCommutative? : () -> Boolean if A has FINAALG(R) +--R apply : (Matrix(R),%) -> % if A has FRNAALG(R) +--R associative? : () -> Boolean if A has FINAALG(R) +--R associatorDependence : () -> List(Vector(R)) if A has FINAALG(R) and R has INTDOM or A has FRNAALG(R) and R has INTDOM +--R basis : () -> Vector(%) if A has FRNAALG(R) +--R commutative? : () -> Boolean if A has FINAALG(R) +--R conditionsForIdempotents : Vector(%) -> List(Polynomial(R)) if A has FINAALG(R) +--R conditionsForIdempotents : () -> List(Polynomial(R)) if A has FRNAALG(R) +--R convert : % -> Vector(R) if A has FRNAALG(R) +--R convert : Vector(R) -> % if A has FRNAALG(R) +--R coordinates : (%,Vector(%)) -> Vector(R) if A has FINAALG(R) +--R coordinates : (Vector(%),Vector(%)) -> Matrix(R) if A has FINAALG(R) +--R coordinates : % -> Vector(R) if A has FRNAALG(R) +--R coordinates : Vector(%) -> Matrix(R) if A has FRNAALG(R) +--R ?.? : (%,Integer) -> R if A has FRNAALG(R) +--R flexible? : () -> Boolean if A has FINAALG(R) +--R jacobiIdentity? : () -> Boolean if A has FINAALG(R) +--R jordanAdmissible? : () -> Boolean if A has FINAALG(R) +--R jordanAlgebra? : () -> Boolean if A has FINAALG(R) +--R leftAlternative? : () -> Boolean if A has FINAALG(R) +--R leftCharacteristicPolynomial : % -> SparseUnivariatePolynomial(R) if A has FINAALG(R) +--R leftDiscriminant : Vector(%) -> R if A has FINAALG(R) +--R leftDiscriminant : () -> R if A has FRNAALG(R) +--R leftMinimalPolynomial : % -> SparseUnivariatePolynomial(R) if A has FINAALG(R) and R has INTDOM or A has FRNAALG(R) and R has INTDOM +--R leftNorm : % -> R if A has FINAALG(R) --R leftPower : (%,PositiveInteger) -> % ---R leftRankPolynomial : () -> SparseUnivariatePolynomial Polynomial R if A has FRNAALG R and R has FIELD ---R leftRecip : % -> Union(%,"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM ---R leftRegularRepresentation : (%,Vector %) -> Matrix R if A has FINAALG R ---R leftRegularRepresentation : % -> Matrix R if A has FRNAALG R ---R leftTrace : % -> R if A has FINAALG R ---R leftTraceMatrix : Vector % -> Matrix R if A has FINAALG R ---R leftTraceMatrix : () -> Matrix R if A has FRNAALG R ---R leftUnit : () -> Union(%,"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM ---R leftUnits : () -> Union(Record(particular: %,basis: List %),"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM ---R lieAdmissible? : () -> Boolean if A has FINAALG R ---R lieAlgebra? : () -> Boolean if A has FINAALG R ---R noncommutativeJordanAlgebra? : () -> Boolean if A has FINAALG R +--R leftRankPolynomial : () -> SparseUnivariatePolynomial(Polynomial(R)) if A has FRNAALG(R) and R has FIELD +--R leftRecip : % -> Union(%,"failed") if A has FINAALG(R) and R has INTDOM or A has FRNAALG(R) and R has INTDOM +--R leftRegularRepresentation : (%,Vector(%)) -> Matrix(R) if A has FINAALG(R) +--R leftRegularRepresentation : % -> Matrix(R) if A has FRNAALG(R) +--R leftTrace : % -> R if A has FINAALG(R) +--R leftTraceMatrix : Vector(%) -> Matrix(R) if A has FINAALG(R) +--R leftTraceMatrix : () -> Matrix(R) if A has FRNAALG(R) +--R leftUnit : () -> Union(%,"failed") if A has FINAALG(R) and R has INTDOM or A has FRNAALG(R) and R has INTDOM +--R leftUnits : () -> Union(Record(particular: %,basis: List(%)),"failed") if A has FINAALG(R) and R has INTDOM or A has FRNAALG(R) and R has INTDOM +--R lieAdmissible? : () -> Boolean if A has FINAALG(R) +--R lieAlgebra? : () -> Boolean if A has FINAALG(R) +--R noncommutativeJordanAlgebra? : () -> Boolean if A has FINAALG(R) --R plenaryPower : (%,PositiveInteger) -> % ---R powerAssociative? : () -> Boolean if A has FINAALG R ---R rank : () -> PositiveInteger if A has FINAALG R ---R recip : % -> Union(%,"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM ---R represents : (Vector R,Vector %) -> % if A has FINAALG R ---R represents : Vector R -> % if A has FRNAALG R ---R rightAlternative? : () -> Boolean if A has FINAALG R ---R rightCharacteristicPolynomial : % -> SparseUnivariatePolynomial R if A has FINAALG R ---R rightDiscriminant : Vector % -> R if A has FINAALG R ---R rightDiscriminant : () -> R if A has FRNAALG R ---R rightMinimalPolynomial : % -> SparseUnivariatePolynomial R if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM ---R rightNorm : % -> R if A has FINAALG R +--R powerAssociative? : () -> Boolean if A has FINAALG(R) +--R rank : () -> PositiveInteger if A has FINAALG(R) +--R recip : % -> Union(%,"failed") if A has FINAALG(R) and R has INTDOM or A has FRNAALG(R) and R has INTDOM +--R represents : (Vector(R),Vector(%)) -> % if A has FINAALG(R) +--R represents : Vector(R) -> % if A has FRNAALG(R) +--R rightAlternative? : () -> Boolean if A has FINAALG(R) +--R rightCharacteristicPolynomial : % -> SparseUnivariatePolynomial(R) if A has FINAALG(R) +--R rightDiscriminant : Vector(%) -> R if A has FINAALG(R) +--R rightDiscriminant : () -> R if A has FRNAALG(R) +--R rightMinimalPolynomial : % -> SparseUnivariatePolynomial(R) if A has FINAALG(R) and R has INTDOM or A has FRNAALG(R) and R has INTDOM +--R rightNorm : % -> R if A has FINAALG(R) --R rightPower : (%,PositiveInteger) -> % ---R rightRankPolynomial : () -> SparseUnivariatePolynomial Polynomial R if A has FRNAALG R and R has FIELD ---R rightRecip : % -> Union(%,"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM ---R rightRegularRepresentation : (%,Vector %) -> Matrix R if A has FINAALG R ---R rightRegularRepresentation : % -> Matrix R if A has FRNAALG R ---R rightTrace : % -> R if A has FINAALG R ---R rightTraceMatrix : Vector % -> Matrix R if A has FINAALG R ---R rightTraceMatrix : () -> Matrix R if A has FRNAALG R ---R rightUnit : () -> Union(%,"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM ---R rightUnits : () -> Union(Record(particular: %,basis: List %),"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM ---R someBasis : () -> Vector % if A has FINAALG R ---R structuralConstants : Vector % -> Vector Matrix R if A has FINAALG R ---R structuralConstants : () -> Vector Matrix R if A has FRNAALG R +--R rightRankPolynomial : () -> SparseUnivariatePolynomial(Polynomial(R)) if A has FRNAALG(R) and R has FIELD +--R rightRecip : % -> Union(%,"failed") if A has FINAALG(R) and R has INTDOM or A has FRNAALG(R) and R has INTDOM +--R rightRegularRepresentation : (%,Vector(%)) -> Matrix(R) if A has FINAALG(R) +--R rightRegularRepresentation : % -> Matrix(R) if A has FRNAALG(R) +--R rightTrace : % -> R if A has FINAALG(R) +--R rightTraceMatrix : Vector(%) -> Matrix(R) if A has FINAALG(R) +--R rightTraceMatrix : () -> Matrix(R) if A has FRNAALG(R) +--R rightUnit : () -> Union(%,"failed") if A has FINAALG(R) and R has INTDOM or A has FRNAALG(R) and R has INTDOM +--R rightUnits : () -> Union(Record(particular: %,basis: List(%)),"failed") if A has FINAALG(R) and R has INTDOM or A has FRNAALG(R) and R has INTDOM +--R someBasis : () -> Vector(%) if A has FINAALG(R) +--R structuralConstants : Vector(%) -> Vector(Matrix(R)) if A has FINAALG(R) +--R structuralConstants : () -> Vector(Matrix(R)) if A has FRNAALG(R) --R subtractIfCan : (%,%) -> Union(%,"failed") ---R unit : () -> Union(%,"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM +--R unit : () -> Union(%,"failed") if A has FINAALG(R) and R has INTDOM or A has FRNAALG(R) and R has INTDOM --R --E 1 @@ -10723,7 +10770,8 @@ AttributeButtons(): E == I where --S 1 of 1 )show Automorphism ---R Automorphism R: Ring is a domain constructor +--R +--R Automorphism(R: Ring) is a domain constructor --R Abbreviation for Automorphism is AUTOMOR --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for AUTOMOR @@ -11231,7 +11279,8 @@ BalancedBinaryTree(S: SetCategory): Exports == Implementation where --S 1 of 1 )show BalancedPAdicInteger ---R BalancedPAdicInteger p: Integer is a domain constructor +--R +--R BalancedPAdicInteger(p: Integer) is a domain constructor --R Abbreviation for BalancedPAdicInteger is BPADIC --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for BPADIC @@ -11245,10 +11294,10 @@ BalancedBinaryTree(S: SetCategory): Exports == Implementation where --R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean --R coerce : % -> % coerce : Integer -> % --R coerce : % -> OutputForm complete : % -> % ---R digits : % -> Stream Integer extend : (%,Integer) -> % ---R gcd : List % -> % gcd : (%,%) -> % +--R digits : % -> Stream(Integer) extend : (%,Integer) -> % +--R gcd : List(%) -> % gcd : (%,%) -> % --R hash : % -> SingleInteger latex : % -> String ---R lcm : List % -> % lcm : (%,%) -> % +--R lcm : List(%) -> % lcm : (%,%) -> % --R moduloP : % -> Integer modulus : () -> Integer --R one? : % -> Boolean order : % -> NonNegativeInteger --R ?quo? : (%,%) -> % quotientByP : % -> % @@ -11264,14 +11313,14 @@ BalancedBinaryTree(S: SetCategory): Exports == Implementation where --R characteristic : () -> NonNegativeInteger --R divide : (%,%) -> Record(quotient: %,remainder: %) --R euclideanSize : % -> NonNegativeInteger ---R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") --R exquo : (%,%) -> Union(%,"failed") --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % ---R multiEuclidean : (List %,%) -> Union(List %,"failed") ---R principalIdeal : List % -> Record(coef: List %,generator: %) ---R root : (SparseUnivariatePolynomial Integer,Integer) -> % +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) +--R root : (SparseUnivariatePolynomial(Integer),Integer) -> % --R subtractIfCan : (%,%) -> Union(%,"failed") --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) --R @@ -11387,13 +11436,14 @@ BalancedPAdicInteger(p:Integer) == InnerPAdicInteger(p,false$Boolean) --S 1 of 1 )show BalancedPAdicRational ---R BalancedPAdicRational p: Integer is a domain constructor +--R +--R BalancedPAdicRational(p: Integer) is a domain constructor --R Abbreviation for BalancedPAdicRational is BPADICRT --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for BPADICRT --R --R------------------------------- Operations -------------------------------- ---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % --R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % @@ -11401,111 +11451,111 @@ BalancedPAdicInteger(p:Integer) == InnerPAdicInteger(p,false$Boolean) --R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % --R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % ---R associates? : (%,%) -> Boolean coerce : Fraction Integer -> % +--R associates? : (%,%) -> Boolean coerce : Fraction(Integer) -> % --R coerce : % -> % coerce : Integer -> % --R coerce : % -> OutputForm denominator : % -> % ---R factor : % -> Factored % gcd : List % -> % +--R factor : % -> Factored(%) gcd : List(%) -> % --R gcd : (%,%) -> % hash : % -> SingleInteger --R inv : % -> % latex : % -> String ---R lcm : List % -> % lcm : (%,%) -> % +--R lcm : List(%) -> % lcm : (%,%) -> % --R numerator : % -> % one? : % -> Boolean --R prime? : % -> Boolean ?quo? : (%,%) -> % --R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % --R removeZeroes : (Integer,%) -> % removeZeroes : % -> % --R sample : () -> % sizeLess? : (%,%) -> Boolean ---R squareFree : % -> Factored % squareFreePart : % -> % +--R squareFree : % -> Factored(%) squareFreePart : % -> % --R unit? : % -> Boolean unitCanonical : % -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (%,BalancedPAdicInteger p) -> % ---R ?*? : (BalancedPAdicInteger p,%) -> % +--R ?*? : (%,BalancedPAdicInteger(p)) -> % +--R ?*? : (BalancedPAdicInteger(p),%) -> % --R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (BalancedPAdicInteger p,BalancedPAdicInteger p) -> % ---R ? Boolean if BalancedPAdicInteger p has ORDSET ---R ?<=? : (%,%) -> Boolean if BalancedPAdicInteger p has ORDSET ---R ?>? : (%,%) -> Boolean if BalancedPAdicInteger p has ORDSET ---R ?>=? : (%,%) -> Boolean if BalancedPAdicInteger p has ORDSET ---R D : (%,(BalancedPAdicInteger p -> BalancedPAdicInteger p)) -> % ---R D : (%,(BalancedPAdicInteger p -> BalancedPAdicInteger p),NonNegativeInteger) -> % ---R D : (%,List Symbol,List NonNegativeInteger) -> % if BalancedPAdicInteger p has PDRING SYMBOL ---R D : (%,Symbol,NonNegativeInteger) -> % if BalancedPAdicInteger p has PDRING SYMBOL ---R D : (%,List Symbol) -> % if BalancedPAdicInteger p has PDRING SYMBOL ---R D : (%,Symbol) -> % if BalancedPAdicInteger p has PDRING SYMBOL ---R D : (%,NonNegativeInteger) -> % if BalancedPAdicInteger p has DIFRING ---R D : % -> % if BalancedPAdicInteger p has DIFRING +--R ?/? : (BalancedPAdicInteger(p),BalancedPAdicInteger(p)) -> % +--R ? Boolean if BalancedPAdicInteger(p) has ORDSET +--R ?<=? : (%,%) -> Boolean if BalancedPAdicInteger(p) has ORDSET +--R ?>? : (%,%) -> Boolean if BalancedPAdicInteger(p) has ORDSET +--R ?>=? : (%,%) -> Boolean if BalancedPAdicInteger(p) has ORDSET +--R D : (%,(BalancedPAdicInteger(p) -> BalancedPAdicInteger(p))) -> % +--R D : (%,(BalancedPAdicInteger(p) -> BalancedPAdicInteger(p)),NonNegativeInteger) -> % +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if BalancedPAdicInteger(p) has PDRING(SYMBOL) +--R D : (%,Symbol,NonNegativeInteger) -> % if BalancedPAdicInteger(p) has PDRING(SYMBOL) +--R D : (%,List(Symbol)) -> % if BalancedPAdicInteger(p) has PDRING(SYMBOL) +--R D : (%,Symbol) -> % if BalancedPAdicInteger(p) has PDRING(SYMBOL) +--R D : (%,NonNegativeInteger) -> % if BalancedPAdicInteger(p) has DIFRING +--R D : % -> % if BalancedPAdicInteger(p) has DIFRING --R ?^? : (%,NonNegativeInteger) -> % ---R abs : % -> % if BalancedPAdicInteger p has OINTDOM ---R approximate : (%,Integer) -> Fraction Integer ---R ceiling : % -> BalancedPAdicInteger p if BalancedPAdicInteger p has INS +--R abs : % -> % if BalancedPAdicInteger(p) has OINTDOM +--R approximate : (%,Integer) -> Fraction(Integer) +--R ceiling : % -> BalancedPAdicInteger(p) if BalancedPAdicInteger(p) has INS --R characteristic : () -> NonNegativeInteger ---R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and BalancedPAdicInteger p has PFECAT or BalancedPAdicInteger p has CHARNZ ---R coerce : Symbol -> % if BalancedPAdicInteger p has RETRACT SYMBOL ---R coerce : BalancedPAdicInteger p -> % ---R conditionP : Matrix % -> Union(Vector %,"failed") if $ has CHARNZ and BalancedPAdicInteger p has PFECAT ---R continuedFraction : % -> ContinuedFraction Fraction Integer ---R convert : % -> DoubleFloat if BalancedPAdicInteger p has REAL ---R convert : % -> Float if BalancedPAdicInteger p has REAL ---R convert : % -> InputForm if BalancedPAdicInteger p has KONVERT INFORM ---R convert : % -> Pattern Float if BalancedPAdicInteger p has KONVERT PATTERN FLOAT ---R convert : % -> Pattern Integer if BalancedPAdicInteger p has KONVERT PATTERN INT ---R denom : % -> BalancedPAdicInteger p ---R differentiate : (%,(BalancedPAdicInteger p -> BalancedPAdicInteger p)) -> % ---R differentiate : (%,(BalancedPAdicInteger p -> BalancedPAdicInteger p),NonNegativeInteger) -> % ---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if BalancedPAdicInteger p has PDRING SYMBOL ---R differentiate : (%,Symbol,NonNegativeInteger) -> % if BalancedPAdicInteger p has PDRING SYMBOL ---R differentiate : (%,List Symbol) -> % if BalancedPAdicInteger p has PDRING SYMBOL ---R differentiate : (%,Symbol) -> % if BalancedPAdicInteger p has PDRING SYMBOL ---R differentiate : (%,NonNegativeInteger) -> % if BalancedPAdicInteger p has DIFRING ---R differentiate : % -> % if BalancedPAdicInteger p has DIFRING +--R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and BalancedPAdicInteger(p) has PFECAT or BalancedPAdicInteger(p) has CHARNZ +--R coerce : Symbol -> % if BalancedPAdicInteger(p) has RETRACT(SYMBOL) +--R coerce : BalancedPAdicInteger(p) -> % +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and BalancedPAdicInteger(p) has PFECAT +--R continuedFraction : % -> ContinuedFraction(Fraction(Integer)) +--R convert : % -> DoubleFloat if BalancedPAdicInteger(p) has REAL +--R convert : % -> Float if BalancedPAdicInteger(p) has REAL +--R convert : % -> InputForm if BalancedPAdicInteger(p) has KONVERT(INFORM) +--R convert : % -> Pattern(Float) if BalancedPAdicInteger(p) has KONVERT(PATTERN(FLOAT)) +--R convert : % -> Pattern(Integer) if BalancedPAdicInteger(p) has KONVERT(PATTERN(INT)) +--R denom : % -> BalancedPAdicInteger(p) +--R differentiate : (%,(BalancedPAdicInteger(p) -> BalancedPAdicInteger(p))) -> % +--R differentiate : (%,(BalancedPAdicInteger(p) -> BalancedPAdicInteger(p)),NonNegativeInteger) -> % +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if BalancedPAdicInteger(p) has PDRING(SYMBOL) +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if BalancedPAdicInteger(p) has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol)) -> % if BalancedPAdicInteger(p) has PDRING(SYMBOL) +--R differentiate : (%,Symbol) -> % if BalancedPAdicInteger(p) has PDRING(SYMBOL) +--R differentiate : (%,NonNegativeInteger) -> % if BalancedPAdicInteger(p) has DIFRING +--R differentiate : % -> % if BalancedPAdicInteger(p) has DIFRING --R divide : (%,%) -> Record(quotient: %,remainder: %) ---R ?.? : (%,BalancedPAdicInteger p) -> % if BalancedPAdicInteger p has ELTAB(BPADIC p,BPADIC p) +--R ?.? : (%,BalancedPAdicInteger(p)) -> % if BalancedPAdicInteger(p) has ELTAB(BPADIC(p),BPADIC(p)) --R euclideanSize : % -> NonNegativeInteger ---R eval : (%,Symbol,BalancedPAdicInteger p) -> % if BalancedPAdicInteger p has IEVALAB(SYMBOL,BPADIC p) ---R eval : (%,List Symbol,List BalancedPAdicInteger p) -> % if BalancedPAdicInteger p has IEVALAB(SYMBOL,BPADIC p) ---R eval : (%,List Equation BalancedPAdicInteger p) -> % if BalancedPAdicInteger p has EVALAB BPADIC p ---R eval : (%,Equation BalancedPAdicInteger p) -> % if BalancedPAdicInteger p has EVALAB BPADIC p ---R eval : (%,BalancedPAdicInteger p,BalancedPAdicInteger p) -> % if BalancedPAdicInteger p has EVALAB BPADIC p ---R eval : (%,List BalancedPAdicInteger p,List BalancedPAdicInteger p) -> % if BalancedPAdicInteger p has EVALAB BPADIC p ---R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R eval : (%,Symbol,BalancedPAdicInteger(p)) -> % if BalancedPAdicInteger(p) has IEVALAB(SYMBOL,BPADIC(p)) +--R eval : (%,List(Symbol),List(BalancedPAdicInteger(p))) -> % if BalancedPAdicInteger(p) has IEVALAB(SYMBOL,BPADIC(p)) +--R eval : (%,List(Equation(BalancedPAdicInteger(p)))) -> % if BalancedPAdicInteger(p) has EVALAB(BPADIC(p)) +--R eval : (%,Equation(BalancedPAdicInteger(p))) -> % if BalancedPAdicInteger(p) has EVALAB(BPADIC(p)) +--R eval : (%,BalancedPAdicInteger(p),BalancedPAdicInteger(p)) -> % if BalancedPAdicInteger(p) has EVALAB(BPADIC(p)) +--R eval : (%,List(BalancedPAdicInteger(p)),List(BalancedPAdicInteger(p))) -> % if BalancedPAdicInteger(p) has EVALAB(BPADIC(p)) +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") --R exquo : (%,%) -> Union(%,"failed") --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) ---R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if BalancedPAdicInteger p has PFECAT ---R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if BalancedPAdicInteger p has PFECAT ---R floor : % -> BalancedPAdicInteger p if BalancedPAdicInteger p has INS ---R fractionPart : % -> % if BalancedPAdicInteger p has EUCDOM ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % ---R init : () -> % if BalancedPAdicInteger p has STEP ---R map : ((BalancedPAdicInteger p -> BalancedPAdicInteger p),%) -> % ---R max : (%,%) -> % if BalancedPAdicInteger p has ORDSET ---R min : (%,%) -> % if BalancedPAdicInteger p has ORDSET ---R multiEuclidean : (List %,%) -> Union(List %,"failed") ---R negative? : % -> Boolean if BalancedPAdicInteger p has OINTDOM ---R nextItem : % -> Union(%,"failed") if BalancedPAdicInteger p has STEP ---R numer : % -> BalancedPAdicInteger p ---R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if BalancedPAdicInteger p has PATMAB FLOAT ---R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if BalancedPAdicInteger p has PATMAB INT ---R positive? : % -> Boolean if BalancedPAdicInteger p has OINTDOM ---R principalIdeal : List % -> Record(coef: List %,generator: %) ---R random : () -> % if BalancedPAdicInteger p has INS ---R reducedSystem : Matrix % -> Matrix BalancedPAdicInteger p ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix BalancedPAdicInteger p,vec: Vector BalancedPAdicInteger p) ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if BalancedPAdicInteger p has LINEXP INT ---R reducedSystem : Matrix % -> Matrix Integer if BalancedPAdicInteger p has LINEXP INT ---R retract : % -> Integer if BalancedPAdicInteger p has RETRACT INT ---R retract : % -> Fraction Integer if BalancedPAdicInteger p has RETRACT INT ---R retract : % -> Symbol if BalancedPAdicInteger p has RETRACT SYMBOL ---R retract : % -> BalancedPAdicInteger p ---R retractIfCan : % -> Union(Integer,"failed") if BalancedPAdicInteger p has RETRACT INT ---R retractIfCan : % -> Union(Fraction Integer,"failed") if BalancedPAdicInteger p has RETRACT INT ---R retractIfCan : % -> Union(Symbol,"failed") if BalancedPAdicInteger p has RETRACT SYMBOL ---R retractIfCan : % -> Union(BalancedPAdicInteger p,"failed") ---R sign : % -> Integer if BalancedPAdicInteger p has OINTDOM ---R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if BalancedPAdicInteger p has PFECAT ---R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if BalancedPAdicInteger p has PFECAT +--R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if BalancedPAdicInteger(p) has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if BalancedPAdicInteger(p) has PFECAT +--R floor : % -> BalancedPAdicInteger(p) if BalancedPAdicInteger(p) has INS +--R fractionPart : % -> % if BalancedPAdicInteger(p) has EUCDOM +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) +--R init : () -> % if BalancedPAdicInteger(p) has STEP +--R map : ((BalancedPAdicInteger(p) -> BalancedPAdicInteger(p)),%) -> % +--R max : (%,%) -> % if BalancedPAdicInteger(p) has ORDSET +--R min : (%,%) -> % if BalancedPAdicInteger(p) has ORDSET +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") +--R negative? : % -> Boolean if BalancedPAdicInteger(p) has OINTDOM +--R nextItem : % -> Union(%,"failed") if BalancedPAdicInteger(p) has STEP +--R numer : % -> BalancedPAdicInteger(p) +--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if BalancedPAdicInteger(p) has PATMAB(FLOAT) +--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if BalancedPAdicInteger(p) has PATMAB(INT) +--R positive? : % -> Boolean if BalancedPAdicInteger(p) has OINTDOM +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) +--R random : () -> % if BalancedPAdicInteger(p) has INS +--R reducedSystem : Matrix(%) -> Matrix(BalancedPAdicInteger(p)) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(BalancedPAdicInteger(p)),vec: Vector(BalancedPAdicInteger(p))) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if BalancedPAdicInteger(p) has LINEXP(INT) +--R reducedSystem : Matrix(%) -> Matrix(Integer) if BalancedPAdicInteger(p) has LINEXP(INT) +--R retract : % -> Integer if BalancedPAdicInteger(p) has RETRACT(INT) +--R retract : % -> Fraction(Integer) if BalancedPAdicInteger(p) has RETRACT(INT) +--R retract : % -> Symbol if BalancedPAdicInteger(p) has RETRACT(SYMBOL) +--R retract : % -> BalancedPAdicInteger(p) +--R retractIfCan : % -> Union(Integer,"failed") if BalancedPAdicInteger(p) has RETRACT(INT) +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if BalancedPAdicInteger(p) has RETRACT(INT) +--R retractIfCan : % -> Union(Symbol,"failed") if BalancedPAdicInteger(p) has RETRACT(SYMBOL) +--R retractIfCan : % -> Union(BalancedPAdicInteger(p),"failed") +--R sign : % -> Integer if BalancedPAdicInteger(p) has OINTDOM +--R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if BalancedPAdicInteger(p) has PFECAT +--R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if BalancedPAdicInteger(p) has PFECAT --R subtractIfCan : (%,%) -> Union(%,"failed") --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) ---R wholePart : % -> BalancedPAdicInteger p if BalancedPAdicInteger p has EUCDOM +--R wholePart : % -> BalancedPAdicInteger(p) if BalancedPAdicInteger(p) has EUCDOM --R --E 1 @@ -11657,16 +11707,17 @@ BalancedPAdicRational(p:Integer) == --S 1 of 1 )show BasicFunctions +--R --R BasicFunctions is a domain constructor --R Abbreviation for BasicFunctions is BFUNCT --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for BFUNCT --R --R------------------------------- Operations -------------------------------- ---R ?=? : (%,%) -> Boolean bfKeys : () -> List Symbol +--R ?=? : (%,%) -> Boolean bfKeys : () -> List(Symbol) --R coerce : % -> OutputForm hash : % -> SingleInteger --R latex : % -> String ?~=? : (%,%) -> Boolean ---R bfEntry : Symbol -> Record(zeros: Stream DoubleFloat,ones: Stream DoubleFloat,singularities: Stream DoubleFloat) +--R bfEntry : Symbol -> Record(zeros: Stream(DoubleFloat),ones: Stream(DoubleFloat),singularities: Stream(DoubleFloat)) --R --E 1 @@ -11795,7 +11846,7 @@ deq := D(y x, x, 2) + D(y x, x) + y x = 0 --R ,, , --R (2) y (x) + y (x) + y(x)= 0 --R ---R Type: Equation Expression Integer +--R Type: Equation(Expression(Integer)) --E 2 --S 3 of 18 @@ -11807,7 +11858,7 @@ solve(deq, y, x) --R x\|3 2 2 x\|3 --R (3) [particular= 0,basis= [cos(-----)%e ,%e sin(-----)]] --R 2 2 ---RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--IType: Union(Record(particular: Expression(Integer),basis: ... --E 3 --S 4 of 18 @@ -12843,7 +12894,7 @@ r + binary(6/7) --R 0.000000100111011, 0.000000100111, --R ____________________________________________________ --R 0.00000010011010100100001110011111011001010110111100011] ---R Type: List BinaryExpansion +--R Type: List(BinaryExpansion) --E 3 --S 4 of 7 @@ -12869,7 +12920,7 @@ p := binary(1/4)*x**2 + binary(2/3)*x + binary(4/9) --R --R 2 __ ______ --R (5) 0.01x + 0.10x + 0.011100 ---R Type: Polynomial BinaryExpansion +--R Type: Polynomial(BinaryExpansion) --E 5 --S 6 of 7 @@ -12878,7 +12929,7 @@ q := D(p, x) --R --R __ --R (6) 0.1x + 0.10 ---R Type: Polynomial BinaryExpansion +--R Type: Polynomial(BinaryExpansion) --E 6 --S 7 of 7 @@ -12887,7 +12938,7 @@ g := gcd(p, q) --R --R __ --R (7) x + 1.01 ---R Type: Polynomial BinaryExpansion +--R Type: Polynomial(BinaryExpansion) --E 7 )spool )lisp (bye) @@ -13299,7 +13350,7 @@ lv := [8,3,5,4,6,2,1,5,7] --R --R --R (1) [8,3,5,4,6,2,1,5,7] ---R Type: List PositiveInteger +--R Type: List(PositiveInteger) --E 1 --S 2 of 12 @@ -13307,7 +13358,7 @@ t := binarySearchTree lv --R --R --R (2) [[[1,2,.],3,[4,5,[5,6,7]]],8,.] ---R Type: BinarySearchTree PositiveInteger +--R Type: BinarySearchTree(PositiveInteger) --E 2 --S 3 of 12 @@ -13315,7 +13366,7 @@ emptybst := empty()$BSTREE(INT) --R --R --R (3) [] ---R Type: BinarySearchTree Integer +--R Type: BinarySearchTree(Integer) --E 3 --S 4 of 12 @@ -13323,7 +13374,7 @@ t1 := insert!(8,emptybst) --R --R --R (4) 8 ---R Type: BinarySearchTree Integer +--R Type: BinarySearchTree(Integer) --E 4 --S 5 of 12 @@ -13331,7 +13382,7 @@ insert!(3,t1) --R --R --R (5) [3,8,.] ---R Type: BinarySearchTree Integer +--R Type: BinarySearchTree(Integer) --E 5 --S 6 of 12 @@ -13339,7 +13390,7 @@ leaves t --R --R --R (6) [1,4,5,7] ---R Type: List PositiveInteger +--R Type: List(PositiveInteger) --E 6 --S 7 of 12 @@ -13347,7 +13398,7 @@ split(3,t) --R --R --R (7) [less= [1,2,.],greater= [[.,3,[4,5,[5,6,7]]],8,.]] ---RType: Record(less: BinarySearchTree PositiveInteger,greater: BinarySearchTree PositiveInteger) +--IType: Record(less: BinarySearchTree(PositiveInteger),greater: ... --E 7 --S 8 of 12 @@ -13373,13 +13424,13 @@ buildFromRoot ls == reduce(insertRoot,ls,emptybst) --S 11 of 12 rt := buildFromRoot reverse lv --R ---R Compiling function buildFromRoot with type List PositiveInteger -> ---R BinarySearchTree Integer ---R Compiling function insertRoot with type (Integer,BinarySearchTree ---R Integer) -> BinarySearchTree Integer +--R Compiling function buildFromRoot with type List(PositiveInteger) -> +--R BinarySearchTree(Integer) +--R Compiling function insertRoot with type (Integer,BinarySearchTree( +--R Integer)) -> BinarySearchTree(Integer) --R --R (11) [[[1,2,.],3,[4,5,[5,6,7]]],8,.] ---R Type: BinarySearchTree Integer +--R Type: BinarySearchTree(Integer) --E 11 --S 12 of 12 @@ -13646,21 +13697,22 @@ both BinaryTree(S) --S 1 of 1 )show BinaryTournament ---R BinaryTournament S: OrderedSet is a domain constructor +--R +--R BinaryTournament(S: OrderedSet) is a domain constructor --R Abbreviation for BinaryTournament is BTOURN --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for BTOURN --R --R------------------------------- Operations -------------------------------- ---R binaryTournament : List S -> % children : % -> List % +--R binaryTournament : List(S) -> % children : % -> List(%) --R copy : % -> % cyclic? : % -> Boolean --R distance : (%,%) -> Integer ?.right : (%,right) -> % --R ?.left : (%,left) -> % ?.value : (%,value) -> S --R empty : () -> % empty? : % -> Boolean --R eq? : (%,%) -> Boolean insert! : (S,%) -> % ---R leaf? : % -> Boolean leaves : % -> List S +--R leaf? : % -> Boolean leaves : % -> List(S) --R left : % -> % map : ((S -> S),%) -> % ---R node : (%,S,%) -> % nodes : % -> List % +--R node : (%,S,%) -> % nodes : % -> List(%) --R right : % -> % sample : () -> % --R value : % -> S --R #? : % -> NonNegativeInteger if $ has finiteAggregate @@ -13670,21 +13722,21 @@ both BinaryTree(S) --R coerce : % -> OutputForm if S has SETCAT --R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT --R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate ---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if S has SETCAT --R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT ---R members : % -> List S if $ has finiteAggregate +--R members : % -> List(S) if $ has finiteAggregate --R more? : (%,NonNegativeInteger) -> Boolean --R node? : (%,%) -> Boolean if S has SETCAT ---R parts : % -> List S if $ has finiteAggregate ---R setchildren! : (%,List %) -> % if $ has shallowlyMutable +--R parts : % -> List(S) if $ has finiteAggregate +--R setchildren! : (%,List(%)) -> % if $ has shallowlyMutable --R setelt : (%,right,%) -> % if $ has shallowlyMutable --R setelt : (%,left,%) -> % if $ has shallowlyMutable --R setelt : (%,value,S) -> S if $ has shallowlyMutable @@ -13826,21 +13878,22 @@ BinaryTournament(S: OrderedSet): Exports == Implementation where --S 1 of 1 )show BinaryTree ---R BinaryTree S: SetCategory is a domain constructor +--R +--R BinaryTree(S: SetCategory) is a domain constructor --R Abbreviation for BinaryTree is BTREE --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for BTREE --R --R------------------------------- Operations -------------------------------- --R binaryTree : (%,S,%) -> % binaryTree : S -> % ---R children : % -> List % copy : % -> % +--R children : % -> List(%) copy : % -> % --R cyclic? : % -> Boolean distance : (%,%) -> Integer --R ?.right : (%,right) -> % ?.left : (%,left) -> % --R ?.value : (%,value) -> S empty : () -> % --R empty? : % -> Boolean eq? : (%,%) -> Boolean ---R leaf? : % -> Boolean leaves : % -> List S +--R leaf? : % -> Boolean leaves : % -> List(S) --R left : % -> % map : ((S -> S),%) -> % ---R node : (%,S,%) -> % nodes : % -> List % +--R node : (%,S,%) -> % nodes : % -> List(%) --R right : % -> % sample : () -> % --R value : % -> S --R #? : % -> NonNegativeInteger if $ has finiteAggregate @@ -13850,21 +13903,21 @@ BinaryTournament(S: OrderedSet): Exports == Implementation where --R coerce : % -> OutputForm if S has SETCAT --R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT --R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate ---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if S has SETCAT --R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT ---R members : % -> List S if $ has finiteAggregate +--R members : % -> List(S) if $ has finiteAggregate --R more? : (%,NonNegativeInteger) -> Boolean --R node? : (%,%) -> Boolean if S has SETCAT ---R parts : % -> List S if $ has finiteAggregate ---R setchildren! : (%,List %) -> % if $ has shallowlyMutable +--R parts : % -> List(S) if $ has finiteAggregate +--R setchildren! : (%,List(%)) -> % if $ has shallowlyMutable --R setelt : (%,right,%) -> % if $ has shallowlyMutable --R setelt : (%,left,%) -> % if $ has shallowlyMutable --R setelt : (%,value,S) -> S if $ has shallowlyMutable @@ -14022,6 +14075,7 @@ BinaryTree(S: SetCategory): Exports == Implementation where --S 1 of 1 )show Bits +--R --R Bits is a domain constructor --R Abbreviation for Bits is BITS --R This constructor is exposed in this frame. @@ -14034,13 +14088,13 @@ BinaryTree(S: SetCategory): Exports == Implementation where --R ?\/? : (%,%) -> % ^? : % -> % --R ?and? : (%,%) -> % coerce : % -> OutputForm --R concat : (%,Boolean) -> % concat : (Boolean,%) -> % ---R concat : (%,%) -> % concat : List % -> % ---R construct : List Boolean -> % copy : % -> % +--R concat : (%,%) -> % concat : List(%) -> % +--R construct : List(Boolean) -> % copy : % -> % --R delete : (%,Integer) -> % ?.? : (%,Integer) -> Boolean --R empty : () -> % empty? : % -> Boolean ---R entries : % -> List Boolean eq? : (%,%) -> Boolean +--R entries : % -> List(Boolean) eq? : (%,%) -> Boolean --R hash : % -> SingleInteger index? : (Integer,%) -> Boolean ---R indices : % -> List Integer insert : (%,%,Integer) -> % +--R indices : % -> List(Integer) insert : (%,%,Integer) -> % --R latex : % -> String max : (%,%) -> % --R min : (%,%) -> % nand : (%,%) -> % --R nor : (%,%) -> % not? : % -> % @@ -14051,18 +14105,18 @@ BinaryTree(S: SetCategory): Exports == Implementation where --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R any? : ((Boolean -> Boolean),%) -> Boolean if $ has finiteAggregate --R bits : (NonNegativeInteger,Boolean) -> % ---R convert : % -> InputForm if Boolean has KONVERT INFORM +--R convert : % -> InputForm if Boolean has KONVERT(INFORM) --R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable --R count : ((Boolean -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate --R count : (Boolean,%) -> NonNegativeInteger if $ has finiteAggregate and Boolean has SETCAT ---R delete : (%,UniversalSegment Integer) -> % +--R delete : (%,UniversalSegment(Integer)) -> % --R elt : (%,Integer,Boolean) -> Boolean ---R ?.? : (%,UniversalSegment Integer) -> % +--R ?.? : (%,UniversalSegment(Integer)) -> % --R entry? : (Boolean,%) -> Boolean if $ has finiteAggregate and Boolean has SETCAT ---R eval : (%,List Equation Boolean) -> % if Boolean has EVALAB BOOLEAN and Boolean has SETCAT ---R eval : (%,Equation Boolean) -> % if Boolean has EVALAB BOOLEAN and Boolean has SETCAT ---R eval : (%,Boolean,Boolean) -> % if Boolean has EVALAB BOOLEAN and Boolean has SETCAT ---R eval : (%,List Boolean,List Boolean) -> % if Boolean has EVALAB BOOLEAN and Boolean has SETCAT +--R eval : (%,List(Equation(Boolean))) -> % if Boolean has EVALAB(BOOLEAN) and Boolean has SETCAT +--R eval : (%,Equation(Boolean)) -> % if Boolean has EVALAB(BOOLEAN) and Boolean has SETCAT +--R eval : (%,Boolean,Boolean) -> % if Boolean has EVALAB(BOOLEAN) and Boolean has SETCAT +--R eval : (%,List(Boolean),List(Boolean)) -> % if Boolean has EVALAB(BOOLEAN) and Boolean has SETCAT --R every? : ((Boolean -> Boolean),%) -> Boolean if $ has finiteAggregate --R fill! : (%,Boolean) -> % if $ has shallowlyMutable --R find : ((Boolean -> Boolean),%) -> Union(Boolean,"failed") @@ -14074,13 +14128,13 @@ BinaryTree(S: SetCategory): Exports == Implementation where --R map! : ((Boolean -> Boolean),%) -> % if $ has shallowlyMutable --R maxIndex : % -> Integer if Integer has ORDSET --R member? : (Boolean,%) -> Boolean if $ has finiteAggregate and Boolean has SETCAT ---R members : % -> List Boolean if $ has finiteAggregate +--R members : % -> List(Boolean) if $ has finiteAggregate --R merge : (((Boolean,Boolean) -> Boolean),%,%) -> % --R merge : (%,%) -> % if Boolean has ORDSET --R minIndex : % -> Integer if Integer has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean --R new : (NonNegativeInteger,Boolean) -> % ---R parts : % -> List Boolean if $ has finiteAggregate +--R parts : % -> List(Boolean) if $ has finiteAggregate --R position : ((Boolean -> Boolean),%) -> Integer --R position : (Boolean,%) -> Integer if Boolean has SETCAT --R position : (Boolean,%,Integer) -> Integer if Boolean has SETCAT @@ -14094,7 +14148,7 @@ BinaryTree(S: SetCategory): Exports == Implementation where --R reverse! : % -> % if $ has shallowlyMutable --R select : ((Boolean -> Boolean),%) -> % if $ has finiteAggregate --R setelt : (%,Integer,Boolean) -> Boolean if $ has shallowlyMutable ---R setelt : (%,UniversalSegment Integer,Boolean) -> Boolean if $ has shallowlyMutable +--R setelt : (%,UniversalSegment(Integer),Boolean) -> Boolean if $ has shallowlyMutable --R size? : (%,NonNegativeInteger) -> Boolean --R sort : (((Boolean,Boolean) -> Boolean),%) -> % --R sort : % -> % if Boolean has ORDSET @@ -14241,6 +14295,7 @@ Bits(): Exports == Implementation where --S 1 of 1 )show BlowUpWithHamburgerNoether +--R --R BlowUpWithHamburgerNoether is a domain constructor --R Abbreviation for BlowUpWithHamburgerNoether is BLHN --R This constructor is exposed in this frame. @@ -14248,7 +14303,7 @@ Bits(): Exports == Implementation where --R --R------------------------------- Operations -------------------------------- --R ?=? : (%,%) -> Boolean chartCoord : % -> Integer ---R coerce : List Integer -> % coerce : % -> OutputForm +--R coerce : List(Integer) -> % coerce : % -> OutputForm --R excepCoord : % -> Integer hash : % -> SingleInteger --R infClsPt? : % -> Boolean latex : % -> String --R quotValuation : % -> Integer ramifMult : % -> Integer @@ -14347,6 +14402,7 @@ BlowUpWithHamburgerNoether: Exports == Implementation where --S 1 of 1 )show BlowUpWithQuadTrans +--R --R BlowUpWithQuadTrans is a domain constructor --R Abbreviation for BlowUpWithQuadTrans is BLQT --R This constructor is exposed in this frame. @@ -14354,7 +14410,7 @@ BlowUpWithHamburgerNoether: Exports == Implementation where --R --R------------------------------- Operations -------------------------------- --R ?=? : (%,%) -> Boolean chartCoord : % -> Integer ---R coerce : List Integer -> % coerce : % -> OutputForm +--R coerce : List(Integer) -> % coerce : % -> OutputForm --R excepCoord : % -> Integer hash : % -> SingleInteger --R infClsPt? : % -> Boolean latex : % -> String --R quotValuation : % -> Integer ramifMult : % -> Integer @@ -14726,7 +14782,7 @@ countable? A1 --R --R --R (12) [4,Aleph(1)] ---R Type: List CardinalNumber +--R Type: List(CardinalNumber) --E 12 --S 13 of 20 @@ -14734,7 +14790,7 @@ countable? A1 --R --R --R (13) [0,2,4,0,Aleph(1),Aleph(1),Aleph(1)] ---R Type: List CardinalNumber +--R Type: List(CardinalNumber) --E 13 --S 14 of 20 @@ -14742,7 +14798,7 @@ countable? A1 --R --R --R (14) [1,2,4,1,Aleph(1),Aleph(1)] ---R Type: List CardinalNumber +--R Type: List(CardinalNumber) --E 14 --S 15 of 20 @@ -14750,7 +14806,7 @@ countable? A1 --R --R --R (15) [1,0,"failed",Aleph(1),Aleph(1),"failed"] ---R Type: List Union(CardinalNumber,"failed") +--R Type: List(Union(CardinalNumber,"failed")) --E 15 --S 16 of 20 @@ -14766,7 +14822,7 @@ generalizedContinuumHypothesisAssumed true --R --R --R (17) [0,1,Aleph(1),Aleph(1),Aleph(2),Aleph(1),Aleph(2)] ---R Type: List CardinalNumber +--R Type: List(CardinalNumber) --E 17 --S 18 of 20 @@ -15355,7 +15411,7 @@ Tmv = m * v --R --R --R (19) [11,32]= [11,32] ---R Type: Equation CartesianTensor(1,2,Integer) +--R Type: Equation(CartesianTensor(1,2,Integer)) --E 19 --S 20 of 48 @@ -15465,7 +15521,7 @@ contract(Tmn,1,2) = trace(m) * n --R +12 18+ +12 18+ --R (32) | |= | | --R +0 6 + +0 6 + ---R Type: Equation CartesianTensor(1,2,Integer) +--R Type: Equation(CartesianTensor(1,2,Integer)) --E 32 --S 33 of 48 @@ -15475,7 +15531,7 @@ contract(Tmn,1,3) = transpose(m) * n --R +2 7 + +2 7 + --R (33) | |= | | --R +4 11+ +4 11+ ---R Type: Equation CartesianTensor(1,2,Integer) +--R Type: Equation(CartesianTensor(1,2,Integer)) --E 33 --S 34 of 48 @@ -15485,7 +15541,7 @@ contract(Tmn,1,4) = transpose(m) * transpose(n) --R +14 4+ +14 4+ --R (34) | |= | | --R +19 5+ +19 5+ ---R Type: Equation CartesianTensor(1,2,Integer) +--R Type: Equation(CartesianTensor(1,2,Integer)) --E 34 --S 35 of 48 @@ -15495,7 +15551,7 @@ contract(Tmn,2,3) = m * n --R +2 5 + +2 5 + --R (35) | |= | | --R +8 17+ +8 17+ ---R Type: Equation CartesianTensor(1,2,Integer) +--R Type: Equation(CartesianTensor(1,2,Integer)) --E 35 --S 36 of 48 @@ -15505,7 +15561,7 @@ contract(Tmn,2,4) = m * transpose(n) --R +8 2+ +8 2+ --R (36) | |= | | --R +23 5+ +23 5+ ---R Type: Equation CartesianTensor(1,2,Integer) +--R Type: Equation(CartesianTensor(1,2,Integer)) --E 36 --S 37 of 48 @@ -15515,7 +15571,7 @@ contract(Tmn,3,4) = trace(n) * m --R +3 6 + +3 6 + --R (37) | |= | | --R +12 15+ +12 15+ ---R Type: Equation CartesianTensor(1,2,Integer) +--R Type: Equation(CartesianTensor(1,2,Integer)) --E 37 --S 38 of 48 @@ -15553,7 +15609,7 @@ transpose Tm = transpose m --R +1 4+ +1 4+ --R (40) | |= | | --R +2 5+ +2 5+ ---R Type: Equation CartesianTensor(1,2,Integer) +--R Type: Equation(CartesianTensor(1,2,Integer)) --E 40 --S 41 of 48 @@ -15623,7 +15679,7 @@ contract(Tmn, 2, delta, 1) = reindex(Tmn, [1,3,4,2]) --R |+8 10+ +0 0+| |+8 10+ +0 0+| --R || | | || || | | || --R ++12 15+ +4 5++ ++12 15+ +4 5++ ---R Type: Equation CartesianTensor(1,2,Integer) +--R Type: Equation(CartesianTensor(1,2,Integer)) --E 46 --S 47 of 48 @@ -15641,7 +15697,7 @@ contract(epsilon*Tm*epsilon, 1,2) = 2 * determinant m --R --R --R (48) - 6= - 6 ---R Type: Equation CartesianTensor(1,2,Integer) +--R Type: Equation(CartesianTensor(1,2,Integer)) --E 48 )spool )lisp (bye) @@ -16783,7 +16839,7 @@ chars := [char "a", char "A", char "X", char "8", char "+"] --R --R --R (1) [a,A,X,8,+] ---R Type: List Character +--R Type: List(Character) --E 1 --S 2 of 13 @@ -16815,7 +16871,7 @@ escape() --R --R --R (5) [97,65,88,56,43] ---R Type: List Integer +--R Type: List(Integer) --E 5 --S 6 of 13 @@ -16823,7 +16879,7 @@ escape() --R --R --R (6) [A,A,X,8,+] ---R Type: List Character +--R Type: List(Character) --E 6 --S 7 of 13 @@ -16831,7 +16887,7 @@ escape() --R --R --R (7) [a,a,x,8,+] ---R Type: List Character +--R Type: List(Character) --E 7 --S 8 of 13 @@ -16839,7 +16895,7 @@ escape() --R --R --R (8) [true,true,true,false,false] ---R Type: List Boolean +--R Type: List(Boolean) --E 8 --S 9 of 13 @@ -16847,7 +16903,7 @@ escape() --R --R --R (9) [false,true,true,false,false] ---R Type: List Boolean +--R Type: List(Boolean) --E 9 --S 10 of 13 @@ -16855,7 +16911,7 @@ escape() --R --R --R (10) [true,false,false,false,false] ---R Type: List Boolean +--R Type: List(Boolean) --E 10 --S 11 of 13 @@ -16863,7 +16919,7 @@ escape() --R --R --R (11) [false,false,false,true,false] ---R Type: List Boolean +--R Type: List(Boolean) --E 11 --S 12 of 13 @@ -16871,7 +16927,7 @@ escape() --R --R --R (12) [true,true,false,true,false] ---R Type: List Boolean +--R Type: List(Boolean) --E 12 --S 13 of 13 @@ -16879,7 +16935,7 @@ escape() --R --R --R (13) [true,true,true,true,false] ---R Type: List Boolean +--R Type: List(Boolean) --E 13 )spool )lisp (bye) @@ -17786,7 +17842,7 @@ $\mathbb{R}_{m,m}$ & --------$>$ & $\mathbb{R}^{4^m}$ \\ K := Fraction Polynomial Integer --R --R ---R (1) Fraction Polynomial Integer +--R (1) Fraction(Polynomial(Integer)) --R Type: Domain --E 1 @@ -17795,14 +17851,14 @@ m := matrix [ [-1] ] --R --R --R (2) [- 1] ---R Type: Matrix Integer +--R Type: Matrix(Integer) --E 2 --S 3 of 36 C := CliffordAlgebra(1, K, quadraticForm m) --R --R ---R (3) CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX) +--R (3) CliffordAlgebra(1,Fraction(Polynomial(Integer)),[[-1]]) --R Type: Domain --E 3 @@ -17812,7 +17868,7 @@ i: C := e(1) --R --R (4) e --R 1 ---R Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX) +--R Type: CliffordAlgebra(1,Fraction(Polynomial(Integer)),[[-1]]) --E 4 --S 5 of 36 @@ -17821,7 +17877,7 @@ x := a + b * i --R --R (5) a + b e --R 1 ---R Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX) +--R Type: CliffordAlgebra(1,Fraction(Polynomial(Integer)),[[-1]]) --E 5 --S 6 of 36 @@ -17830,7 +17886,7 @@ y := c + d * i --R --R (6) c + d e --R 1 ---R Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX) +--R Type: CliffordAlgebra(1,Fraction(Polynomial(Integer)),[[-1]]) --E 6 --S 7 of 36 @@ -17839,7 +17895,7 @@ x * y --R --R (7) - b d + a c + (a d + b c)e --R 1 ---R Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX) +--R Type: CliffordAlgebra(1,Fraction(Polynomial(Integer)),[[-1]]) --E 7 )clear all @@ -17847,7 +17903,7 @@ x * y K := Fraction Polynomial Integer --R --R ---R (1) Fraction Polynomial Integer +--R (1) Fraction(Polynomial(Integer)) --R Type: Domain --E 8 @@ -17858,14 +17914,14 @@ m := matrix [ [-1,0],[0,-1] ] --R +- 1 0 + --R (2) | | --R + 0 - 1+ ---R Type: Matrix Integer +--R Type: Matrix(Integer) --E 9 --S 10 of 36 H := CliffordAlgebra(2, K, quadraticForm m) --R --R ---R (3) CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) +--R (3) CliffordAlgebra(2,Fraction(Polynomial(Integer)),[[-1,0],[0,-1]]) --R Type: Domain --E 10 @@ -17875,7 +17931,7 @@ i: H := e(1) --R --R (4) e --R 1 ---R Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) +--R Type: CliffordAlgebra(2,Fraction(Polynomial(Integer)),[[-1,0],[0,-1]]) --E 11 --S 12 of 36 @@ -17884,7 +17940,7 @@ j: H := e(2) --R --R (5) e --R 2 ---R Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) +--R Type: CliffordAlgebra(2,Fraction(Polynomial(Integer)),[[-1,0],[0,-1]]) --E 12 --S 13 of 36 @@ -17893,7 +17949,7 @@ k: H := i * j --R --R (6) e e --R 1 2 ---R Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) +--R Type: CliffordAlgebra(2,Fraction(Polynomial(Integer)),[[-1,0],[0,-1]]) --E 13 --S 14 of 36 @@ -17902,7 +17958,7 @@ x := a + b * i + c * j + d * k --R --R (7) a + b e + c e + d e e --R 1 2 1 2 ---R Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) +--R Type: CliffordAlgebra(2,Fraction(Polynomial(Integer)),[[-1,0],[0,-1]]) --E 14 --S 15 of 36 @@ -17911,7 +17967,7 @@ y := e + f * i + g * j + h * k --R --R (8) e + f e + g e + h e e --R 1 2 1 2 ---R Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) +--R Type: CliffordAlgebra(2,Fraction(Polynomial(Integer)),[[-1,0],[0,-1]]) --E 15 --S 16 of 36 @@ -17920,7 +17976,7 @@ x + y --R --R (9) e + a + (f + b)e + (g + c)e + (h + d)e e --R 1 2 1 2 ---R Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) +--R Type: CliffordAlgebra(2,Fraction(Polynomial(Integer)),[[-1,0],[0,-1]]) --E 16 --S 17 of 36 @@ -17933,7 +17989,7 @@ x * y --R + --R (- b h + a g + d f + c e)e + (a h + b g - c f + d e)e e --R 2 1 2 ---R Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) +--R Type: CliffordAlgebra(2,Fraction(Polynomial(Integer)),[[-1,0],[0,-1]]) --E 17 --S 18 of 36 @@ -17946,7 +18002,7 @@ y * x --R + --R (b h + a g - d f + c e)e + (a h - b g + c f + d e)e e --R 2 1 2 ---R Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) +--R Type: CliffordAlgebra(2,Fraction(Polynomial(Integer)),[[-1,0],[0,-1]]) --E 18 )clear all @@ -17954,7 +18010,7 @@ y * x K := Fraction Polynomial Integer --R --R ---R (1) Fraction Polynomial Integer +--R (1) Fraction(Polynomial(Integer)) --R Type: Domain --E 19 @@ -17962,7 +18018,8 @@ K := Fraction Polynomial Integer Ext := CliffordAlgebra(3, K, quadraticForm 0) --R --R ---R (2) CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX) +--R (2) +--R CliffordAlgebra(3,Fraction(Polynomial(Integer)),[[0,0,0],[0,0,0],[0,0,0]]) --R Type: Domain --E 20 @@ -17972,7 +18029,7 @@ i: Ext := e(1) --R --R (3) e --R 1 ---R Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX) +--RType: CliffordAlgebra(3,Fraction(Polynomial(Integer)),[[0,0,0],[0,0,0],[0,0,0]]) --E 21 --S 22 of 36 @@ -17981,7 +18038,7 @@ j: Ext := e(2) --R --R (4) e --R 2 ---R Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX) +--RType: CliffordAlgebra(3,Fraction(Polynomial(Integer)),[[0,0,0],[0,0,0],[0,0,0]]) --E 22 --S 23 of 36 @@ -17990,7 +18047,7 @@ k: Ext := e(3) --R --R (5) e --R 3 ---R Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX) +--RType: CliffordAlgebra(3,Fraction(Polynomial(Integer)),[[0,0,0],[0,0,0],[0,0,0]]) --E 23 --S 24 of 36 @@ -17999,7 +18056,7 @@ x := x1*i + x2*j + x3*k --R --R (6) x1 e + x2 e + x3 e --R 1 2 3 ---R Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX) +--RType: CliffordAlgebra(3,Fraction(Polynomial(Integer)),[[0,0,0],[0,0,0],[0,0,0]]) --E 24 --S 25 of 36 @@ -18008,7 +18065,7 @@ y := y1*i + y2*j + y3*k --R --R (7) y1 e + y2 e + y3 e --R 1 2 3 ---R Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX) +--RType: CliffordAlgebra(3,Fraction(Polynomial(Integer)),[[0,0,0],[0,0,0],[0,0,0]]) --E 25 --S 26 of 36 @@ -18017,7 +18074,7 @@ x + y --R --R (8) (y1 + x1)e + (y2 + x2)e + (y3 + x3)e --R 1 2 3 ---R Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX) +--RType: CliffordAlgebra(3,Fraction(Polynomial(Integer)),[[0,0,0],[0,0,0],[0,0,0]]) --E 26 --S 27 of 36 @@ -18025,7 +18082,7 @@ x * y + y * x --R --R --R (9) 0 ---R Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX) +--RType: CliffordAlgebra(3,Fraction(Polynomial(Integer)),[[0,0,0],[0,0,0],[0,0,0]]) --E 27 --S 28 of 36 @@ -18037,13 +18094,14 @@ dual2 a == coefficient(a,[2,3]) * i + coefficient(a,[3,1]) * j + coefficient(a,[ --S 29 of 36 dual2(x*y) --R ---R Compiling function dual2 with type CliffordAlgebra(3,Fraction ---R Polynomial Integer,MATRIX) -> CliffordAlgebra(3,Fraction ---R Polynomial Integer,MATRIX) +--R Compiling function dual2 with type CliffordAlgebra(3,Fraction( +--R Polynomial(Integer)),[[0,0,0],[0,0,0],[0,0,0]]) -> +--R CliffordAlgebra(3,Fraction(Polynomial(Integer)),[[0,0,0],[0,0,0], +--R [0,0,0]]) --R --R (11) (x2 y3 - x3 y2)e + (- x1 y3 + x3 y1)e + (x1 y2 - x2 y1)e --R 1 2 3 ---R Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX) +--RType: CliffordAlgebra(3,Fraction(Polynomial(Integer)),[[0,0,0],[0,0,0],[0,0,0]]) --E 29 )clear all @@ -18051,7 +18109,7 @@ dual2(x*y) K := Fraction Integer --R --R ---R (1) Fraction Integer +--R (1) Fraction(Integer) --R Type: Domain --E 30 @@ -18066,14 +18124,16 @@ g := matrix [ [1,0,0,0], [0,-1,0,0], [0,0,-1,0], [0,0,0,-1] ] --R |0 0 - 1 0 | --R | | --R +0 0 0 - 1+ ---R Type: Matrix Integer +--R Type: Matrix(Integer) --E 31 --S 32 of 36 D := CliffordAlgebra(4,K, quadraticForm g) --R --R ---R (3) CliffordAlgebra(4,Fraction Integer,MATRIX) +--R (3) +--R CliffordAlgebra(4,Fraction(Integer),[[1,0,0,0],[0,-1,0,0],[0,0,-1,0],[0,0,0,- +--R 1]]) --R Type: Domain --E 32 @@ -18083,7 +18143,7 @@ gam := [e(i)$D for i in 1..4] --R --R (4) [e ,e ,e ,e ] --R 1 2 3 4 ---R Type: List CliffordAlgebra(4,Fraction Integer,MATRIX) +--RType: List(CliffordAlgebra(4,Fraction(Integer),[[1,0,0,0],[0,-1,0,0],[0,0,-1,0],[0,0,0,-1]])) --E 33 --S 34 of 36 @@ -18099,7 +18159,7 @@ lhs := reduce(+, [reduce(+, [ g(l,t)*gam(l)*gam(m)*gam(n)*gam(r)*gam(s)*gam(t) f --R --R (6) - 4e e e e --R 1 2 3 4 ---R Type: CliffordAlgebra(4,Fraction Integer,MATRIX) +--RType: CliffordAlgebra(4,Fraction(Integer),[[1,0,0,0],[0,-1,0,0],[0,0,-1,0],[0,0,0,-1]]) --E 35 --S 36 of 36 @@ -18108,7 +18168,7 @@ rhs := 2*(gam s * gam m*gam n*gam r + gam r*gam n*gam m*gam s) --R --R (7) - 4e e e e --R 1 2 3 4 ---R Type: CliffordAlgebra(4,Fraction Integer,MATRIX) +--RType: CliffordAlgebra(4,Fraction(Integer),[[1,0,0,0],[0,-1,0,0],[0,0,-1,0],[0,0,0,-1]]) --E 36 )spool )lisp (bye) @@ -18925,7 +18985,7 @@ a := complex(4/3,5/2) --R 4 5 --R (1) - + - %i --R 3 2 ---R Type: Complex Fraction Integer +--R Type: Complex(Fraction(Integer)) --E 1 --S 2 of 16 @@ -18935,7 +18995,7 @@ b := complex(4/3,-5/2) --R 4 5 --R (2) - - - %i --R 3 2 ---R Type: Complex Fraction Integer +--R Type: Complex(Fraction(Integer)) --E 2 --S 3 of 16 @@ -18945,7 +19005,7 @@ a + b --R 8 --R (3) - --R 3 ---R Type: Complex Fraction Integer +--R Type: Complex(Fraction(Integer)) --E 3 --S 4 of 16 @@ -18953,7 +19013,7 @@ a - b --R --R --R (4) 5%i ---R Type: Complex Fraction Integer +--R Type: Complex(Fraction(Integer)) --E 4 --S 5 of 16 @@ -18963,7 +19023,7 @@ a * b --R 289 --R (5) --- --R 36 ---R Type: Complex Fraction Integer +--R Type: Complex(Fraction(Integer)) --E 5 --S 6 of 16 @@ -18973,7 +19033,7 @@ a / b --R 161 240 --R (6) - --- + --- %i --R 289 289 ---R Type: Complex Fraction Integer +--R Type: Complex(Fraction(Integer)) --E 6 --S 7 of 16 @@ -18983,7 +19043,7 @@ a / b --R - 15 + 8%i --R (7) ---------- --R 15 + 8%i ---R Type: Fraction Complex Integer +--R Type: Fraction(Complex(Integer)) --E 7 --S 8 of 16 @@ -18991,7 +19051,7 @@ a / b --R --R --R (8) 3.4 + 6.7 %i ---R Type: Complex Float +--R Type: Complex(Float) --E 8 --S 9 of 16 @@ -19001,7 +19061,7 @@ conjugate a --R 4 5 --R (9) - - - %i --R 3 2 ---R Type: Complex Fraction Integer +--R Type: Complex(Fraction(Integer)) --E 9 --S 10 of 16 @@ -19011,7 +19071,7 @@ norm a --R 289 --R (10) --- --R 36 ---R Type: Fraction Integer +--R Type: Fraction(Integer) --E 10 --S 11 of 16 @@ -19021,7 +19081,7 @@ real a --R 4 --R (11) - --R 3 ---R Type: Fraction Integer +--R Type: Fraction(Integer) --E 11 --S 12 of 16 @@ -19031,7 +19091,7 @@ imag a --R 5 --R (12) - --R 2 ---R Type: Fraction Integer +--R Type: Fraction(Integer) --E 12 --S 13 of 16 @@ -19039,7 +19099,7 @@ gcd(13 - 13*%i,31 + 27*%i) --R --R --R (13) 5 + %i ---R Type: Complex Integer +--R Type: Complex(Integer) --E 13 --S 14 of 16 @@ -19047,7 +19107,7 @@ lcm(13 - 13*%i,31 + 27*%i) --R --R --R (14) 143 - 39%i ---R Type: Complex Integer +--R Type: Complex(Integer) --E 14 --S 15 of 16 @@ -19055,7 +19115,7 @@ factor(13 - 13*%i) --R --R --R (15) - (1 + %i)(2 + 3%i)(3 + 2%i) ---R Type: Factored Complex Integer +--R Type: Factored(Complex(Integer)) --E 15 --S 16 of 16 @@ -19064,7 +19124,7 @@ factor complex(2,0) --R --R 2 --R (16) - %i (1 + %i) ---R Type: Factored Complex Integer +--R Type: Factored(Complex(Integer)) --E 16 )spool )lisp (bye) @@ -19439,6 +19499,7 @@ Complex(R:CommutativeRing): ComplexCategory(R) with --S 1 of 6 )show ComplexDoubleFloatMatrix +--R --R ComplexDoubleFloatMatrix is a domain constructor --R Abbreviation for ComplexDoubleFloatMatrix is CDFMAT --R This constructor is exposed in this frame. @@ -19449,7 +19510,7 @@ Complex(R:CommutativeRing): ComplexCategory(R) with --R ?+? : (%,%) -> % -? : % -> % --R ?-? : (%,%) -> % antisymmetric? : % -> Boolean --R copy : % -> % diagonal? : % -> Boolean ---R diagonalMatrix : List % -> % empty : () -> % +--R diagonalMatrix : List(%) -> % empty : () -> % --R empty? : % -> Boolean eq? : (%,%) -> Boolean --R horizConcat : (%,%) -> % maxColIndex : % -> Integer --R maxRowIndex : % -> Integer minColIndex : % -> Integer @@ -19461,60 +19522,60 @@ Complex(R:CommutativeRing): ComplexCategory(R) with --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?*? : (ComplexDoubleFloatVector,%) -> ComplexDoubleFloatVector --R ?*? : (%,ComplexDoubleFloatVector) -> ComplexDoubleFloatVector ---R ?*? : (%,Complex DoubleFloat) -> % ---R ?*? : (Complex DoubleFloat,%) -> % ---R ?**? : (%,Integer) -> % if Complex DoubleFloat has FIELD +--R ?*? : (%,Complex(DoubleFloat)) -> % +--R ?*? : (Complex(DoubleFloat),%) -> % +--R ?**? : (%,Integer) -> % if Complex(DoubleFloat) has FIELD --R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (%,Complex DoubleFloat) -> % if Complex DoubleFloat has FIELD ---R ?=? : (%,%) -> Boolean if Complex DoubleFloat has SETCAT ---R any? : ((Complex DoubleFloat -> Boolean),%) -> Boolean if $ has finiteAggregate +--R ?/? : (%,Complex(DoubleFloat)) -> % if Complex(DoubleFloat) has FIELD +--R ?=? : (%,%) -> Boolean if Complex(DoubleFloat) has SETCAT +--R any? : ((Complex(DoubleFloat) -> Boolean),%) -> Boolean if $ has finiteAggregate --R coerce : ComplexDoubleFloatVector -> % ---R coerce : % -> OutputForm if Complex DoubleFloat has SETCAT +--R coerce : % -> OutputForm if Complex(DoubleFloat) has SETCAT --R column : (%,Integer) -> ComplexDoubleFloatVector ---R columnSpace : % -> List ComplexDoubleFloatVector if Complex DoubleFloat has EUCDOM ---R count : (Complex DoubleFloat,%) -> NonNegativeInteger if $ has finiteAggregate and Complex DoubleFloat has SETCAT ---R count : ((Complex DoubleFloat -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate ---R determinant : % -> Complex DoubleFloat if Complex DoubleFloat has commutative * ---R diagonalMatrix : List Complex DoubleFloat -> % ---R elt : (%,List Integer,List Integer) -> % ---R elt : (%,Integer,Integer,Complex DoubleFloat) -> Complex DoubleFloat ---R elt : (%,Integer,Integer) -> Complex DoubleFloat ---R eval : (%,List Complex DoubleFloat,List Complex DoubleFloat) -> % if Complex DoubleFloat has EVALAB COMPLEX DFLOAT and Complex DoubleFloat has SETCAT ---R eval : (%,Complex DoubleFloat,Complex DoubleFloat) -> % if Complex DoubleFloat has EVALAB COMPLEX DFLOAT and Complex DoubleFloat has SETCAT ---R eval : (%,Equation Complex DoubleFloat) -> % if Complex DoubleFloat has EVALAB COMPLEX DFLOAT and Complex DoubleFloat has SETCAT ---R eval : (%,List Equation Complex DoubleFloat) -> % if Complex DoubleFloat has EVALAB COMPLEX DFLOAT and Complex DoubleFloat has SETCAT ---R every? : ((Complex DoubleFloat -> Boolean),%) -> Boolean if $ has finiteAggregate ---R exquo : (%,Complex DoubleFloat) -> Union(%,"failed") if Complex DoubleFloat has INTDOM ---R fill! : (%,Complex DoubleFloat) -> % ---R hash : % -> SingleInteger if Complex DoubleFloat has SETCAT ---R inverse : % -> Union(%,"failed") if Complex DoubleFloat has FIELD ---R latex : % -> String if Complex DoubleFloat has SETCAT +--R columnSpace : % -> List(ComplexDoubleFloatVector) if Complex(DoubleFloat) has EUCDOM +--R count : (Complex(DoubleFloat),%) -> NonNegativeInteger if $ has finiteAggregate and Complex(DoubleFloat) has SETCAT +--R count : ((Complex(DoubleFloat) -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R determinant : % -> Complex(DoubleFloat) if Complex(DoubleFloat) has commutative(*) +--R diagonalMatrix : List(Complex(DoubleFloat)) -> % +--R elt : (%,List(Integer),List(Integer)) -> % +--R elt : (%,Integer,Integer,Complex(DoubleFloat)) -> Complex(DoubleFloat) +--R elt : (%,Integer,Integer) -> Complex(DoubleFloat) +--R eval : (%,List(Complex(DoubleFloat)),List(Complex(DoubleFloat))) -> % if Complex(DoubleFloat) has EVALAB(COMPLEX(DFLOAT)) and Complex(DoubleFloat) has SETCAT +--R eval : (%,Complex(DoubleFloat),Complex(DoubleFloat)) -> % if Complex(DoubleFloat) has EVALAB(COMPLEX(DFLOAT)) and Complex(DoubleFloat) has SETCAT +--R eval : (%,Equation(Complex(DoubleFloat))) -> % if Complex(DoubleFloat) has EVALAB(COMPLEX(DFLOAT)) and Complex(DoubleFloat) has SETCAT +--R eval : (%,List(Equation(Complex(DoubleFloat)))) -> % if Complex(DoubleFloat) has EVALAB(COMPLEX(DFLOAT)) and Complex(DoubleFloat) has SETCAT +--R every? : ((Complex(DoubleFloat) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R exquo : (%,Complex(DoubleFloat)) -> Union(%,"failed") if Complex(DoubleFloat) has INTDOM +--R fill! : (%,Complex(DoubleFloat)) -> % +--R hash : % -> SingleInteger if Complex(DoubleFloat) has SETCAT +--R inverse : % -> Union(%,"failed") if Complex(DoubleFloat) has FIELD +--R latex : % -> String if Complex(DoubleFloat) has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean ---R listOfLists : % -> List List Complex DoubleFloat ---R map : (((Complex DoubleFloat,Complex DoubleFloat) -> Complex DoubleFloat),%,%,Complex DoubleFloat) -> % ---R map : (((Complex DoubleFloat,Complex DoubleFloat) -> Complex DoubleFloat),%,%) -> % ---R map : ((Complex DoubleFloat -> Complex DoubleFloat),%) -> % ---R map! : ((Complex DoubleFloat -> Complex DoubleFloat),%) -> % ---R matrix : List List Complex DoubleFloat -> % ---R member? : (Complex DoubleFloat,%) -> Boolean if $ has finiteAggregate and Complex DoubleFloat has SETCAT ---R members : % -> List Complex DoubleFloat if $ has finiteAggregate ---R minordet : % -> Complex DoubleFloat if Complex DoubleFloat has commutative * +--R listOfLists : % -> List(List(Complex(DoubleFloat))) +--R map : (((Complex(DoubleFloat),Complex(DoubleFloat)) -> Complex(DoubleFloat)),%,%,Complex(DoubleFloat)) -> % +--R map : (((Complex(DoubleFloat),Complex(DoubleFloat)) -> Complex(DoubleFloat)),%,%) -> % +--R map : ((Complex(DoubleFloat) -> Complex(DoubleFloat)),%) -> % +--R map! : ((Complex(DoubleFloat) -> Complex(DoubleFloat)),%) -> % +--R matrix : List(List(Complex(DoubleFloat))) -> % +--R member? : (Complex(DoubleFloat),%) -> Boolean if $ has finiteAggregate and Complex(DoubleFloat) has SETCAT +--R members : % -> List(Complex(DoubleFloat)) if $ has finiteAggregate +--R minordet : % -> Complex(DoubleFloat) if Complex(DoubleFloat) has commutative(*) --R more? : (%,NonNegativeInteger) -> Boolean ---R new : (NonNegativeInteger,NonNegativeInteger,Complex DoubleFloat) -> % ---R nullSpace : % -> List ComplexDoubleFloatVector if Complex DoubleFloat has INTDOM ---R nullity : % -> NonNegativeInteger if Complex DoubleFloat has INTDOM ---R parts : % -> List Complex DoubleFloat ---R pfaffian : % -> Complex DoubleFloat if Complex DoubleFloat has COMRING ---R qelt : (%,Integer,Integer) -> Complex DoubleFloat ---R qsetelt! : (%,Integer,Integer,Complex DoubleFloat) -> Complex DoubleFloat ---R rank : % -> NonNegativeInteger if Complex DoubleFloat has INTDOM +--R new : (NonNegativeInteger,NonNegativeInteger,Complex(DoubleFloat)) -> % +--R nullSpace : % -> List(ComplexDoubleFloatVector) if Complex(DoubleFloat) has INTDOM +--R nullity : % -> NonNegativeInteger if Complex(DoubleFloat) has INTDOM +--R parts : % -> List(Complex(DoubleFloat)) +--R pfaffian : % -> Complex(DoubleFloat) if Complex(DoubleFloat) has COMRING +--R qelt : (%,Integer,Integer) -> Complex(DoubleFloat) +--R qsetelt! : (%,Integer,Integer,Complex(DoubleFloat)) -> Complex(DoubleFloat) +--R rank : % -> NonNegativeInteger if Complex(DoubleFloat) has INTDOM --R row : (%,Integer) -> ComplexDoubleFloatVector ---R rowEchelon : % -> % if Complex DoubleFloat has EUCDOM ---R scalarMatrix : (NonNegativeInteger,Complex DoubleFloat) -> % +--R rowEchelon : % -> % if Complex(DoubleFloat) has EUCDOM +--R scalarMatrix : (NonNegativeInteger,Complex(DoubleFloat)) -> % --R setColumn! : (%,Integer,ComplexDoubleFloatVector) -> % --R setRow! : (%,Integer,ComplexDoubleFloatVector) -> % ---R setelt : (%,List Integer,List Integer,%) -> % ---R setelt : (%,Integer,Integer,Complex DoubleFloat) -> Complex DoubleFloat +--R setelt : (%,List(Integer),List(Integer),%) -> % +--R setelt : (%,Integer,Integer,Complex(DoubleFloat)) -> Complex(DoubleFloat) --R setsubMatrix! : (%,Integer,Integer,%) -> % --R size? : (%,NonNegativeInteger) -> Boolean --R subMatrix : (%,Integer,Integer,Integer,Integer) -> % @@ -19522,7 +19583,7 @@ Complex(R:CommutativeRing): ComplexCategory(R) with --R swapRows! : (%,Integer,Integer) -> % --R transpose : ComplexDoubleFloatVector -> % --R zero : (NonNegativeInteger,NonNegativeInteger) -> % ---R ?~=? : (%,%) -> Boolean if Complex DoubleFloat has SETCAT +--R ?~=? : (%,%) -> Boolean if Complex(DoubleFloat) has SETCAT --R --E 1 @@ -19539,7 +19600,7 @@ a:CDFMAT:=qnew(2,3) qsetelt!(a,1,1,1.0+2*%i) --R --R (2) 1. + 2. %i ---R Type: Complex DoubleFloat +--R Type: Complex(DoubleFloat) --E 3 --S 4 of 6 @@ -19555,7 +19616,7 @@ a qsetelt!(a,0,0,2.0+4*%i) --R --R (4) 2. + 4. %i ---R Type: Complex DoubleFloat +--R Type: Complex(DoubleFloat) --E 5 --S 6 of 6 @@ -19755,103 +19816,104 @@ ComplexDoubleFloatMatrix : MatrixCategory(Complex DoubleFloat, --S 1 of 6 )show ComplexDoubleFloatVector +--R --R ComplexDoubleFloatVector is a domain constructor --R Abbreviation for ComplexDoubleFloatVector is CDFVEC --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for CDFVEC --R --R------------------------------- Operations -------------------------------- ---R concat : List % -> % concat : (%,%) -> % +--R concat : List(%) -> % concat : (%,%) -> % --R copy : % -> % delete : (%,Integer) -> % --R empty : () -> % empty? : % -> Boolean --R eq? : (%,%) -> Boolean index? : (Integer,%) -> Boolean ---R indices : % -> List Integer insert : (%,%,Integer) -> % +--R indices : % -> List(Integer) insert : (%,%,Integer) -> % --R qnew : Integer -> % reverse : % -> % --R sample : () -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate ---R ?*? : (%,Complex DoubleFloat) -> % if Complex DoubleFloat has MONOID ---R ?*? : (Complex DoubleFloat,%) -> % if Complex DoubleFloat has MONOID ---R ?*? : (Integer,%) -> % if Complex DoubleFloat has ABELGRP ---R ?+? : (%,%) -> % if Complex DoubleFloat has ABELSG ---R ?-? : (%,%) -> % if Complex DoubleFloat has ABELGRP ---R -? : % -> % if Complex DoubleFloat has ABELGRP ---R ? Boolean if Complex DoubleFloat has ORDSET ---R ?<=? : (%,%) -> Boolean if Complex DoubleFloat has ORDSET ---R ?=? : (%,%) -> Boolean if Complex DoubleFloat has SETCAT ---R ?>? : (%,%) -> Boolean if Complex DoubleFloat has ORDSET ---R ?>=? : (%,%) -> Boolean if Complex DoubleFloat has ORDSET ---R any? : ((Complex DoubleFloat -> Boolean),%) -> Boolean if $ has finiteAggregate ---R coerce : % -> OutputForm if Complex DoubleFloat has SETCAT ---R concat : (Complex DoubleFloat,%) -> % ---R concat : (%,Complex DoubleFloat) -> % ---R construct : List Complex DoubleFloat -> % ---R convert : % -> InputForm if Complex DoubleFloat has KONVERT INFORM +--R ?*? : (%,Complex(DoubleFloat)) -> % if Complex(DoubleFloat) has MONOID +--R ?*? : (Complex(DoubleFloat),%) -> % if Complex(DoubleFloat) has MONOID +--R ?*? : (Integer,%) -> % if Complex(DoubleFloat) has ABELGRP +--R ?+? : (%,%) -> % if Complex(DoubleFloat) has ABELSG +--R ?-? : (%,%) -> % if Complex(DoubleFloat) has ABELGRP +--R -? : % -> % if Complex(DoubleFloat) has ABELGRP +--R ? Boolean if Complex(DoubleFloat) has ORDSET +--R ?<=? : (%,%) -> Boolean if Complex(DoubleFloat) has ORDSET +--R ?=? : (%,%) -> Boolean if Complex(DoubleFloat) has SETCAT +--R ?>? : (%,%) -> Boolean if Complex(DoubleFloat) has ORDSET +--R ?>=? : (%,%) -> Boolean if Complex(DoubleFloat) has ORDSET +--R any? : ((Complex(DoubleFloat) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if Complex(DoubleFloat) has SETCAT +--R concat : (Complex(DoubleFloat),%) -> % +--R concat : (%,Complex(DoubleFloat)) -> % +--R construct : List(Complex(DoubleFloat)) -> % +--R convert : % -> InputForm if Complex(DoubleFloat) has KONVERT(INFORM) --R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable ---R count : (Complex DoubleFloat,%) -> NonNegativeInteger if $ has finiteAggregate and Complex DoubleFloat has SETCAT ---R count : ((Complex DoubleFloat -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate ---R cross : (%,%) -> % if Complex DoubleFloat has RING ---R delete : (%,UniversalSegment Integer) -> % ---R dot : (%,%) -> Complex DoubleFloat if Complex DoubleFloat has RING ---R ?.? : (%,UniversalSegment Integer) -> % ---R ?.? : (%,Integer) -> Complex DoubleFloat ---R elt : (%,Integer,Complex DoubleFloat) -> Complex DoubleFloat ---R entries : % -> List Complex DoubleFloat ---R entry? : (Complex DoubleFloat,%) -> Boolean if $ has finiteAggregate and Complex DoubleFloat has SETCAT ---R eval : (%,List Complex DoubleFloat,List Complex DoubleFloat) -> % if Complex DoubleFloat has EVALAB COMPLEX DFLOAT and Complex DoubleFloat has SETCAT ---R eval : (%,Complex DoubleFloat,Complex DoubleFloat) -> % if Complex DoubleFloat has EVALAB COMPLEX DFLOAT and Complex DoubleFloat has SETCAT ---R eval : (%,Equation Complex DoubleFloat) -> % if Complex DoubleFloat has EVALAB COMPLEX DFLOAT and Complex DoubleFloat has SETCAT ---R eval : (%,List Equation Complex DoubleFloat) -> % if Complex DoubleFloat has EVALAB COMPLEX DFLOAT and Complex DoubleFloat has SETCAT ---R every? : ((Complex DoubleFloat -> Boolean),%) -> Boolean if $ has finiteAggregate ---R fill! : (%,Complex DoubleFloat) -> % if $ has shallowlyMutable ---R find : ((Complex DoubleFloat -> Boolean),%) -> Union(Complex DoubleFloat,"failed") ---R first : % -> Complex DoubleFloat if Integer has ORDSET ---R hash : % -> SingleInteger if Complex DoubleFloat has SETCAT ---R insert : (Complex DoubleFloat,%,Integer) -> % ---R latex : % -> String if Complex DoubleFloat has SETCAT ---R length : % -> Complex DoubleFloat if Complex DoubleFloat has RADCAT and Complex DoubleFloat has RING +--R count : (Complex(DoubleFloat),%) -> NonNegativeInteger if $ has finiteAggregate and Complex(DoubleFloat) has SETCAT +--R count : ((Complex(DoubleFloat) -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R cross : (%,%) -> % if Complex(DoubleFloat) has RING +--R delete : (%,UniversalSegment(Integer)) -> % +--R dot : (%,%) -> Complex(DoubleFloat) if Complex(DoubleFloat) has RING +--R ?.? : (%,UniversalSegment(Integer)) -> % +--R ?.? : (%,Integer) -> Complex(DoubleFloat) +--R elt : (%,Integer,Complex(DoubleFloat)) -> Complex(DoubleFloat) +--R entries : % -> List(Complex(DoubleFloat)) +--R entry? : (Complex(DoubleFloat),%) -> Boolean if $ has finiteAggregate and Complex(DoubleFloat) has SETCAT +--R eval : (%,List(Complex(DoubleFloat)),List(Complex(DoubleFloat))) -> % if Complex(DoubleFloat) has EVALAB(COMPLEX(DFLOAT)) and Complex(DoubleFloat) has SETCAT +--R eval : (%,Complex(DoubleFloat),Complex(DoubleFloat)) -> % if Complex(DoubleFloat) has EVALAB(COMPLEX(DFLOAT)) and Complex(DoubleFloat) has SETCAT +--R eval : (%,Equation(Complex(DoubleFloat))) -> % if Complex(DoubleFloat) has EVALAB(COMPLEX(DFLOAT)) and Complex(DoubleFloat) has SETCAT +--R eval : (%,List(Equation(Complex(DoubleFloat)))) -> % if Complex(DoubleFloat) has EVALAB(COMPLEX(DFLOAT)) and Complex(DoubleFloat) has SETCAT +--R every? : ((Complex(DoubleFloat) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,Complex(DoubleFloat)) -> % if $ has shallowlyMutable +--R find : ((Complex(DoubleFloat) -> Boolean),%) -> Union(Complex(DoubleFloat),"failed") +--R first : % -> Complex(DoubleFloat) if Integer has ORDSET +--R hash : % -> SingleInteger if Complex(DoubleFloat) has SETCAT +--R insert : (Complex(DoubleFloat),%,Integer) -> % +--R latex : % -> String if Complex(DoubleFloat) has SETCAT +--R length : % -> Complex(DoubleFloat) if Complex(DoubleFloat) has RADCAT and Complex(DoubleFloat) has RING --R less? : (%,NonNegativeInteger) -> Boolean ---R magnitude : % -> Complex DoubleFloat if Complex DoubleFloat has RADCAT and Complex DoubleFloat has RING ---R map : (((Complex DoubleFloat,Complex DoubleFloat) -> Complex DoubleFloat),%,%) -> % ---R map : ((Complex DoubleFloat -> Complex DoubleFloat),%) -> % ---R map! : ((Complex DoubleFloat -> Complex DoubleFloat),%) -> % if $ has shallowlyMutable ---R max : (%,%) -> % if Complex DoubleFloat has ORDSET +--R magnitude : % -> Complex(DoubleFloat) if Complex(DoubleFloat) has RADCAT and Complex(DoubleFloat) has RING +--R map : (((Complex(DoubleFloat),Complex(DoubleFloat)) -> Complex(DoubleFloat)),%,%) -> % +--R map : ((Complex(DoubleFloat) -> Complex(DoubleFloat)),%) -> % +--R map! : ((Complex(DoubleFloat) -> Complex(DoubleFloat)),%) -> % if $ has shallowlyMutable +--R max : (%,%) -> % if Complex(DoubleFloat) has ORDSET --R maxIndex : % -> Integer if Integer has ORDSET ---R member? : (Complex DoubleFloat,%) -> Boolean if $ has finiteAggregate and Complex DoubleFloat has SETCAT ---R members : % -> List Complex DoubleFloat if $ has finiteAggregate ---R merge : (%,%) -> % if Complex DoubleFloat has ORDSET ---R merge : (((Complex DoubleFloat,Complex DoubleFloat) -> Boolean),%,%) -> % ---R min : (%,%) -> % if Complex DoubleFloat has ORDSET +--R member? : (Complex(DoubleFloat),%) -> Boolean if $ has finiteAggregate and Complex(DoubleFloat) has SETCAT +--R members : % -> List(Complex(DoubleFloat)) if $ has finiteAggregate +--R merge : (%,%) -> % if Complex(DoubleFloat) has ORDSET +--R merge : (((Complex(DoubleFloat),Complex(DoubleFloat)) -> Boolean),%,%) -> % +--R min : (%,%) -> % if Complex(DoubleFloat) has ORDSET --R minIndex : % -> Integer if Integer has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean ---R new : (NonNegativeInteger,Complex DoubleFloat) -> % ---R outerProduct : (%,%) -> Matrix Complex DoubleFloat if Complex DoubleFloat has RING ---R parts : % -> List Complex DoubleFloat if $ has finiteAggregate ---R position : (Complex DoubleFloat,%,Integer) -> Integer if Complex DoubleFloat has SETCAT ---R position : (Complex DoubleFloat,%) -> Integer if Complex DoubleFloat has SETCAT ---R position : ((Complex DoubleFloat -> Boolean),%) -> Integer ---R qelt : (%,Integer) -> Complex DoubleFloat ---R qsetelt! : (%,Integer,Complex DoubleFloat) -> Complex DoubleFloat if $ has shallowlyMutable ---R reduce : (((Complex DoubleFloat,Complex DoubleFloat) -> Complex DoubleFloat),%) -> Complex DoubleFloat if $ has finiteAggregate ---R reduce : (((Complex DoubleFloat,Complex DoubleFloat) -> Complex DoubleFloat),%,Complex DoubleFloat) -> Complex DoubleFloat if $ has finiteAggregate ---R reduce : (((Complex DoubleFloat,Complex DoubleFloat) -> Complex DoubleFloat),%,Complex DoubleFloat,Complex DoubleFloat) -> Complex DoubleFloat if $ has finiteAggregate and Complex DoubleFloat has SETCAT ---R remove : ((Complex DoubleFloat -> Boolean),%) -> % if $ has finiteAggregate ---R remove : (Complex DoubleFloat,%) -> % if $ has finiteAggregate and Complex DoubleFloat has SETCAT ---R removeDuplicates : % -> % if $ has finiteAggregate and Complex DoubleFloat has SETCAT +--R new : (NonNegativeInteger,Complex(DoubleFloat)) -> % +--R outerProduct : (%,%) -> Matrix(Complex(DoubleFloat)) if Complex(DoubleFloat) has RING +--R parts : % -> List(Complex(DoubleFloat)) if $ has finiteAggregate +--R position : (Complex(DoubleFloat),%,Integer) -> Integer if Complex(DoubleFloat) has SETCAT +--R position : (Complex(DoubleFloat),%) -> Integer if Complex(DoubleFloat) has SETCAT +--R position : ((Complex(DoubleFloat) -> Boolean),%) -> Integer +--R qelt : (%,Integer) -> Complex(DoubleFloat) +--R qsetelt! : (%,Integer,Complex(DoubleFloat)) -> Complex(DoubleFloat) if $ has shallowlyMutable +--R reduce : (((Complex(DoubleFloat),Complex(DoubleFloat)) -> Complex(DoubleFloat)),%) -> Complex(DoubleFloat) if $ has finiteAggregate +--R reduce : (((Complex(DoubleFloat),Complex(DoubleFloat)) -> Complex(DoubleFloat)),%,Complex(DoubleFloat)) -> Complex(DoubleFloat) if $ has finiteAggregate +--R reduce : (((Complex(DoubleFloat),Complex(DoubleFloat)) -> Complex(DoubleFloat)),%,Complex(DoubleFloat),Complex(DoubleFloat)) -> Complex(DoubleFloat) if $ has finiteAggregate and Complex(DoubleFloat) has SETCAT +--R remove : ((Complex(DoubleFloat) -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (Complex(DoubleFloat),%) -> % if $ has finiteAggregate and Complex(DoubleFloat) has SETCAT +--R removeDuplicates : % -> % if $ has finiteAggregate and Complex(DoubleFloat) has SETCAT --R reverse! : % -> % if $ has shallowlyMutable ---R select : ((Complex DoubleFloat -> Boolean),%) -> % if $ has finiteAggregate ---R setelt : (%,UniversalSegment Integer,Complex DoubleFloat) -> Complex DoubleFloat if $ has shallowlyMutable ---R setelt : (%,Integer,Complex DoubleFloat) -> Complex DoubleFloat if $ has shallowlyMutable +--R select : ((Complex(DoubleFloat) -> Boolean),%) -> % if $ has finiteAggregate +--R setelt : (%,UniversalSegment(Integer),Complex(DoubleFloat)) -> Complex(DoubleFloat) if $ has shallowlyMutable +--R setelt : (%,Integer,Complex(DoubleFloat)) -> Complex(DoubleFloat) if $ has shallowlyMutable --R size? : (%,NonNegativeInteger) -> Boolean ---R sort : % -> % if Complex DoubleFloat has ORDSET ---R sort : (((Complex DoubleFloat,Complex DoubleFloat) -> Boolean),%) -> % ---R sort! : % -> % if $ has shallowlyMutable and Complex DoubleFloat has ORDSET ---R sort! : (((Complex DoubleFloat,Complex DoubleFloat) -> Boolean),%) -> % if $ has shallowlyMutable ---R sorted? : % -> Boolean if Complex DoubleFloat has ORDSET ---R sorted? : (((Complex DoubleFloat,Complex DoubleFloat) -> Boolean),%) -> Boolean +--R sort : % -> % if Complex(DoubleFloat) has ORDSET +--R sort : (((Complex(DoubleFloat),Complex(DoubleFloat)) -> Boolean),%) -> % +--R sort! : % -> % if $ has shallowlyMutable and Complex(DoubleFloat) has ORDSET +--R sort! : (((Complex(DoubleFloat),Complex(DoubleFloat)) -> Boolean),%) -> % if $ has shallowlyMutable +--R sorted? : % -> Boolean if Complex(DoubleFloat) has ORDSET +--R sorted? : (((Complex(DoubleFloat),Complex(DoubleFloat)) -> Boolean),%) -> Boolean --R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable ---R vector : List Complex DoubleFloat -> % ---R zero : NonNegativeInteger -> % if Complex DoubleFloat has ABELMON ---R ?~=? : (%,%) -> Boolean if Complex DoubleFloat has SETCAT +--R vector : List(Complex(DoubleFloat)) -> % +--R zero : NonNegativeInteger -> % if Complex(DoubleFloat) has ABELMON +--R ?~=? : (%,%) -> Boolean if Complex(DoubleFloat) has SETCAT --R --E 1 @@ -19867,7 +19929,7 @@ t1:CDFVEC:=qnew(5) t1.1:=1.0+2*%i --R --R (2) 1. + 2. %i ---R Type: Complex DoubleFloat +--R Type: Complex(DoubleFloat) --E 3 --S 4 of 6 @@ -19881,7 +19943,7 @@ t1 t1.0:=3.0+4.0*%i --R --R (4) 3. + 4. %i ---R Type: Complex DoubleFloat +--R Type: Complex(DoubleFloat) --E 5 --S 6 of 6 @@ -20079,7 +20141,7 @@ c := continuedFraction(314159/100000) --R 1 | 1 | 1 | 1 | 1 | 1 | 1 | --R (1) 3 + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+ --R | 7 | 15 | 1 | 25 | 1 | 7 | 4 ---R Type: ContinuedFraction Integer +--R Type: ContinuedFraction(Integer) --E 1 --S 2 of 22 @@ -20087,7 +20149,7 @@ partialQuotients c --R --R --R (2) [3,7,15,1,25,1,7,4] ---R Type: Stream Integer +--R Type: Stream(Integer) --E 2 --S 3 of 22 @@ -20097,7 +20159,7 @@ convergents c --R 22 333 355 9208 9563 76149 314159 --R (3) [3,--,---,---,----,----,-----,------] --R 7 106 113 2931 3044 24239 100000 ---R Type: Stream Fraction Integer +--R Type: Stream(Fraction(Integer)) --E 3 --S 4 of 22 @@ -20108,7 +20170,7 @@ approximants c --R 22 333 355 9208 9563 76149 314159 --R (4) [3,--,---,---,----,----,-----,------] --R 7 106 113 2931 3044 24239 100000 ---R Type: Stream Fraction Integer +--R Type: Stream(Fraction(Integer)) --E 4 --S 5 of 22 @@ -20116,7 +20178,7 @@ pq := partialQuotients(1/c) --R --R --R (5) [0,3,7,15,1,25,1,7,4] ---R Type: Stream Integer +--R Type: Stream(Integer) --E 5 --S 6 of 22 @@ -20126,7 +20188,7 @@ continuedFraction(first pq,repeating [1],rest pq) --R 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | --R (6) +---+ + +---+ + +----+ + +---+ + +----+ + +---+ + +---+ + +---+ --R | 3 | 7 | 15 | 1 | 25 | 1 | 7 | 4 ---R Type: ContinuedFraction Integer +--R Type: ContinuedFraction(Integer) --E 6 --S 7 of 22 @@ -20141,7 +20203,7 @@ z:=continuedFraction(3,repeating [1],repeating [3,6]) --R 1 | --R +---+ + ... --R | 6 ---R Type: ContinuedFraction Integer +--R Type: ContinuedFraction(Integer) --E 7 --S 8 of 22 @@ -20149,7 +20211,7 @@ dens:Stream Integer := cons(1,generate((x+->x+4),6)) --R --R --R (8) [1,6,10,14,18,22,26,30,34,38,...] ---R Type: Stream Integer +--R Type: Stream(Integer) --E 8 --S 9 of 22 @@ -20164,7 +20226,7 @@ cf := continuedFraction(0,repeating [1],dens) --R 1 | 1 | --R +----+ + +----+ + ... --R | 34 | 38 ---R Type: ContinuedFraction Integer +--R Type: ContinuedFraction(Integer) --E 9 --S 10 of 22 @@ -20174,7 +20236,7 @@ ccf := convergents cf --R 6 61 860 15541 342762 8927353 268163352 9126481321 --R (10) [0,1,-,--,----,-----,------,--------,---------,-----------,...] --R 7 71 1001 18089 398959 10391023 312129649 10622799089 ---R Type: Stream Fraction Integer +--R Type: Stream(Fraction(Integer)) --E 10 --S 11 of 22 @@ -20184,7 +20246,7 @@ eConvergents := [2*e + 1 for e in ccf] --R 19 193 2721 49171 1084483 28245729 848456353 28875761731 --R (11) [1,3,--,---,----,-----,-------,--------,---------,-----------,...] --R 7 71 1001 18089 398959 10391023 312129649 10622799089 ---R Type: Stream Fraction Integer +--R Type: Stream(Fraction(Integer)) --E 11 --S 12 of 22 @@ -20196,7 +20258,7 @@ eConvergents :: Stream Float --R 2.7182817182 817182817, 2.7182818287 356957267, 2.7182818284 585634113, --R 2.7182818284 590458514, 2.7182818284 590452348, 2.7182818284 590452354, --R ...] ---R Type: Stream Float +--R Type: Stream(Float) --E 12 --S 13 of 22 @@ -20219,7 +20281,7 @@ cf := continuedFraction(1,[(2*i+1)**2 for i in 0..],repeating [2]) --R 289 | 361 | --R +-----+ + +-----+ + ... --R | 2 | 2 ---R Type: ContinuedFraction Integer +--R Type: ContinuedFraction(Integer) --E 14 --S 15 of 22 @@ -20229,7 +20291,7 @@ ccf := convergents cf --R 3 15 105 315 3465 45045 45045 765765 14549535 --R (15) [1,-,--,---,---,----,-----,-----,------,--------,...] --R 2 13 76 263 2578 36979 33976 622637 11064338 ---R Type: Stream Fraction Integer +--R Type: Stream(Fraction(Integer)) --E 15 --S 16 of 22 @@ -20239,7 +20301,7 @@ piConvergents := [4/p for p in ccf] --R 8 52 304 1052 10312 147916 135904 2490548 44257352 --R (16) [4,-,--,---,----,-----,------,------,-------,--------,...] --R 3 15 105 315 3465 45045 45045 765765 14549535 ---R Type: Stream Fraction Integer +--R Type: Stream(Fraction(Integer)) --E 16 --S 17 of 22 @@ -20251,7 +20313,7 @@ piConvergents :: Stream Float --R 2.8952380952 380952381, 3.3396825396 825396825, 2.9760461760 461760462, --R 3.2837384837 384837385, 3.0170718170 718170718, 3.2523659347 188758953, --R 3.0418396189 294022111, ...] ---R Type: Stream Float +--R Type: Stream(Float) --E 17 --S 18 of 22 @@ -20261,7 +20323,7 @@ continuedFraction((- 122 + 597*%i)/(4 - 4*%i)) --R 1 | 1 | --R (18) - 90 + 59%i + +---------+ + +-----------+ --R | 1 - 2%i | - 1 + 2%i ---R Type: ContinuedFraction Complex Integer +--R Type: ContinuedFraction(Complex(Integer)) --E 18 --S 19 of 22 @@ -20279,7 +20341,7 @@ r := ((x - 1) * (x - 2)) / ((x-3) * (x-4)) --R (20) ------------ --R 2 --R x - 7x + 12 ---R Type: Fraction UnivariatePolynomial(x,Fraction Integer) +--R Type: Fraction(UnivariatePolynomial(x,Fraction(Integer))) --E 20 --S 21 of 22 @@ -20291,7 +20353,7 @@ continuedFraction r --R | 1 9 | 16 40 --R | - x - - | -- x - -- --R | 4 8 | 3 3 ---R Type: ContinuedFraction UnivariatePolynomial(x,Fraction Integer) +--R Type: ContinuedFraction(UnivariatePolynomial(x,Fraction(Integer))) --E 21 --S 22 of 22 @@ -20303,7 +20365,7 @@ continuedFraction r --R 10.9999860763 98799786, 11.0000006979 29731039, 10.9999999650 15834446, --R 11.0000000017 53603304, 10.9999999999 12099531, 11.0000000000 04406066, --R ...] ---R Type: Stream Float +--R Type: Stream(Float) --E 22 )spool )lisp (bye) @@ -21023,7 +21085,8 @@ ContinuedFraction(R): Exports == Implementation where --S 1 of 1 )show Database ---R Database S where +--R +--R Database(S) where --R S: OrderedSet with --R ?.? : (%,Symbol) -> String --R display : % -> Void @@ -21034,12 +21097,12 @@ ContinuedFraction(R): Exports == Implementation where --R --R------------------------------- Operations -------------------------------- --R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R ?=? : (%,%) -> Boolean coerce : List S -> % +--R ?=? : (%,%) -> Boolean coerce : List(S) -> % --R coerce : % -> OutputForm display : % -> Void --R ?.? : (%,QueryEquation) -> % fullDisplay : % -> Void --R hash : % -> SingleInteger latex : % -> String --R ?~=? : (%,%) -> Boolean ---R ?.? : (%,Symbol) -> DataList String +--R ?.? : (%,Symbol) -> DataList(String) --R fullDisplay : (%,PositiveInteger,PositiveInteger) -> Void --R --E 1 @@ -21149,35 +21212,36 @@ Database(S): Exports == Implementation where --S 1 of 1 )show DataList ---R DataList S: OrderedSet is a domain constructor +--R +--R DataList(S: OrderedSet) is a domain constructor --R Abbreviation for DataList is DLIST --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for DLIST --R --R------------------------------- Operations -------------------------------- ---R children : % -> List % coerce : % -> List S ---R coerce : List S -> % concat : (%,S) -> % ---R concat : List % -> % concat : (S,%) -> % +--R children : % -> List(%) coerce : % -> List(S) +--R coerce : List(S) -> % concat : (%,S) -> % +--R concat : List(%) -> % concat : (S,%) -> % --R concat : (%,%) -> % concat! : (%,S) -> % ---R concat! : (%,%) -> % construct : List S -> % +--R concat! : (%,%) -> % construct : List(S) -> % --R copy : % -> % cycleEntry : % -> % --R cycleTail : % -> % cyclic? : % -> Boolean ---R datalist : List S -> % delete : (%,Integer) -> % +--R datalist : List(S) -> % delete : (%,Integer) -> % --R delete! : (%,Integer) -> % distance : (%,%) -> Integer --R ?.sort : (%,sort) -> % ?.unique : (%,unique) -> % --R elt : (%,Integer,S) -> S ?.? : (%,Integer) -> S --R ?.last : (%,last) -> S ?.rest : (%,rest) -> % --R ?.first : (%,first) -> S ?.value : (%,value) -> S --R empty : () -> % empty? : % -> Boolean ---R entries : % -> List S eq? : (%,%) -> Boolean +--R entries : % -> List(S) eq? : (%,%) -> Boolean --R explicitlyFinite? : % -> Boolean first : % -> S ---R index? : (Integer,%) -> Boolean indices : % -> List Integer +--R index? : (Integer,%) -> Boolean indices : % -> List(Integer) --R insert : (S,%,Integer) -> % insert : (%,%,Integer) -> % --R insert! : (S,%,Integer) -> % insert! : (%,%,Integer) -> % --R last : % -> S leaf? : % -> Boolean ---R leaves : % -> List S list : S -> % +--R leaves : % -> List(S) list : S -> % --R map : (((S,S) -> S),%,%) -> % map : ((S -> S),%) -> % ---R new : (NonNegativeInteger,S) -> % nodes : % -> List % +--R new : (NonNegativeInteger,S) -> % nodes : % -> List(%) --R possiblyInfinite? : % -> Boolean qelt : (%,Integer) -> S --R rest : % -> % reverse : % -> % --R sample : () -> % second : % -> S @@ -21192,21 +21256,21 @@ Database(S): Exports == Implementation where --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R child? : (%,%) -> Boolean if S has SETCAT --R coerce : % -> OutputForm if S has SETCAT ---R convert : % -> InputForm if S has KONVERT INFORM +--R convert : % -> InputForm if S has KONVERT(INFORM) --R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable --R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT --R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate --R cycleLength : % -> NonNegativeInteger --R cycleSplit! : % -> % if $ has shallowlyMutable ---R delete : (%,UniversalSegment Integer) -> % ---R delete! : (%,UniversalSegment Integer) -> % +--R delete : (%,UniversalSegment(Integer)) -> % +--R delete! : (%,UniversalSegment(Integer)) -> % --R ?.count : (%,count) -> NonNegativeInteger ---R ?.? : (%,UniversalSegment Integer) -> % +--R ?.? : (%,UniversalSegment(Integer)) -> % --R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT ---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R fill! : (%,S) -> % if $ has shallowlyMutable --R find : ((S -> Boolean),%) -> Union(S,"failed") @@ -21219,7 +21283,7 @@ Database(S): Exports == Implementation where --R max : (%,%) -> % if S has ORDSET --R maxIndex : % -> Integer if Integer has ORDSET --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT ---R members : % -> List S if $ has finiteAggregate +--R members : % -> List(S) if $ has finiteAggregate --R merge : (((S,S) -> Boolean),%,%) -> % --R merge : (%,%) -> % if S has ORDSET --R merge! : (((S,S) -> Boolean),%,%) -> % @@ -21228,7 +21292,7 @@ Database(S): Exports == Implementation where --R minIndex : % -> Integer if Integer has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean --R node? : (%,%) -> Boolean if S has SETCAT ---R parts : % -> List S if $ has finiteAggregate +--R parts : % -> List(S) if $ has finiteAggregate --R position : ((S -> Boolean),%) -> Integer --R position : (S,%) -> Integer if S has SETCAT --R position : (S,%,Integer) -> Integer if S has SETCAT @@ -21246,9 +21310,9 @@ Database(S): Exports == Implementation where --R reverse! : % -> % if $ has shallowlyMutable --R select : ((S -> Boolean),%) -> % if $ has finiteAggregate --R select! : ((S -> Boolean),%) -> % ---R setchildren! : (%,List %) -> % if $ has shallowlyMutable +--R setchildren! : (%,List(%)) -> % if $ has shallowlyMutable --R setelt : (%,Integer,S) -> S if $ has shallowlyMutable ---R setelt : (%,UniversalSegment Integer,S) -> S if $ has shallowlyMutable +--R setelt : (%,UniversalSegment(Integer),S) -> S if $ has shallowlyMutable --R setelt : (%,last,S) -> S if $ has shallowlyMutable --R setelt : (%,rest,%) -> % if $ has shallowlyMutable --R setelt : (%,first,S) -> S if $ has shallowlyMutable @@ -21472,7 +21536,7 @@ r + decimal(6/7) --R [0.00285714, 0.002849, 0.0028409, 0.00283286118980169971671388101983, --R __________________________________________________________ --R 0.00282485875706214689265536723163841807909604519774011299435] ---R Type: List DecimalExpansion +--R Type: List(DecimalExpansion) --E 3 --S 4 of 7 @@ -21496,7 +21560,7 @@ p := decimal(1/4)*x**2 + decimal(2/3)*x + decimal(4/9) --R --R 2 _ _ --R (5) 0.25x + 0.6x + 0.4 ---R Type: Polynomial DecimalExpansion +--R Type: Polynomial(DecimalExpansion) --E 5 --S 6 of 7 @@ -21505,7 +21569,7 @@ q := differentiate(p, x) --R --R _ --R (6) 0.5x + 0.6 ---R Type: Polynomial DecimalExpansion +--R Type: Polynomial(DecimalExpansion) --E 6 --S 7 of 7 @@ -21514,7 +21578,7 @@ g := gcd(p, q) --R --R _ --R (7) x + 1.3 ---R Type: Polynomial DecimalExpansion +--R Type: Polynomial(DecimalExpansion) --E 7 )spool )lisp (bye) @@ -23505,7 +23569,7 @@ a:Dequeue INT:= dequeue [1,2,3,4,5] --R --R --R (1) [1,2,3,4,5] ---R Type: Dequeue Integer +--R Type: Dequeue(Integer) --E 1 --S 2 of 63 @@ -23521,7 +23585,7 @@ a --R --R --R (3) [2,3,4,5] ---R Type: Dequeue Integer +--R Type: Dequeue(Integer) --E 3 --S 4 of 63 @@ -23537,7 +23601,7 @@ a --R --R --R (5) [3,4,5] ---R Type: Dequeue Integer +--R Type: Dequeue(Integer) --E 5 --S 6 of 63 @@ -23553,7 +23617,7 @@ a --R --R --R (7) [3,4,5,9] ---R Type: Dequeue Integer +--R Type: Dequeue(Integer) --E 7 --S 8 of 63 @@ -23561,7 +23625,7 @@ insert!(8,a) --R --R --R (8) [3,4,5,9,8] ---R Type: Dequeue Integer +--R Type: Dequeue(Integer) --E 8 --S 9 of 63 @@ -23569,7 +23633,7 @@ a --R --R --R (9) [3,4,5,9,8] ---R Type: Dequeue Integer +--R Type: Dequeue(Integer) --E 9 --S 10 of 63 @@ -23601,7 +23665,7 @@ a --R --R --R (13) [3,4,5,9] ---R Type: Dequeue Integer +--R Type: Dequeue(Integer) --E 13 --S 14 of 63 @@ -23633,7 +23697,7 @@ a --R --R --R (17) [3,4,5,9,6] ---R Type: Dequeue Integer +--R Type: Dequeue(Integer) --E 17 --S 18 of 63 @@ -23649,7 +23713,7 @@ a --R --R --R (19) [3,4,5,9] ---R Type: Dequeue Integer +--R Type: Dequeue(Integer) --E 19 --S 20 of 63 @@ -23665,7 +23729,7 @@ a --R --R --R (21) [7,3,4,5,9] ---R Type: Dequeue Integer +--R Type: Dequeue(Integer) --E 21 --S 22 of 63 @@ -23681,7 +23745,7 @@ a --R --R --R (23) [3,4,5,9] ---R Type: Dequeue Integer +--R Type: Dequeue(Integer) --E 23 --S 24 of 63 @@ -23697,7 +23761,7 @@ a --R --R --R (25) [3,4,5,9] ---R Type: Dequeue Integer +--R Type: Dequeue(Integer) --E 25 --S 26 of 63 @@ -23713,7 +23777,7 @@ a --R --R --R (27) [4,5,9] ---R Type: Dequeue Integer +--R Type: Dequeue(Integer) --E 27 --S 28 of 63 @@ -23721,7 +23785,7 @@ reverse! a --R --R --R (28) [9,5,4] ---R Type: Dequeue Integer +--R Type: Dequeue(Integer) --E 28 --S 29 of 63 @@ -23729,7 +23793,7 @@ rotate! a --R --R --R (29) [5,4,9] ---R Type: Dequeue Integer +--R Type: Dequeue(Integer) --E 29 --S 30 of 63 @@ -23801,7 +23865,7 @@ parts a --R --R --R (38) [5,4,9] ---R Type: List Integer +--R Type: List(Integer) --E 38 --S 39 of 63 @@ -23809,7 +23873,7 @@ bag([1,2,3,4,5])$Dequeue(INT) --R --R --R (39) [1,2,3,4,5] ---R Type: Dequeue Integer +--R Type: Dequeue(Integer) --E 39 --S 40 of 63 @@ -23817,7 +23881,7 @@ b:=empty()$(Dequeue INT) --R --R --R (40) [] ---R Type: Dequeue Integer +--R Type: Dequeue(Integer) --E 40 --S 41 of 63 @@ -23833,7 +23897,7 @@ sample()$Dequeue(INT) --R --R --R (42) [] ---R Type: Dequeue Integer +--R Type: Dequeue(Integer) --E 42 --S 43 of 63 @@ -23841,7 +23905,7 @@ c:=copy a --R --R --R (43) [5,4,9] ---R Type: Dequeue Integer +--R Type: Dequeue(Integer) --E 43 --S 44 of 63 @@ -23929,7 +23993,7 @@ map(x+->x+10,a) --R --R --R (54) [15,14,19] ---R Type: Dequeue Integer +--R Type: Dequeue(Integer) --E 54 --S 55 of 63 @@ -23937,7 +24001,7 @@ a --R --R --R (55) [5,4,9] ---R Type: Dequeue Integer +--R Type: Dequeue(Integer) --E 55 --S 56 of 63 @@ -23945,7 +24009,7 @@ map!(x+->x+10,a) --R --R --R (56) [15,14,19] ---R Type: Dequeue Integer +--R Type: Dequeue(Integer) --E 56 --S 57 of 63 @@ -23953,7 +24017,7 @@ a --R --R --R (57) [15,14,19] ---R Type: Dequeue Integer +--R Type: Dequeue(Integer) --E 57 --S 58 of 63 @@ -23961,7 +24025,7 @@ members a --R --R --R (58) [15,14,19] ---R Type: List Integer +--R Type: List(Integer) --E 58 --S 59 of 63 @@ -23999,15 +24063,15 @@ latex a --S 63 of 63 )show Dequeue --R ---R Dequeue S: SetCategory is a domain constructor +--R Dequeue(S: SetCategory) is a domain constructor --R Abbreviation for Dequeue is DEQUEUE --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for DEQUEUE --R --R------------------------------- Operations -------------------------------- ---R back : % -> S bag : List S -> % +--R back : % -> S bag : List(S) -> % --R bottom! : % -> S copy : % -> % ---R depth : % -> NonNegativeInteger dequeue : List S -> % +--R depth : % -> NonNegativeInteger dequeue : List(S) -> % --R dequeue : () -> % dequeue! : % -> S --R empty : () -> % empty? : % -> Boolean --R enqueue! : (S,%) -> S eq? : (%,%) -> Boolean @@ -24026,19 +24090,19 @@ latex a --R coerce : % -> OutputForm if S has SETCAT --R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT --R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate ---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if S has SETCAT --R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT ---R members : % -> List S if $ has finiteAggregate +--R members : % -> List(S) if $ has finiteAggregate --R more? : (%,NonNegativeInteger) -> Boolean ---R parts : % -> List S if $ has finiteAggregate +--R parts : % -> List(S) if $ has finiteAggregate --R size? : (%,NonNegativeInteger) -> Boolean --R ?~=? : (%,%) -> Boolean if S has SETCAT --R @@ -24722,7 +24786,7 @@ lv : List Symbol := [x,y,z] --R --R --R (2) [x,y,z] ---R Type: List Symbol +--R Type: List(Symbol) --E 2 --S 3 of 34 @@ -24737,7 +24801,7 @@ der := DERHAM(coefRing,lv) R := Expression coefRing --R --R ---R (4) Expression Integer +--R (4) Expression(Integer) --R Type: Domain --E 4 @@ -24747,7 +24811,7 @@ f : R := x**2*y*z-5*x**3*y**2*z**5 --R --R 3 2 5 2 --R (5) - 5x y z + x y z ---R Type: Expression Integer +--R Type: Expression(Integer) --E 5 --S 6 of 34 @@ -24756,7 +24820,7 @@ g : R := z**2*y*cos(z)-7*sin(x**3*y**2)*z**2 --R --R 2 3 2 2 --R (6) - 7z sin(x y ) + y z cos(z) ---R Type: Expression Integer +--R Type: Expression(Integer) --E 6 --S 7 of 34 @@ -24765,7 +24829,7 @@ h : R :=x*y*z-2*x**3*y*z**2 --R --R 3 2 --R (7) - 2x y z + x y z ---R Type: Expression Integer +--R Type: Expression(Integer) --E 7 --S 8 of 34 @@ -24797,7 +24861,7 @@ dz : der := generator(3) --R --R --R (11) [dx,dy,dz] ---R Type: List DeRhamComplex(Integer,[x,y,z]) +--R Type: List(DeRhamComplex(Integer,[x,y,z])) --E 11 --S 12 of 34 @@ -24997,7 +25061,7 @@ coefficient(gamma, dx*dy) --R --R 2 3 2 2 4 2 5 3 --R (31) (7z sin(x y ) - y z cos(z))cos(tan(x y z) + x y z) - 5x y z + x y z ---R Type: Expression Integer +--R Type: Expression(Integer) --E 31 --S 32 of 34 @@ -25005,7 +25069,7 @@ coefficient(gamma, one) --R --R --R (32) 0 ---R Type: Expression Integer +--R Type: Expression(Integer) --E 32 --S 33 of 34 @@ -25013,7 +25077,7 @@ coefficient(g1,one) --R --R --R (33) a(x,t,y,u,v,z,e) ---R Type: Expression Integer +--R Type: Expression(Integer) --E 33 --S 34 of 34 @@ -25455,22 +25519,23 @@ DeRhamComplex(CoefRing,listIndVar:List Symbol): Export == Implement where --S 1 of 1 )show DesingTree ---R DesingTree S: SetCategory is a domain constructor +--R +--R DesingTree(S: SetCategory) is a domain constructor --R Abbreviation for DesingTree is DSTREE --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for DSTREE --R --R------------------------------- Operations -------------------------------- ---R children : % -> List % copy : % -> % +--R children : % -> List(%) copy : % -> % --R cyclic? : % -> Boolean distance : (%,%) -> Integer --R ?.value : (%,value) -> S empty : () -> % --R empty? : % -> Boolean encode : % -> String --R eq? : (%,%) -> Boolean fullOut : % -> OutputForm --R fullOutput : () -> Boolean fullOutput : Boolean -> Boolean ---R leaf? : % -> Boolean leaves : % -> List S ---R map : ((S -> S),%) -> % nodes : % -> List % ---R sample : () -> % tree : List S -> % ---R tree : S -> % tree : (S,List %) -> % +--R leaf? : % -> Boolean leaves : % -> List(S) +--R map : ((S -> S),%) -> % nodes : % -> List(%) +--R sample : () -> % tree : List(S) -> % +--R tree : S -> % tree : (S,List(%)) -> % --R value : % -> S --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if S has SETCAT @@ -25479,21 +25544,21 @@ DeRhamComplex(CoefRing,listIndVar:List Symbol): Export == Implement where --R coerce : % -> OutputForm if S has SETCAT --R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT --R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate ---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if S has SETCAT --R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT ---R members : % -> List S if $ has finiteAggregate +--R members : % -> List(S) if $ has finiteAggregate --R more? : (%,NonNegativeInteger) -> Boolean --R node? : (%,%) -> Boolean if S has SETCAT ---R parts : % -> List S if $ has finiteAggregate ---R setchildren! : (%,List %) -> % if $ has shallowlyMutable +--R parts : % -> List(S) if $ has finiteAggregate +--R setchildren! : (%,List(%)) -> % if $ has shallowlyMutable --R setelt : (%,value,S) -> S if $ has shallowlyMutable --R setvalue! : (%,S) -> S if $ has shallowlyMutable --R size? : (%,NonNegativeInteger) -> Boolean @@ -25653,7 +25718,8 @@ DesingTree(S: SetCategory): T==C where --S 1 of 1 )show DifferentialSparseMultivariatePolynomial ---R DifferentialSparseMultivariatePolynomial(R: Ring,S: OrderedSet,V: DifferentialVariableCategory S) is a domain constructor +--R +--R DifferentialSparseMultivariatePolynomial(R: Ring,S: OrderedSet,V: DifferentialVariableCategory(S)) is a domain constructor --R Abbreviation for DifferentialSparseMultivariatePolynomial is DSMP --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for DSMP @@ -25665,32 +25731,31 @@ DesingTree(S: SetCategory): T==C where --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R D : (%,(R -> R)) -> % D : % -> % if R has DIFRING ---R D : (%,List V) -> % D : (%,V) -> % +--R D : (%,List(V)) -> % D : (%,V) -> % --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coefficients : % -> List R +--R ?^? : (%,PositiveInteger) -> % coefficients : % -> List(R) --R coerce : S -> % coerce : V -> % --R coerce : R -> % coerce : Integer -> % ---R coerce : % -> OutputForm degree : % -> IndexedExponents V ---R differentiate : (%,List V) -> % differentiate : (%,V) -> % ---R eval : (%,List V,List %) -> % eval : (%,V,%) -> % ---R eval : (%,List V,List R) -> % eval : (%,V,R) -> % ---R eval : (%,List %,List %) -> % eval : (%,%,%) -> % ---R eval : (%,Equation %) -> % eval : (%,List Equation %) -> % +--R coerce : % -> OutputForm degree : % -> IndexedExponents(V) +--R differentiate : (%,List(V)) -> % differentiate : (%,V) -> % +--R eval : (%,List(V),List(%)) -> % eval : (%,V,%) -> % +--R eval : (%,List(V),List(R)) -> % eval : (%,V,R) -> % +--R eval : (%,%,%) -> % eval : (%,Equation(%)) -> % --R ground : % -> R ground? : % -> Boolean --R hash : % -> SingleInteger initial : % -> % --R isobaric? : % -> Boolean latex : % -> String --R leader : % -> V leadingCoefficient : % -> R --R leadingMonomial : % -> % map : ((R -> R),%) -> % ---R monomial? : % -> Boolean monomials : % -> List % +--R monomial? : % -> Boolean monomials : % -> List(%) --R one? : % -> Boolean order : % -> NonNegativeInteger ---R primitiveMonomials : % -> List % recip : % -> Union(%,"failed") ---R reductum : % -> % retract : % -> S ---R retract : % -> V retract : % -> R ---R sample : () -> % separant : % -> % ---R variables : % -> List V weight : % -> NonNegativeInteger ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (Fraction Integer,%) -> % if R has ALGEBRA FRAC INT ---R ?*? : (%,Fraction Integer) -> % if R has ALGEBRA FRAC INT +--R recip : % -> Union(%,"failed") reductum : % -> % +--R retract : % -> S retract : % -> V +--R retract : % -> R sample : () -> % +--R separant : % -> % variables : % -> List(V) +--R weight : % -> NonNegativeInteger zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT)) +--R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) --R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,R) -> % if R has FIELD @@ -25699,114 +25764,117 @@ DesingTree(S: SetCategory): T==C where --R ?>? : (%,%) -> Boolean if R has ORDSET --R ?>=? : (%,%) -> Boolean if R has ORDSET --R D : (%,(R -> R),NonNegativeInteger) -> % ---R D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL ---R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL ---R D : (%,List Symbol) -> % if R has PDRING SYMBOL ---R D : (%,Symbol) -> % if R has PDRING SYMBOL +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) +--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) +--R D : (%,List(Symbol)) -> % if R has PDRING(SYMBOL) +--R D : (%,Symbol) -> % if R has PDRING(SYMBOL) --R D : (%,NonNegativeInteger) -> % if R has DIFRING ---R D : (%,List V,List NonNegativeInteger) -> % +--R D : (%,List(V),List(NonNegativeInteger)) -> % --R D : (%,V,NonNegativeInteger) -> % --R ?^? : (%,NonNegativeInteger) -> % --R associates? : (%,%) -> Boolean if R has INTDOM --R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and R has PFECAT or R has CHARNZ ---R coefficient : (%,List V,List NonNegativeInteger) -> % +--R coefficient : (%,List(V),List(NonNegativeInteger)) -> % --R coefficient : (%,V,NonNegativeInteger) -> % ---R coefficient : (%,IndexedExponents V) -> R +--R coefficient : (%,IndexedExponents(V)) -> R --R coerce : % -> % if R has INTDOM ---R coerce : Fraction Integer -> % if R has ALGEBRA FRAC INT or R has RETRACT FRAC INT +--R coerce : Fraction(Integer) -> % if R has ALGEBRA(FRAC(INT)) or R has RETRACT(FRAC(INT)) --R coerce : SparseMultivariatePolynomial(R,S) -> % ---R conditionP : Matrix % -> Union(Vector %,"failed") if $ has CHARNZ and R has PFECAT +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and R has PFECAT --R content : (%,V) -> % if R has GCDDOM --R content : % -> R if R has GCDDOM ---R convert : % -> InputForm if R has KONVERT INFORM and V has KONVERT INFORM ---R convert : % -> Pattern Integer if R has KONVERT PATTERN INT and V has KONVERT PATTERN INT ---R convert : % -> Pattern Float if R has KONVERT PATTERN FLOAT and V has KONVERT PATTERN FLOAT +--R convert : % -> InputForm if R has KONVERT(INFORM) and V has KONVERT(INFORM) +--R convert : % -> Pattern(Integer) if R has KONVERT(PATTERN(INT)) and V has KONVERT(PATTERN(INT)) +--R convert : % -> Pattern(Float) if R has KONVERT(PATTERN(FLOAT)) and V has KONVERT(PATTERN(FLOAT)) --R degree : (%,S) -> NonNegativeInteger ---R degree : (%,List V) -> List NonNegativeInteger +--R degree : (%,List(V)) -> List(NonNegativeInteger) --R degree : (%,V) -> NonNegativeInteger ---R differentialVariables : % -> List S +--R differentialVariables : % -> List(S) --R differentiate : (%,(R -> R)) -> % --R differentiate : (%,(R -> R),NonNegativeInteger) -> % ---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL ---R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL ---R differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL ---R differentiate : (%,Symbol) -> % if R has PDRING SYMBOL +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol)) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,Symbol) -> % if R has PDRING(SYMBOL) --R differentiate : (%,NonNegativeInteger) -> % if R has DIFRING --R differentiate : % -> % if R has DIFRING ---R differentiate : (%,List V,List NonNegativeInteger) -> % +--R differentiate : (%,List(V),List(NonNegativeInteger)) -> % --R differentiate : (%,V,NonNegativeInteger) -> % --R discriminant : (%,V) -> % if R has COMRING ---R eval : (%,List S,List R) -> % if R has DIFRING +--R eval : (%,List(S),List(R)) -> % if R has DIFRING --R eval : (%,S,R) -> % if R has DIFRING ---R eval : (%,List S,List %) -> % if R has DIFRING +--R eval : (%,List(S),List(%)) -> % if R has DIFRING --R eval : (%,S,%) -> % if R has DIFRING +--R eval : (%,List(%),List(%)) -> % +--R eval : (%,List(Equation(%))) -> % --R exquo : (%,%) -> Union(%,"failed") if R has INTDOM --R exquo : (%,R) -> Union(%,"failed") if R has INTDOM ---R factor : % -> Factored % if R has PFECAT ---R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT ---R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R factor : % -> Factored(%) if R has PFECAT +--R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT --R gcd : (%,%) -> % if R has GCDDOM ---R gcd : List % -> % if R has GCDDOM ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has GCDDOM +--R gcd : List(%) -> % if R has GCDDOM +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has GCDDOM --R isExpt : % -> Union(Record(var: V,exponent: NonNegativeInteger),"failed") ---R isPlus : % -> Union(List %,"failed") ---R isTimes : % -> Union(List %,"failed") +--R isPlus : % -> Union(List(%),"failed") +--R isTimes : % -> Union(List(%),"failed") --R lcm : (%,%) -> % if R has GCDDOM ---R lcm : List % -> % if R has GCDDOM +--R lcm : List(%) -> % if R has GCDDOM --R mainVariable : % -> Union(V,"failed") --R makeVariable : % -> (NonNegativeInteger -> %) if R has DIFRING --R makeVariable : S -> (NonNegativeInteger -> %) ---R mapExponents : ((IndexedExponents V -> IndexedExponents V),%) -> % +--R mapExponents : ((IndexedExponents(V) -> IndexedExponents(V)),%) -> % --R max : (%,%) -> % if R has ORDSET --R min : (%,%) -> % if R has ORDSET ---R minimumDegree : (%,List V) -> List NonNegativeInteger +--R minimumDegree : (%,List(V)) -> List(NonNegativeInteger) --R minimumDegree : (%,V) -> NonNegativeInteger ---R minimumDegree : % -> IndexedExponents V +--R minimumDegree : % -> IndexedExponents(V) --R monicDivide : (%,%,V) -> Record(quotient: %,remainder: %) ---R monomial : (%,List V,List NonNegativeInteger) -> % +--R monomial : (%,List(V),List(NonNegativeInteger)) -> % --R monomial : (%,V,NonNegativeInteger) -> % ---R monomial : (R,IndexedExponents V) -> % ---R multivariate : (SparseUnivariatePolynomial %,V) -> % ---R multivariate : (SparseUnivariatePolynomial R,V) -> % +--R monomial : (R,IndexedExponents(V)) -> % +--R multivariate : (SparseUnivariatePolynomial(%),V) -> % +--R multivariate : (SparseUnivariatePolynomial(R),V) -> % --R numberOfMonomials : % -> NonNegativeInteger --R order : (%,S) -> NonNegativeInteger ---R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if R has PATMAB INT and V has PATMAB INT ---R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if R has PATMAB FLOAT and V has PATMAB FLOAT ---R pomopo! : (%,R,IndexedExponents V,%) -> % +--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if R has PATMAB(INT) and V has PATMAB(INT) +--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if R has PATMAB(FLOAT) and V has PATMAB(FLOAT) +--R pomopo! : (%,R,IndexedExponents(V),%) -> % --R prime? : % -> Boolean if R has PFECAT +--R primitiveMonomials : % -> List(%) --R primitivePart : (%,V) -> % if R has GCDDOM --R primitivePart : % -> % if R has GCDDOM ---R reducedSystem : Matrix % -> Matrix R ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT ---R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT +--R reducedSystem : Matrix(%) -> Matrix(R) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT) +--R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT) --R resultant : (%,%,V) -> % if R has COMRING --R retract : % -> SparseMultivariatePolynomial(R,S) ---R retract : % -> Integer if R has RETRACT INT ---R retract : % -> Fraction Integer if R has RETRACT FRAC INT +--R retract : % -> Integer if R has RETRACT(INT) +--R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT)) --R retractIfCan : % -> Union(SparseMultivariatePolynomial(R,S),"failed") --R retractIfCan : % -> Union(S,"failed") --R retractIfCan : % -> Union(V,"failed") ---R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT ---R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT) +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT)) --R retractIfCan : % -> Union(R,"failed") ---R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if R has PFECAT ---R squareFree : % -> Factored % if R has GCDDOM +--R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if R has PFECAT +--R squareFree : % -> Factored(%) if R has GCDDOM --R squareFreePart : % -> % if R has GCDDOM ---R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT --R subtractIfCan : (%,%) -> Union(%,"failed") ---R totalDegree : (%,List V) -> NonNegativeInteger +--R totalDegree : (%,List(V)) -> NonNegativeInteger --R totalDegree : % -> NonNegativeInteger --R unit? : % -> Boolean if R has INTDOM --R unitCanonical : % -> % if R has INTDOM --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM ---R univariate : % -> SparseUnivariatePolynomial R ---R univariate : (%,V) -> SparseUnivariatePolynomial % +--R univariate : % -> SparseUnivariatePolynomial(R) +--R univariate : (%,V) -> SparseUnivariatePolynomial(%) --R weight : (%,S) -> NonNegativeInteger ---R weights : (%,S) -> List NonNegativeInteger ---R weights : % -> List NonNegativeInteger +--R weights : (%,S) -> List(NonNegativeInteger) +--R weights : % -> List(NonNegativeInteger) --R --E 1 @@ -25990,6 +26058,7 @@ DifferentialSparseMultivariatePolynomial(R, S, V): --S 1 of 1 )show DirectProduct +--R --R DirectProduct(dim: NonNegativeInteger,R: Type) is a domain constructor --R Abbreviation for DirectProduct is DIRPROD --R This constructor is not exposed in this frame. @@ -25997,12 +26066,12 @@ DifferentialSparseMultivariatePolynomial(R, S, V): --R --R------------------------------- Operations -------------------------------- --R -? : % -> % if R has RING 1 : () -> % if R has MONOID ---R 0 : () -> % if R has CABMON coerce : % -> Vector R ---R copy : % -> % directProduct : Vector R -> % +--R 0 : () -> % if R has CABMON coerce : % -> Vector(R) +--R copy : % -> % directProduct : Vector(R) -> % --R ?.? : (%,Integer) -> R elt : (%,Integer,R) -> R --R empty : () -> % empty? : % -> Boolean ---R entries : % -> List R eq? : (%,%) -> Boolean ---R index? : (Integer,%) -> Boolean indices : % -> List Integer +--R entries : % -> List(R) eq? : (%,%) -> Boolean +--R index? : (Integer,%) -> Boolean indices : % -> List(Integer) --R map : ((R -> R),%) -> % qelt : (%,Integer) -> R --R sample : () -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate @@ -26024,10 +26093,10 @@ DifferentialSparseMultivariatePolynomial(R, S, V): --R ?>=? : (%,%) -> Boolean if R has OAMONS or R has ORDRING --R D : (%,(R -> R)) -> % if R has RING --R D : (%,(R -> R),NonNegativeInteger) -> % if R has RING ---R D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL and R has RING ---R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL and R has RING ---R D : (%,List Symbol) -> % if R has PDRING SYMBOL and R has RING ---R D : (%,Symbol) -> % if R has PDRING SYMBOL and R has RING +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) and R has RING +--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) and R has RING +--R D : (%,List(Symbol)) -> % if R has PDRING(SYMBOL) and R has RING +--R D : (%,Symbol) -> % if R has PDRING(SYMBOL) and R has RING --R D : (%,NonNegativeInteger) -> % if R has DIFRING and R has RING --R D : % -> % if R has DIFRING and R has RING --R ?^? : (%,PositiveInteger) -> % if R has MONOID @@ -26036,26 +26105,26 @@ DifferentialSparseMultivariatePolynomial(R, S, V): --R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate --R characteristic : () -> NonNegativeInteger if R has RING --R coerce : R -> % if R has SETCAT ---R coerce : Fraction Integer -> % if R has RETRACT FRAC INT and R has SETCAT ---R coerce : Integer -> % if R has RETRACT INT and R has SETCAT or R has RING +--R coerce : Fraction(Integer) -> % if R has RETRACT(FRAC(INT)) and R has SETCAT +--R coerce : Integer -> % if R has RETRACT(INT) and R has SETCAT or R has RING --R coerce : % -> OutputForm if R has SETCAT --R count : (R,%) -> NonNegativeInteger if $ has finiteAggregate and R has SETCAT --R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate --R differentiate : (%,(R -> R)) -> % if R has RING --R differentiate : (%,(R -> R),NonNegativeInteger) -> % if R has RING ---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL and R has RING ---R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL and R has RING ---R differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL and R has RING ---R differentiate : (%,Symbol) -> % if R has PDRING SYMBOL and R has RING +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) and R has RING +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) and R has RING +--R differentiate : (%,List(Symbol)) -> % if R has PDRING(SYMBOL) and R has RING +--R differentiate : (%,Symbol) -> % if R has PDRING(SYMBOL) and R has RING --R differentiate : (%,NonNegativeInteger) -> % if R has DIFRING and R has RING --R differentiate : % -> % if R has DIFRING and R has RING --R dimension : () -> CardinalNumber if R has FIELD --R dot : (%,%) -> R if R has RING --R entry? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT ---R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT ---R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT ---R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT ---R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,List(R),List(R)) -> % if R has EVALAB(R) and R has SETCAT +--R eval : (%,R,R) -> % if R has EVALAB(R) and R has SETCAT +--R eval : (%,Equation(R)) -> % if R has EVALAB(R) and R has SETCAT +--R eval : (%,List(Equation(R))) -> % if R has EVALAB(R) and R has SETCAT --R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate --R fill! : (%,R) -> % if $ has shallowlyMutable --R first : % -> R if Integer has ORDSET @@ -26068,27 +26137,27 @@ DifferentialSparseMultivariatePolynomial(R, S, V): --R max : (%,%) -> % if R has OAMONS or R has ORDRING --R maxIndex : % -> Integer if Integer has ORDSET --R member? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT ---R members : % -> List R if $ has finiteAggregate +--R members : % -> List(R) if $ has finiteAggregate --R min : (%,%) -> % if R has OAMONS or R has ORDRING --R minIndex : % -> Integer if Integer has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean --R negative? : % -> Boolean if R has ORDRING --R one? : % -> Boolean if R has MONOID ---R parts : % -> List R if $ has finiteAggregate +--R parts : % -> List(R) if $ has finiteAggregate --R positive? : % -> Boolean if R has ORDRING --R qsetelt! : (%,Integer,R) -> R if $ has shallowlyMutable --R random : () -> % if R has FINITE --R recip : % -> Union(%,"failed") if R has MONOID ---R reducedSystem : Matrix % -> Matrix R if R has RING ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) if R has RING ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT and R has RING ---R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT and R has RING +--R reducedSystem : Matrix(%) -> Matrix(R) if R has RING +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) if R has RING +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT) and R has RING +--R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT) and R has RING --R retract : % -> R if R has SETCAT ---R retract : % -> Fraction Integer if R has RETRACT FRAC INT and R has SETCAT ---R retract : % -> Integer if R has RETRACT INT and R has SETCAT +--R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT)) and R has SETCAT +--R retract : % -> Integer if R has RETRACT(INT) and R has SETCAT --R retractIfCan : % -> Union(R,"failed") if R has SETCAT ---R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT and R has SETCAT ---R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT and R has SETCAT +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT)) and R has SETCAT +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT) and R has SETCAT --R setelt : (%,Integer,R) -> R if $ has shallowlyMutable --R sign : % -> Integer if R has ORDRING --R size : () -> NonNegativeInteger if R has FINITE @@ -26317,7 +26386,8 @@ DirectProduct(dim:NonNegativeInteger, R:Type): --S 1 of 1 )show DirectProductMatrixModule ---R DirectProductMatrixModule(n: PositiveInteger,R: Ring,M: SquareMatrixCategory(n,R,DirectProduct(n,R),DirectProduct(n,R)),S: LeftModule R) is a domain constructor +--R +--R DirectProductMatrixModule(n: PositiveInteger,R: Ring,M: SquareMatrixCategory(n,R,DirectProduct(n,R),DirectProduct(n,R)),S: LeftModule(R)) is a domain constructor --R Abbreviation for DirectProductMatrixModule is DPMM --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for DPMM @@ -26328,22 +26398,22 @@ DirectProduct(dim:NonNegativeInteger, R:Type): --R ?+? : (%,%) -> % -? : % -> % --R ?-? : (%,%) -> % ?=? : (%,%) -> Boolean --R 0 : () -> % coerce : % -> OutputForm ---R coerce : % -> Vector S copy : % -> % ---R directProduct : Vector S -> % ?.? : (%,Integer) -> S +--R coerce : % -> Vector(S) copy : % -> % +--R directProduct : Vector(S) -> % ?.? : (%,Integer) -> S --R elt : (%,Integer,S) -> S empty : () -> % ---R empty? : % -> Boolean entries : % -> List S +--R empty? : % -> Boolean entries : % -> List(S) --R eq? : (%,%) -> Boolean hash : % -> SingleInteger ---R index? : (Integer,%) -> Boolean indices : % -> List Integer +--R index? : (Integer,%) -> Boolean indices : % -> List(Integer) --R latex : % -> String map : ((S -> S),%) -> % --R qelt : (%,Integer) -> S sample : () -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R #? : % -> NonNegativeInteger if $ has finiteAggregate ---R ?*? : (%,%) -> % if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING +--R ?*? : (%,%) -> % if S has DIFRING and S has RING or S has LINEXP(INT) and S has RING or S has MONOID or S has PDRING(SYMBOL) and S has RING --R ?*? : (S,%) -> % if S has RING --R ?*? : (%,S) -> % if S has RING --R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,PositiveInteger) -> % if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING ---R ?**? : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING +--R ?**? : (%,PositiveInteger) -> % if S has DIFRING and S has RING or S has LINEXP(INT) and S has RING or S has MONOID or S has PDRING(SYMBOL) and S has RING +--R ?**? : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING or S has LINEXP(INT) and S has RING or S has MONOID or S has PDRING(SYMBOL) and S has RING --R ?/? : (%,S) -> % if S has FIELD --R ? Boolean if S has OAMONS or S has ORDRING --R ?<=? : (%,%) -> Boolean if S has OAMONS or S has ORDRING @@ -26351,38 +26421,38 @@ DirectProduct(dim:NonNegativeInteger, R:Type): --R ?>=? : (%,%) -> Boolean if S has OAMONS or S has ORDRING --R D : % -> % if S has DIFRING and S has RING --R D : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING ---R D : (%,Symbol) -> % if S has PDRING SYMBOL and S has RING ---R D : (%,List Symbol) -> % if S has PDRING SYMBOL and S has RING ---R D : (%,Symbol,NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING ---R D : (%,List Symbol,List NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING +--R D : (%,Symbol) -> % if S has PDRING(SYMBOL) and S has RING +--R D : (%,List(Symbol)) -> % if S has PDRING(SYMBOL) and S has RING +--R D : (%,Symbol,NonNegativeInteger) -> % if S has PDRING(SYMBOL) and S has RING +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if S has PDRING(SYMBOL) and S has RING --R D : (%,(S -> S)) -> % if S has RING --R D : (%,(S -> S),NonNegativeInteger) -> % if S has RING ---R 1 : () -> % if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING ---R ?^? : (%,PositiveInteger) -> % if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING ---R ?^? : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING +--R 1 : () -> % if S has DIFRING and S has RING or S has LINEXP(INT) and S has RING or S has MONOID or S has PDRING(SYMBOL) and S has RING +--R ?^? : (%,PositiveInteger) -> % if S has DIFRING and S has RING or S has LINEXP(INT) and S has RING or S has MONOID or S has PDRING(SYMBOL) and S has RING +--R ?^? : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING or S has LINEXP(INT) and S has RING or S has MONOID or S has PDRING(SYMBOL) and S has RING --R abs : % -> % if S has ORDRING --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R characteristic : () -> NonNegativeInteger if S has RING ---R coerce : Fraction Integer -> % if S has RETRACT FRAC INT and S has SETCAT ---R coerce : Integer -> % if S has RETRACT INT and S has SETCAT or S has RING +--R coerce : Fraction(Integer) -> % if S has RETRACT(FRAC(INT)) and S has SETCAT +--R coerce : Integer -> % if S has RETRACT(INT) and S has SETCAT or S has RING --R coerce : S -> % if S has SETCAT --R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT --R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate --R differentiate : % -> % if S has DIFRING and S has RING --R differentiate : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING ---R differentiate : (%,Symbol) -> % if S has PDRING SYMBOL and S has RING ---R differentiate : (%,List Symbol) -> % if S has PDRING SYMBOL and S has RING ---R differentiate : (%,Symbol,NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING ---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING +--R differentiate : (%,Symbol) -> % if S has PDRING(SYMBOL) and S has RING +--R differentiate : (%,List(Symbol)) -> % if S has PDRING(SYMBOL) and S has RING +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if S has PDRING(SYMBOL) and S has RING +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if S has PDRING(SYMBOL) and S has RING --R differentiate : (%,(S -> S)) -> % if S has RING --R differentiate : (%,(S -> S),NonNegativeInteger) -> % if S has RING --R dimension : () -> CardinalNumber if S has FIELD --R dot : (%,%) -> S if S has RING --R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT ---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R fill! : (%,S) -> % if $ has shallowlyMutable --R first : % -> S if Integer has ORDSET @@ -26393,26 +26463,26 @@ DirectProduct(dim:NonNegativeInteger, R:Type): --R max : (%,%) -> % if S has OAMONS or S has ORDRING --R maxIndex : % -> Integer if Integer has ORDSET --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT ---R members : % -> List S if $ has finiteAggregate +--R members : % -> List(S) if $ has finiteAggregate --R min : (%,%) -> % if S has OAMONS or S has ORDRING --R minIndex : % -> Integer if Integer has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean --R negative? : % -> Boolean if S has ORDRING ---R one? : % -> Boolean if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING ---R parts : % -> List S if $ has finiteAggregate +--R one? : % -> Boolean if S has DIFRING and S has RING or S has LINEXP(INT) and S has RING or S has MONOID or S has PDRING(SYMBOL) and S has RING +--R parts : % -> List(S) if $ has finiteAggregate --R positive? : % -> Boolean if S has ORDRING --R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable --R random : () -> % if S has FINITE ---R recip : % -> Union(%,"failed") if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING ---R reducedSystem : Matrix % -> Matrix Integer if S has LINEXP INT and S has RING ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if S has LINEXP INT and S has RING ---R reducedSystem : Matrix % -> Matrix S if S has RING ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix S,vec: Vector S) if S has RING ---R retract : % -> Fraction Integer if S has RETRACT FRAC INT and S has SETCAT ---R retract : % -> Integer if S has RETRACT INT and S has SETCAT +--R recip : % -> Union(%,"failed") if S has DIFRING and S has RING or S has LINEXP(INT) and S has RING or S has MONOID or S has PDRING(SYMBOL) and S has RING +--R reducedSystem : Matrix(%) -> Matrix(Integer) if S has LINEXP(INT) and S has RING +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if S has LINEXP(INT) and S has RING +--R reducedSystem : Matrix(%) -> Matrix(S) if S has RING +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(S),vec: Vector(S)) if S has RING +--R retract : % -> Fraction(Integer) if S has RETRACT(FRAC(INT)) and S has SETCAT +--R retract : % -> Integer if S has RETRACT(INT) and S has SETCAT --R retract : % -> S if S has SETCAT ---R retractIfCan : % -> Union(Fraction Integer,"failed") if S has RETRACT FRAC INT and S has SETCAT ---R retractIfCan : % -> Union(Integer,"failed") if S has RETRACT INT and S has SETCAT +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if S has RETRACT(FRAC(INT)) and S has SETCAT +--R retractIfCan : % -> Union(Integer,"failed") if S has RETRACT(INT) and S has SETCAT --R retractIfCan : % -> Union(S,"failed") if S has SETCAT --R setelt : (%,Integer,S) -> S if $ has shallowlyMutable --R sign : % -> Integer if S has ORDRING @@ -26575,7 +26645,8 @@ DirectProductMatrixModule(n, R, M, S): DPcategory == DPcapsule where --S 1 of 1 )show DirectProductModule ---R DirectProductModule(n: NonNegativeInteger,R: Ring,S: LeftModule R) is a domain constructor +--R +--R DirectProductModule(n: NonNegativeInteger,R: Ring,S: LeftModule(R)) is a domain constructor --R Abbreviation for DirectProductModule is DPMO --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for DPMO @@ -26585,23 +26656,23 @@ DirectProductMatrixModule(n, R, M, S): DPcategory == DPcapsule where --R ?*? : (R,%) -> % ?+? : (%,%) -> % --R -? : % -> % ?-? : (%,%) -> % --R ?=? : (%,%) -> Boolean 0 : () -> % ---R coerce : % -> OutputForm coerce : % -> Vector S ---R copy : % -> % directProduct : Vector S -> % +--R coerce : % -> OutputForm coerce : % -> Vector(S) +--R copy : % -> % directProduct : Vector(S) -> % --R ?.? : (%,Integer) -> S elt : (%,Integer,S) -> S --R empty : () -> % empty? : % -> Boolean ---R entries : % -> List S eq? : (%,%) -> Boolean +--R entries : % -> List(S) eq? : (%,%) -> Boolean --R hash : % -> SingleInteger index? : (Integer,%) -> Boolean ---R indices : % -> List Integer latex : % -> String +--R indices : % -> List(Integer) latex : % -> String --R map : ((S -> S),%) -> % qelt : (%,Integer) -> S --R sample : () -> % zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean --R #? : % -> NonNegativeInteger if $ has finiteAggregate ---R ?*? : (%,%) -> % if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING +--R ?*? : (%,%) -> % if S has DIFRING and S has RING or S has LINEXP(INT) and S has RING or S has MONOID or S has PDRING(SYMBOL) and S has RING --R ?*? : (S,%) -> % if S has RING --R ?*? : (%,S) -> % if S has RING --R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,PositiveInteger) -> % if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING ---R ?**? : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING +--R ?**? : (%,PositiveInteger) -> % if S has DIFRING and S has RING or S has LINEXP(INT) and S has RING or S has MONOID or S has PDRING(SYMBOL) and S has RING +--R ?**? : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING or S has LINEXP(INT) and S has RING or S has MONOID or S has PDRING(SYMBOL) and S has RING --R ?/? : (%,S) -> % if S has FIELD --R ? Boolean if S has OAMONS or S has ORDRING --R ?<=? : (%,%) -> Boolean if S has OAMONS or S has ORDRING @@ -26609,38 +26680,38 @@ DirectProductMatrixModule(n, R, M, S): DPcategory == DPcapsule where --R ?>=? : (%,%) -> Boolean if S has OAMONS or S has ORDRING --R D : % -> % if S has DIFRING and S has RING --R D : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING ---R D : (%,Symbol) -> % if S has PDRING SYMBOL and S has RING ---R D : (%,List Symbol) -> % if S has PDRING SYMBOL and S has RING ---R D : (%,Symbol,NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING ---R D : (%,List Symbol,List NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING +--R D : (%,Symbol) -> % if S has PDRING(SYMBOL) and S has RING +--R D : (%,List(Symbol)) -> % if S has PDRING(SYMBOL) and S has RING +--R D : (%,Symbol,NonNegativeInteger) -> % if S has PDRING(SYMBOL) and S has RING +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if S has PDRING(SYMBOL) and S has RING --R D : (%,(S -> S)) -> % if S has RING --R D : (%,(S -> S),NonNegativeInteger) -> % if S has RING ---R 1 : () -> % if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING ---R ?^? : (%,PositiveInteger) -> % if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING ---R ?^? : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING +--R 1 : () -> % if S has DIFRING and S has RING or S has LINEXP(INT) and S has RING or S has MONOID or S has PDRING(SYMBOL) and S has RING +--R ?^? : (%,PositiveInteger) -> % if S has DIFRING and S has RING or S has LINEXP(INT) and S has RING or S has MONOID or S has PDRING(SYMBOL) and S has RING +--R ?^? : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING or S has LINEXP(INT) and S has RING or S has MONOID or S has PDRING(SYMBOL) and S has RING --R abs : % -> % if S has ORDRING --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R characteristic : () -> NonNegativeInteger if S has RING ---R coerce : Fraction Integer -> % if S has RETRACT FRAC INT and S has SETCAT ---R coerce : Integer -> % if S has RETRACT INT and S has SETCAT or S has RING +--R coerce : Fraction(Integer) -> % if S has RETRACT(FRAC(INT)) and S has SETCAT +--R coerce : Integer -> % if S has RETRACT(INT) and S has SETCAT or S has RING --R coerce : S -> % if S has SETCAT --R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT --R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate --R differentiate : % -> % if S has DIFRING and S has RING --R differentiate : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING ---R differentiate : (%,Symbol) -> % if S has PDRING SYMBOL and S has RING ---R differentiate : (%,List Symbol) -> % if S has PDRING SYMBOL and S has RING ---R differentiate : (%,Symbol,NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING ---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING +--R differentiate : (%,Symbol) -> % if S has PDRING(SYMBOL) and S has RING +--R differentiate : (%,List(Symbol)) -> % if S has PDRING(SYMBOL) and S has RING +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if S has PDRING(SYMBOL) and S has RING +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if S has PDRING(SYMBOL) and S has RING --R differentiate : (%,(S -> S)) -> % if S has RING --R differentiate : (%,(S -> S),NonNegativeInteger) -> % if S has RING --R dimension : () -> CardinalNumber if S has FIELD --R dot : (%,%) -> S if S has RING --R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT ---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R fill! : (%,S) -> % if $ has shallowlyMutable --R first : % -> S if Integer has ORDSET @@ -26651,26 +26722,26 @@ DirectProductMatrixModule(n, R, M, S): DPcategory == DPcapsule where --R max : (%,%) -> % if S has OAMONS or S has ORDRING --R maxIndex : % -> Integer if Integer has ORDSET --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT ---R members : % -> List S if $ has finiteAggregate +--R members : % -> List(S) if $ has finiteAggregate --R min : (%,%) -> % if S has OAMONS or S has ORDRING --R minIndex : % -> Integer if Integer has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean --R negative? : % -> Boolean if S has ORDRING ---R one? : % -> Boolean if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING ---R parts : % -> List S if $ has finiteAggregate +--R one? : % -> Boolean if S has DIFRING and S has RING or S has LINEXP(INT) and S has RING or S has MONOID or S has PDRING(SYMBOL) and S has RING +--R parts : % -> List(S) if $ has finiteAggregate --R positive? : % -> Boolean if S has ORDRING --R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable --R random : () -> % if S has FINITE ---R recip : % -> Union(%,"failed") if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING ---R reducedSystem : Matrix % -> Matrix Integer if S has LINEXP INT and S has RING ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if S has LINEXP INT and S has RING ---R reducedSystem : Matrix % -> Matrix S if S has RING ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix S,vec: Vector S) if S has RING ---R retract : % -> Fraction Integer if S has RETRACT FRAC INT and S has SETCAT ---R retract : % -> Integer if S has RETRACT INT and S has SETCAT +--R recip : % -> Union(%,"failed") if S has DIFRING and S has RING or S has LINEXP(INT) and S has RING or S has MONOID or S has PDRING(SYMBOL) and S has RING +--R reducedSystem : Matrix(%) -> Matrix(Integer) if S has LINEXP(INT) and S has RING +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if S has LINEXP(INT) and S has RING +--R reducedSystem : Matrix(%) -> Matrix(S) if S has RING +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(S),vec: Vector(S)) if S has RING +--R retract : % -> Fraction(Integer) if S has RETRACT(FRAC(INT)) and S has SETCAT +--R retract : % -> Integer if S has RETRACT(INT) and S has SETCAT --R retract : % -> S if S has SETCAT ---R retractIfCan : % -> Union(Fraction Integer,"failed") if S has RETRACT FRAC INT and S has SETCAT ---R retractIfCan : % -> Union(Integer,"failed") if S has RETRACT INT and S has SETCAT +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if S has RETRACT(FRAC(INT)) and S has SETCAT +--R retractIfCan : % -> Union(Integer,"failed") if S has RETRACT(INT) and S has SETCAT --R retractIfCan : % -> Union(S,"failed") if S has SETCAT --R setelt : (%,Integer,S) -> S if $ has shallowlyMutable --R sign : % -> Integer if S has ORDRING @@ -26850,7 +26921,7 @@ t1:DIRRING INT := (n:PI):INT +-> moebiusMu n --R --R --R (1) [1,- 1,- 1,0,- 1,1,- 1,0,0,1,...] ---R Type: DirichletRing Integer +--R Type: DirichletRing(Integer) --E 1 --S 2 of 21 @@ -26858,7 +26929,7 @@ t1:DIRRING INT := (n:PI):INT +-> moebiusMu n --R --R --R (2) [1,- 1,- 1,0] ---R Type: List Integer +--R Type: List(Integer) --E 2 --S 3 of 21 @@ -26866,7 +26937,7 @@ t2:DIRRING INT := [moebiusMu n for n in 1..] --R --R --R (3) [1,- 1,- 1,0,- 1,1,- 1,0,0,1,...] ---R Type: DirichletRing Integer +--R Type: DirichletRing(Integer) --E 3 --S 4 of 21 @@ -26874,7 +26945,7 @@ t2:DIRRING INT := [moebiusMu n for n in 1..] --R --R --R (4) [1,- 1,- 1,0] ---R Type: List Integer +--R Type: List(Integer) --E 4 --S 5 of 21 @@ -26890,7 +26961,7 @@ mu:DIRRING FRAC INT := (n:PI):FRAC INT +-> moebiusMu n --R --R --R (6) [1,- 1,- 1,0,- 1,1,- 1,0,0,1,...] ---R Type: DirichletRing Fraction Integer +--R Type: DirichletRing(Fraction(Integer)) --E 6 --S 7 of 21 @@ -26898,7 +26969,7 @@ phi:DIRRING FRAC INT := (n:PI):FRAC INT +-> eulerPhi n --R --R --R (7) [1,1,2,2,4,2,6,4,6,4,...] ---R Type: DirichletRing Fraction Integer +--R Type: DirichletRing(Fraction(Integer)) --E 7 --S 8 of 21 @@ -26906,7 +26977,7 @@ t3:=[(recip mu * phi).n for n in 1..10] --R --R --R (8) [1,2,3,4,5,6,7,8,9,10] ---R Type: List Fraction Integer +--R Type: List(Fraction(Integer)) --E 8 --S 9 of 21 @@ -26914,7 +26985,7 @@ t4:=[(phi * recip mu).n for n in 1..10] --R --R --R (9) [1,2,3,4,5,6,7,8,9,10] ---R Type: List Fraction Integer +--R Type: List(Fraction(Integer)) --E 9 --S 10 of 21 @@ -26940,7 +27011,7 @@ t5:=[(1/2 * phi).n for n in 1..10] --R 1 1 --R (12) [-,-,1,1,2,1,3,2,3,2] --R 2 2 ---R Type: List Fraction Integer +--R Type: List(Fraction(Integer)) --E 12 --S 13 of 21 @@ -26950,7 +27021,7 @@ t6:=[eulerPhi n/2 for n in 1..10] --R 1 1 --R (13) [-,-,1,1,2,1,3,2,3,2] --R 2 2 ---R Type: List Fraction Integer +--R Type: List(Fraction(Integer)) --E 13 --S 14 of 21 @@ -26966,7 +27037,7 @@ t7:=[(recip mu).n for n in 1..10] --R --R --R (15) [1,1,1,1,1,1,1,1,1,1] ---R Type: List Fraction Integer +--R Type: List(Fraction(Integer)) --E 15 --S 16 of 21 @@ -26974,7 +27045,7 @@ t8:=[1 for n in 1..10] --R --R --R (16) [1,1,1,1,1,1,1,1,1,1] ---R Type: List PositiveInteger +--R Type: List(PositiveInteger) --E 16 --S 17 of 21 @@ -26990,7 +27061,7 @@ t9:=[(recip mu * phi).n for n in 1..10] --R --R --R (18) [1,2,3,4,5,6,7,8,9,10] ---R Type: List Fraction Integer +--R Type: List(Fraction(Integer)) --E 18 --S 19 of 21 @@ -26998,7 +27069,7 @@ t10:=[n for n in 1..10] --R --R --R (19) [1,2,3,4,5,6,7,8,9,10] ---R Type: List PositiveInteger +--R Type: List(PositiveInteger) --E 19 --S 20 of 21 @@ -27011,7 +27082,8 @@ reduce(_and,[(x = y)@Boolean for x in t9 for y in t10]) --S 21 of 21 )show DirichletRing ---R DirichletRing Coef: Ring is a domain constructor +--R +--R DirichletRing(Coef: Ring) is a domain constructor --R Abbreviation for DirichletRing is DIRRING --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for DIRRING @@ -27022,8 +27094,8 @@ reduce(_and,[(x = y)@Boolean for x in t9 for y in t10]) --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coerce : % -> Stream Coef ---R coerce : Stream Coef -> % coerce : Integer -> % +--R ?^? : (%,PositiveInteger) -> % coerce : % -> Stream(Coef) +--R coerce : Stream(Coef) -> % coerce : Integer -> % --R coerce : % -> OutputForm ?.? : (%,PositiveInteger) -> Coef --R hash : % -> SingleInteger latex : % -> String --R one? : % -> Boolean recip : % -> Union(%,"failed") @@ -27259,7 +27331,7 @@ d1 := -4*z + 4*y**2*x + 16*x**2 + 1 --R --R 2 2 --R (2) - 4z + 4y x + 16x + 1 ---R Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer) +--R Type: DistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 2 --S 3 of 10 @@ -27268,7 +27340,7 @@ d2 := 2*z*y**2 + 4*x + 1 --R --R 2 --R (3) 2z y + 4x + 1 ---R Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer) +--R Type: DistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 3 --S 4 of 10 @@ -27277,7 +27349,7 @@ d3 := 2*z*x**2 - 2*y**2 - x --R --R 2 2 --R (4) 2z x - 2y - x ---R Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer) +--R Type: DistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 4 --S 5 of 10 @@ -27294,7 +27366,7 @@ groebner [d1,d2,d3] --R 7 29 6 17 4 11 3 1 2 15 1 --R x + -- x - -- x - -- x + -- x + -- x + -] --R 4 16 8 32 16 4 ---R Type: List DistributedMultivariatePolynomial([z,y,x],Fraction Integer) +--R Type: List(DistributedMultivariatePolynomial([z,y,x],Fraction(Integer))) --E 5 --S 6 of 10 @@ -27309,7 +27381,7 @@ n1 := d1 --R --R 2 2 --R (7) 4y x + 16x - 4z + 1 ---R Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer) +--RType: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 7 --S 8 of 10 @@ -27318,7 +27390,7 @@ n2 := d2 --R --R 2 --R (8) 2z y + 4x + 1 ---R Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer) +--RType: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 8 --S 9 of 10 @@ -27327,7 +27399,7 @@ n3 := d3 --R --R 2 2 --R (9) 2z x - 2y - x ---R Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer) +--RType: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 9 --S 10 of 10 @@ -27344,7 +27416,7 @@ groebner [n1,n2,n3] --R 2 2 2 1 3 --R z - 4y + 2x - - z - - x] --R 4 2 ---RType: List HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer) +--RType: List(HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction(Integer))) --E 10 )spool )lisp (bye) @@ -27600,7 +27672,8 @@ DistributedMultivariatePolynomial(vl,R): public == private where --S 1 of 1 )show Divisor ---R Divisor S: SetCategoryWithDegree is a domain constructor +--R +--R Divisor(S: SetCategoryWithDegree) is a domain constructor --R Abbreviation for Divisor is DIV --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for DIV @@ -27621,9 +27694,9 @@ DistributedMultivariatePolynomial(vl,R): public == private where --R mapGen : ((S -> S),%) -> % nthCoef : (%,Integer) -> Integer --R nthFactor : (%,Integer) -> S reductum : % -> % --R retract : % -> S sample : () -> % ---R size : % -> NonNegativeInteger split : % -> List % ---R supp : % -> List S suppOfPole : % -> List S ---R suppOfZero : % -> List S zero? : % -> Boolean +--R size : % -> NonNegativeInteger split : % -> List(%) +--R supp : % -> List(S) suppOfPole : % -> List(S) +--R suppOfZero : % -> List(S) zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean --R ?*? : (NonNegativeInteger,%) -> % --R head : % -> Record(gen: S,exp: Integer) @@ -27631,7 +27704,7 @@ DistributedMultivariatePolynomial(vl,R): public == private where --R mapCoef : ((Integer -> Integer),%) -> % --R retractIfCan : % -> Union(S,"failed") --R subtractIfCan : (%,%) -> Union(%,"failed") ---R terms : % -> List Record(gen: S,exp: Integer) +--R terms : % -> List(Record(gen: S,exp: Integer)) --R --E 1 @@ -28054,7 +28127,7 @@ avg l == --S 7 of 13 avg [] --R ---R Compiling function avg with type List DoubleFloat -> DoubleFloat +--R Compiling function avg with type List(DoubleFloat) -> DoubleFloat --R --R (7) 0. --R Type: DoubleFloat @@ -28097,7 +28170,7 @@ integerDecode a --R --R --R (12) [6004799503160662,- 54,- 1] ---R Type: List Integer +--R Type: List(Integer) --E 12 --S 13 of 13 @@ -28107,7 +28180,7 @@ machineFraction a --R 3002399751580331 --R (13) - ---------------- --R 9007199254740992 ---R Type: Fraction Integer +--R Type: Fraction(Integer) --E 13 )spool @@ -28715,6 +28788,7 @@ DoubleFloat(): Join(FloatingPointSystem, DifferentialRing, OpenMath, --S 1 of 6 )show DoubleFloatMatrix +--R --R DoubleFloatMatrix is a domain constructor --R Abbreviation for DoubleFloatMatrix is DFMAT --R This constructor is exposed in this frame. @@ -28726,13 +28800,13 @@ DoubleFloat(): Join(FloatingPointSystem, DifferentialRing, OpenMath, --R ?+? : (%,%) -> % -? : % -> % --R ?-? : (%,%) -> % antisymmetric? : % -> Boolean --R coerce : DoubleFloatVector -> % copy : % -> % ---R diagonal? : % -> Boolean diagonalMatrix : List % -> % +--R diagonal? : % -> Boolean diagonalMatrix : List(%) -> % --R empty : () -> % empty? : % -> Boolean --R eq? : (%,%) -> Boolean fill! : (%,DoubleFloat) -> % --R horizConcat : (%,%) -> % maxColIndex : % -> Integer --R maxRowIndex : % -> Integer minColIndex : % -> Integer --R minRowIndex : % -> Integer ncols : % -> NonNegativeInteger ---R nrows : % -> NonNegativeInteger parts : % -> List DoubleFloat +--R nrows : % -> NonNegativeInteger parts : % -> List(DoubleFloat) --R qnew : (Integer,Integer) -> % sample : () -> % --R square? : % -> Boolean squareTop : % -> % --R symmetric? : % -> Boolean transpose : % -> % @@ -28747,36 +28821,36 @@ DoubleFloat(): Join(FloatingPointSystem, DifferentialRing, OpenMath, --R any? : ((DoubleFloat -> Boolean),%) -> Boolean if $ has finiteAggregate --R coerce : % -> OutputForm if DoubleFloat has SETCAT --R column : (%,Integer) -> DoubleFloatVector ---R columnSpace : % -> List DoubleFloatVector if DoubleFloat has EUCDOM +--R columnSpace : % -> List(DoubleFloatVector) if DoubleFloat has EUCDOM --R count : (DoubleFloat,%) -> NonNegativeInteger if $ has finiteAggregate and DoubleFloat has SETCAT --R count : ((DoubleFloat -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate ---R determinant : % -> DoubleFloat if DoubleFloat has commutative * ---R diagonalMatrix : List DoubleFloat -> % ---R elt : (%,List Integer,List Integer) -> % +--R determinant : % -> DoubleFloat if DoubleFloat has commutative(*) +--R diagonalMatrix : List(DoubleFloat) -> % +--R elt : (%,List(Integer),List(Integer)) -> % --R elt : (%,Integer,Integer,DoubleFloat) -> DoubleFloat --R elt : (%,Integer,Integer) -> DoubleFloat ---R eval : (%,List DoubleFloat,List DoubleFloat) -> % if DoubleFloat has EVALAB DFLOAT and DoubleFloat has SETCAT ---R eval : (%,DoubleFloat,DoubleFloat) -> % if DoubleFloat has EVALAB DFLOAT and DoubleFloat has SETCAT ---R eval : (%,Equation DoubleFloat) -> % if DoubleFloat has EVALAB DFLOAT and DoubleFloat has SETCAT ---R eval : (%,List Equation DoubleFloat) -> % if DoubleFloat has EVALAB DFLOAT and DoubleFloat has SETCAT +--R eval : (%,List(DoubleFloat),List(DoubleFloat)) -> % if DoubleFloat has EVALAB(DFLOAT) and DoubleFloat has SETCAT +--R eval : (%,DoubleFloat,DoubleFloat) -> % if DoubleFloat has EVALAB(DFLOAT) and DoubleFloat has SETCAT +--R eval : (%,Equation(DoubleFloat)) -> % if DoubleFloat has EVALAB(DFLOAT) and DoubleFloat has SETCAT +--R eval : (%,List(Equation(DoubleFloat))) -> % if DoubleFloat has EVALAB(DFLOAT) and DoubleFloat has SETCAT --R every? : ((DoubleFloat -> Boolean),%) -> Boolean if $ has finiteAggregate --R exquo : (%,DoubleFloat) -> Union(%,"failed") if DoubleFloat has INTDOM --R hash : % -> SingleInteger if DoubleFloat has SETCAT --R inverse : % -> Union(%,"failed") if DoubleFloat has FIELD --R latex : % -> String if DoubleFloat has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean ---R listOfLists : % -> List List DoubleFloat +--R listOfLists : % -> List(List(DoubleFloat)) --R map : (((DoubleFloat,DoubleFloat) -> DoubleFloat),%,%,DoubleFloat) -> % --R map : (((DoubleFloat,DoubleFloat) -> DoubleFloat),%,%) -> % --R map : ((DoubleFloat -> DoubleFloat),%) -> % --R map! : ((DoubleFloat -> DoubleFloat),%) -> % ---R matrix : List List DoubleFloat -> % +--R matrix : List(List(DoubleFloat)) -> % --R member? : (DoubleFloat,%) -> Boolean if $ has finiteAggregate and DoubleFloat has SETCAT ---R members : % -> List DoubleFloat if $ has finiteAggregate ---R minordet : % -> DoubleFloat if DoubleFloat has commutative * +--R members : % -> List(DoubleFloat) if $ has finiteAggregate +--R minordet : % -> DoubleFloat if DoubleFloat has commutative(*) --R more? : (%,NonNegativeInteger) -> Boolean --R new : (NonNegativeInteger,NonNegativeInteger,DoubleFloat) -> % ---R nullSpace : % -> List DoubleFloatVector if DoubleFloat has INTDOM +--R nullSpace : % -> List(DoubleFloatVector) if DoubleFloat has INTDOM --R nullity : % -> NonNegativeInteger if DoubleFloat has INTDOM --R pfaffian : % -> DoubleFloat if DoubleFloat has COMRING --R qelt : (%,Integer,Integer) -> DoubleFloat @@ -28787,7 +28861,7 @@ DoubleFloat(): Join(FloatingPointSystem, DifferentialRing, OpenMath, --R scalarMatrix : (NonNegativeInteger,DoubleFloat) -> % --R setColumn! : (%,Integer,DoubleFloatVector) -> % --R setRow! : (%,Integer,DoubleFloatVector) -> % ---R setelt : (%,List Integer,List Integer,%) -> % +--R setelt : (%,List(Integer),List(Integer),%) -> % --R setelt : (%,Integer,Integer,DoubleFloat) -> DoubleFloat --R setsubMatrix! : (%,Integer,Integer,%) -> % --R size? : (%,NonNegativeInteger) -> Boolean @@ -29038,22 +29112,22 @@ DoubleFloatMatrix : MatrixCategory(DoubleFloat, --S 1 of 6 )show DoubleFloatVector +--R --R DoubleFloatVector is a domain constructor --R Abbreviation for DoubleFloatVector is DFVEC --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for DFVEC --R --R------------------------------- Operations -------------------------------- ---R concat : List % -> % concat : (%,%) -> % +--R concat : List(%) -> % concat : (%,%) -> % --R concat : (DoubleFloat,%) -> % concat : (%,DoubleFloat) -> % ---R construct : List DoubleFloat -> % copy : % -> % ---R delete : (%,Integer) -> % ?.? : (%,Integer) -> DoubleFloat ---R empty : () -> % empty? : % -> Boolean ---R entries : % -> List DoubleFloat eq? : (%,%) -> Boolean ---R index? : (Integer,%) -> Boolean indices : % -> List Integer ---R insert : (%,%,Integer) -> % qelt : (%,Integer) -> DoubleFloat ---R qnew : Integer -> % reverse : % -> % ---R sample : () -> % +--R copy : % -> % delete : (%,Integer) -> % +--R ?.? : (%,Integer) -> DoubleFloat empty : () -> % +--R empty? : % -> Boolean entries : % -> List(DoubleFloat) +--R eq? : (%,%) -> Boolean index? : (Integer,%) -> Boolean +--R indices : % -> List(Integer) insert : (%,%,Integer) -> % +--R qelt : (%,Integer) -> DoubleFloat qnew : Integer -> % +--R reverse : % -> % sample : () -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?*? : (%,DoubleFloat) -> % if DoubleFloat has MONOID --R ?*? : (DoubleFloat,%) -> % if DoubleFloat has MONOID @@ -29068,20 +29142,21 @@ DoubleFloatMatrix : MatrixCategory(DoubleFloat, --R ?>=? : (%,%) -> Boolean if DoubleFloat has ORDSET --R any? : ((DoubleFloat -> Boolean),%) -> Boolean if $ has finiteAggregate --R coerce : % -> OutputForm if DoubleFloat has SETCAT ---R convert : % -> InputForm if DoubleFloat has KONVERT INFORM +--R construct : List(DoubleFloat) -> % +--R convert : % -> InputForm if DoubleFloat has KONVERT(INFORM) --R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable --R count : (DoubleFloat,%) -> NonNegativeInteger if $ has finiteAggregate and DoubleFloat has SETCAT --R count : ((DoubleFloat -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate --R cross : (%,%) -> % if DoubleFloat has RING ---R delete : (%,UniversalSegment Integer) -> % +--R delete : (%,UniversalSegment(Integer)) -> % --R dot : (%,%) -> DoubleFloat if DoubleFloat has RING ---R ?.? : (%,UniversalSegment Integer) -> % +--R ?.? : (%,UniversalSegment(Integer)) -> % --R elt : (%,Integer,DoubleFloat) -> DoubleFloat --R entry? : (DoubleFloat,%) -> Boolean if $ has finiteAggregate and DoubleFloat has SETCAT ---R eval : (%,List DoubleFloat,List DoubleFloat) -> % if DoubleFloat has EVALAB DFLOAT and DoubleFloat has SETCAT ---R eval : (%,DoubleFloat,DoubleFloat) -> % if DoubleFloat has EVALAB DFLOAT and DoubleFloat has SETCAT ---R eval : (%,Equation DoubleFloat) -> % if DoubleFloat has EVALAB DFLOAT and DoubleFloat has SETCAT ---R eval : (%,List Equation DoubleFloat) -> % if DoubleFloat has EVALAB DFLOAT and DoubleFloat has SETCAT +--R eval : (%,List(DoubleFloat),List(DoubleFloat)) -> % if DoubleFloat has EVALAB(DFLOAT) and DoubleFloat has SETCAT +--R eval : (%,DoubleFloat,DoubleFloat) -> % if DoubleFloat has EVALAB(DFLOAT) and DoubleFloat has SETCAT +--R eval : (%,Equation(DoubleFloat)) -> % if DoubleFloat has EVALAB(DFLOAT) and DoubleFloat has SETCAT +--R eval : (%,List(Equation(DoubleFloat))) -> % if DoubleFloat has EVALAB(DFLOAT) and DoubleFloat has SETCAT --R every? : ((DoubleFloat -> Boolean),%) -> Boolean if $ has finiteAggregate --R fill! : (%,DoubleFloat) -> % if $ has shallowlyMutable --R find : ((DoubleFloat -> Boolean),%) -> Union(DoubleFloat,"failed") @@ -29098,15 +29173,15 @@ DoubleFloatMatrix : MatrixCategory(DoubleFloat, --R max : (%,%) -> % if DoubleFloat has ORDSET --R maxIndex : % -> Integer if Integer has ORDSET --R member? : (DoubleFloat,%) -> Boolean if $ has finiteAggregate and DoubleFloat has SETCAT ---R members : % -> List DoubleFloat if $ has finiteAggregate +--R members : % -> List(DoubleFloat) if $ has finiteAggregate --R merge : (%,%) -> % if DoubleFloat has ORDSET --R merge : (((DoubleFloat,DoubleFloat) -> Boolean),%,%) -> % --R min : (%,%) -> % if DoubleFloat has ORDSET --R minIndex : % -> Integer if Integer has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean --R new : (NonNegativeInteger,DoubleFloat) -> % ---R outerProduct : (%,%) -> Matrix DoubleFloat if DoubleFloat has RING ---R parts : % -> List DoubleFloat if $ has finiteAggregate +--R outerProduct : (%,%) -> Matrix(DoubleFloat) if DoubleFloat has RING +--R parts : % -> List(DoubleFloat) if $ has finiteAggregate --R position : (DoubleFloat,%,Integer) -> Integer if DoubleFloat has SETCAT --R position : (DoubleFloat,%) -> Integer if DoubleFloat has SETCAT --R position : ((DoubleFloat -> Boolean),%) -> Integer @@ -29119,7 +29194,7 @@ DoubleFloatMatrix : MatrixCategory(DoubleFloat, --R removeDuplicates : % -> % if $ has finiteAggregate and DoubleFloat has SETCAT --R reverse! : % -> % if $ has shallowlyMutable --R select : ((DoubleFloat -> Boolean),%) -> % if $ has finiteAggregate ---R setelt : (%,UniversalSegment Integer,DoubleFloat) -> DoubleFloat if $ has shallowlyMutable +--R setelt : (%,UniversalSegment(Integer),DoubleFloat) -> DoubleFloat if $ has shallowlyMutable --R setelt : (%,Integer,DoubleFloat) -> DoubleFloat if $ has shallowlyMutable --R size? : (%,NonNegativeInteger) -> Boolean --R sort : % -> % if DoubleFloat has ORDSET @@ -29347,6 +29422,7 @@ DoubleFloatVector : VectorCategory DoubleFloat with --S 1 of 1 )show DrawOption +--R --R DrawOption is a domain constructor --R Abbreviation for DrawOption is DROPT --R This constructor is exposed in this frame. @@ -29354,25 +29430,26 @@ DoubleFloatVector : VectorCategory DoubleFloat with --R --R------------------------------- Operations -------------------------------- --R ?=? : (%,%) -> Boolean adaptive : Boolean -> % ---R clip : List Segment Float -> % clip : Boolean -> % +--R clip : List(Segment(Float)) -> % clip : Boolean -> % --R coerce : % -> OutputForm curveColor : Palette -> % --R curveColor : Float -> % hash : % -> SingleInteger --R latex : % -> String pointColor : Palette -> % ---R pointColor : Float -> % range : List Segment Float -> % ---R ranges : List Segment Float -> % style : String -> % ---R title : String -> % toScale : Boolean -> % ---R tubePoints : PositiveInteger -> % tubeRadius : Float -> % ---R unit : List Float -> % var1Steps : PositiveInteger -> % ---R var2Steps : PositiveInteger -> % ?~=? : (%,%) -> Boolean +--R pointColor : Float -> % range : List(Segment(Float)) -> % +--R style : String -> % title : String -> % +--R toScale : Boolean -> % tubePoints : PositiveInteger -> % +--R tubeRadius : Float -> % unit : List(Float) -> % +--R var1Steps : PositiveInteger -> % var2Steps : PositiveInteger -> % +--R ?~=? : (%,%) -> Boolean --R colorFunction : ((DoubleFloat,DoubleFloat,DoubleFloat) -> DoubleFloat) -> % --R colorFunction : ((DoubleFloat,DoubleFloat) -> DoubleFloat) -> % --R colorFunction : (DoubleFloat -> DoubleFloat) -> % ---R coord : (Point DoubleFloat -> Point DoubleFloat) -> % ---R coordinates : (Point DoubleFloat -> Point DoubleFloat) -> % ---R option : (List %,Symbol) -> Union(Any,"failed") ---R option? : (List %,Symbol) -> Boolean ---R range : List Segment Fraction Integer -> % ---R space : ThreeSpace DoubleFloat -> % +--R coord : (Point(DoubleFloat) -> Point(DoubleFloat)) -> % +--R coordinates : (Point(DoubleFloat) -> Point(DoubleFloat)) -> % +--R option : (List(%),Symbol) -> Union(Any,"failed") +--R option? : (List(%),Symbol) -> Boolean +--R range : List(Segment(Fraction(Integer))) -> % +--R ranges : List(Segment(Float)) -> % +--R space : ThreeSpace(DoubleFloat) -> % --R viewpoint : Record(theta: DoubleFloat,phi: DoubleFloat,scale: DoubleFloat,scaleX: DoubleFloat,scaleY: DoubleFloat,scaleZ: DoubleFloat,deltaX: DoubleFloat,deltaY: DoubleFloat) -> % --R --E 1 @@ -29655,6 +29732,7 @@ DrawOption(): Exports == Implementation where --S 1 of 1 )show d01ajfAnnaType +--R --R d01ajfAnnaType is a domain constructor --R Abbreviation for d01ajfAnnaType is D01AJFA --R This constructor is exposed in this frame. @@ -29664,10 +29742,10 @@ DrawOption(): Exports == Implementation where --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R ?~=? : (%,%) -> Boolean ---R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) ---R measure : (RoutinesTable,Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) ---R numericalIntegration : (Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result ---R numericalIntegration : (Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R measure : (RoutinesTable,Record(fn: Expression(DoubleFloat),range: List(Segment(OrderedCompletion(DoubleFloat))),abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R measure : (RoutinesTable,Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R numericalIntegration : (Record(fn: Expression(DoubleFloat),range: List(Segment(OrderedCompletion(DoubleFloat))),abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R numericalIntegration : (Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result --R --E 1 @@ -29772,6 +29850,7 @@ d01ajfAnnaType(): NumericalIntegrationCategory == Result add --S 1 of 1 )show d01akfAnnaType +--R --R d01akfAnnaType is a domain constructor --R Abbreviation for d01akfAnnaType is D01AKFA --R This constructor is exposed in this frame. @@ -29781,10 +29860,10 @@ d01ajfAnnaType(): NumericalIntegrationCategory == Result add --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R ?~=? : (%,%) -> Boolean ---R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) ---R measure : (RoutinesTable,Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) ---R numericalIntegration : (Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result ---R numericalIntegration : (Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R measure : (RoutinesTable,Record(fn: Expression(DoubleFloat),range: List(Segment(OrderedCompletion(DoubleFloat))),abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R measure : (RoutinesTable,Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R numericalIntegration : (Record(fn: Expression(DoubleFloat),range: List(Segment(OrderedCompletion(DoubleFloat))),abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R numericalIntegration : (Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result --R --E 1 @@ -29894,6 +29973,7 @@ d01akfAnnaType(): NumericalIntegrationCategory == Result add --S 1 of 1 )show d01alfAnnaType +--R --R d01alfAnnaType is a domain constructor --R Abbreviation for d01alfAnnaType is D01ALFA --R This constructor is exposed in this frame. @@ -29903,10 +29983,10 @@ d01akfAnnaType(): NumericalIntegrationCategory == Result add --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R ?~=? : (%,%) -> Boolean ---R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) ---R measure : (RoutinesTable,Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) ---R numericalIntegration : (Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result ---R numericalIntegration : (Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R measure : (RoutinesTable,Record(fn: Expression(DoubleFloat),range: List(Segment(OrderedCompletion(DoubleFloat))),abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R measure : (RoutinesTable,Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R numericalIntegration : (Record(fn: Expression(DoubleFloat),range: List(Segment(OrderedCompletion(DoubleFloat))),abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R numericalIntegration : (Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result --R --E 1 @@ -30028,6 +30108,7 @@ d01alfAnnaType(): NumericalIntegrationCategory == Result add --S 1 of 1 )show d01amfAnnaType +--R --R d01amfAnnaType is a domain constructor --R Abbreviation for d01amfAnnaType is D01AMFA --R This constructor is exposed in this frame. @@ -30037,10 +30118,10 @@ d01alfAnnaType(): NumericalIntegrationCategory == Result add --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R ?~=? : (%,%) -> Boolean ---R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) ---R measure : (RoutinesTable,Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) ---R numericalIntegration : (Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result ---R numericalIntegration : (Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R measure : (RoutinesTable,Record(fn: Expression(DoubleFloat),range: List(Segment(OrderedCompletion(DoubleFloat))),abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R measure : (RoutinesTable,Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R numericalIntegration : (Record(fn: Expression(DoubleFloat),range: List(Segment(OrderedCompletion(DoubleFloat))),abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R numericalIntegration : (Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result --R --E 1 @@ -30158,6 +30239,7 @@ d01amfAnnaType(): NumericalIntegrationCategory == Result add --S 1 of 1 )show d01anfAnnaType +--R --R d01anfAnnaType is a domain constructor --R Abbreviation for d01anfAnnaType is D01ANFA --R This constructor is exposed in this frame. @@ -30167,10 +30249,10 @@ d01amfAnnaType(): NumericalIntegrationCategory == Result add --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R ?~=? : (%,%) -> Boolean ---R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) ---R measure : (RoutinesTable,Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) ---R numericalIntegration : (Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result ---R numericalIntegration : (Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R measure : (RoutinesTable,Record(fn: Expression(DoubleFloat),range: List(Segment(OrderedCompletion(DoubleFloat))),abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R measure : (RoutinesTable,Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R numericalIntegration : (Record(fn: Expression(DoubleFloat),range: List(Segment(OrderedCompletion(DoubleFloat))),abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R numericalIntegration : (Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result --R --E 1 @@ -30290,6 +30372,7 @@ d01anfAnnaType(): NumericalIntegrationCategory == Result add --S 1 of 1 )show d01apfAnnaType +--R --R d01apfAnnaType is a domain constructor --R Abbreviation for d01apfAnnaType is D01APFA --R This constructor is exposed in this frame. @@ -30299,10 +30382,10 @@ d01anfAnnaType(): NumericalIntegrationCategory == Result add --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R ?~=? : (%,%) -> Boolean ---R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) ---R measure : (RoutinesTable,Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) ---R numericalIntegration : (Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result ---R numericalIntegration : (Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R measure : (RoutinesTable,Record(fn: Expression(DoubleFloat),range: List(Segment(OrderedCompletion(DoubleFloat))),abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R measure : (RoutinesTable,Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R numericalIntegration : (Record(fn: Expression(DoubleFloat),range: List(Segment(OrderedCompletion(DoubleFloat))),abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R numericalIntegration : (Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result --R --E 1 @@ -30435,6 +30518,7 @@ d01apfAnnaType(): NumericalIntegrationCategory == Result add --S 1 of 1 )show d01aqfAnnaType +--R --R d01aqfAnnaType is a domain constructor --R Abbreviation for d01aqfAnnaType is D01AQFA --R This constructor is exposed in this frame. @@ -30444,10 +30528,10 @@ d01apfAnnaType(): NumericalIntegrationCategory == Result add --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R ?~=? : (%,%) -> Boolean ---R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) ---R measure : (RoutinesTable,Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) ---R numericalIntegration : (Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result ---R numericalIntegration : (Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R measure : (RoutinesTable,Record(fn: Expression(DoubleFloat),range: List(Segment(OrderedCompletion(DoubleFloat))),abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R measure : (RoutinesTable,Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R numericalIntegration : (Record(fn: Expression(DoubleFloat),range: List(Segment(OrderedCompletion(DoubleFloat))),abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R numericalIntegration : (Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result --R --E 1 @@ -30576,6 +30660,7 @@ d01aqfAnnaType(): NumericalIntegrationCategory == Result add --S 1 of 1 )show d01asfAnnaType +--R --R d01asfAnnaType is a domain constructor --R Abbreviation for d01asfAnnaType is D01ASFA --R This constructor is exposed in this frame. @@ -30585,10 +30670,10 @@ d01aqfAnnaType(): NumericalIntegrationCategory == Result add --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R ?~=? : (%,%) -> Boolean ---R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) ---R measure : (RoutinesTable,Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) ---R numericalIntegration : (Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result ---R numericalIntegration : (Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R measure : (RoutinesTable,Record(fn: Expression(DoubleFloat),range: List(Segment(OrderedCompletion(DoubleFloat))),abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R measure : (RoutinesTable,Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R numericalIntegration : (Record(fn: Expression(DoubleFloat),range: List(Segment(OrderedCompletion(DoubleFloat))),abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R numericalIntegration : (Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result --R --E 1 @@ -30714,6 +30799,7 @@ d01asfAnnaType(): NumericalIntegrationCategory == Result add --S 1 of 1 )show d01fcfAnnaType +--R --R d01fcfAnnaType is a domain constructor --R Abbreviation for d01fcfAnnaType is D01FCFA --R This constructor is exposed in this frame. @@ -30723,10 +30809,10 @@ d01asfAnnaType(): NumericalIntegrationCategory == Result add --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R ?~=? : (%,%) -> Boolean ---R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) ---R measure : (RoutinesTable,Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) ---R numericalIntegration : (Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result ---R numericalIntegration : (Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R measure : (RoutinesTable,Record(fn: Expression(DoubleFloat),range: List(Segment(OrderedCompletion(DoubleFloat))),abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R measure : (RoutinesTable,Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R numericalIntegration : (Record(fn: Expression(DoubleFloat),range: List(Segment(OrderedCompletion(DoubleFloat))),abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R numericalIntegration : (Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result --R --E 1 @@ -30842,6 +30928,7 @@ d01fcfAnnaType(): NumericalIntegrationCategory == Result add --S 1 of 1 )show d01gbfAnnaType +--R --R d01gbfAnnaType is a domain constructor --R Abbreviation for d01gbfAnnaType is D01GBFA --R This constructor is exposed in this frame. @@ -30851,10 +30938,10 @@ d01fcfAnnaType(): NumericalIntegrationCategory == Result add --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R ?~=? : (%,%) -> Boolean ---R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) ---R measure : (RoutinesTable,Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) ---R numericalIntegration : (Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result ---R numericalIntegration : (Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R measure : (RoutinesTable,Record(fn: Expression(DoubleFloat),range: List(Segment(OrderedCompletion(DoubleFloat))),abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R measure : (RoutinesTable,Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R numericalIntegration : (Record(fn: Expression(DoubleFloat),range: List(Segment(OrderedCompletion(DoubleFloat))),abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R numericalIntegration : (Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result --R --E 1 @@ -30976,6 +31063,7 @@ d01gbfAnnaType(): NumericalIntegrationCategory == Result add --S 1 of 1 )show d01TransformFunctionType +--R --R d01TransformFunctionType is a domain constructor --R Abbreviation for d01TransformFunctionType is D01TRNS --R This constructor is exposed in this frame. @@ -30985,10 +31073,10 @@ d01gbfAnnaType(): NumericalIntegrationCategory == Result add --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R ?~=? : (%,%) -> Boolean ---R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) ---R measure : (RoutinesTable,Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) ---R numericalIntegration : (Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result ---R numericalIntegration : (Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R measure : (RoutinesTable,Record(fn: Expression(DoubleFloat),range: List(Segment(OrderedCompletion(DoubleFloat))),abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R measure : (RoutinesTable,Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R numericalIntegration : (Record(fn: Expression(DoubleFloat),range: List(Segment(OrderedCompletion(DoubleFloat))),abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R numericalIntegration : (Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result --R --E 1 @@ -31196,6 +31284,7 @@ d01TransformFunctionType():NumericalIntegrationCategory == Result add --S 1 of 1 )show d02bbfAnnaType +--R --R d02bbfAnnaType is a domain constructor --R Abbreviation for d02bbfAnnaType is D02BBFA --R This constructor is exposed in this frame. @@ -31205,8 +31294,8 @@ d01TransformFunctionType():NumericalIntegrationCategory == Result add --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R ?~=? : (%,%) -> Boolean ---R ODESolve : Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat) -> Result ---R measure : (RoutinesTable,Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String) +--R ODESolve : Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector(Expression(DoubleFloat)),yinit: List(DoubleFloat),intvals: List(DoubleFloat),g: Expression(DoubleFloat),abserr: DoubleFloat,relerr: DoubleFloat) -> Result +--R measure : (RoutinesTable,Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector(Expression(DoubleFloat)),yinit: List(DoubleFloat),intvals: List(DoubleFloat),g: Expression(DoubleFloat),abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String) --R --E 1 @@ -31347,6 +31436,7 @@ d02bbfAnnaType():OrdinaryDifferentialEquationsSolverCategory == Result add --S 1 of 1 )show d02bhfAnnaType +--R --R d02bhfAnnaType is a domain constructor --R Abbreviation for d02bhfAnnaType is D02BHFA --R This constructor is exposed in this frame. @@ -31356,8 +31446,8 @@ d02bbfAnnaType():OrdinaryDifferentialEquationsSolverCategory == Result add --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R ?~=? : (%,%) -> Boolean ---R ODESolve : Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat) -> Result ---R measure : (RoutinesTable,Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String) +--R ODESolve : Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector(Expression(DoubleFloat)),yinit: List(DoubleFloat),intvals: List(DoubleFloat),g: Expression(DoubleFloat),abserr: DoubleFloat,relerr: DoubleFloat) -> Result +--R measure : (RoutinesTable,Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector(Expression(DoubleFloat)),yinit: List(DoubleFloat),intvals: List(DoubleFloat),g: Expression(DoubleFloat),abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String) --R --E 1 @@ -31495,6 +31585,7 @@ d02bhfAnnaType():OrdinaryDifferentialEquationsSolverCategory == Result add --S 1 of 1 )show d02cjfAnnaType +--R --R d02cjfAnnaType is a domain constructor --R Abbreviation for d02cjfAnnaType is D02CJFA --R This constructor is exposed in this frame. @@ -31504,8 +31595,8 @@ d02bhfAnnaType():OrdinaryDifferentialEquationsSolverCategory == Result add --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R ?~=? : (%,%) -> Boolean ---R ODESolve : Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat) -> Result ---R measure : (RoutinesTable,Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String) +--R ODESolve : Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector(Expression(DoubleFloat)),yinit: List(DoubleFloat),intvals: List(DoubleFloat),g: Expression(DoubleFloat),abserr: DoubleFloat,relerr: DoubleFloat) -> Result +--R measure : (RoutinesTable,Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector(Expression(DoubleFloat)),yinit: List(DoubleFloat),intvals: List(DoubleFloat),g: Expression(DoubleFloat),abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String) --R --E 1 @@ -31636,6 +31727,7 @@ d02cjfAnnaType():OrdinaryDifferentialEquationsSolverCategory == Result add --S 1 of 1 )show d02ejfAnnaType +--R --R d02ejfAnnaType is a domain constructor --R Abbreviation for d02ejfAnnaType is D02EJFA --R This constructor is exposed in this frame. @@ -31645,8 +31737,8 @@ d02cjfAnnaType():OrdinaryDifferentialEquationsSolverCategory == Result add --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R ?~=? : (%,%) -> Boolean ---R ODESolve : Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat) -> Result ---R measure : (RoutinesTable,Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String) +--R ODESolve : Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector(Expression(DoubleFloat)),yinit: List(DoubleFloat),intvals: List(DoubleFloat),g: Expression(DoubleFloat),abserr: DoubleFloat,relerr: DoubleFloat) -> Result +--R measure : (RoutinesTable,Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector(Expression(DoubleFloat)),yinit: List(DoubleFloat),intvals: List(DoubleFloat),g: Expression(DoubleFloat),abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String) --R --E 1 @@ -31808,6 +31900,7 @@ d02ejfAnnaType():OrdinaryDifferentialEquationsSolverCategory == Result add --S 1 of 1 )show d03eefAnnaType +--R --R d03eefAnnaType is a domain constructor --R Abbreviation for d03eefAnnaType is D03EEFA --R This constructor is exposed in this frame. @@ -31817,8 +31910,8 @@ d02ejfAnnaType():OrdinaryDifferentialEquationsSolverCategory == Result add --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R ?~=? : (%,%) -> Boolean ---R PDESolve : Record(pde: List Expression DoubleFloat,constraints: List Record(start: DoubleFloat,finish: DoubleFloat,grid: NonNegativeInteger,boundaryType: Integer,dStart: Matrix DoubleFloat,dFinish: Matrix DoubleFloat),f: List List Expression DoubleFloat,st: String,tol: DoubleFloat) -> Result ---R measure : (RoutinesTable,Record(pde: List Expression DoubleFloat,constraints: List Record(start: DoubleFloat,finish: DoubleFloat,grid: NonNegativeInteger,boundaryType: Integer,dStart: Matrix DoubleFloat,dFinish: Matrix DoubleFloat),f: List List Expression DoubleFloat,st: String,tol: DoubleFloat)) -> Record(measure: Float,explanations: String) +--R PDESolve : Record(pde: List(Expression(DoubleFloat)),constraints: List(Record(start: DoubleFloat,finish: DoubleFloat,grid: NonNegativeInteger,boundaryType: Integer,dStart: Matrix(DoubleFloat),dFinish: Matrix(DoubleFloat))),f: List(List(Expression(DoubleFloat))),st: String,tol: DoubleFloat) -> Result +--R measure : (RoutinesTable,Record(pde: List(Expression(DoubleFloat)),constraints: List(Record(start: DoubleFloat,finish: DoubleFloat,grid: NonNegativeInteger,boundaryType: Integer,dStart: Matrix(DoubleFloat),dFinish: Matrix(DoubleFloat))),f: List(List(Expression(DoubleFloat))),st: String,tol: DoubleFloat)) -> Record(measure: Float,explanations: String) --R --E 1 @@ -31940,6 +32033,7 @@ d03eefAnnaType():PartialDifferentialEquationsSolverCategory == Result add --S 1 of 1 )show d03fafAnnaType +--R --R d03fafAnnaType is a domain constructor --R Abbreviation for d03fafAnnaType is D03FAFA --R This constructor is exposed in this frame. @@ -31949,8 +32043,8 @@ d03eefAnnaType():PartialDifferentialEquationsSolverCategory == Result add --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R ?~=? : (%,%) -> Boolean ---R PDESolve : Record(pde: List Expression DoubleFloat,constraints: List Record(start: DoubleFloat,finish: DoubleFloat,grid: NonNegativeInteger,boundaryType: Integer,dStart: Matrix DoubleFloat,dFinish: Matrix DoubleFloat),f: List List Expression DoubleFloat,st: String,tol: DoubleFloat) -> Result ---R measure : (RoutinesTable,Record(pde: List Expression DoubleFloat,constraints: List Record(start: DoubleFloat,finish: DoubleFloat,grid: NonNegativeInteger,boundaryType: Integer,dStart: Matrix DoubleFloat,dFinish: Matrix DoubleFloat),f: List List Expression DoubleFloat,st: String,tol: DoubleFloat)) -> Record(measure: Float,explanations: String) +--R PDESolve : Record(pde: List(Expression(DoubleFloat)),constraints: List(Record(start: DoubleFloat,finish: DoubleFloat,grid: NonNegativeInteger,boundaryType: Integer,dStart: Matrix(DoubleFloat),dFinish: Matrix(DoubleFloat))),f: List(List(Expression(DoubleFloat))),st: String,tol: DoubleFloat) -> Result +--R measure : (RoutinesTable,Record(pde: List(Expression(DoubleFloat)),constraints: List(Record(start: DoubleFloat,finish: DoubleFloat,grid: NonNegativeInteger,boundaryType: Integer,dStart: Matrix(DoubleFloat),dFinish: Matrix(DoubleFloat))),f: List(List(Expression(DoubleFloat))),st: String,tol: DoubleFloat)) -> Record(measure: Float,explanations: String) --R --E 1 @@ -32043,7 +32137,7 @@ eq1 := 3*x + 4*y = 5 --R --R --R (1) 4y + 3x= 5 ---R Type: Equation Polynomial Integer +--R Type: Equation(Polynomial(Integer)) --E 1 --S 2 of 12 @@ -32051,7 +32145,7 @@ eq2 := 2*x + 2*y = 3 --R --R --R (2) 2y + 2x= 3 ---R Type: Equation Polynomial Integer +--R Type: Equation(Polynomial(Integer)) --E 2 --S 3 of 12 @@ -32059,7 +32153,7 @@ lhs eq1 --R --R --R (3) 4y + 3x ---R Type: Polynomial Integer +--R Type: Polynomial(Integer) --E 3 --S 4 of 12 @@ -32067,7 +32161,7 @@ rhs eq1 --R --R --R (4) 5 ---R Type: Polynomial Integer +--R Type: Polynomial(Integer) --E 4 --S 5 of 12 @@ -32075,7 +32169,7 @@ eq1 + eq2 --R --R --R (5) 6y + 5x= 8 ---R Type: Equation Polynomial Integer +--R Type: Equation(Polynomial(Integer)) --E 5 --S 6 of 12 @@ -32084,7 +32178,7 @@ eq1 * eq2 --R --R 2 2 --R (6) 8y + 14x y + 6x = 15 ---R Type: Equation Polynomial Integer +--R Type: Equation(Polynomial(Integer)) --E 6 --S 7 of 12 @@ -32092,7 +32186,7 @@ eq1 * eq2 --R --R --R (7) x= 1 ---R Type: Equation Polynomial Integer +--R Type: Equation(Polynomial(Integer)) --E 7 --S 8 of 12 @@ -32101,7 +32195,7 @@ eq1**2 --R --R 2 2 --R (8) 16y + 24x y + 9x = 25 ---R Type: Equation Polynomial Integer +--R Type: Equation(Polynomial(Integer)) --E 8 --S 9 of 12 @@ -32117,7 +32211,7 @@ eqpol := x+1 = y --R --R --R (10) x + 1= y ---R Type: Equation Polynomial Integer +--R Type: Equation(Polynomial(Integer)) --E 10 --S 11 of 12 @@ -32501,7 +32595,7 @@ e: EqTable(List Integer, Integer) := table() --R --R --R (1) table() ---R Type: EqTable(List Integer,Integer) +--R Type: EqTable(List(Integer),Integer) --E 1 --S 2 of 6 @@ -32509,7 +32603,7 @@ l1 := [1,2,3] --R --R --R (2) [1,2,3] ---R Type: List PositiveInteger +--R Type: List(PositiveInteger) --E 2 --S 3 of 6 @@ -32517,7 +32611,7 @@ l2 := [1,2,3] --R --R --R (3) [1,2,3] ---R Type: List PositiveInteger +--R Type: List(PositiveInteger) --E 3 --S 4 of 6 @@ -32702,7 +32796,8 @@ EqTable(Key: SetCategory, Entry: SetCategory) == --S 1 of 1 )show EuclideanModularRing ---R EuclideanModularRing(S: CommutativeRing,R: UnivariatePolynomialCategory S,Mod: AbelianMonoid,reduction: ((R,Mod) -> R),merge: ((Mod,Mod) -> Union(Mod,"failed")),exactQuo: ((R,R,Mod) -> Union(R,"failed"))) is a domain constructor +--R +--R EuclideanModularRing(S: CommutativeRing,R: UnivariatePolynomialCategory(S),Mod: AbelianMonoid,reduction: ((R,Mod) -> R),merge: ((Mod,Mod) -> Union(Mod,"failed")),exactQuo: ((R,R,Mod) -> Union(R,"failed"))) is a domain constructor --R Abbreviation for EuclideanModularRing is EMR --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for EMR @@ -32716,10 +32811,10 @@ EqTable(Key: SetCategory, Entry: SetCategory) == --R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean --R coerce : % -> R coerce : % -> % --R coerce : Integer -> % coerce : % -> OutputForm ---R ?.? : (%,R) -> R gcd : List % -> % +--R ?.? : (%,R) -> R gcd : List(%) -> % --R gcd : (%,%) -> % hash : % -> SingleInteger --R inv : % -> % latex : % -> String ---R lcm : List % -> % lcm : (%,%) -> % +--R lcm : List(%) -> % lcm : (%,%) -> % --R modulus : % -> Mod one? : % -> Boolean --R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") --R reduce : (R,Mod) -> % ?rem? : (%,%) -> % @@ -32733,13 +32828,13 @@ EqTable(Key: SetCategory, Entry: SetCategory) == --R divide : (%,%) -> Record(quotient: %,remainder: %) --R euclideanSize : % -> NonNegativeInteger --R exQuo : (%,%) -> Union(%,"failed") ---R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") --R exquo : (%,%) -> Union(%,"failed") --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % ---R multiEuclidean : (List %,%) -> Union(List %,"failed") ---R principalIdeal : List % -> Record(coef: List %,generator: %) +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) --R subtractIfCan : (%,%) -> Union(%,"failed") --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) --R @@ -33083,13 +33178,14 @@ Exit: SetCategory == add --S 1 of 1 )show ExponentialExpansion ---R ExponentialExpansion(R: Join(OrderedSet,RetractableTo Integer,LinearlyExplicitRingOver Integer,GcdDomain),FE: Join(AlgebraicallyClosedField,TranscendentalFunctionCategory,FunctionSpace R),var: Symbol,cen: FE) is a domain constructor +--R +--R ExponentialExpansion(R: Join(OrderedSet,RetractableTo(Integer),LinearlyExplicitRingOver(Integer),GcdDomain),FE: Join(AlgebraicallyClosedField,TranscendentalFunctionCategory,FunctionSpace(R)),var: Symbol,cen: FE) is a domain constructor --R Abbreviation for ExponentialExpansion is EXPEXPAN --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for EXPEXPAN --R --R------------------------------- Operations -------------------------------- ---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % --R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % @@ -33097,18 +33193,18 @@ Exit: SetCategory == add --R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % --R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % ---R associates? : (%,%) -> Boolean coerce : Fraction Integer -> % +--R associates? : (%,%) -> Boolean coerce : Fraction(Integer) -> % --R coerce : % -> % coerce : Integer -> % --R coerce : % -> OutputForm denominator : % -> % ---R factor : % -> Factored % gcd : List % -> % +--R factor : % -> Factored(%) gcd : List(%) -> % --R gcd : (%,%) -> % hash : % -> SingleInteger --R inv : % -> % latex : % -> String ---R lcm : List % -> % lcm : (%,%) -> % +--R lcm : List(%) -> % lcm : (%,%) -> % --R numerator : % -> % one? : % -> Boolean --R prime? : % -> Boolean ?quo? : (%,%) -> % --R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % --R sample : () -> % sizeLess? : (%,%) -> Boolean ---R squareFree : % -> Factored % squareFreePart : % -> % +--R squareFree : % -> Factored(%) squareFreePart : % -> % --R unit? : % -> Boolean unitCanonical : % -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (%,UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)) -> % @@ -33122,10 +33218,10 @@ Exit: SetCategory == add --R ?>=? : (%,%) -> Boolean if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has ORDSET --R D : (%,(UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) -> UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen))) -> % --R D : (%,(UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) -> UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)),NonNegativeInteger) -> % ---R D : (%,List Symbol,List NonNegativeInteger) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PDRING SYMBOL ---R D : (%,Symbol,NonNegativeInteger) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PDRING SYMBOL ---R D : (%,List Symbol) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PDRING SYMBOL ---R D : (%,Symbol) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PDRING SYMBOL +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PDRING(SYMBOL) +--R D : (%,Symbol,NonNegativeInteger) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PDRING(SYMBOL) +--R D : (%,List(Symbol)) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PDRING(SYMBOL) +--R D : (%,Symbol) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PDRING(SYMBOL) --R D : (%,NonNegativeInteger) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has DIFRING --R D : % -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has DIFRING --R ?^? : (%,NonNegativeInteger) -> % @@ -33134,72 +33230,72 @@ Exit: SetCategory == add --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PFECAT or UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has CHARNZ --R coerce : UnivariatePuiseuxSeries(FE,var,cen) -> % ---R coerce : Symbol -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has RETRACT SYMBOL +--R coerce : Symbol -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has RETRACT(SYMBOL) --R coerce : UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) -> % ---R conditionP : Matrix % -> Union(Vector %,"failed") if $ has CHARNZ and UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PFECAT +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PFECAT --R convert : % -> DoubleFloat if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has REAL --R convert : % -> Float if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has REAL ---R convert : % -> InputForm if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has KONVERT INFORM ---R convert : % -> Pattern Float if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has KONVERT PATTERN FLOAT ---R convert : % -> Pattern Integer if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has KONVERT PATTERN INT +--R convert : % -> InputForm if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has KONVERT(INFORM) +--R convert : % -> Pattern(Float) if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has KONVERT(PATTERN(FLOAT)) +--R convert : % -> Pattern(Integer) if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has KONVERT(PATTERN(INT)) --R denom : % -> UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) --R differentiate : (%,(UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) -> UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen))) -> % --R differentiate : (%,(UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) -> UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)),NonNegativeInteger) -> % ---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PDRING SYMBOL ---R differentiate : (%,Symbol,NonNegativeInteger) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PDRING SYMBOL ---R differentiate : (%,List Symbol) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PDRING SYMBOL ---R differentiate : (%,Symbol) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PDRING SYMBOL +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PDRING(SYMBOL) +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol)) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PDRING(SYMBOL) +--R differentiate : (%,Symbol) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PDRING(SYMBOL) --R differentiate : (%,NonNegativeInteger) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has DIFRING --R differentiate : % -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has DIFRING --R divide : (%,%) -> Record(quotient: %,remainder: %) --R ?.? : (%,UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has ELTAB(UPXSSING(R,FE,var,cen),UPXSSING(R,FE,var,cen)) --R euclideanSize : % -> NonNegativeInteger --R eval : (%,Symbol,UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has IEVALAB(SYMBOL,UPXSSING(R,FE,var,cen)) ---R eval : (%,List Symbol,List UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has IEVALAB(SYMBOL,UPXSSING(R,FE,var,cen)) ---R eval : (%,List Equation UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has EVALAB UPXSSING(R,FE,var,cen) ---R eval : (%,Equation UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has EVALAB UPXSSING(R,FE,var,cen) ---R eval : (%,UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen),UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has EVALAB UPXSSING(R,FE,var,cen) ---R eval : (%,List UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen),List UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has EVALAB UPXSSING(R,FE,var,cen) ---R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R eval : (%,List(Symbol),List(UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen))) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has IEVALAB(SYMBOL,UPXSSING(R,FE,var,cen)) +--R eval : (%,List(Equation(UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)))) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has EVALAB(UPXSSING(R,FE,var,cen)) +--R eval : (%,Equation(UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen))) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has EVALAB(UPXSSING(R,FE,var,cen)) +--R eval : (%,UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen),UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has EVALAB(UPXSSING(R,FE,var,cen)) +--R eval : (%,List(UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)),List(UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen))) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has EVALAB(UPXSSING(R,FE,var,cen)) +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") --R exquo : (%,%) -> Union(%,"failed") --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) ---R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PFECAT ---R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PFECAT +--R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PFECAT --R floor : % -> UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has INS --R fractionPart : % -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has EUCDOM ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) --R init : () -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has STEP ---R limitPlus : % -> Union(OrderedCompletion FE,"failed") +--R limitPlus : % -> Union(OrderedCompletion(FE),"failed") --R map : ((UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) -> UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)),%) -> % --R max : (%,%) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has ORDSET --R min : (%,%) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has ORDSET ---R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") --R negative? : % -> Boolean if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has OINTDOM --R nextItem : % -> Union(%,"failed") if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has STEP --R numer : % -> UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) ---R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PATMAB FLOAT ---R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PATMAB INT +--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PATMAB(FLOAT) +--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PATMAB(INT) --R positive? : % -> Boolean if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has OINTDOM ---R principalIdeal : List % -> Record(coef: List %,generator: %) +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) --R random : () -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has INS ---R reducedSystem : Matrix % -> Matrix UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen),vec: Vector UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)) ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has LINEXP INT ---R reducedSystem : Matrix % -> Matrix Integer if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has LINEXP INT +--R reducedSystem : Matrix(%) -> Matrix(UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)),vec: Vector(UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen))) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has LINEXP(INT) +--R reducedSystem : Matrix(%) -> Matrix(Integer) if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has LINEXP(INT) --R retract : % -> UnivariatePuiseuxSeries(FE,var,cen) ---R retract : % -> Integer if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has RETRACT INT ---R retract : % -> Fraction Integer if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has RETRACT INT ---R retract : % -> Symbol if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has RETRACT SYMBOL +--R retract : % -> Integer if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has RETRACT(INT) +--R retract : % -> Fraction(Integer) if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has RETRACT(INT) +--R retract : % -> Symbol if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has RETRACT(SYMBOL) --R retract : % -> UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) --R retractIfCan : % -> Union(UnivariatePuiseuxSeries(FE,var,cen),"failed") ---R retractIfCan : % -> Union(Integer,"failed") if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has RETRACT INT ---R retractIfCan : % -> Union(Fraction Integer,"failed") if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has RETRACT INT ---R retractIfCan : % -> Union(Symbol,"failed") if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has RETRACT SYMBOL +--R retractIfCan : % -> Union(Integer,"failed") if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has RETRACT(INT) +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has RETRACT(INT) +--R retractIfCan : % -> Union(Symbol,"failed") if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has RETRACT(SYMBOL) --R retractIfCan : % -> Union(UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen),"failed") --R sign : % -> Integer if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has OINTDOM ---R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PFECAT ---R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PFECAT +--R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PFECAT +--R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PFECAT --R subtractIfCan : (%,%) -> Union(%,"failed") --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) --R wholePart : % -> UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has EUCDOM @@ -33480,7 +33576,7 @@ sin(x) + 3*cos(x)**2 --R --R 2 --R (1) sin(x) + 3cos(x) ---R Type: Expression Integer +--R Type: Expression(Integer) --E 1 --S 2 of 23 @@ -33488,7 +33584,7 @@ tan(x) - 3.45*x --R --R --R (2) tan(x) - 3.45 x ---R Type: Expression Float +--R Type: Expression(Float) --E 2 --S 3 of 23 @@ -33499,7 +33595,7 @@ tan(x) - 3.45*x --R - tan(\|7 ) + 2sin(\|11 )tan(\|7 ) - sin(\|11 ) --R (3) ------------------------------------------------- --R cos(y - x) - 4 ---R Type: Expression Integer +--R Type: Expression(Integer) --E 3 --S 4 of 23 @@ -33507,7 +33603,7 @@ log(exp x)@Expression(Integer) --R --R --R (4) x ---R Type: Expression Integer +--R Type: Expression(Integer) --E 4 --S 5 of 23 @@ -33516,7 +33612,7 @@ log(exp x)@Expression(Complex Integer) --R --R x --R (5) log(%e ) ---R Type: Expression Complex Integer +--R Type: Expression(Complex(Integer)) --E 5 --S 6 of 23 @@ -33536,7 +33632,7 @@ sqrt 3 + sqrt(2 + sqrt(-5)) --R +----------+ --R | +---+ +-+ --R (7) \|\|- 5 + 2 + \|3 ---R Type: Expression Integer +--R Type: Expression(Integer) --E 7 --S 8 of 23 @@ -33556,7 +33652,7 @@ e := (sin(x) - 4)**2 / ( 1 - 2*y*sqrt(- y) ) --R (9) ------------------------ --R +---+ --R 2y\|- y - 1 ---R Type: Expression Integer +--R Type: Expression(Integer) --E 9 --S 10 of 23 @@ -33565,7 +33661,7 @@ numer e --R --R 2 --R (10) - sin(x) + 8sin(x) - 16 ---R Type: SparseMultivariatePolynomial(Integer,Kernel Expression Integer) +--R Type: SparseMultivariatePolynomial(Integer,Kernel(Expression(Integer))) --E 10 --S 11 of 23 @@ -33574,7 +33670,7 @@ denom e --R --R +---+ --R (11) 2y\|- y - 1 ---R Type: SparseMultivariatePolynomial(Integer,Kernel Expression Integer) +--R Type: SparseMultivariatePolynomial(Integer,Kernel(Expression(Integer))) --E 11 --S 12 of 23 @@ -33586,7 +33682,7 @@ D(e, x) --R (12) -------------------------------------------------------------- --R +---+ 3 --R 4y\|- y + 4y - 1 ---R Type: Expression Integer +--R Type: Expression(Integer) --E 12 --S 13 of 23 @@ -33608,7 +33704,7 @@ D(e, [x, y], [1, 2]) --R + --R 2 --R 16y ---R Type: Expression Integer +--R Type: Expression(Integer) --E 13 --S 14 of 23 @@ -33616,7 +33712,7 @@ complexNumeric(cos(2 - 3*%i)) --R --R --R (14) - 4.1896256909 688072301 + 9.1092278937 55336598 %i ---R Type: Complex Float +--R Type: Complex(Float) --E 14 --S 15 of 23 @@ -33633,7 +33729,7 @@ e2 := cos(x**2 - y + 3) --R --R 2 --R (16) cos(y - x - 3) ---R Type: Expression Integer +--R Type: Expression(Integer) --E 16 --S 17 of 23 @@ -33642,7 +33738,7 @@ e3 := asin(e2) - %pi/2 --R --R 2 --R (17) - y + x + 3 ---R Type: Expression Integer +--R Type: Expression(Integer) --E 17 --S 18 of 23 @@ -33651,7 +33747,7 @@ e3 :: Polynomial Integer --R --R 2 --R (18) - y + x + 3 ---R Type: Polynomial Integer +--R Type: Polynomial(Integer) --E 18 --S 19 of 23 @@ -33668,7 +33764,7 @@ sin %pi --R --R --R (20) 0 ---R Type: Expression Integer +--R Type: Expression(Integer) --E 20 --S 21 of 23 @@ -33679,7 +33775,7 @@ cos(%pi / 4) --R \|2 --R (21) ---- --R 2 ---R Type: Expression Integer +--R Type: Expression(Integer) --E 21 --S 22 of 23 @@ -33688,7 +33784,7 @@ tan(x)**6 + 3*tan(x)**4 + 3*tan(x)**2 + 1 --R --R 6 4 2 --R (22) tan(x) + 3tan(x) + 3tan(x) + 1 ---R Type: Expression Integer +--R Type: Expression(Integer) --E 22 --S 23 of 23 @@ -33699,7 +33795,7 @@ simplify % --R (23) ------- --R 6 --R cos(x) ---R Type: Expression Integer +--R Type: Expression(Integer) --E 23 )spool )lisp (bye) @@ -34556,6 +34652,7 @@ Expression(R:OrderedSet): Exports == Implementation where --S 1 of 1 )show ExponentialOfUnivariatePuiseuxSeries +--R --R ExponentialOfUnivariatePuiseuxSeries(FE: Join(Field,OrderedSet),var: Symbol,cen: FE) is a domain constructor --R Abbreviation for ExponentialOfUnivariatePuiseuxSeries is EXPUPXS --R This constructor is not exposed in this frame. @@ -34572,120 +34669,120 @@ Expression(R:OrderedSet): Exports == Implementation where --R 1 : () -> % 0 : () -> % --R ?^? : (%,PositiveInteger) -> % center : % -> FE --R coerce : Integer -> % coerce : % -> OutputForm ---R complete : % -> % degree : % -> Fraction Integer ---R ?.? : (%,Fraction Integer) -> FE hash : % -> SingleInteger +--R complete : % -> % degree : % -> Fraction(Integer) +--R ?.? : (%,Fraction(Integer)) -> FE hash : % -> SingleInteger --R inv : % -> % if FE has FIELD latex : % -> String --R leadingCoefficient : % -> FE leadingMonomial : % -> % --R map : ((FE -> FE),%) -> % max : (%,%) -> % --R min : (%,%) -> % monomial? : % -> Boolean ---R one? : % -> Boolean order : % -> Fraction Integer +--R one? : % -> Boolean order : % -> Fraction(Integer) --R pole? : % -> Boolean recip : % -> Union(%,"failed") --R reductum : % -> % sample : () -> % --R variable : % -> Symbol zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean ---R ?*? : (%,Fraction Integer) -> % if FE has ALGEBRA FRAC INT ---R ?*? : (Fraction Integer,%) -> % if FE has ALGEBRA FRAC INT +--R ?*? : (%,Fraction(Integer)) -> % if FE has ALGEBRA(FRAC(INT)) +--R ?*? : (Fraction(Integer),%) -> % if FE has ALGEBRA(FRAC(INT)) --R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,Fraction Integer) -> % if FE has ALGEBRA FRAC INT ---R ?**? : (%,%) -> % if FE has ALGEBRA FRAC INT +--R ?**? : (%,Fraction(Integer)) -> % if FE has ALGEBRA(FRAC(INT)) +--R ?**? : (%,%) -> % if FE has ALGEBRA(FRAC(INT)) --R ?**? : (%,Integer) -> % if FE has FIELD --R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,%) -> % if FE has FIELD --R ?/? : (%,FE) -> % if FE has FIELD ---R D : % -> % if FE has *: (Fraction Integer,FE) -> FE ---R D : (%,NonNegativeInteger) -> % if FE has *: (Fraction Integer,FE) -> FE ---R D : (%,Symbol) -> % if FE has *: (Fraction Integer,FE) -> FE and FE has PDRING SYMBOL ---R D : (%,List Symbol) -> % if FE has *: (Fraction Integer,FE) -> FE and FE has PDRING SYMBOL ---R D : (%,Symbol,NonNegativeInteger) -> % if FE has *: (Fraction Integer,FE) -> FE and FE has PDRING SYMBOL ---R D : (%,List Symbol,List NonNegativeInteger) -> % if FE has *: (Fraction Integer,FE) -> FE and FE has PDRING SYMBOL +--R D : % -> % if FE has *: (Fraction(Integer),FE) -> FE +--R D : (%,NonNegativeInteger) -> % if FE has *: (Fraction(Integer),FE) -> FE +--R D : (%,Symbol) -> % if FE has *: (Fraction(Integer),FE) -> FE and FE has PDRING(SYMBOL) +--R D : (%,List(Symbol)) -> % if FE has *: (Fraction(Integer),FE) -> FE and FE has PDRING(SYMBOL) +--R D : (%,Symbol,NonNegativeInteger) -> % if FE has *: (Fraction(Integer),FE) -> FE and FE has PDRING(SYMBOL) +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if FE has *: (Fraction(Integer),FE) -> FE and FE has PDRING(SYMBOL) --R ?^? : (%,Integer) -> % if FE has FIELD --R ?^? : (%,NonNegativeInteger) -> % ---R acos : % -> % if FE has ALGEBRA FRAC INT ---R acosh : % -> % if FE has ALGEBRA FRAC INT ---R acot : % -> % if FE has ALGEBRA FRAC INT ---R acoth : % -> % if FE has ALGEBRA FRAC INT ---R acsc : % -> % if FE has ALGEBRA FRAC INT ---R acsch : % -> % if FE has ALGEBRA FRAC INT ---R approximate : (%,Fraction Integer) -> FE if FE has **: (FE,Fraction Integer) -> FE and FE has coerce: Symbol -> FE ---R asec : % -> % if FE has ALGEBRA FRAC INT ---R asech : % -> % if FE has ALGEBRA FRAC INT ---R asin : % -> % if FE has ALGEBRA FRAC INT ---R asinh : % -> % if FE has ALGEBRA FRAC INT +--R acos : % -> % if FE has ALGEBRA(FRAC(INT)) +--R acosh : % -> % if FE has ALGEBRA(FRAC(INT)) +--R acot : % -> % if FE has ALGEBRA(FRAC(INT)) +--R acoth : % -> % if FE has ALGEBRA(FRAC(INT)) +--R acsc : % -> % if FE has ALGEBRA(FRAC(INT)) +--R acsch : % -> % if FE has ALGEBRA(FRAC(INT)) +--R approximate : (%,Fraction(Integer)) -> FE if FE has **: (FE,Fraction(Integer)) -> FE and FE has coerce: Symbol -> FE +--R asec : % -> % if FE has ALGEBRA(FRAC(INT)) +--R asech : % -> % if FE has ALGEBRA(FRAC(INT)) +--R asin : % -> % if FE has ALGEBRA(FRAC(INT)) +--R asinh : % -> % if FE has ALGEBRA(FRAC(INT)) --R associates? : (%,%) -> Boolean if FE has INTDOM ---R atan : % -> % if FE has ALGEBRA FRAC INT ---R atanh : % -> % if FE has ALGEBRA FRAC INT +--R atan : % -> % if FE has ALGEBRA(FRAC(INT)) +--R atanh : % -> % if FE has ALGEBRA(FRAC(INT)) --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if FE has CHARNZ ---R coefficient : (%,Fraction Integer) -> FE +--R coefficient : (%,Fraction(Integer)) -> FE --R coerce : % -> % if FE has INTDOM ---R coerce : Fraction Integer -> % if FE has ALGEBRA FRAC INT +--R coerce : Fraction(Integer) -> % if FE has ALGEBRA(FRAC(INT)) --R coerce : FE -> % if FE has COMRING ---R cos : % -> % if FE has ALGEBRA FRAC INT ---R cosh : % -> % if FE has ALGEBRA FRAC INT ---R cot : % -> % if FE has ALGEBRA FRAC INT ---R coth : % -> % if FE has ALGEBRA FRAC INT ---R csc : % -> % if FE has ALGEBRA FRAC INT ---R csch : % -> % if FE has ALGEBRA FRAC INT ---R differentiate : % -> % if FE has *: (Fraction Integer,FE) -> FE ---R differentiate : (%,NonNegativeInteger) -> % if FE has *: (Fraction Integer,FE) -> FE ---R differentiate : (%,Symbol) -> % if FE has *: (Fraction Integer,FE) -> FE and FE has PDRING SYMBOL ---R differentiate : (%,List Symbol) -> % if FE has *: (Fraction Integer,FE) -> FE and FE has PDRING SYMBOL ---R differentiate : (%,Symbol,NonNegativeInteger) -> % if FE has *: (Fraction Integer,FE) -> FE and FE has PDRING SYMBOL ---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if FE has *: (Fraction Integer,FE) -> FE and FE has PDRING SYMBOL +--R cos : % -> % if FE has ALGEBRA(FRAC(INT)) +--R cosh : % -> % if FE has ALGEBRA(FRAC(INT)) +--R cot : % -> % if FE has ALGEBRA(FRAC(INT)) +--R coth : % -> % if FE has ALGEBRA(FRAC(INT)) +--R csc : % -> % if FE has ALGEBRA(FRAC(INT)) +--R csch : % -> % if FE has ALGEBRA(FRAC(INT)) +--R differentiate : % -> % if FE has *: (Fraction(Integer),FE) -> FE +--R differentiate : (%,NonNegativeInteger) -> % if FE has *: (Fraction(Integer),FE) -> FE +--R differentiate : (%,Symbol) -> % if FE has *: (Fraction(Integer),FE) -> FE and FE has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol)) -> % if FE has *: (Fraction(Integer),FE) -> FE and FE has PDRING(SYMBOL) +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if FE has *: (Fraction(Integer),FE) -> FE and FE has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if FE has *: (Fraction(Integer),FE) -> FE and FE has PDRING(SYMBOL) --R divide : (%,%) -> Record(quotient: %,remainder: %) if FE has FIELD ---R ?.? : (%,%) -> % if Fraction Integer has SGROUP +--R ?.? : (%,%) -> % if Fraction(Integer) has SGROUP --R euclideanSize : % -> NonNegativeInteger if FE has FIELD ---R eval : (%,FE) -> Stream FE if FE has **: (FE,Fraction Integer) -> FE ---R exp : % -> % if FE has ALGEBRA FRAC INT +--R eval : (%,FE) -> Stream(FE) if FE has **: (FE,Fraction(Integer)) -> FE +--R exp : % -> % if FE has ALGEBRA(FRAC(INT)) --R exponent : % -> UnivariatePuiseuxSeries(FE,var,cen) --R exponential : UnivariatePuiseuxSeries(FE,var,cen) -> % ---R exponentialOrder : % -> Fraction Integer ---R expressIdealMember : (List %,%) -> Union(List %,"failed") if FE has FIELD +--R exponentialOrder : % -> Fraction(Integer) +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if FE has FIELD --R exquo : (%,%) -> Union(%,"failed") if FE has INTDOM ---R extend : (%,Fraction Integer) -> % +--R extend : (%,Fraction(Integer)) -> % --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if FE has FIELD --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if FE has FIELD ---R factor : % -> Factored % if FE has FIELD +--R factor : % -> Factored(%) if FE has FIELD --R gcd : (%,%) -> % if FE has FIELD ---R gcd : List % -> % if FE has FIELD ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if FE has FIELD ---R integrate : (%,Symbol) -> % if FE has integrate: (FE,Symbol) -> FE and FE has variables: FE -> List Symbol and FE has ALGEBRA FRAC INT or FE has ACFS INT and FE has ALGEBRA FRAC INT and FE has PRIMCAT and FE has TRANFUN ---R integrate : % -> % if FE has ALGEBRA FRAC INT +--R gcd : List(%) -> % if FE has FIELD +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if FE has FIELD +--R integrate : (%,Symbol) -> % if FE has integrate: (FE,Symbol) -> FE and FE has variables: FE -> List(Symbol) and FE has ALGEBRA(FRAC(INT)) or FE has ACFS(INT) and FE has ALGEBRA(FRAC(INT)) and FE has PRIMCAT and FE has TRANFUN +--R integrate : % -> % if FE has ALGEBRA(FRAC(INT)) --R lcm : (%,%) -> % if FE has FIELD ---R lcm : List % -> % if FE has FIELD ---R log : % -> % if FE has ALGEBRA FRAC INT ---R monomial : (%,List SingletonAsOrderedSet,List Fraction Integer) -> % ---R monomial : (%,SingletonAsOrderedSet,Fraction Integer) -> % ---R monomial : (FE,Fraction Integer) -> % ---R multiEuclidean : (List %,%) -> Union(List %,"failed") if FE has FIELD ---R multiplyExponents : (%,Fraction Integer) -> % +--R lcm : List(%) -> % if FE has FIELD +--R log : % -> % if FE has ALGEBRA(FRAC(INT)) +--R monomial : (%,List(SingletonAsOrderedSet),List(Fraction(Integer))) -> % +--R monomial : (%,SingletonAsOrderedSet,Fraction(Integer)) -> % +--R monomial : (FE,Fraction(Integer)) -> % +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") if FE has FIELD +--R multiplyExponents : (%,Fraction(Integer)) -> % --R multiplyExponents : (%,PositiveInteger) -> % ---R nthRoot : (%,Integer) -> % if FE has ALGEBRA FRAC INT ---R order : (%,Fraction Integer) -> Fraction Integer ---R pi : () -> % if FE has ALGEBRA FRAC INT +--R nthRoot : (%,Integer) -> % if FE has ALGEBRA(FRAC(INT)) +--R order : (%,Fraction(Integer)) -> Fraction(Integer) +--R pi : () -> % if FE has ALGEBRA(FRAC(INT)) --R prime? : % -> Boolean if FE has FIELD ---R principalIdeal : List % -> Record(coef: List %,generator: %) if FE has FIELD +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if FE has FIELD --R ?quo? : (%,%) -> % if FE has FIELD --R ?rem? : (%,%) -> % if FE has FIELD ---R sec : % -> % if FE has ALGEBRA FRAC INT ---R sech : % -> % if FE has ALGEBRA FRAC INT ---R series : (NonNegativeInteger,Stream Record(k: Fraction Integer,c: FE)) -> % ---R sin : % -> % if FE has ALGEBRA FRAC INT ---R sinh : % -> % if FE has ALGEBRA FRAC INT +--R sec : % -> % if FE has ALGEBRA(FRAC(INT)) +--R sech : % -> % if FE has ALGEBRA(FRAC(INT)) +--R series : (NonNegativeInteger,Stream(Record(k: Fraction(Integer),c: FE))) -> % +--R sin : % -> % if FE has ALGEBRA(FRAC(INT)) +--R sinh : % -> % if FE has ALGEBRA(FRAC(INT)) --R sizeLess? : (%,%) -> Boolean if FE has FIELD ---R sqrt : % -> % if FE has ALGEBRA FRAC INT ---R squareFree : % -> Factored % if FE has FIELD +--R sqrt : % -> % if FE has ALGEBRA(FRAC(INT)) +--R squareFree : % -> Factored(%) if FE has FIELD --R squareFreePart : % -> % if FE has FIELD --R subtractIfCan : (%,%) -> Union(%,"failed") ---R tan : % -> % if FE has ALGEBRA FRAC INT ---R tanh : % -> % if FE has ALGEBRA FRAC INT ---R terms : % -> Stream Record(k: Fraction Integer,c: FE) ---R truncate : (%,Fraction Integer,Fraction Integer) -> % ---R truncate : (%,Fraction Integer) -> % +--R tan : % -> % if FE has ALGEBRA(FRAC(INT)) +--R tanh : % -> % if FE has ALGEBRA(FRAC(INT)) +--R terms : % -> Stream(Record(k: Fraction(Integer),c: FE)) +--R truncate : (%,Fraction(Integer),Fraction(Integer)) -> % +--R truncate : (%,Fraction(Integer)) -> % --R unit? : % -> Boolean if FE has INTDOM --R unitCanonical : % -> % if FE has INTDOM --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if FE has INTDOM ---R variables : % -> List SingletonAsOrderedSet +--R variables : % -> List(SingletonAsOrderedSet) --R --E 1 @@ -34910,6 +35007,7 @@ ExponentialOfUnivariatePuiseuxSeries(FE,var,cen):_ --S 1 of 1 )show ExtAlgBasis +--R --R ExtAlgBasis is a domain constructor --R Abbreviation for ExtAlgBasis is EAB --R This constructor is not exposed in this frame. @@ -34919,8 +35017,8 @@ ExponentialOfUnivariatePuiseuxSeries(FE,var,cen):_ --R ? Boolean ?<=? : (%,%) -> Boolean --R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean --R ?>=? : (%,%) -> Boolean Nul : NonNegativeInteger -> % ---R coerce : List Integer -> % coerce : % -> OutputForm ---R degree : % -> NonNegativeInteger exponents : % -> List Integer +--R coerce : List(Integer) -> % coerce : % -> OutputForm +--R degree : % -> NonNegativeInteger exponents : % -> List(Integer) --R hash : % -> SingleInteger latex : % -> String --R max : (%,%) -> % min : (%,%) -> % --R ?~=? : (%,%) -> Boolean @@ -35065,6 +35163,7 @@ ExtAlgBasis(): Export == Implement where --S 1 of 1 )show e04dgfAnnaType +--R --R e04dgfAnnaType is a domain constructor --R Abbreviation for e04dgfAnnaType is E04DGFA --R This constructor is exposed in this frame. @@ -35074,10 +35173,10 @@ ExtAlgBasis(): Export == Implement where --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R ?~=? : (%,%) -> Boolean ---R measure : (RoutinesTable,Record(lfn: List Expression DoubleFloat,init: List DoubleFloat)) -> Record(measure: Float,explanations: String) ---R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat)) -> Record(measure: Float,explanations: String) ---R numericalOptimization : Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat) -> Result ---R numericalOptimization : Record(lfn: List Expression DoubleFloat,init: List DoubleFloat) -> Result +--R measure : (RoutinesTable,Record(lfn: List(Expression(DoubleFloat)),init: List(DoubleFloat))) -> Record(measure: Float,explanations: String) +--R measure : (RoutinesTable,Record(fn: Expression(DoubleFloat),init: List(DoubleFloat),lb: List(OrderedCompletion(DoubleFloat)),cf: List(Expression(DoubleFloat)),ub: List(OrderedCompletion(DoubleFloat)))) -> Record(measure: Float,explanations: String) +--R numericalOptimization : Record(fn: Expression(DoubleFloat),init: List(DoubleFloat),lb: List(OrderedCompletion(DoubleFloat)),cf: List(Expression(DoubleFloat)),ub: List(OrderedCompletion(DoubleFloat))) -> Result +--R numericalOptimization : Record(lfn: List(Expression(DoubleFloat)),init: List(DoubleFloat)) -> Result --R --E 1 @@ -35204,6 +35303,7 @@ e04dgfAnnaType(): NumericalOptimizationCategory == Result add --S 1 of 1 )show e04fdfAnnaType +--R --R e04fdfAnnaType is a domain constructor --R Abbreviation for e04fdfAnnaType is E04FDFA --R This constructor is exposed in this frame. @@ -35213,10 +35313,10 @@ e04dgfAnnaType(): NumericalOptimizationCategory == Result add --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R ?~=? : (%,%) -> Boolean ---R measure : (RoutinesTable,Record(lfn: List Expression DoubleFloat,init: List DoubleFloat)) -> Record(measure: Float,explanations: String) ---R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat)) -> Record(measure: Float,explanations: String) ---R numericalOptimization : Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat) -> Result ---R numericalOptimization : Record(lfn: List Expression DoubleFloat,init: List DoubleFloat) -> Result +--R measure : (RoutinesTable,Record(lfn: List(Expression(DoubleFloat)),init: List(DoubleFloat))) -> Record(measure: Float,explanations: String) +--R measure : (RoutinesTable,Record(fn: Expression(DoubleFloat),init: List(DoubleFloat),lb: List(OrderedCompletion(DoubleFloat)),cf: List(Expression(DoubleFloat)),ub: List(OrderedCompletion(DoubleFloat)))) -> Record(measure: Float,explanations: String) +--R numericalOptimization : Record(fn: Expression(DoubleFloat),init: List(DoubleFloat),lb: List(OrderedCompletion(DoubleFloat)),cf: List(Expression(DoubleFloat)),ub: List(OrderedCompletion(DoubleFloat))) -> Result +--R numericalOptimization : Record(lfn: List(Expression(DoubleFloat)),init: List(DoubleFloat)) -> Result --R --E 1 @@ -35369,6 +35469,7 @@ e04fdfAnnaType(): NumericalOptimizationCategory == Result add --S 1 of 1 )show e04gcfAnnaType +--R --R e04gcfAnnaType is a domain constructor --R Abbreviation for e04gcfAnnaType is E04GCFA --R This constructor is exposed in this frame. @@ -35378,10 +35479,10 @@ e04fdfAnnaType(): NumericalOptimizationCategory == Result add --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R ?~=? : (%,%) -> Boolean ---R measure : (RoutinesTable,Record(lfn: List Expression DoubleFloat,init: List DoubleFloat)) -> Record(measure: Float,explanations: String) ---R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat)) -> Record(measure: Float,explanations: String) ---R numericalOptimization : Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat) -> Result ---R numericalOptimization : Record(lfn: List Expression DoubleFloat,init: List DoubleFloat) -> Result +--R measure : (RoutinesTable,Record(lfn: List(Expression(DoubleFloat)),init: List(DoubleFloat))) -> Record(measure: Float,explanations: String) +--R measure : (RoutinesTable,Record(fn: Expression(DoubleFloat),init: List(DoubleFloat),lb: List(OrderedCompletion(DoubleFloat)),cf: List(Expression(DoubleFloat)),ub: List(OrderedCompletion(DoubleFloat)))) -> Record(measure: Float,explanations: String) +--R numericalOptimization : Record(fn: Expression(DoubleFloat),init: List(DoubleFloat),lb: List(OrderedCompletion(DoubleFloat)),cf: List(Expression(DoubleFloat)),ub: List(OrderedCompletion(DoubleFloat))) -> Result +--R numericalOptimization : Record(lfn: List(Expression(DoubleFloat)),init: List(DoubleFloat)) -> Result --R --E 1 @@ -35550,6 +35651,7 @@ e04gcfAnnaType(): NumericalOptimizationCategory == Result add --S 1 of 1 )show e04jafAnnaType +--R --R e04jafAnnaType is a domain constructor --R Abbreviation for e04jafAnnaType is E04JAFA --R This constructor is exposed in this frame. @@ -35559,10 +35661,10 @@ e04gcfAnnaType(): NumericalOptimizationCategory == Result add --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R ?~=? : (%,%) -> Boolean ---R measure : (RoutinesTable,Record(lfn: List Expression DoubleFloat,init: List DoubleFloat)) -> Record(measure: Float,explanations: String) ---R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat)) -> Record(measure: Float,explanations: String) ---R numericalOptimization : Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat) -> Result ---R numericalOptimization : Record(lfn: List Expression DoubleFloat,init: List DoubleFloat) -> Result +--R measure : (RoutinesTable,Record(lfn: List(Expression(DoubleFloat)),init: List(DoubleFloat))) -> Record(measure: Float,explanations: String) +--R measure : (RoutinesTable,Record(fn: Expression(DoubleFloat),init: List(DoubleFloat),lb: List(OrderedCompletion(DoubleFloat)),cf: List(Expression(DoubleFloat)),ub: List(OrderedCompletion(DoubleFloat)))) -> Record(measure: Float,explanations: String) +--R numericalOptimization : Record(fn: Expression(DoubleFloat),init: List(DoubleFloat),lb: List(OrderedCompletion(DoubleFloat)),cf: List(Expression(DoubleFloat)),ub: List(OrderedCompletion(DoubleFloat))) -> Result +--R numericalOptimization : Record(lfn: List(Expression(DoubleFloat)),init: List(DoubleFloat)) -> Result --R --E 1 @@ -35706,6 +35808,7 @@ e04jafAnnaType(): NumericalOptimizationCategory == Result add --S 1 of 1 )show e04mbfAnnaType +--R --R e04mbfAnnaType is a domain constructor --R Abbreviation for e04mbfAnnaType is E04MBFA --R This constructor is exposed in this frame. @@ -35715,10 +35818,10 @@ e04jafAnnaType(): NumericalOptimizationCategory == Result add --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R ?~=? : (%,%) -> Boolean ---R measure : (RoutinesTable,Record(lfn: List Expression DoubleFloat,init: List DoubleFloat)) -> Record(measure: Float,explanations: String) ---R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat)) -> Record(measure: Float,explanations: String) ---R numericalOptimization : Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat) -> Result ---R numericalOptimization : Record(lfn: List Expression DoubleFloat,init: List DoubleFloat) -> Result +--R measure : (RoutinesTable,Record(lfn: List(Expression(DoubleFloat)),init: List(DoubleFloat))) -> Record(measure: Float,explanations: String) +--R measure : (RoutinesTable,Record(fn: Expression(DoubleFloat),init: List(DoubleFloat),lb: List(OrderedCompletion(DoubleFloat)),cf: List(Expression(DoubleFloat)),ub: List(OrderedCompletion(DoubleFloat)))) -> Record(measure: Float,explanations: String) +--R numericalOptimization : Record(fn: Expression(DoubleFloat),init: List(DoubleFloat),lb: List(OrderedCompletion(DoubleFloat)),cf: List(Expression(DoubleFloat)),ub: List(OrderedCompletion(DoubleFloat))) -> Result +--R numericalOptimization : Record(lfn: List(Expression(DoubleFloat)),init: List(DoubleFloat)) -> Result --R --E 1 @@ -35848,6 +35951,7 @@ e04mbfAnnaType(): NumericalOptimizationCategory == Result add --S 1 of 1 )show e04nafAnnaType +--R --R e04nafAnnaType is a domain constructor --R Abbreviation for e04nafAnnaType is E04NAFA --R This constructor is exposed in this frame. @@ -35857,10 +35961,10 @@ e04mbfAnnaType(): NumericalOptimizationCategory == Result add --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R ?~=? : (%,%) -> Boolean ---R measure : (RoutinesTable,Record(lfn: List Expression DoubleFloat,init: List DoubleFloat)) -> Record(measure: Float,explanations: String) ---R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat)) -> Record(measure: Float,explanations: String) ---R numericalOptimization : Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat) -> Result ---R numericalOptimization : Record(lfn: List Expression DoubleFloat,init: List DoubleFloat) -> Result +--R measure : (RoutinesTable,Record(lfn: List(Expression(DoubleFloat)),init: List(DoubleFloat))) -> Record(measure: Float,explanations: String) +--R measure : (RoutinesTable,Record(fn: Expression(DoubleFloat),init: List(DoubleFloat),lb: List(OrderedCompletion(DoubleFloat)),cf: List(Expression(DoubleFloat)),ub: List(OrderedCompletion(DoubleFloat)))) -> Record(measure: Float,explanations: String) +--R numericalOptimization : Record(fn: Expression(DoubleFloat),init: List(DoubleFloat),lb: List(OrderedCompletion(DoubleFloat)),cf: List(Expression(DoubleFloat)),ub: List(OrderedCompletion(DoubleFloat))) -> Result +--R numericalOptimization : Record(lfn: List(Expression(DoubleFloat)),init: List(DoubleFloat)) -> Result --R --E 1 @@ -36005,6 +36109,7 @@ e04nafAnnaType(): NumericalOptimizationCategory == Result add --S 1 of 1 )show e04ucfAnnaType +--R --R e04ucfAnnaType is a domain constructor --R Abbreviation for e04ucfAnnaType is E04UCFA --R This constructor is exposed in this frame. @@ -36014,10 +36119,10 @@ e04nafAnnaType(): NumericalOptimizationCategory == Result add --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R ?~=? : (%,%) -> Boolean ---R measure : (RoutinesTable,Record(lfn: List Expression DoubleFloat,init: List DoubleFloat)) -> Record(measure: Float,explanations: String) ---R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat)) -> Record(measure: Float,explanations: String) ---R numericalOptimization : Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat) -> Result ---R numericalOptimization : Record(lfn: List Expression DoubleFloat,init: List DoubleFloat) -> Result +--R measure : (RoutinesTable,Record(lfn: List(Expression(DoubleFloat)),init: List(DoubleFloat))) -> Record(measure: Float,explanations: String) +--R measure : (RoutinesTable,Record(fn: Expression(DoubleFloat),init: List(DoubleFloat),lb: List(OrderedCompletion(DoubleFloat)),cf: List(Expression(DoubleFloat)),ub: List(OrderedCompletion(DoubleFloat)))) -> Record(measure: Float,explanations: String) +--R numericalOptimization : Record(fn: Expression(DoubleFloat),init: List(DoubleFloat),lb: List(OrderedCompletion(DoubleFloat)),cf: List(Expression(DoubleFloat)),ub: List(OrderedCompletion(DoubleFloat))) -> Result +--R numericalOptimization : Record(lfn: List(Expression(DoubleFloat)),init: List(DoubleFloat)) -> Result --R --E 1 @@ -36183,7 +36288,7 @@ g := factor(4312) --R --R 3 2 --R (1) 2 7 11 ---R Type: Factored Integer +--R Type: Factored(Integer) --E 1 --S 2 of 38 @@ -36207,7 +36312,7 @@ numberOfFactors(g) --R --R --R (4) [2,7,11] ---R Type: List Integer +--R Type: List(Integer) --E 4 --S 5 of 38 @@ -36215,7 +36320,7 @@ numberOfFactors(g) --R --R --R (5) [3,2,1] ---R Type: List Integer +--R Type: List(Integer) --E 5 --S 6 of 38 @@ -36223,7 +36328,7 @@ numberOfFactors(g) --R --R --R (6) ["prime","prime","prime"] ---R Type: List Union("nil","sqfr","irred","prime") +--R Type: List(Union("nil","sqfr","irred","prime")) --E 6 --S 7 of 38 @@ -36233,7 +36338,7 @@ factorList(g) --R (7) --R [[flg= "prime",fctr= 2,xpnt= 3], [flg= "prime",fctr= 7,xpnt= 2], --R [flg= "prime",fctr= 11,xpnt= 1]] ---RType: List Record(flg: Union("nil","sqfr","irred","prime"),fctr: Integer,xpnt: Integer) +--RType: List(Record(flg: Union("nil","sqfr","irred","prime"),fctr: Integer,xpnt: Integer)) --E 7 --S 8 of 38 @@ -36242,7 +36347,7 @@ factors(g) --R --R (8) --R [[factor= 2,exponent= 3],[factor= 7,exponent= 2],[factor= 11,exponent= 1]] ---R Type: List Record(factor: Integer,exponent: Integer) +--R Type: List(Record(factor: Integer,exponent: Integer)) --E 8 --S 9 of 38 @@ -36259,7 +36364,7 @@ g := factor(4312) --R --R 3 2 --R (10) 2 7 11 ---R Type: Factored Integer +--R Type: Factored(Integer) --E 10 --S 11 of 38 @@ -36284,7 +36389,7 @@ g := factor(4312) --R --R 3 2 --R (13) 2 7 11 ---R Type: Factored Integer +--R Type: Factored(Integer) --E 13 --S 14 of 38 @@ -36293,7 +36398,7 @@ f := factor(246960) --R --R 4 2 3 --R (14) 2 3 5 7 ---R Type: Factored Integer +--R Type: Factored(Integer) --E 14 --S 15 of 38 @@ -36302,7 +36407,7 @@ f * g --R --R 7 2 5 --R (15) 2 3 5 7 11 ---R Type: Factored Integer +--R Type: Factored(Integer) --E 15 --S 16 of 38 @@ -36311,7 +36416,7 @@ f**500 --R --R 2000 1000 500 1500 --R (16) 2 3 5 7 ---R Type: Factored Integer +--R Type: Factored(Integer) --E 16 --S 17 of 38 @@ -36320,7 +36425,7 @@ gcd(f,g) --R --R 3 2 --R (17) 2 7 ---R Type: Factored Integer +--R Type: Factored(Integer) --E 17 --S 18 of 38 @@ -36329,7 +36434,7 @@ lcm(f,g) --R --R 4 2 3 --R (18) 2 3 5 7 11 ---R Type: Factored Integer +--R Type: Factored(Integer) --E 18 --S 19 of 38 @@ -36338,7 +36443,7 @@ f + g --R --R 3 2 --R (19) 2 7 641 ---R Type: Factored Integer +--R Type: Factored(Integer) --E 19 --S 20 of 38 @@ -36347,7 +36452,7 @@ f - g --R --R 3 2 --R (20) 2 7 619 ---R Type: Factored Integer +--R Type: Factored(Integer) --E 20 --S 21 of 38 @@ -36387,7 +36492,7 @@ one?(f) --R --R --R (25) 0 ---R Type: Factored Integer +--R Type: Factored(Integer) --E 25 --S 26 of 38 @@ -36395,7 +36500,7 @@ one?(f) --R --R --R (26) 1 ---R Type: Factored Integer +--R Type: Factored(Integer) --E 26 --S 27 of 38 @@ -36404,7 +36509,7 @@ nilFactor(24,2) --R --R 2 --R (27) 24 ---R Type: Factored Integer +--R Type: Factored(Integer) --E 27 --S 28 of 38 @@ -36421,7 +36526,7 @@ sqfrFactor(30,2) --R --R 2 --R (29) 30 ---R Type: Factored Integer +--R Type: Factored(Integer) --E 29 --S 30 of 38 @@ -36430,7 +36535,7 @@ irreducibleFactor(13,10) --R --R 10 --R (30) 13 ---R Type: Factored Integer +--R Type: Factored(Integer) --E 30 --S 31 of 38 @@ -36439,7 +36544,7 @@ primeFactor(11,5) --R --R 5 --R (31) 11 ---R Type: Factored Integer +--R Type: Factored(Integer) --E 31 --S 32 of 38 @@ -36448,7 +36553,7 @@ h := factor(-720) --R --R 4 2 --R (32) - 2 3 5 ---R Type: Factored Integer +--R Type: Factored(Integer) --E 32 --S 33 of 38 @@ -36456,7 +36561,7 @@ h - makeFR(unit(h),factorList(h)) --R --R --R (33) 0 ---R Type: Factored Integer +--R Type: Factored(Integer) --E 33 --S 34 of 38 @@ -36465,7 +36570,7 @@ p := (4*x*x-12*x+9)*y*y + (4*x*x-12*x+9)*y + 28*x*x - 84*x + 63 --R --R 2 2 2 2 --R (34) (4x - 12x + 9)y + (4x - 12x + 9)y + 28x - 84x + 63 ---R Type: Polynomial Integer +--R Type: Polynomial(Integer) --E 34 --S 35 of 38 @@ -36474,7 +36579,7 @@ fp := factor(p) --R --R 2 2 --R (35) (2x - 3) (y + y + 7) ---R Type: Factored Polynomial Integer +--R Type: Factored(Polynomial(Integer)) --E 35 --S 36 of 38 @@ -36483,7 +36588,7 @@ D(p,x) --R --R 2 --R (36) (8x - 12)y + (8x - 12)y + 56x - 84 ---R Type: Polynomial Integer +--R Type: Polynomial(Integer) --E 36 --S 37 of 38 @@ -36492,7 +36597,7 @@ D(fp,x) --R --R 2 --R (37) 4(2x - 3)(y + y + 7) ---R Type: Factored Polynomial Integer +--R Type: Factored(Polynomial(Integer)) --E 37 --S 38 of 38 @@ -37424,7 +37529,7 @@ ifile:File List Integer:=open("jazz1","output") --R --R --R (1) "jazz1" ---R Type: File List Integer +--R Type: File(List(Integer)) --E 1 --S 2 of 12 @@ -37432,7 +37537,7 @@ write!(ifile, [-1,2,3]) --R --R --R (2) [- 1,2,3] ---R Type: List Integer +--R Type: List(Integer) --E 2 --S 3 of 12 @@ -37440,7 +37545,7 @@ write!(ifile, [10,-10,0,111]) --R --R --R (3) [10,- 10,0,111] ---R Type: List Integer +--R Type: List(Integer) --E 3 --S 4 of 12 @@ -37448,7 +37553,7 @@ write!(ifile, [7]) --R --R --R (4) [7] ---R Type: List Integer +--R Type: List(Integer) --E 4 --S 5 of 12 @@ -37456,7 +37561,7 @@ reopen!(ifile, "input") --R --R --R (5) "jazz1" ---R Type: File List Integer +--R Type: File(List(Integer)) --E 5 --S 6 of 12 @@ -37464,7 +37569,7 @@ read! ifile --R --R --R (6) [- 1,2,3] ---R Type: List Integer +--R Type: List(Integer) --E 6 --S 7 of 12 @@ -37472,7 +37577,7 @@ read! ifile --R --R --R (7) [10,- 10,0,111] ---R Type: List Integer +--R Type: List(Integer) --E 7 --S 8 of 12 @@ -37480,7 +37585,7 @@ readIfCan! ifile --R --R --R (8) [7] ---R Type: Union(List Integer,...) +--R Type: Union(List(Integer),...) --E 8 --S 9 of 12 @@ -37512,7 +37617,7 @@ close! ifile --R --R --R (12) "jazz1" ---R Type: File List Integer +--R Type: File(List(Integer)) --E 12 )system rm jazz1 )spool @@ -38084,7 +38189,8 @@ FileName(): FileNameCategory == add --S 1 of 1 )show FiniteDivisor ---R FiniteDivisor(F: Field,UP: UnivariatePolynomialCategory F,UPUP: UnivariatePolynomialCategory Fraction UP,R: FunctionFieldCategory(F,UP,UPUP)) is a domain constructor +--R +--R FiniteDivisor(F: Field,UP: UnivariatePolynomialCategory(F),UPUP: UnivariatePolynomialCategory(Fraction(UP)),R: FunctionFieldCategory(F,UP,UPUP)) is a domain constructor --R Abbreviation for FiniteDivisor is FDIV --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for FDIV @@ -38096,16 +38202,16 @@ FileName(): FileNameCategory == add --R 0 : () -> % coerce : % -> OutputForm --R divisor : (R,UP,UP,UP,F) -> % divisor : (F,F,Integer) -> % --R divisor : (F,F) -> % divisor : R -> % ---R finiteBasis : % -> Vector R hash : % -> SingleInteger ---R lSpaceBasis : % -> Vector R latex : % -> String +--R finiteBasis : % -> Vector(R) hash : % -> SingleInteger +--R lSpaceBasis : % -> Vector(R) latex : % -> String --R principal? : % -> Boolean reduce : % -> % --R sample : () -> % zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean --R ?*? : (NonNegativeInteger,%) -> % ---R decompose : % -> Record(id: FractionalIdeal(UP,Fraction UP,UPUP,R),principalPart: R) ---R divisor : FractionalIdeal(UP,Fraction UP,UPUP,R) -> % +--R decompose : % -> Record(id: FractionalIdeal(UP,Fraction(UP),UPUP,R),principalPart: R) +--R divisor : FractionalIdeal(UP,Fraction(UP),UPUP,R) -> % --R generator : % -> Union(R,"failed") ---R ideal : % -> FractionalIdeal(UP,Fraction UP,UPUP,R) +--R ideal : % -> FractionalIdeal(UP,Fraction(UP),UPUP,R) --R subtractIfCan : (%,%) -> Union(%,"failed") --R --E 1 @@ -38303,102 +38409,103 @@ FiniteDivisor(F, UP, UPUP, R): Exports == Implementation where --S 1 of 1 )show FiniteField +--R --R FiniteField(p: PositiveInteger,n: PositiveInteger) is a domain constructor --R Abbreviation for FiniteField is FF --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for FF --R --R------------------------------- Operations -------------------------------- ---R ?*? : (PrimeField p,%) -> % ?*? : (%,PrimeField p) -> % ---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (PrimeField(p),%) -> % ?*? : (%,PrimeField(p)) -> % +--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % --R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % ---R ?/? : (%,PrimeField p) -> % ?/? : (%,%) -> % +--R ?/? : (%,PrimeField(p)) -> % ?/? : (%,%) -> % --R ?=? : (%,%) -> Boolean 1 : () -> % --R 0 : () -> % ?^? : (%,Integer) -> % --R ?^? : (%,PositiveInteger) -> % algebraic? : % -> Boolean ---R associates? : (%,%) -> Boolean basis : () -> Vector % ---R coerce : PrimeField p -> % coerce : Fraction Integer -> % +--R associates? : (%,%) -> Boolean basis : () -> Vector(%) +--R coerce : PrimeField(p) -> % coerce : Fraction(Integer) -> % --R coerce : % -> % coerce : Integer -> % --R coerce : % -> OutputForm degree : % -> PositiveInteger ---R dimension : () -> CardinalNumber factor : % -> Factored % ---R gcd : List % -> % gcd : (%,%) -> % +--R dimension : () -> CardinalNumber factor : % -> Factored(%) +--R gcd : List(%) -> % gcd : (%,%) -> % --R hash : % -> SingleInteger inGroundField? : % -> Boolean --R inv : % -> % latex : % -> String ---R lcm : List % -> % lcm : (%,%) -> % ---R norm : % -> PrimeField p one? : % -> Boolean +--R lcm : List(%) -> % lcm : (%,%) -> % +--R norm : % -> PrimeField(p) one? : % -> Boolean --R prime? : % -> Boolean ?quo? : (%,%) -> % --R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % ---R retract : % -> PrimeField p sample : () -> % ---R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored % ---R squareFreePart : % -> % trace : % -> PrimeField p +--R retract : % -> PrimeField(p) sample : () -> % +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) +--R squareFreePart : % -> % trace : % -> PrimeField(p) --R transcendent? : % -> Boolean unit? : % -> Boolean --R unitCanonical : % -> % zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean --R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,NonNegativeInteger) -> % ---R D : (%,NonNegativeInteger) -> % if PrimeField p has FINITE ---R D : % -> % if PrimeField p has FINITE ---R Frobenius : (%,NonNegativeInteger) -> % if PrimeField p has FINITE ---R Frobenius : % -> % if PrimeField p has FINITE +--R D : (%,NonNegativeInteger) -> % if PrimeField(p) has FINITE +--R D : % -> % if PrimeField(p) has FINITE +--R Frobenius : (%,NonNegativeInteger) -> % if PrimeField(p) has FINITE +--R Frobenius : % -> % if PrimeField(p) has FINITE --R ?^? : (%,NonNegativeInteger) -> % ---R basis : PositiveInteger -> Vector % +--R basis : PositiveInteger -> Vector(%) --R characteristic : () -> NonNegativeInteger ---R charthRoot : % -> Union(%,"failed") if PrimeField p has CHARNZ or PrimeField p has FINITE ---R charthRoot : % -> % if PrimeField p has FINITE ---R conditionP : Matrix % -> Union(Vector %,"failed") if PrimeField p has FINITE ---R coordinates : Vector % -> Matrix PrimeField p ---R coordinates : % -> Vector PrimeField p ---R createNormalElement : () -> % if PrimeField p has FINITE ---R createPrimitiveElement : () -> % if PrimeField p has FINITE ---R definingPolynomial : () -> SparseUnivariatePolynomial PrimeField p ---R degree : % -> OnePointCompletion PositiveInteger ---R differentiate : (%,NonNegativeInteger) -> % if PrimeField p has FINITE ---R differentiate : % -> % if PrimeField p has FINITE ---R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if PrimeField p has CHARNZ or PrimeField p has FINITE ---R discreteLog : % -> NonNegativeInteger if PrimeField p has FINITE +--R charthRoot : % -> Union(%,"failed") if PrimeField(p) has CHARNZ or PrimeField(p) has FINITE +--R charthRoot : % -> % if PrimeField(p) has FINITE +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if PrimeField(p) has FINITE +--R coordinates : Vector(%) -> Matrix(PrimeField(p)) +--R coordinates : % -> Vector(PrimeField(p)) +--R createNormalElement : () -> % if PrimeField(p) has FINITE +--R createPrimitiveElement : () -> % if PrimeField(p) has FINITE +--R definingPolynomial : () -> SparseUnivariatePolynomial(PrimeField(p)) +--R degree : % -> OnePointCompletion(PositiveInteger) +--R differentiate : (%,NonNegativeInteger) -> % if PrimeField(p) has FINITE +--R differentiate : % -> % if PrimeField(p) has FINITE +--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if PrimeField(p) has CHARNZ or PrimeField(p) has FINITE +--R discreteLog : % -> NonNegativeInteger if PrimeField(p) has FINITE --R divide : (%,%) -> Record(quotient: %,remainder: %) --R euclideanSize : % -> NonNegativeInteger ---R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") --R exquo : (%,%) -> Union(%,"failed") --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) --R extensionDegree : () -> PositiveInteger ---R extensionDegree : () -> OnePointCompletion PositiveInteger ---R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if PrimeField p has FINITE ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % ---R generator : () -> % if PrimeField p has FINITE ---R index : PositiveInteger -> % if PrimeField p has FINITE ---R init : () -> % if PrimeField p has FINITE ---R linearAssociatedExp : (%,SparseUnivariatePolynomial PrimeField p) -> % if PrimeField p has FINITE ---R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial PrimeField p,"failed") if PrimeField p has FINITE ---R linearAssociatedLog : % -> SparseUnivariatePolynomial PrimeField p if PrimeField p has FINITE ---R linearAssociatedOrder : % -> SparseUnivariatePolynomial PrimeField p if PrimeField p has FINITE ---R lookup : % -> PositiveInteger if PrimeField p has FINITE ---R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial % if PrimeField p has FINITE ---R minimalPolynomial : % -> SparseUnivariatePolynomial PrimeField p ---R multiEuclidean : (List %,%) -> Union(List %,"failed") ---R nextItem : % -> Union(%,"failed") if PrimeField p has FINITE ---R norm : (%,PositiveInteger) -> % if PrimeField p has FINITE ---R normal? : % -> Boolean if PrimeField p has FINITE ---R normalElement : () -> % if PrimeField p has FINITE ---R order : % -> OnePointCompletion PositiveInteger if PrimeField p has CHARNZ or PrimeField p has FINITE ---R order : % -> PositiveInteger if PrimeField p has FINITE ---R primeFrobenius : % -> % if PrimeField p has CHARNZ or PrimeField p has FINITE ---R primeFrobenius : (%,NonNegativeInteger) -> % if PrimeField p has CHARNZ or PrimeField p has FINITE ---R primitive? : % -> Boolean if PrimeField p has FINITE ---R primitiveElement : () -> % if PrimeField p has FINITE ---R principalIdeal : List % -> Record(coef: List %,generator: %) ---R random : () -> % if PrimeField p has FINITE ---R representationType : () -> Union("prime",polynomial,normal,cyclic) if PrimeField p has FINITE ---R represents : Vector PrimeField p -> % ---R retractIfCan : % -> Union(PrimeField p,"failed") ---R size : () -> NonNegativeInteger if PrimeField p has FINITE +--R extensionDegree : () -> OnePointCompletion(PositiveInteger) +--R factorsOfCyclicGroupSize : () -> List(Record(factor: Integer,exponent: Integer)) if PrimeField(p) has FINITE +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) +--R generator : () -> % if PrimeField(p) has FINITE +--R index : PositiveInteger -> % if PrimeField(p) has FINITE +--R init : () -> % if PrimeField(p) has FINITE +--R linearAssociatedExp : (%,SparseUnivariatePolynomial(PrimeField(p))) -> % if PrimeField(p) has FINITE +--R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial(PrimeField(p)),"failed") if PrimeField(p) has FINITE +--R linearAssociatedLog : % -> SparseUnivariatePolynomial(PrimeField(p)) if PrimeField(p) has FINITE +--R linearAssociatedOrder : % -> SparseUnivariatePolynomial(PrimeField(p)) if PrimeField(p) has FINITE +--R lookup : % -> PositiveInteger if PrimeField(p) has FINITE +--R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial(%) if PrimeField(p) has FINITE +--R minimalPolynomial : % -> SparseUnivariatePolynomial(PrimeField(p)) +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") +--R nextItem : % -> Union(%,"failed") if PrimeField(p) has FINITE +--R norm : (%,PositiveInteger) -> % if PrimeField(p) has FINITE +--R normal? : % -> Boolean if PrimeField(p) has FINITE +--R normalElement : () -> % if PrimeField(p) has FINITE +--R order : % -> OnePointCompletion(PositiveInteger) if PrimeField(p) has CHARNZ or PrimeField(p) has FINITE +--R order : % -> PositiveInteger if PrimeField(p) has FINITE +--R primeFrobenius : % -> % if PrimeField(p) has CHARNZ or PrimeField(p) has FINITE +--R primeFrobenius : (%,NonNegativeInteger) -> % if PrimeField(p) has CHARNZ or PrimeField(p) has FINITE +--R primitive? : % -> Boolean if PrimeField(p) has FINITE +--R primitiveElement : () -> % if PrimeField(p) has FINITE +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) +--R random : () -> % if PrimeField(p) has FINITE +--R representationType : () -> Union("prime",polynomial,normal,cyclic) if PrimeField(p) has FINITE +--R represents : Vector(PrimeField(p)) -> % +--R retractIfCan : % -> Union(PrimeField(p),"failed") +--R size : () -> NonNegativeInteger if PrimeField(p) has FINITE --R subtractIfCan : (%,%) -> Union(%,"failed") ---R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if PrimeField p has FINITE ---R trace : (%,PositiveInteger) -> % if PrimeField p has FINITE +--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if PrimeField(p) has FINITE +--R trace : (%,PositiveInteger) -> % if PrimeField(p) has FINITE --R transcendenceDegree : () -> NonNegativeInteger --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) --R @@ -38562,103 +38669,104 @@ FiniteField(p:PositiveInteger, n:PositiveInteger): _ --S 1 of 1 )show FiniteFieldCyclicGroup +--R --R FiniteFieldCyclicGroup(p: PositiveInteger,extdeg: PositiveInteger) is a domain constructor --R Abbreviation for FiniteFieldCyclicGroup is FFCG --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for FFCG --R --R------------------------------- Operations -------------------------------- ---R ?*? : (PrimeField p,%) -> % ?*? : (%,PrimeField p) -> % ---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (PrimeField(p),%) -> % ?*? : (%,PrimeField(p)) -> % +--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % --R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % ---R ?/? : (%,PrimeField p) -> % ?/? : (%,%) -> % +--R ?/? : (%,PrimeField(p)) -> % ?/? : (%,%) -> % --R ?=? : (%,%) -> Boolean 1 : () -> % --R 0 : () -> % ?^? : (%,Integer) -> % --R ?^? : (%,PositiveInteger) -> % algebraic? : % -> Boolean ---R associates? : (%,%) -> Boolean basis : () -> Vector % ---R coerce : PrimeField p -> % coerce : Fraction Integer -> % +--R associates? : (%,%) -> Boolean basis : () -> Vector(%) +--R coerce : PrimeField(p) -> % coerce : Fraction(Integer) -> % --R coerce : % -> % coerce : Integer -> % --R coerce : % -> OutputForm degree : % -> PositiveInteger ---R dimension : () -> CardinalNumber factor : % -> Factored % ---R gcd : List % -> % gcd : (%,%) -> % +--R dimension : () -> CardinalNumber factor : % -> Factored(%) +--R gcd : List(%) -> % gcd : (%,%) -> % --R hash : % -> SingleInteger inGroundField? : % -> Boolean --R inv : % -> % latex : % -> String ---R lcm : List % -> % lcm : (%,%) -> % ---R norm : % -> PrimeField p one? : % -> Boolean +--R lcm : List(%) -> % lcm : (%,%) -> % +--R norm : % -> PrimeField(p) one? : % -> Boolean --R prime? : % -> Boolean ?quo? : (%,%) -> % --R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % ---R retract : % -> PrimeField p sample : () -> % ---R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored % ---R squareFreePart : % -> % trace : % -> PrimeField p +--R retract : % -> PrimeField(p) sample : () -> % +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) +--R squareFreePart : % -> % trace : % -> PrimeField(p) --R transcendent? : % -> Boolean unit? : % -> Boolean --R unitCanonical : % -> % zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean --R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,NonNegativeInteger) -> % ---R D : (%,NonNegativeInteger) -> % if PrimeField p has FINITE ---R D : % -> % if PrimeField p has FINITE ---R Frobenius : (%,NonNegativeInteger) -> % if PrimeField p has FINITE ---R Frobenius : % -> % if PrimeField p has FINITE +--R D : (%,NonNegativeInteger) -> % if PrimeField(p) has FINITE +--R D : % -> % if PrimeField(p) has FINITE +--R Frobenius : (%,NonNegativeInteger) -> % if PrimeField(p) has FINITE +--R Frobenius : % -> % if PrimeField(p) has FINITE --R ?^? : (%,NonNegativeInteger) -> % ---R basis : PositiveInteger -> Vector % +--R basis : PositiveInteger -> Vector(%) --R characteristic : () -> NonNegativeInteger ---R charthRoot : % -> Union(%,"failed") if PrimeField p has CHARNZ or PrimeField p has FINITE ---R charthRoot : % -> % if PrimeField p has FINITE ---R conditionP : Matrix % -> Union(Vector %,"failed") if PrimeField p has FINITE ---R coordinates : Vector % -> Matrix PrimeField p ---R coordinates : % -> Vector PrimeField p ---R createNormalElement : () -> % if PrimeField p has FINITE ---R createPrimitiveElement : () -> % if PrimeField p has FINITE ---R definingPolynomial : () -> SparseUnivariatePolynomial PrimeField p ---R degree : % -> OnePointCompletion PositiveInteger ---R differentiate : (%,NonNegativeInteger) -> % if PrimeField p has FINITE ---R differentiate : % -> % if PrimeField p has FINITE ---R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if PrimeField p has CHARNZ or PrimeField p has FINITE ---R discreteLog : % -> NonNegativeInteger if PrimeField p has FINITE +--R charthRoot : % -> Union(%,"failed") if PrimeField(p) has CHARNZ or PrimeField(p) has FINITE +--R charthRoot : % -> % if PrimeField(p) has FINITE +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if PrimeField(p) has FINITE +--R coordinates : Vector(%) -> Matrix(PrimeField(p)) +--R coordinates : % -> Vector(PrimeField(p)) +--R createNormalElement : () -> % if PrimeField(p) has FINITE +--R createPrimitiveElement : () -> % if PrimeField(p) has FINITE +--R definingPolynomial : () -> SparseUnivariatePolynomial(PrimeField(p)) +--R degree : % -> OnePointCompletion(PositiveInteger) +--R differentiate : (%,NonNegativeInteger) -> % if PrimeField(p) has FINITE +--R differentiate : % -> % if PrimeField(p) has FINITE +--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if PrimeField(p) has CHARNZ or PrimeField(p) has FINITE +--R discreteLog : % -> NonNegativeInteger if PrimeField(p) has FINITE --R divide : (%,%) -> Record(quotient: %,remainder: %) --R euclideanSize : % -> NonNegativeInteger ---R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") --R exquo : (%,%) -> Union(%,"failed") --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) --R extensionDegree : () -> PositiveInteger ---R extensionDegree : () -> OnePointCompletion PositiveInteger ---R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if PrimeField p has FINITE ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % ---R generator : () -> % if PrimeField p has FINITE ---R getZechTable : () -> PrimitiveArray SingleInteger ---R index : PositiveInteger -> % if PrimeField p has FINITE ---R init : () -> % if PrimeField p has FINITE ---R linearAssociatedExp : (%,SparseUnivariatePolynomial PrimeField p) -> % if PrimeField p has FINITE ---R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial PrimeField p,"failed") if PrimeField p has FINITE ---R linearAssociatedLog : % -> SparseUnivariatePolynomial PrimeField p if PrimeField p has FINITE ---R linearAssociatedOrder : % -> SparseUnivariatePolynomial PrimeField p if PrimeField p has FINITE ---R lookup : % -> PositiveInteger if PrimeField p has FINITE ---R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial % if PrimeField p has FINITE ---R minimalPolynomial : % -> SparseUnivariatePolynomial PrimeField p ---R multiEuclidean : (List %,%) -> Union(List %,"failed") ---R nextItem : % -> Union(%,"failed") if PrimeField p has FINITE ---R norm : (%,PositiveInteger) -> % if PrimeField p has FINITE ---R normal? : % -> Boolean if PrimeField p has FINITE ---R normalElement : () -> % if PrimeField p has FINITE ---R order : % -> OnePointCompletion PositiveInteger if PrimeField p has CHARNZ or PrimeField p has FINITE ---R order : % -> PositiveInteger if PrimeField p has FINITE ---R primeFrobenius : % -> % if PrimeField p has CHARNZ or PrimeField p has FINITE ---R primeFrobenius : (%,NonNegativeInteger) -> % if PrimeField p has CHARNZ or PrimeField p has FINITE ---R primitive? : % -> Boolean if PrimeField p has FINITE ---R primitiveElement : () -> % if PrimeField p has FINITE ---R principalIdeal : List % -> Record(coef: List %,generator: %) ---R random : () -> % if PrimeField p has FINITE ---R representationType : () -> Union("prime",polynomial,normal,cyclic) if PrimeField p has FINITE ---R represents : Vector PrimeField p -> % ---R retractIfCan : % -> Union(PrimeField p,"failed") ---R size : () -> NonNegativeInteger if PrimeField p has FINITE +--R extensionDegree : () -> OnePointCompletion(PositiveInteger) +--R factorsOfCyclicGroupSize : () -> List(Record(factor: Integer,exponent: Integer)) if PrimeField(p) has FINITE +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) +--R generator : () -> % if PrimeField(p) has FINITE +--R getZechTable : () -> PrimitiveArray(SingleInteger) +--R index : PositiveInteger -> % if PrimeField(p) has FINITE +--R init : () -> % if PrimeField(p) has FINITE +--R linearAssociatedExp : (%,SparseUnivariatePolynomial(PrimeField(p))) -> % if PrimeField(p) has FINITE +--R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial(PrimeField(p)),"failed") if PrimeField(p) has FINITE +--R linearAssociatedLog : % -> SparseUnivariatePolynomial(PrimeField(p)) if PrimeField(p) has FINITE +--R linearAssociatedOrder : % -> SparseUnivariatePolynomial(PrimeField(p)) if PrimeField(p) has FINITE +--R lookup : % -> PositiveInteger if PrimeField(p) has FINITE +--R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial(%) if PrimeField(p) has FINITE +--R minimalPolynomial : % -> SparseUnivariatePolynomial(PrimeField(p)) +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") +--R nextItem : % -> Union(%,"failed") if PrimeField(p) has FINITE +--R norm : (%,PositiveInteger) -> % if PrimeField(p) has FINITE +--R normal? : % -> Boolean if PrimeField(p) has FINITE +--R normalElement : () -> % if PrimeField(p) has FINITE +--R order : % -> OnePointCompletion(PositiveInteger) if PrimeField(p) has CHARNZ or PrimeField(p) has FINITE +--R order : % -> PositiveInteger if PrimeField(p) has FINITE +--R primeFrobenius : % -> % if PrimeField(p) has CHARNZ or PrimeField(p) has FINITE +--R primeFrobenius : (%,NonNegativeInteger) -> % if PrimeField(p) has CHARNZ or PrimeField(p) has FINITE +--R primitive? : % -> Boolean if PrimeField(p) has FINITE +--R primitiveElement : () -> % if PrimeField(p) has FINITE +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) +--R random : () -> % if PrimeField(p) has FINITE +--R representationType : () -> Union("prime",polynomial,normal,cyclic) if PrimeField(p) has FINITE +--R represents : Vector(PrimeField(p)) -> % +--R retractIfCan : % -> Union(PrimeField(p),"failed") +--R size : () -> NonNegativeInteger if PrimeField(p) has FINITE --R subtractIfCan : (%,%) -> Union(%,"failed") ---R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if PrimeField p has FINITE ---R trace : (%,PositiveInteger) -> % if PrimeField p has FINITE +--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if PrimeField(p) has FINITE +--R trace : (%,PositiveInteger) -> % if PrimeField(p) has FINITE --R transcendenceDegree : () -> NonNegativeInteger --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) --R @@ -38832,6 +38940,7 @@ FiniteFieldCyclicGroup(p,extdeg):_ --S 1 of 1 )show FiniteFieldCyclicGroupExtension +--R --R FiniteFieldCyclicGroupExtension(GF: FiniteFieldCategory,extdeg: PositiveInteger) is a domain constructor --R Abbreviation for FiniteFieldCyclicGroupExtension is FFCGX --R This constructor is not exposed in this frame. @@ -38839,7 +38948,7 @@ FiniteFieldCyclicGroup(p,extdeg):_ --R --R------------------------------- Operations -------------------------------- --R ?*? : (GF,%) -> % ?*? : (%,GF) -> % ---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % --R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % @@ -38849,21 +38958,21 @@ FiniteFieldCyclicGroup(p,extdeg):_ --R 1 : () -> % 0 : () -> % --R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % --R algebraic? : % -> Boolean associates? : (%,%) -> Boolean ---R basis : () -> Vector % coerce : GF -> % ---R coerce : Fraction Integer -> % coerce : % -> % +--R basis : () -> Vector(%) coerce : GF -> % +--R coerce : Fraction(Integer) -> % coerce : % -> % --R coerce : Integer -> % coerce : % -> OutputForm ---R coordinates : % -> Vector GF degree : % -> PositiveInteger ---R dimension : () -> CardinalNumber factor : % -> Factored % ---R gcd : List % -> % gcd : (%,%) -> % +--R coordinates : % -> Vector(GF) degree : % -> PositiveInteger +--R dimension : () -> CardinalNumber factor : % -> Factored(%) +--R gcd : List(%) -> % gcd : (%,%) -> % --R hash : % -> SingleInteger inGroundField? : % -> Boolean --R inv : % -> % latex : % -> String ---R lcm : List % -> % lcm : (%,%) -> % +--R lcm : List(%) -> % lcm : (%,%) -> % --R norm : % -> GF one? : % -> Boolean --R prime? : % -> Boolean ?quo? : (%,%) -> % --R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % ---R represents : Vector GF -> % retract : % -> GF +--R represents : Vector(GF) -> % retract : % -> GF --R sample : () -> % sizeLess? : (%,%) -> Boolean ---R squareFree : % -> Factored % squareFreePart : % -> % +--R squareFree : % -> Factored(%) squareFreePart : % -> % --R trace : % -> GF transcendent? : % -> Boolean --R unit? : % -> Boolean unitCanonical : % -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean @@ -38873,53 +38982,53 @@ FiniteFieldCyclicGroup(p,extdeg):_ --R Frobenius : (%,NonNegativeInteger) -> % if GF has FINITE --R Frobenius : % -> % if GF has FINITE --R ?^? : (%,NonNegativeInteger) -> % ---R basis : PositiveInteger -> Vector % +--R basis : PositiveInteger -> Vector(%) --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if GF has CHARNZ or GF has FINITE --R charthRoot : % -> % if GF has FINITE ---R conditionP : Matrix % -> Union(Vector %,"failed") if GF has FINITE ---R coordinates : Vector % -> Matrix GF +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if GF has FINITE +--R coordinates : Vector(%) -> Matrix(GF) --R createNormalElement : () -> % if GF has FINITE --R createPrimitiveElement : () -> % if GF has FINITE ---R definingPolynomial : () -> SparseUnivariatePolynomial GF ---R degree : % -> OnePointCompletion PositiveInteger +--R definingPolynomial : () -> SparseUnivariatePolynomial(GF) +--R degree : % -> OnePointCompletion(PositiveInteger) --R differentiate : (%,NonNegativeInteger) -> % if GF has FINITE --R differentiate : % -> % if GF has FINITE --R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if GF has CHARNZ or GF has FINITE --R discreteLog : % -> NonNegativeInteger if GF has FINITE --R divide : (%,%) -> Record(quotient: %,remainder: %) --R euclideanSize : % -> NonNegativeInteger ---R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") --R exquo : (%,%) -> Union(%,"failed") --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) --R extensionDegree : () -> PositiveInteger ---R extensionDegree : () -> OnePointCompletion PositiveInteger ---R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if GF has FINITE ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R extensionDegree : () -> OnePointCompletion(PositiveInteger) +--R factorsOfCyclicGroupSize : () -> List(Record(factor: Integer,exponent: Integer)) if GF has FINITE +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) --R generator : () -> % if GF has FINITE ---R getZechTable : () -> PrimitiveArray SingleInteger +--R getZechTable : () -> PrimitiveArray(SingleInteger) --R index : PositiveInteger -> % if GF has FINITE --R init : () -> % if GF has FINITE ---R linearAssociatedExp : (%,SparseUnivariatePolynomial GF) -> % if GF has FINITE ---R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial GF,"failed") if GF has FINITE ---R linearAssociatedLog : % -> SparseUnivariatePolynomial GF if GF has FINITE ---R linearAssociatedOrder : % -> SparseUnivariatePolynomial GF if GF has FINITE +--R linearAssociatedExp : (%,SparseUnivariatePolynomial(GF)) -> % if GF has FINITE +--R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial(GF),"failed") if GF has FINITE +--R linearAssociatedLog : % -> SparseUnivariatePolynomial(GF) if GF has FINITE +--R linearAssociatedOrder : % -> SparseUnivariatePolynomial(GF) if GF has FINITE --R lookup : % -> PositiveInteger if GF has FINITE ---R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial % if GF has FINITE ---R minimalPolynomial : % -> SparseUnivariatePolynomial GF ---R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial(%) if GF has FINITE +--R minimalPolynomial : % -> SparseUnivariatePolynomial(GF) +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") --R nextItem : % -> Union(%,"failed") if GF has FINITE --R norm : (%,PositiveInteger) -> % if GF has FINITE --R normal? : % -> Boolean if GF has FINITE --R normalElement : () -> % if GF has FINITE ---R order : % -> OnePointCompletion PositiveInteger if GF has CHARNZ or GF has FINITE +--R order : % -> OnePointCompletion(PositiveInteger) if GF has CHARNZ or GF has FINITE --R order : % -> PositiveInteger if GF has FINITE --R primeFrobenius : % -> % if GF has CHARNZ or GF has FINITE --R primeFrobenius : (%,NonNegativeInteger) -> % if GF has CHARNZ or GF has FINITE --R primitive? : % -> Boolean if GF has FINITE --R primitiveElement : () -> % if GF has FINITE ---R principalIdeal : List % -> Record(coef: List %,generator: %) +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) --R random : () -> % if GF has FINITE --R representationType : () -> Union("prime",polynomial,normal,cyclic) if GF has FINITE --R retractIfCan : % -> Union(GF,"failed") @@ -39102,14 +39211,15 @@ FiniteFieldCyclicGroupExtension(GF,extdeg):_ --S 1 of 1 )show FiniteFieldCyclicGroupExtensionByPolynomial ---R FiniteFieldCyclicGroupExtensionByPolynomial(GF: FiniteFieldCategory,defpol: SparseUnivariatePolynomial GF) is a domain constructor +--R +--R FiniteFieldCyclicGroupExtensionByPolynomial(GF: FiniteFieldCategory,defpol: SparseUnivariatePolynomial(GF)) is a domain constructor --R Abbreviation for FiniteFieldCyclicGroupExtensionByPolynomial is FFCGP --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for FFCGP --R --R------------------------------- Operations -------------------------------- --R ?*? : (GF,%) -> % ?*? : (%,GF) -> % ---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % --R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % @@ -39119,21 +39229,21 @@ FiniteFieldCyclicGroupExtension(GF,extdeg):_ --R 1 : () -> % 0 : () -> % --R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % --R algebraic? : % -> Boolean associates? : (%,%) -> Boolean ---R basis : () -> Vector % coerce : GF -> % ---R coerce : Fraction Integer -> % coerce : % -> % +--R basis : () -> Vector(%) coerce : GF -> % +--R coerce : Fraction(Integer) -> % coerce : % -> % --R coerce : Integer -> % coerce : % -> OutputForm ---R coordinates : % -> Vector GF degree : % -> PositiveInteger ---R dimension : () -> CardinalNumber factor : % -> Factored % ---R gcd : List % -> % gcd : (%,%) -> % +--R coordinates : % -> Vector(GF) degree : % -> PositiveInteger +--R dimension : () -> CardinalNumber factor : % -> Factored(%) +--R gcd : List(%) -> % gcd : (%,%) -> % --R hash : % -> SingleInteger inGroundField? : % -> Boolean --R inv : % -> % latex : % -> String ---R lcm : List % -> % lcm : (%,%) -> % +--R lcm : List(%) -> % lcm : (%,%) -> % --R norm : % -> GF one? : % -> Boolean --R prime? : % -> Boolean ?quo? : (%,%) -> % --R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % ---R represents : Vector GF -> % retract : % -> GF +--R represents : Vector(GF) -> % retract : % -> GF --R sample : () -> % sizeLess? : (%,%) -> Boolean ---R squareFree : % -> Factored % squareFreePart : % -> % +--R squareFree : % -> Factored(%) squareFreePart : % -> % --R trace : % -> GF transcendent? : % -> Boolean --R unit? : % -> Boolean unitCanonical : % -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean @@ -39143,53 +39253,53 @@ FiniteFieldCyclicGroupExtension(GF,extdeg):_ --R Frobenius : (%,NonNegativeInteger) -> % if GF has FINITE --R Frobenius : % -> % if GF has FINITE --R ?^? : (%,NonNegativeInteger) -> % ---R basis : PositiveInteger -> Vector % +--R basis : PositiveInteger -> Vector(%) --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if GF has CHARNZ or GF has FINITE --R charthRoot : % -> % if GF has FINITE ---R conditionP : Matrix % -> Union(Vector %,"failed") if GF has FINITE ---R coordinates : Vector % -> Matrix GF +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if GF has FINITE +--R coordinates : Vector(%) -> Matrix(GF) --R createNormalElement : () -> % if GF has FINITE --R createPrimitiveElement : () -> % if GF has FINITE ---R definingPolynomial : () -> SparseUnivariatePolynomial GF ---R degree : % -> OnePointCompletion PositiveInteger +--R definingPolynomial : () -> SparseUnivariatePolynomial(GF) +--R degree : % -> OnePointCompletion(PositiveInteger) --R differentiate : (%,NonNegativeInteger) -> % if GF has FINITE --R differentiate : % -> % if GF has FINITE --R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if GF has CHARNZ or GF has FINITE --R discreteLog : % -> NonNegativeInteger if GF has FINITE --R divide : (%,%) -> Record(quotient: %,remainder: %) --R euclideanSize : % -> NonNegativeInteger ---R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") --R exquo : (%,%) -> Union(%,"failed") --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) --R extensionDegree : () -> PositiveInteger ---R extensionDegree : () -> OnePointCompletion PositiveInteger ---R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if GF has FINITE ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R extensionDegree : () -> OnePointCompletion(PositiveInteger) +--R factorsOfCyclicGroupSize : () -> List(Record(factor: Integer,exponent: Integer)) if GF has FINITE +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) --R generator : () -> % if GF has FINITE ---R getZechTable : () -> PrimitiveArray SingleInteger +--R getZechTable : () -> PrimitiveArray(SingleInteger) --R index : PositiveInteger -> % if GF has FINITE --R init : () -> % if GF has FINITE ---R linearAssociatedExp : (%,SparseUnivariatePolynomial GF) -> % if GF has FINITE ---R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial GF,"failed") if GF has FINITE ---R linearAssociatedLog : % -> SparseUnivariatePolynomial GF if GF has FINITE ---R linearAssociatedOrder : % -> SparseUnivariatePolynomial GF if GF has FINITE +--R linearAssociatedExp : (%,SparseUnivariatePolynomial(GF)) -> % if GF has FINITE +--R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial(GF),"failed") if GF has FINITE +--R linearAssociatedLog : % -> SparseUnivariatePolynomial(GF) if GF has FINITE +--R linearAssociatedOrder : % -> SparseUnivariatePolynomial(GF) if GF has FINITE --R lookup : % -> PositiveInteger if GF has FINITE ---R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial % if GF has FINITE ---R minimalPolynomial : % -> SparseUnivariatePolynomial GF ---R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial(%) if GF has FINITE +--R minimalPolynomial : % -> SparseUnivariatePolynomial(GF) +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") --R nextItem : % -> Union(%,"failed") if GF has FINITE --R norm : (%,PositiveInteger) -> % if GF has FINITE --R normal? : % -> Boolean if GF has FINITE --R normalElement : () -> % if GF has FINITE ---R order : % -> OnePointCompletion PositiveInteger if GF has CHARNZ or GF has FINITE +--R order : % -> OnePointCompletion(PositiveInteger) if GF has CHARNZ or GF has FINITE --R order : % -> PositiveInteger if GF has FINITE --R primeFrobenius : % -> % if GF has CHARNZ or GF has FINITE --R primeFrobenius : (%,NonNegativeInteger) -> % if GF has CHARNZ or GF has FINITE --R primitive? : % -> Boolean if GF has FINITE --R primitiveElement : () -> % if GF has FINITE ---R principalIdeal : List % -> Record(coef: List %,generator: %) +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) --R random : () -> % if GF has FINITE --R representationType : () -> Union("prime",polynomial,normal,cyclic) if GF has FINITE --R retractIfCan : % -> Union(GF,"failed") @@ -39638,6 +39748,7 @@ FiniteFieldCyclicGroupExtensionByPolynomial(GF,defpol):_ --S 1 of 1 )show FiniteFieldExtension +--R --R FiniteFieldExtension(GF: FiniteFieldCategory,n: PositiveInteger) is a domain constructor --R Abbreviation for FiniteFieldExtension is FFX --R This constructor is not exposed in this frame. @@ -39645,7 +39756,7 @@ FiniteFieldCyclicGroupExtensionByPolynomial(GF,defpol):_ --R --R------------------------------- Operations -------------------------------- --R ?*? : (GF,%) -> % ?*? : (%,GF) -> % ---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % --R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % @@ -39655,21 +39766,21 @@ FiniteFieldCyclicGroupExtensionByPolynomial(GF,defpol):_ --R 1 : () -> % 0 : () -> % --R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % --R algebraic? : % -> Boolean associates? : (%,%) -> Boolean ---R basis : () -> Vector % coerce : GF -> % ---R coerce : Fraction Integer -> % coerce : % -> % +--R basis : () -> Vector(%) coerce : GF -> % +--R coerce : Fraction(Integer) -> % coerce : % -> % --R coerce : Integer -> % coerce : % -> OutputForm ---R coordinates : % -> Vector GF degree : % -> PositiveInteger ---R dimension : () -> CardinalNumber factor : % -> Factored % ---R gcd : List % -> % gcd : (%,%) -> % +--R coordinates : % -> Vector(GF) degree : % -> PositiveInteger +--R dimension : () -> CardinalNumber factor : % -> Factored(%) +--R gcd : List(%) -> % gcd : (%,%) -> % --R hash : % -> SingleInteger inGroundField? : % -> Boolean --R inv : % -> % latex : % -> String ---R lcm : List % -> % lcm : (%,%) -> % +--R lcm : List(%) -> % lcm : (%,%) -> % --R norm : % -> GF one? : % -> Boolean --R prime? : % -> Boolean ?quo? : (%,%) -> % --R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % ---R represents : Vector GF -> % retract : % -> GF +--R represents : Vector(GF) -> % retract : % -> GF --R sample : () -> % sizeLess? : (%,%) -> Boolean ---R squareFree : % -> Factored % squareFreePart : % -> % +--R squareFree : % -> Factored(%) squareFreePart : % -> % --R trace : % -> GF transcendent? : % -> Boolean --R unit? : % -> Boolean unitCanonical : % -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean @@ -39679,52 +39790,52 @@ FiniteFieldCyclicGroupExtensionByPolynomial(GF,defpol):_ --R Frobenius : (%,NonNegativeInteger) -> % if GF has FINITE --R Frobenius : % -> % if GF has FINITE --R ?^? : (%,NonNegativeInteger) -> % ---R basis : PositiveInteger -> Vector % +--R basis : PositiveInteger -> Vector(%) --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if GF has CHARNZ or GF has FINITE --R charthRoot : % -> % if GF has FINITE ---R conditionP : Matrix % -> Union(Vector %,"failed") if GF has FINITE ---R coordinates : Vector % -> Matrix GF +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if GF has FINITE +--R coordinates : Vector(%) -> Matrix(GF) --R createNormalElement : () -> % if GF has FINITE --R createPrimitiveElement : () -> % if GF has FINITE ---R definingPolynomial : () -> SparseUnivariatePolynomial GF ---R degree : % -> OnePointCompletion PositiveInteger +--R definingPolynomial : () -> SparseUnivariatePolynomial(GF) +--R degree : % -> OnePointCompletion(PositiveInteger) --R differentiate : (%,NonNegativeInteger) -> % if GF has FINITE --R differentiate : % -> % if GF has FINITE --R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if GF has CHARNZ or GF has FINITE --R discreteLog : % -> NonNegativeInteger if GF has FINITE --R divide : (%,%) -> Record(quotient: %,remainder: %) --R euclideanSize : % -> NonNegativeInteger ---R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") --R exquo : (%,%) -> Union(%,"failed") --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) --R extensionDegree : () -> PositiveInteger ---R extensionDegree : () -> OnePointCompletion PositiveInteger ---R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if GF has FINITE ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R extensionDegree : () -> OnePointCompletion(PositiveInteger) +--R factorsOfCyclicGroupSize : () -> List(Record(factor: Integer,exponent: Integer)) if GF has FINITE +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) --R generator : () -> % if GF has FINITE --R index : PositiveInteger -> % if GF has FINITE --R init : () -> % if GF has FINITE ---R linearAssociatedExp : (%,SparseUnivariatePolynomial GF) -> % if GF has FINITE ---R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial GF,"failed") if GF has FINITE ---R linearAssociatedLog : % -> SparseUnivariatePolynomial GF if GF has FINITE ---R linearAssociatedOrder : % -> SparseUnivariatePolynomial GF if GF has FINITE +--R linearAssociatedExp : (%,SparseUnivariatePolynomial(GF)) -> % if GF has FINITE +--R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial(GF),"failed") if GF has FINITE +--R linearAssociatedLog : % -> SparseUnivariatePolynomial(GF) if GF has FINITE +--R linearAssociatedOrder : % -> SparseUnivariatePolynomial(GF) if GF has FINITE --R lookup : % -> PositiveInteger if GF has FINITE ---R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial % if GF has FINITE ---R minimalPolynomial : % -> SparseUnivariatePolynomial GF ---R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial(%) if GF has FINITE +--R minimalPolynomial : % -> SparseUnivariatePolynomial(GF) +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") --R nextItem : % -> Union(%,"failed") if GF has FINITE --R norm : (%,PositiveInteger) -> % if GF has FINITE --R normal? : % -> Boolean if GF has FINITE --R normalElement : () -> % if GF has FINITE ---R order : % -> OnePointCompletion PositiveInteger if GF has CHARNZ or GF has FINITE +--R order : % -> OnePointCompletion(PositiveInteger) if GF has CHARNZ or GF has FINITE --R order : % -> PositiveInteger if GF has FINITE --R primeFrobenius : % -> % if GF has CHARNZ or GF has FINITE --R primeFrobenius : (%,NonNegativeInteger) -> % if GF has CHARNZ or GF has FINITE --R primitive? : % -> Boolean if GF has FINITE --R primitiveElement : () -> % if GF has FINITE ---R principalIdeal : List % -> Record(coef: List %,generator: %) +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) --R random : () -> % if GF has FINITE --R representationType : () -> Union("prime",polynomial,normal,cyclic) if GF has FINITE --R retractIfCan : % -> Union(GF,"failed") @@ -39901,14 +40012,15 @@ FiniteFieldExtension(GF, n): Exports == Implementation where --S 1 of 1 )show FiniteFieldExtensionByPolynomial ---R FiniteFieldExtensionByPolynomial(GF: FiniteFieldCategory,defpol: SparseUnivariatePolynomial GF) is a domain constructor +--R +--R FiniteFieldExtensionByPolynomial(GF: FiniteFieldCategory,defpol: SparseUnivariatePolynomial(GF)) is a domain constructor --R Abbreviation for FiniteFieldExtensionByPolynomial is FFP --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for FFP --R --R------------------------------- Operations -------------------------------- --R ?*? : (GF,%) -> % ?*? : (%,GF) -> % ---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % --R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % @@ -39918,21 +40030,21 @@ FiniteFieldExtension(GF, n): Exports == Implementation where --R 1 : () -> % 0 : () -> % --R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % --R algebraic? : % -> Boolean associates? : (%,%) -> Boolean ---R basis : () -> Vector % coerce : GF -> % ---R coerce : Fraction Integer -> % coerce : % -> % +--R basis : () -> Vector(%) coerce : GF -> % +--R coerce : Fraction(Integer) -> % coerce : % -> % --R coerce : Integer -> % coerce : % -> OutputForm ---R coordinates : % -> Vector GF degree : % -> PositiveInteger ---R dimension : () -> CardinalNumber factor : % -> Factored % ---R gcd : List % -> % gcd : (%,%) -> % +--R coordinates : % -> Vector(GF) degree : % -> PositiveInteger +--R dimension : () -> CardinalNumber factor : % -> Factored(%) +--R gcd : List(%) -> % gcd : (%,%) -> % --R hash : % -> SingleInteger inGroundField? : % -> Boolean --R inv : % -> % latex : % -> String ---R lcm : List % -> % lcm : (%,%) -> % +--R lcm : List(%) -> % lcm : (%,%) -> % --R norm : % -> GF one? : % -> Boolean --R prime? : % -> Boolean ?quo? : (%,%) -> % --R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % ---R represents : Vector GF -> % retract : % -> GF +--R represents : Vector(GF) -> % retract : % -> GF --R sample : () -> % sizeLess? : (%,%) -> Boolean ---R squareFree : % -> Factored % squareFreePart : % -> % +--R squareFree : % -> Factored(%) squareFreePart : % -> % --R trace : % -> GF transcendent? : % -> Boolean --R unit? : % -> Boolean unitCanonical : % -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean @@ -39942,52 +40054,52 @@ FiniteFieldExtension(GF, n): Exports == Implementation where --R Frobenius : (%,NonNegativeInteger) -> % if GF has FINITE --R Frobenius : % -> % if GF has FINITE --R ?^? : (%,NonNegativeInteger) -> % ---R basis : PositiveInteger -> Vector % +--R basis : PositiveInteger -> Vector(%) --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if GF has CHARNZ or GF has FINITE --R charthRoot : % -> % if GF has FINITE ---R conditionP : Matrix % -> Union(Vector %,"failed") if GF has FINITE ---R coordinates : Vector % -> Matrix GF +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if GF has FINITE +--R coordinates : Vector(%) -> Matrix(GF) --R createNormalElement : () -> % if GF has FINITE --R createPrimitiveElement : () -> % if GF has FINITE ---R definingPolynomial : () -> SparseUnivariatePolynomial GF ---R degree : % -> OnePointCompletion PositiveInteger +--R definingPolynomial : () -> SparseUnivariatePolynomial(GF) +--R degree : % -> OnePointCompletion(PositiveInteger) --R differentiate : (%,NonNegativeInteger) -> % if GF has FINITE --R differentiate : % -> % if GF has FINITE --R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if GF has CHARNZ or GF has FINITE --R discreteLog : % -> NonNegativeInteger if GF has FINITE --R divide : (%,%) -> Record(quotient: %,remainder: %) --R euclideanSize : % -> NonNegativeInteger ---R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") --R exquo : (%,%) -> Union(%,"failed") --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) --R extensionDegree : () -> PositiveInteger ---R extensionDegree : () -> OnePointCompletion PositiveInteger ---R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if GF has FINITE ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R extensionDegree : () -> OnePointCompletion(PositiveInteger) +--R factorsOfCyclicGroupSize : () -> List(Record(factor: Integer,exponent: Integer)) if GF has FINITE +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) --R generator : () -> % if GF has FINITE --R index : PositiveInteger -> % if GF has FINITE --R init : () -> % if GF has FINITE ---R linearAssociatedExp : (%,SparseUnivariatePolynomial GF) -> % if GF has FINITE ---R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial GF,"failed") if GF has FINITE ---R linearAssociatedLog : % -> SparseUnivariatePolynomial GF if GF has FINITE ---R linearAssociatedOrder : % -> SparseUnivariatePolynomial GF if GF has FINITE +--R linearAssociatedExp : (%,SparseUnivariatePolynomial(GF)) -> % if GF has FINITE +--R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial(GF),"failed") if GF has FINITE +--R linearAssociatedLog : % -> SparseUnivariatePolynomial(GF) if GF has FINITE +--R linearAssociatedOrder : % -> SparseUnivariatePolynomial(GF) if GF has FINITE --R lookup : % -> PositiveInteger if GF has FINITE ---R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial % if GF has FINITE ---R minimalPolynomial : % -> SparseUnivariatePolynomial GF ---R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial(%) if GF has FINITE +--R minimalPolynomial : % -> SparseUnivariatePolynomial(GF) +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") --R nextItem : % -> Union(%,"failed") if GF has FINITE --R norm : (%,PositiveInteger) -> % if GF has FINITE --R normal? : % -> Boolean if GF has FINITE --R normalElement : () -> % if GF has FINITE ---R order : % -> OnePointCompletion PositiveInteger if GF has CHARNZ or GF has FINITE +--R order : % -> OnePointCompletion(PositiveInteger) if GF has CHARNZ or GF has FINITE --R order : % -> PositiveInteger if GF has FINITE --R primeFrobenius : % -> % if GF has CHARNZ or GF has FINITE --R primeFrobenius : (%,NonNegativeInteger) -> % if GF has CHARNZ or GF has FINITE --R primitive? : % -> Boolean if GF has FINITE --R primitiveElement : () -> % if GF has FINITE ---R principalIdeal : List % -> Record(coef: List %,generator: %) +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) --R random : () -> % if GF has FINITE --R representationType : () -> Union("prime",polynomial,normal,cyclic) if GF has FINITE --R retractIfCan : % -> Union(GF,"failed") @@ -40362,105 +40474,106 @@ FiniteFieldExtensionByPolynomial(GF:FiniteFieldCategory,_ --S 1 of 1 )show FiniteFieldNormalBasis +--R --R FiniteFieldNormalBasis(p: PositiveInteger,extdeg: PositiveInteger) is a domain constructor --R Abbreviation for FiniteFieldNormalBasis is FFNB --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for FFNB --R --R------------------------------- Operations -------------------------------- ---R ?*? : (PrimeField p,%) -> % ?*? : (%,PrimeField p) -> % ---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (PrimeField(p),%) -> % ?*? : (%,PrimeField(p)) -> % +--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % --R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % ---R ?/? : (%,PrimeField p) -> % ?/? : (%,%) -> % +--R ?/? : (%,PrimeField(p)) -> % ?/? : (%,%) -> % --R ?=? : (%,%) -> Boolean 1 : () -> % --R 0 : () -> % ?^? : (%,Integer) -> % --R ?^? : (%,PositiveInteger) -> % algebraic? : % -> Boolean ---R associates? : (%,%) -> Boolean basis : () -> Vector % ---R coerce : PrimeField p -> % coerce : Fraction Integer -> % +--R associates? : (%,%) -> Boolean basis : () -> Vector(%) +--R coerce : PrimeField(p) -> % coerce : Fraction(Integer) -> % --R coerce : % -> % coerce : Integer -> % --R coerce : % -> OutputForm degree : % -> PositiveInteger ---R dimension : () -> CardinalNumber factor : % -> Factored % ---R gcd : List % -> % gcd : (%,%) -> % +--R dimension : () -> CardinalNumber factor : % -> Factored(%) +--R gcd : List(%) -> % gcd : (%,%) -> % --R hash : % -> SingleInteger inGroundField? : % -> Boolean --R inv : % -> % latex : % -> String ---R lcm : List % -> % lcm : (%,%) -> % ---R norm : % -> PrimeField p one? : % -> Boolean +--R lcm : List(%) -> % lcm : (%,%) -> % +--R norm : % -> PrimeField(p) one? : % -> Boolean --R prime? : % -> Boolean ?quo? : (%,%) -> % --R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % ---R retract : % -> PrimeField p sample : () -> % ---R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored % ---R squareFreePart : % -> % trace : % -> PrimeField p +--R retract : % -> PrimeField(p) sample : () -> % +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) +--R squareFreePart : % -> % trace : % -> PrimeField(p) --R transcendent? : % -> Boolean unit? : % -> Boolean --R unitCanonical : % -> % zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean --R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,NonNegativeInteger) -> % ---R D : (%,NonNegativeInteger) -> % if PrimeField p has FINITE ---R D : % -> % if PrimeField p has FINITE ---R Frobenius : (%,NonNegativeInteger) -> % if PrimeField p has FINITE ---R Frobenius : % -> % if PrimeField p has FINITE +--R D : (%,NonNegativeInteger) -> % if PrimeField(p) has FINITE +--R D : % -> % if PrimeField(p) has FINITE +--R Frobenius : (%,NonNegativeInteger) -> % if PrimeField(p) has FINITE +--R Frobenius : % -> % if PrimeField(p) has FINITE --R ?^? : (%,NonNegativeInteger) -> % ---R basis : PositiveInteger -> Vector % +--R basis : PositiveInteger -> Vector(%) --R characteristic : () -> NonNegativeInteger ---R charthRoot : % -> Union(%,"failed") if PrimeField p has CHARNZ or PrimeField p has FINITE ---R charthRoot : % -> % if PrimeField p has FINITE ---R conditionP : Matrix % -> Union(Vector %,"failed") if PrimeField p has FINITE ---R coordinates : Vector % -> Matrix PrimeField p ---R coordinates : % -> Vector PrimeField p ---R createNormalElement : () -> % if PrimeField p has FINITE ---R createPrimitiveElement : () -> % if PrimeField p has FINITE ---R definingPolynomial : () -> SparseUnivariatePolynomial PrimeField p ---R degree : % -> OnePointCompletion PositiveInteger ---R differentiate : (%,NonNegativeInteger) -> % if PrimeField p has FINITE ---R differentiate : % -> % if PrimeField p has FINITE ---R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if PrimeField p has CHARNZ or PrimeField p has FINITE ---R discreteLog : % -> NonNegativeInteger if PrimeField p has FINITE +--R charthRoot : % -> Union(%,"failed") if PrimeField(p) has CHARNZ or PrimeField(p) has FINITE +--R charthRoot : % -> % if PrimeField(p) has FINITE +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if PrimeField(p) has FINITE +--R coordinates : Vector(%) -> Matrix(PrimeField(p)) +--R coordinates : % -> Vector(PrimeField(p)) +--R createNormalElement : () -> % if PrimeField(p) has FINITE +--R createPrimitiveElement : () -> % if PrimeField(p) has FINITE +--R definingPolynomial : () -> SparseUnivariatePolynomial(PrimeField(p)) +--R degree : % -> OnePointCompletion(PositiveInteger) +--R differentiate : (%,NonNegativeInteger) -> % if PrimeField(p) has FINITE +--R differentiate : % -> % if PrimeField(p) has FINITE +--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if PrimeField(p) has CHARNZ or PrimeField(p) has FINITE +--R discreteLog : % -> NonNegativeInteger if PrimeField(p) has FINITE --R divide : (%,%) -> Record(quotient: %,remainder: %) --R euclideanSize : % -> NonNegativeInteger ---R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") --R exquo : (%,%) -> Union(%,"failed") --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) --R extensionDegree : () -> PositiveInteger ---R extensionDegree : () -> OnePointCompletion PositiveInteger ---R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if PrimeField p has FINITE ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % ---R generator : () -> % if PrimeField p has FINITE ---R getMultiplicationMatrix : () -> Matrix PrimeField p ---R getMultiplicationTable : () -> Vector List Record(value: PrimeField p,index: SingleInteger) ---R index : PositiveInteger -> % if PrimeField p has FINITE ---R init : () -> % if PrimeField p has FINITE ---R linearAssociatedExp : (%,SparseUnivariatePolynomial PrimeField p) -> % if PrimeField p has FINITE ---R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial PrimeField p,"failed") if PrimeField p has FINITE ---R linearAssociatedLog : % -> SparseUnivariatePolynomial PrimeField p if PrimeField p has FINITE ---R linearAssociatedOrder : % -> SparseUnivariatePolynomial PrimeField p if PrimeField p has FINITE ---R lookup : % -> PositiveInteger if PrimeField p has FINITE ---R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial % if PrimeField p has FINITE ---R minimalPolynomial : % -> SparseUnivariatePolynomial PrimeField p ---R multiEuclidean : (List %,%) -> Union(List %,"failed") ---R nextItem : % -> Union(%,"failed") if PrimeField p has FINITE ---R norm : (%,PositiveInteger) -> % if PrimeField p has FINITE ---R normal? : % -> Boolean if PrimeField p has FINITE ---R normalElement : () -> % if PrimeField p has FINITE ---R order : % -> OnePointCompletion PositiveInteger if PrimeField p has CHARNZ or PrimeField p has FINITE ---R order : % -> PositiveInteger if PrimeField p has FINITE ---R primeFrobenius : % -> % if PrimeField p has CHARNZ or PrimeField p has FINITE ---R primeFrobenius : (%,NonNegativeInteger) -> % if PrimeField p has CHARNZ or PrimeField p has FINITE ---R primitive? : % -> Boolean if PrimeField p has FINITE ---R primitiveElement : () -> % if PrimeField p has FINITE ---R principalIdeal : List % -> Record(coef: List %,generator: %) ---R random : () -> % if PrimeField p has FINITE ---R representationType : () -> Union("prime",polynomial,normal,cyclic) if PrimeField p has FINITE ---R represents : Vector PrimeField p -> % ---R retractIfCan : % -> Union(PrimeField p,"failed") ---R size : () -> NonNegativeInteger if PrimeField p has FINITE +--R extensionDegree : () -> OnePointCompletion(PositiveInteger) +--R factorsOfCyclicGroupSize : () -> List(Record(factor: Integer,exponent: Integer)) if PrimeField(p) has FINITE +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) +--R generator : () -> % if PrimeField(p) has FINITE +--R getMultiplicationMatrix : () -> Matrix(PrimeField(p)) +--R getMultiplicationTable : () -> Vector(List(Record(value: PrimeField(p),index: SingleInteger))) +--R index : PositiveInteger -> % if PrimeField(p) has FINITE +--R init : () -> % if PrimeField(p) has FINITE +--R linearAssociatedExp : (%,SparseUnivariatePolynomial(PrimeField(p))) -> % if PrimeField(p) has FINITE +--R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial(PrimeField(p)),"failed") if PrimeField(p) has FINITE +--R linearAssociatedLog : % -> SparseUnivariatePolynomial(PrimeField(p)) if PrimeField(p) has FINITE +--R linearAssociatedOrder : % -> SparseUnivariatePolynomial(PrimeField(p)) if PrimeField(p) has FINITE +--R lookup : % -> PositiveInteger if PrimeField(p) has FINITE +--R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial(%) if PrimeField(p) has FINITE +--R minimalPolynomial : % -> SparseUnivariatePolynomial(PrimeField(p)) +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") +--R nextItem : % -> Union(%,"failed") if PrimeField(p) has FINITE +--R norm : (%,PositiveInteger) -> % if PrimeField(p) has FINITE +--R normal? : % -> Boolean if PrimeField(p) has FINITE +--R normalElement : () -> % if PrimeField(p) has FINITE +--R order : % -> OnePointCompletion(PositiveInteger) if PrimeField(p) has CHARNZ or PrimeField(p) has FINITE +--R order : % -> PositiveInteger if PrimeField(p) has FINITE +--R primeFrobenius : % -> % if PrimeField(p) has CHARNZ or PrimeField(p) has FINITE +--R primeFrobenius : (%,NonNegativeInteger) -> % if PrimeField(p) has CHARNZ or PrimeField(p) has FINITE +--R primitive? : % -> Boolean if PrimeField(p) has FINITE +--R primitiveElement : () -> % if PrimeField(p) has FINITE +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) +--R random : () -> % if PrimeField(p) has FINITE +--R representationType : () -> Union("prime",polynomial,normal,cyclic) if PrimeField(p) has FINITE +--R represents : Vector(PrimeField(p)) -> % +--R retractIfCan : % -> Union(PrimeField(p),"failed") +--R size : () -> NonNegativeInteger if PrimeField(p) has FINITE --R sizeMultiplication : () -> NonNegativeInteger --R subtractIfCan : (%,%) -> Union(%,"failed") ---R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if PrimeField p has FINITE ---R trace : (%,PositiveInteger) -> % if PrimeField p has FINITE +--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if PrimeField(p) has FINITE +--R trace : (%,PositiveInteger) -> % if PrimeField(p) has FINITE --R transcendenceDegree : () -> NonNegativeInteger --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) --R @@ -40646,6 +40759,7 @@ FiniteFieldNormalBasis(p,extdeg):_ --S 1 of 1 )show FiniteFieldNormalBasisExtension +--R --R FiniteFieldNormalBasisExtension(GF: FiniteFieldCategory,extdeg: PositiveInteger) is a domain constructor --R Abbreviation for FiniteFieldNormalBasisExtension is FFNBX --R This constructor is not exposed in this frame. @@ -40653,7 +40767,7 @@ FiniteFieldNormalBasis(p,extdeg):_ --R --R------------------------------- Operations -------------------------------- --R ?*? : (GF,%) -> % ?*? : (%,GF) -> % ---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % --R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % @@ -40663,21 +40777,21 @@ FiniteFieldNormalBasis(p,extdeg):_ --R 1 : () -> % 0 : () -> % --R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % --R algebraic? : % -> Boolean associates? : (%,%) -> Boolean ---R basis : () -> Vector % coerce : GF -> % ---R coerce : Fraction Integer -> % coerce : % -> % +--R basis : () -> Vector(%) coerce : GF -> % +--R coerce : Fraction(Integer) -> % coerce : % -> % --R coerce : Integer -> % coerce : % -> OutputForm ---R coordinates : % -> Vector GF degree : % -> PositiveInteger ---R dimension : () -> CardinalNumber factor : % -> Factored % ---R gcd : List % -> % gcd : (%,%) -> % +--R coordinates : % -> Vector(GF) degree : % -> PositiveInteger +--R dimension : () -> CardinalNumber factor : % -> Factored(%) +--R gcd : List(%) -> % gcd : (%,%) -> % --R hash : % -> SingleInteger inGroundField? : % -> Boolean --R inv : % -> % latex : % -> String ---R lcm : List % -> % lcm : (%,%) -> % +--R lcm : List(%) -> % lcm : (%,%) -> % --R norm : % -> GF one? : % -> Boolean --R prime? : % -> Boolean ?quo? : (%,%) -> % --R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % ---R represents : Vector GF -> % retract : % -> GF +--R represents : Vector(GF) -> % retract : % -> GF --R sample : () -> % sizeLess? : (%,%) -> Boolean ---R squareFree : % -> Factored % squareFreePart : % -> % +--R squareFree : % -> Factored(%) squareFreePart : % -> % --R trace : % -> GF transcendent? : % -> Boolean --R unit? : % -> Boolean unitCanonical : % -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean @@ -40687,54 +40801,54 @@ FiniteFieldNormalBasis(p,extdeg):_ --R Frobenius : (%,NonNegativeInteger) -> % if GF has FINITE --R Frobenius : % -> % if GF has FINITE --R ?^? : (%,NonNegativeInteger) -> % ---R basis : PositiveInteger -> Vector % +--R basis : PositiveInteger -> Vector(%) --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if GF has CHARNZ or GF has FINITE --R charthRoot : % -> % if GF has FINITE ---R conditionP : Matrix % -> Union(Vector %,"failed") if GF has FINITE ---R coordinates : Vector % -> Matrix GF +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if GF has FINITE +--R coordinates : Vector(%) -> Matrix(GF) --R createNormalElement : () -> % if GF has FINITE --R createPrimitiveElement : () -> % if GF has FINITE ---R definingPolynomial : () -> SparseUnivariatePolynomial GF ---R degree : % -> OnePointCompletion PositiveInteger +--R definingPolynomial : () -> SparseUnivariatePolynomial(GF) +--R degree : % -> OnePointCompletion(PositiveInteger) --R differentiate : (%,NonNegativeInteger) -> % if GF has FINITE --R differentiate : % -> % if GF has FINITE --R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if GF has CHARNZ or GF has FINITE --R discreteLog : % -> NonNegativeInteger if GF has FINITE --R divide : (%,%) -> Record(quotient: %,remainder: %) --R euclideanSize : % -> NonNegativeInteger ---R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") --R exquo : (%,%) -> Union(%,"failed") --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) --R extensionDegree : () -> PositiveInteger ---R extensionDegree : () -> OnePointCompletion PositiveInteger ---R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if GF has FINITE ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R extensionDegree : () -> OnePointCompletion(PositiveInteger) +--R factorsOfCyclicGroupSize : () -> List(Record(factor: Integer,exponent: Integer)) if GF has FINITE +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) --R generator : () -> % if GF has FINITE ---R getMultiplicationMatrix : () -> Matrix GF ---R getMultiplicationTable : () -> Vector List Record(value: GF,index: SingleInteger) +--R getMultiplicationMatrix : () -> Matrix(GF) +--R getMultiplicationTable : () -> Vector(List(Record(value: GF,index: SingleInteger))) --R index : PositiveInteger -> % if GF has FINITE --R init : () -> % if GF has FINITE ---R linearAssociatedExp : (%,SparseUnivariatePolynomial GF) -> % if GF has FINITE ---R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial GF,"failed") if GF has FINITE ---R linearAssociatedLog : % -> SparseUnivariatePolynomial GF if GF has FINITE ---R linearAssociatedOrder : % -> SparseUnivariatePolynomial GF if GF has FINITE +--R linearAssociatedExp : (%,SparseUnivariatePolynomial(GF)) -> % if GF has FINITE +--R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial(GF),"failed") if GF has FINITE +--R linearAssociatedLog : % -> SparseUnivariatePolynomial(GF) if GF has FINITE +--R linearAssociatedOrder : % -> SparseUnivariatePolynomial(GF) if GF has FINITE --R lookup : % -> PositiveInteger if GF has FINITE ---R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial % if GF has FINITE ---R minimalPolynomial : % -> SparseUnivariatePolynomial GF ---R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial(%) if GF has FINITE +--R minimalPolynomial : % -> SparseUnivariatePolynomial(GF) +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") --R nextItem : % -> Union(%,"failed") if GF has FINITE --R norm : (%,PositiveInteger) -> % if GF has FINITE --R normal? : % -> Boolean if GF has FINITE --R normalElement : () -> % if GF has FINITE ---R order : % -> OnePointCompletion PositiveInteger if GF has CHARNZ or GF has FINITE +--R order : % -> OnePointCompletion(PositiveInteger) if GF has CHARNZ or GF has FINITE --R order : % -> PositiveInteger if GF has FINITE --R primeFrobenius : % -> % if GF has CHARNZ or GF has FINITE --R primeFrobenius : (%,NonNegativeInteger) -> % if GF has CHARNZ or GF has FINITE --R primitive? : % -> Boolean if GF has FINITE --R primitiveElement : () -> % if GF has FINITE ---R principalIdeal : List % -> Record(coef: List %,generator: %) +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) --R random : () -> % if GF has FINITE --R representationType : () -> Union("prime",polynomial,normal,cyclic) if GF has FINITE --R retractIfCan : % -> Union(GF,"failed") @@ -40928,14 +41042,15 @@ FiniteFieldNormalBasisExtension(GF,extdeg):_ --S 1 of 1 )show FiniteFieldNormalBasisExtensionByPolynomial ---R FiniteFieldNormalBasisExtensionByPolynomial(GF: FiniteFieldCategory,uni: Union(SparseUnivariatePolynomial GF,Vector List Record(value: GF,index: SingleInteger))) is a domain constructor +--R +--R FiniteFieldNormalBasisExtensionByPolynomial(GF: FiniteFieldCategory,uni: Union(SparseUnivariatePolynomial(GF),Vector(List(Record(value: GF,index: SingleInteger))))) is a domain constructor --R Abbreviation for FiniteFieldNormalBasisExtensionByPolynomial is FFNBP --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for FFNBP --R --R------------------------------- Operations -------------------------------- --R ?*? : (GF,%) -> % ?*? : (%,GF) -> % ---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % --R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % @@ -40945,21 +41060,21 @@ FiniteFieldNormalBasisExtension(GF,extdeg):_ --R 1 : () -> % 0 : () -> % --R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % --R algebraic? : % -> Boolean associates? : (%,%) -> Boolean ---R basis : () -> Vector % coerce : GF -> % ---R coerce : Fraction Integer -> % coerce : % -> % +--R basis : () -> Vector(%) coerce : GF -> % +--R coerce : Fraction(Integer) -> % coerce : % -> % --R coerce : Integer -> % coerce : % -> OutputForm ---R coordinates : % -> Vector GF degree : % -> PositiveInteger ---R dimension : () -> CardinalNumber factor : % -> Factored % ---R gcd : List % -> % gcd : (%,%) -> % +--R coordinates : % -> Vector(GF) degree : % -> PositiveInteger +--R dimension : () -> CardinalNumber factor : % -> Factored(%) +--R gcd : List(%) -> % gcd : (%,%) -> % --R hash : % -> SingleInteger inGroundField? : % -> Boolean --R inv : % -> % latex : % -> String ---R lcm : List % -> % lcm : (%,%) -> % +--R lcm : List(%) -> % lcm : (%,%) -> % --R norm : % -> GF one? : % -> Boolean --R prime? : % -> Boolean ?quo? : (%,%) -> % --R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % ---R represents : Vector GF -> % retract : % -> GF +--R represents : Vector(GF) -> % retract : % -> GF --R sample : () -> % sizeLess? : (%,%) -> Boolean ---R squareFree : % -> Factored % squareFreePart : % -> % +--R squareFree : % -> Factored(%) squareFreePart : % -> % --R trace : % -> GF transcendent? : % -> Boolean --R unit? : % -> Boolean unitCanonical : % -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean @@ -40969,54 +41084,54 @@ FiniteFieldNormalBasisExtension(GF,extdeg):_ --R Frobenius : (%,NonNegativeInteger) -> % if GF has FINITE --R Frobenius : % -> % if GF has FINITE --R ?^? : (%,NonNegativeInteger) -> % ---R basis : PositiveInteger -> Vector % +--R basis : PositiveInteger -> Vector(%) --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if GF has CHARNZ or GF has FINITE --R charthRoot : % -> % if GF has FINITE ---R conditionP : Matrix % -> Union(Vector %,"failed") if GF has FINITE ---R coordinates : Vector % -> Matrix GF +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if GF has FINITE +--R coordinates : Vector(%) -> Matrix(GF) --R createNormalElement : () -> % if GF has FINITE --R createPrimitiveElement : () -> % if GF has FINITE ---R definingPolynomial : () -> SparseUnivariatePolynomial GF ---R degree : % -> OnePointCompletion PositiveInteger +--R definingPolynomial : () -> SparseUnivariatePolynomial(GF) +--R degree : % -> OnePointCompletion(PositiveInteger) --R differentiate : (%,NonNegativeInteger) -> % if GF has FINITE --R differentiate : % -> % if GF has FINITE --R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if GF has CHARNZ or GF has FINITE --R discreteLog : % -> NonNegativeInteger if GF has FINITE --R divide : (%,%) -> Record(quotient: %,remainder: %) --R euclideanSize : % -> NonNegativeInteger ---R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") --R exquo : (%,%) -> Union(%,"failed") --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) --R extensionDegree : () -> PositiveInteger ---R extensionDegree : () -> OnePointCompletion PositiveInteger ---R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if GF has FINITE ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R extensionDegree : () -> OnePointCompletion(PositiveInteger) +--R factorsOfCyclicGroupSize : () -> List(Record(factor: Integer,exponent: Integer)) if GF has FINITE +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) --R generator : () -> % if GF has FINITE ---R getMultiplicationMatrix : () -> Matrix GF ---R getMultiplicationTable : () -> Vector List Record(value: GF,index: SingleInteger) +--R getMultiplicationMatrix : () -> Matrix(GF) +--R getMultiplicationTable : () -> Vector(List(Record(value: GF,index: SingleInteger))) --R index : PositiveInteger -> % if GF has FINITE --R init : () -> % if GF has FINITE ---R linearAssociatedExp : (%,SparseUnivariatePolynomial GF) -> % if GF has FINITE ---R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial GF,"failed") if GF has FINITE ---R linearAssociatedLog : % -> SparseUnivariatePolynomial GF if GF has FINITE ---R linearAssociatedOrder : % -> SparseUnivariatePolynomial GF if GF has FINITE +--R linearAssociatedExp : (%,SparseUnivariatePolynomial(GF)) -> % if GF has FINITE +--R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial(GF),"failed") if GF has FINITE +--R linearAssociatedLog : % -> SparseUnivariatePolynomial(GF) if GF has FINITE +--R linearAssociatedOrder : % -> SparseUnivariatePolynomial(GF) if GF has FINITE --R lookup : % -> PositiveInteger if GF has FINITE ---R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial % if GF has FINITE ---R minimalPolynomial : % -> SparseUnivariatePolynomial GF ---R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial(%) if GF has FINITE +--R minimalPolynomial : % -> SparseUnivariatePolynomial(GF) +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") --R nextItem : % -> Union(%,"failed") if GF has FINITE --R norm : (%,PositiveInteger) -> % if GF has FINITE --R normal? : % -> Boolean if GF has FINITE --R normalElement : () -> % if GF has FINITE ---R order : % -> OnePointCompletion PositiveInteger if GF has CHARNZ or GF has FINITE +--R order : % -> OnePointCompletion(PositiveInteger) if GF has CHARNZ or GF has FINITE --R order : % -> PositiveInteger if GF has FINITE --R primeFrobenius : % -> % if GF has CHARNZ or GF has FINITE --R primeFrobenius : (%,NonNegativeInteger) -> % if GF has CHARNZ or GF has FINITE --R primitive? : % -> Boolean if GF has FINITE --R primitiveElement : () -> % if GF has FINITE ---R principalIdeal : List % -> Record(coef: List %,generator: %) +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) --R random : () -> % if GF has FINITE --R representationType : () -> Union("prime",polynomial,normal,cyclic) if GF has FINITE --R retractIfCan : % -> Union(GF,"failed") @@ -41522,7 +41637,7 @@ flexibleArray [i for i in 1..6] --R --R --R (1) [1,2,3,4,5,6] ---R Type: FlexibleArray PositiveInteger +--R Type: FlexibleArray(PositiveInteger) --E 1 --S 2 of 16 @@ -41530,7 +41645,7 @@ f : FARRAY INT := new(6,0) --R --R --R (2) [0,0,0,0,0,0] ---R Type: FlexibleArray Integer +--R Type: FlexibleArray(Integer) --E 2 --S 3 of 16 @@ -41538,7 +41653,7 @@ for i in 1..6 repeat f.i := i; f --R --R --R (3) [1,2,3,4,5,6] ---R Type: FlexibleArray Integer +--R Type: FlexibleArray(Integer) --E 3 --S 4 of 16 @@ -41554,7 +41669,7 @@ concat!(f,11) --R --R --R (5) [1,2,3,4,5,6,11] ---R Type: FlexibleArray Integer +--R Type: FlexibleArray(Integer) --E 5 --S 6 of 16 @@ -41570,7 +41685,7 @@ physicalLength!(f,15) --R --R --R (7) [1,2,3,4,5,6,11] ---R Type: FlexibleArray Integer +--R Type: FlexibleArray(Integer) --E 7 --S 8 of 16 @@ -41578,7 +41693,7 @@ concat!(f,f) --R --R --R (8) [1,2,3,4,5,6,11,1,2,3,4,5,6,11] ---R Type: FlexibleArray Integer +--R Type: FlexibleArray(Integer) --E 8 --S 9 of 16 @@ -41586,7 +41701,7 @@ insert!(22,f,1) --R --R --R (9) [22,1,2,3,4,5,6,11,1,2,3,4,5,6,11] ---R Type: FlexibleArray Integer +--R Type: FlexibleArray(Integer) --E 9 --S 10 of 16 @@ -41594,7 +41709,7 @@ g := f(10..) --R --R --R (10) [2,3,4,5,6,11] ---R Type: FlexibleArray Integer +--R Type: FlexibleArray(Integer) --E 10 --S 11 of 16 @@ -41602,7 +41717,7 @@ insert!(g,f,1) --R --R --R (11) [2,3,4,5,6,11,22,1,2,3,4,5,6,11,1,2,3,4,5,6,11] ---R Type: FlexibleArray Integer +--R Type: FlexibleArray(Integer) --E 11 --S 12 of 16 @@ -41610,7 +41725,7 @@ merge!(sort! f, sort! g) --R --R --R (12) [1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6,6,6,6,11,11,11,11,22] ---R Type: FlexibleArray Integer +--R Type: FlexibleArray(Integer) --E 12 --S 13 of 16 @@ -41618,7 +41733,7 @@ removeDuplicates! f --R --R --R (13) [1,2,3,4,5,6,11,22] ---R Type: FlexibleArray Integer +--R Type: FlexibleArray(Integer) --E 13 --S 14 of 16 @@ -41626,7 +41741,7 @@ select!(i +-> even? i,f) --R --R --R (14) [2,4,6,22] ---R Type: FlexibleArray Integer +--R Type: FlexibleArray(Integer) --E 14 --S 15 of 16 @@ -41972,7 +42087,7 @@ i :: Fraction Integer --R --R --R (6) 3 ---R Type: Fraction Integer +--R Type: Fraction(Integer) --E 6 --S 7 of 64 @@ -41990,7 +42105,7 @@ r :: Fraction Integer --R 3 --R (8) - --R 7 ---R Type: Fraction Integer +--R Type: Fraction(Integer) --E 8 --S 9 of 64 @@ -42204,7 +42319,7 @@ a: Matrix Fraction Integer := matrix [ [1/(i+j+1) for j in 0..9] for i in 0..9] --R | 1 1 1 1 1 1 1 1 1 1| --R |-- -- -- -- -- -- -- -- -- --| --R +10 11 12 13 14 15 16 17 18 19+ ---R Type: Matrix Fraction Integer +--R Type: Matrix(Fraction(Integer)) --E 29 --S 30 of 64 @@ -42214,7 +42329,7 @@ d:= determinant a --R 1 --R (29) ----------------------------------------------------- --R 46206893947914691316295628839036278726983680000000000 ---R Type: Fraction Integer +--R Type: Fraction(Integer) --E 30 --S 31 of 64 @@ -42282,7 +42397,7 @@ b: Matrix DoubleFloat := matrix [ [1/(i+j+1$DoubleFloat) for j in 0..9] for i in --R 6.25E-2, 5.8823529411764705E-2, 5.5555555555555552E-2, --R 5.2631578947368418E-2] --R ] ---R Type: Matrix DoubleFloat +--R Type: Matrix(DoubleFloat) --E 32 --S 33 of 64 @@ -42392,7 +42507,7 @@ c: Matrix Float := matrix [ [1/(i+j+1$Float) for j in 0..9] for i in 0..9] --R 0.05555 55555 55555 55555 55555 55555 55555 55555 6, --R 0.05263 15789 47368 42105 26315 78947 36842 10526 3] --R ] ---R Type: Matrix Float +--R Type: Matrix(Float) --E 35 --S 36 of 64 @@ -44058,6 +44173,7 @@ Float(): --S 1 of 1 )show FortranCode +--R --R FortranCode is a domain constructor --R Abbreviation for FortranCode is FC --R This constructor is exposed in this frame. @@ -44065,57 +44181,58 @@ Float(): --R --R------------------------------- Operations -------------------------------- --R ?=? : (%,%) -> Boolean assign : (Symbol,String) -> % ---R block : List % -> % call : String -> % ---R coerce : % -> OutputForm comment : List String -> % +--R block : List(%) -> % call : String -> % +--R coerce : % -> OutputForm comment : List(String) -> % --R comment : String -> % cond : (Switch,%,%) -> % --R cond : (Switch,%) -> % continue : SingleInteger -> % --R getCode : % -> SExpression goto : SingleInteger -> % --R hash : % -> SingleInteger latex : % -> String ---R printCode : % -> Void returns : Expression Integer -> % ---R returns : Expression Float -> % returns : () -> % ---R save : () -> % stop : () -> % ---R whileLoop : (Switch,%) -> % ?~=? : (%,%) -> Boolean ---R assign : (Symbol,List Polynomial Integer,Expression Complex Float) -> % ---R assign : (Symbol,List Polynomial Integer,Expression Float) -> % ---R assign : (Symbol,List Polynomial Integer,Expression Integer) -> % ---R assign : (Symbol,Vector Expression Complex Float) -> % ---R assign : (Symbol,Vector Expression Float) -> % ---R assign : (Symbol,Vector Expression Integer) -> % ---R assign : (Symbol,Matrix Expression Complex Float) -> % ---R assign : (Symbol,Matrix Expression Float) -> % ---R assign : (Symbol,Matrix Expression Integer) -> % ---R assign : (Symbol,Expression Complex Float) -> % ---R assign : (Symbol,Expression Float) -> % ---R assign : (Symbol,Expression Integer) -> % ---R assign : (Symbol,List Polynomial Integer,Expression MachineComplex) -> % ---R assign : (Symbol,List Polynomial Integer,Expression MachineFloat) -> % ---R assign : (Symbol,List Polynomial Integer,Expression MachineInteger) -> % ---R assign : (Symbol,Vector Expression MachineComplex) -> % ---R assign : (Symbol,Vector Expression MachineFloat) -> % ---R assign : (Symbol,Vector Expression MachineInteger) -> % ---R assign : (Symbol,Matrix Expression MachineComplex) -> % ---R assign : (Symbol,Matrix Expression MachineFloat) -> % ---R assign : (Symbol,Matrix Expression MachineInteger) -> % ---R assign : (Symbol,Vector MachineComplex) -> % ---R assign : (Symbol,Vector MachineFloat) -> % ---R assign : (Symbol,Vector MachineInteger) -> % ---R assign : (Symbol,Matrix MachineComplex) -> % ---R assign : (Symbol,Matrix MachineFloat) -> % ---R assign : (Symbol,Matrix MachineInteger) -> % ---R assign : (Symbol,Expression MachineComplex) -> % ---R assign : (Symbol,Expression MachineFloat) -> % ---R assign : (Symbol,Expression MachineInteger) -> % ---R code : % -> Union(nullBranch: null,assignmentBranch: Record(var: Symbol,arrayIndex: List Polynomial Integer,rand: Record(ints2Floats?: Boolean,expr: OutputForm)),arrayAssignmentBranch: Record(var: Symbol,rand: OutputForm,ints2Floats?: Boolean),conditionalBranch: Record(switch: Switch,thenClause: %,elseClause: %),returnBranch: Record(empty?: Boolean,value: Record(ints2Floats?: Boolean,expr: OutputForm)),blockBranch: List %,commentBranch: List String,callBranch: String,forBranch: Record(range: SegmentBinding Polynomial Integer,span: Polynomial Integer,body: %),labelBranch: SingleInteger,loopBranch: Record(switch: Switch,body: %),commonBranch: Record(name: Symbol,contents: List Symbol),printBranch: List OutputForm) ---R common : (Symbol,List Symbol) -> % ---R forLoop : (SegmentBinding Polynomial Integer,Polynomial Integer,%) -> % ---R forLoop : (SegmentBinding Polynomial Integer,%) -> % +--R printCode : % -> Void returns : Expression(Float) -> % +--R returns : () -> % save : () -> % +--R stop : () -> % whileLoop : (Switch,%) -> % +--R ?~=? : (%,%) -> Boolean +--R assign : (Symbol,List(Polynomial(Integer)),Expression(Complex(Float))) -> % +--R assign : (Symbol,List(Polynomial(Integer)),Expression(Float)) -> % +--R assign : (Symbol,List(Polynomial(Integer)),Expression(Integer)) -> % +--R assign : (Symbol,Vector(Expression(Complex(Float)))) -> % +--R assign : (Symbol,Vector(Expression(Float))) -> % +--R assign : (Symbol,Vector(Expression(Integer))) -> % +--R assign : (Symbol,Matrix(Expression(Complex(Float)))) -> % +--R assign : (Symbol,Matrix(Expression(Float))) -> % +--R assign : (Symbol,Matrix(Expression(Integer))) -> % +--R assign : (Symbol,Expression(Complex(Float))) -> % +--R assign : (Symbol,Expression(Float)) -> % +--R assign : (Symbol,Expression(Integer)) -> % +--R assign : (Symbol,List(Polynomial(Integer)),Expression(MachineComplex)) -> % +--R assign : (Symbol,List(Polynomial(Integer)),Expression(MachineFloat)) -> % +--R assign : (Symbol,List(Polynomial(Integer)),Expression(MachineInteger)) -> % +--R assign : (Symbol,Vector(Expression(MachineComplex))) -> % +--R assign : (Symbol,Vector(Expression(MachineFloat))) -> % +--R assign : (Symbol,Vector(Expression(MachineInteger))) -> % +--R assign : (Symbol,Matrix(Expression(MachineComplex))) -> % +--R assign : (Symbol,Matrix(Expression(MachineFloat))) -> % +--R assign : (Symbol,Matrix(Expression(MachineInteger))) -> % +--R assign : (Symbol,Vector(MachineComplex)) -> % +--R assign : (Symbol,Vector(MachineFloat)) -> % +--R assign : (Symbol,Vector(MachineInteger)) -> % +--R assign : (Symbol,Matrix(MachineComplex)) -> % +--R assign : (Symbol,Matrix(MachineFloat)) -> % +--R assign : (Symbol,Matrix(MachineInteger)) -> % +--R assign : (Symbol,Expression(MachineComplex)) -> % +--R assign : (Symbol,Expression(MachineFloat)) -> % +--R assign : (Symbol,Expression(MachineInteger)) -> % +--R code : % -> Union(nullBranch: null,assignmentBranch: Record(var: Symbol,arrayIndex: List(Polynomial(Integer)),rand: Record(ints2Floats?: Boolean,expr: OutputForm)),arrayAssignmentBranch: Record(var: Symbol,rand: OutputForm,ints2Floats?: Boolean),conditionalBranch: Record(switch: Switch,thenClause: %,elseClause: %),returnBranch: Record(empty?: Boolean,value: Record(ints2Floats?: Boolean,expr: OutputForm)),blockBranch: List(%),commentBranch: List(String),callBranch: String,forBranch: Record(range: SegmentBinding(Polynomial(Integer)),span: Polynomial(Integer),body: %),labelBranch: SingleInteger,loopBranch: Record(switch: Switch,body: %),commonBranch: Record(name: Symbol,contents: List(Symbol)),printBranch: List(OutputForm)) +--R common : (Symbol,List(Symbol)) -> % +--R forLoop : (SegmentBinding(Polynomial(Integer)),Polynomial(Integer),%) -> % +--R forLoop : (SegmentBinding(Polynomial(Integer)),%) -> % --R operation : % -> Union(Null: null,Assignment: assignment,Conditional: conditional,Return: return,Block: block,Comment: comment,Call: call,For: for,While: while,Repeat: repeat,Goto: goto,Continue: continue,ArrayAssignment: arrayAssignment,Save: save,Stop: stop,Common: common,Print: print) ---R printStatement : List OutputForm -> % +--R printStatement : List(OutputForm) -> % --R repeatUntilLoop : (Switch,%) -> % ---R returns : Expression Complex Float -> % ---R returns : Expression MachineComplex -> % ---R returns : Expression MachineInteger -> % ---R returns : Expression MachineFloat -> % +--R returns : Expression(Complex(Float)) -> % +--R returns : Expression(Integer) -> % +--R returns : Expression(MachineComplex) -> % +--R returns : Expression(MachineInteger) -> % +--R returns : Expression(MachineFloat) -> % --R setLabelValue : SingleInteger -> SingleInteger --R --E 1 @@ -44784,7 +44901,8 @@ FortranCode(): public == private where --S 1 of 1 )show FortranExpression ---R FortranExpression(basicSymbols: List Symbol,subscriptedSymbols: List Symbol,R: FortranMachineTypeCategory) is a domain constructor +--R +--R FortranExpression(basicSymbols: List(Symbol),subscriptedSymbols: List(Symbol),R: FortranMachineTypeCategory) is a domain constructor --R Abbreviation for FortranExpression is FEXPR --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for FEXPR @@ -44797,86 +44915,88 @@ FortranCode(): public == private where --R ?-? : (%,%) -> % ? Boolean --R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean --R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean ---R D : (%,Symbol) -> % D : (%,List Symbol) -> % +--R D : (%,Symbol) -> % D : (%,List(Symbol)) -> % --R 1 : () -> % 0 : () -> % --R ?^? : (%,PositiveInteger) -> % abs : % -> % --R acos : % -> % asin : % -> % --R atan : % -> % belong? : BasicOperator -> Boolean ---R box : List % -> % box : % -> % ---R coerce : % -> Expression R coerce : Integer -> % ---R coerce : R -> % coerce : Kernel % -> % +--R box : List(%) -> % box : % -> % +--R coerce : % -> Expression(R) coerce : Integer -> % +--R coerce : R -> % coerce : Kernel(%) -> % --R coerce : % -> OutputForm cos : % -> % --R cosh : % -> % differentiate : (%,Symbol) -> % --R distribute : (%,%) -> % distribute : % -> % --R elt : (BasicOperator,%,%) -> % elt : (BasicOperator,%) -> % ---R eval : (%,List %,List %) -> % eval : (%,%,%) -> % ---R eval : (%,Equation %) -> % eval : (%,List Equation %) -> % ---R eval : (%,Kernel %,%) -> % exp : % -> % +--R eval : (%,%,%) -> % eval : (%,Equation(%)) -> % +--R eval : (%,Kernel(%),%) -> % exp : % -> % --R freeOf? : (%,Symbol) -> Boolean freeOf? : (%,%) -> Boolean --R hash : % -> SingleInteger height : % -> NonNegativeInteger --R is? : (%,Symbol) -> Boolean kernel : (BasicOperator,%) -> % ---R kernels : % -> List Kernel % latex : % -> String +--R kernels : % -> List(Kernel(%)) latex : % -> String --R log : % -> % log10 : % -> % ---R map : ((% -> %),Kernel %) -> % max : (%,%) -> % ---R min : (%,%) -> % one? : % -> Boolean ---R paren : List % -> % paren : % -> % ---R pi : () -> % recip : % -> Union(%,"failed") ---R retract : Symbol -> % retract : Expression R -> % ---R retract : % -> R retract : % -> Kernel % ---R sample : () -> % sin : % -> % ---R sinh : % -> % sqrt : % -> % ---R subst : (%,Equation %) -> % tan : % -> % ---R tanh : % -> % tower : % -> List Kernel % ---R useNagFunctions : () -> Boolean variables : % -> List Symbol ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R max : (%,%) -> % min : (%,%) -> % +--R one? : % -> Boolean paren : List(%) -> % +--R paren : % -> % pi : () -> % +--R recip : % -> Union(%,"failed") retract : Symbol -> % +--R retract : Expression(R) -> % retract : % -> R +--R retract : % -> Kernel(%) sample : () -> % +--R sin : % -> % sinh : % -> % +--R sqrt : % -> % subst : (%,Equation(%)) -> % +--R tan : % -> % tanh : % -> % +--R tower : % -> List(Kernel(%)) useNagFunctions : () -> Boolean +--R variables : % -> List(Symbol) zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,NonNegativeInteger) -> % --R D : (%,Symbol,NonNegativeInteger) -> % ---R D : (%,List Symbol,List NonNegativeInteger) -> % +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % --R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger --R definingPolynomial : % -> % if $ has RING ---R differentiate : (%,List Symbol) -> % +--R differentiate : (%,List(Symbol)) -> % --R differentiate : (%,Symbol,NonNegativeInteger) -> % ---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % ---R elt : (BasicOperator,List %) -> % +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % +--R elt : (BasicOperator,List(%)) -> % --R elt : (BasicOperator,%,%,%,%) -> % --R elt : (BasicOperator,%,%,%) -> % --R eval : (%,BasicOperator,(% -> %)) -> % ---R eval : (%,BasicOperator,(List % -> %)) -> % ---R eval : (%,List BasicOperator,List (List % -> %)) -> % ---R eval : (%,List BasicOperator,List (% -> %)) -> % +--R eval : (%,BasicOperator,(List(%) -> %)) -> % +--R eval : (%,List(BasicOperator),List((List(%) -> %))) -> % +--R eval : (%,List(BasicOperator),List((% -> %))) -> % --R eval : (%,Symbol,(% -> %)) -> % ---R eval : (%,Symbol,(List % -> %)) -> % ---R eval : (%,List Symbol,List (List % -> %)) -> % ---R eval : (%,List Symbol,List (% -> %)) -> % ---R eval : (%,List Kernel %,List %) -> % ---R even? : % -> Boolean if $ has RETRACT INT +--R eval : (%,Symbol,(List(%) -> %)) -> % +--R eval : (%,List(Symbol),List((List(%) -> %))) -> % +--R eval : (%,List(Symbol),List((% -> %))) -> % +--R eval : (%,List(%),List(%)) -> % +--R eval : (%,List(Equation(%))) -> % +--R eval : (%,List(Kernel(%)),List(%)) -> % +--R even? : % -> Boolean if $ has RETRACT(INT) --R is? : (%,BasicOperator) -> Boolean ---R kernel : (BasicOperator,List %) -> % ---R mainKernel : % -> Union(Kernel %,"failed") ---R minPoly : Kernel % -> SparseUnivariatePolynomial % if $ has RING ---R odd? : % -> Boolean if $ has RETRACT INT +--R kernel : (BasicOperator,List(%)) -> % +--R mainKernel : % -> Union(Kernel(%),"failed") +--R map : ((% -> %),Kernel(%)) -> % +--R minPoly : Kernel(%) -> SparseUnivariatePolynomial(%) if $ has RING +--R odd? : % -> Boolean if $ has RETRACT(INT) --R operator : BasicOperator -> BasicOperator ---R operators : % -> List BasicOperator ---R retract : Polynomial Float -> % if R has RETRACT FLOAT ---R retract : Fraction Polynomial Float -> % if R has RETRACT FLOAT ---R retract : Expression Float -> % if R has RETRACT FLOAT ---R retract : Polynomial Integer -> % if R has RETRACT INT ---R retract : Fraction Polynomial Integer -> % if R has RETRACT INT ---R retract : Expression Integer -> % if R has RETRACT INT ---R retractIfCan : Polynomial Float -> Union(%,"failed") if R has RETRACT FLOAT ---R retractIfCan : Fraction Polynomial Float -> Union(%,"failed") if R has RETRACT FLOAT ---R retractIfCan : Expression Float -> Union(%,"failed") if R has RETRACT FLOAT ---R retractIfCan : Polynomial Integer -> Union(%,"failed") if R has RETRACT INT ---R retractIfCan : Fraction Polynomial Integer -> Union(%,"failed") if R has RETRACT INT ---R retractIfCan : Expression Integer -> Union(%,"failed") if R has RETRACT INT +--R operators : % -> List(BasicOperator) +--R retract : Polynomial(Float) -> % if R has RETRACT(FLOAT) +--R retract : Fraction(Polynomial(Float)) -> % if R has RETRACT(FLOAT) +--R retract : Expression(Float) -> % if R has RETRACT(FLOAT) +--R retract : Polynomial(Integer) -> % if R has RETRACT(INT) +--R retract : Fraction(Polynomial(Integer)) -> % if R has RETRACT(INT) +--R retract : Expression(Integer) -> % if R has RETRACT(INT) +--R retractIfCan : Polynomial(Float) -> Union(%,"failed") if R has RETRACT(FLOAT) +--R retractIfCan : Fraction(Polynomial(Float)) -> Union(%,"failed") if R has RETRACT(FLOAT) +--R retractIfCan : Expression(Float) -> Union(%,"failed") if R has RETRACT(FLOAT) +--R retractIfCan : Polynomial(Integer) -> Union(%,"failed") if R has RETRACT(INT) +--R retractIfCan : Fraction(Polynomial(Integer)) -> Union(%,"failed") if R has RETRACT(INT) +--R retractIfCan : Expression(Integer) -> Union(%,"failed") if R has RETRACT(INT) --R retractIfCan : Symbol -> Union(%,"failed") ---R retractIfCan : Expression R -> Union(%,"failed") +--R retractIfCan : Expression(R) -> Union(%,"failed") --R retractIfCan : % -> Union(R,"failed") ---R retractIfCan : % -> Union(Kernel %,"failed") ---R subst : (%,List Kernel %,List %) -> % ---R subst : (%,List Equation %) -> % +--R retractIfCan : % -> Union(Kernel(%),"failed") +--R subst : (%,List(Kernel(%)),List(%)) -> % +--R subst : (%,List(Equation(%))) -> % --R subtractIfCan : (%,%) -> Union(%,"failed") --R useNagFunctions : Boolean -> Boolean --R @@ -45342,26 +45462,27 @@ FortranExpression(basicSymbols,subscriptedSymbols,R): --S 1 of 1 )show FortranProgram ---R FortranProgram(name: Symbol,returnType: Union(fst: FortranScalarType,void: void),arguments: List Symbol,symbols: SymbolTable) is a domain constructor +--R +--R FortranProgram(name: Symbol,returnType: Union(fst: FortranScalarType,void: void),arguments: List(Symbol),symbols: SymbolTable) is a domain constructor --R Abbreviation for FortranProgram is FORTRAN --R This constructor is exposed in this frame. --R Issue )edit NIL to see algebra source code for FORTRAN --R --R------------------------------- Operations -------------------------------- ---R coerce : Expression Float -> % coerce : Expression Integer -> % ---R coerce : List FortranCode -> % coerce : FortranCode -> % +--R coerce : Expression(Float) -> % coerce : Expression(Integer) -> % +--R coerce : List(FortranCode) -> % coerce : FortranCode -> % --R coerce : % -> OutputForm outputAsFortran : % -> Void ---R coerce : Equation Expression Complex Float -> % ---R coerce : Equation Expression Float -> % ---R coerce : Equation Expression Integer -> % ---R coerce : Expression Complex Float -> % ---R coerce : Equation Expression MachineComplex -> % ---R coerce : Equation Expression MachineFloat -> % ---R coerce : Equation Expression MachineInteger -> % ---R coerce : Expression MachineComplex -> % ---R coerce : Expression MachineFloat -> % ---R coerce : Expression MachineInteger -> % ---R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R coerce : Equation(Expression(Complex(Float))) -> % +--R coerce : Equation(Expression(Float)) -> % +--R coerce : Equation(Expression(Integer)) -> % +--R coerce : Expression(Complex(Float)) -> % +--R coerce : Equation(Expression(MachineComplex)) -> % +--R coerce : Equation(Expression(MachineFloat)) -> % +--R coerce : Equation(Expression(MachineInteger)) -> % +--R coerce : Expression(MachineComplex) -> % +--R coerce : Expression(MachineFloat) -> % +--R coerce : Expression(MachineInteger) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List(FortranCode)) -> % --R --E 1 @@ -46039,6 +46160,7 @@ FortranTemplate() : specification == implementation where --S 1 of 1 )show FortranType +--R --R FortranType is a domain constructor --R Abbreviation for FortranType is FT --R This constructor is exposed in this frame. @@ -46052,9 +46174,9 @@ FortranTemplate() : specification == implementation where --R fortranInteger : () -> % fortranLogical : () -> % --R fortranReal : () -> % hash : % -> SingleInteger --R latex : % -> String ?~=? : (%,%) -> Boolean ---R construct : (Union(fst: FortranScalarType,void: void),List Polynomial Integer,Boolean) -> % ---R construct : (Union(fst: FortranScalarType,void: void),List Symbol,Boolean) -> % ---R dimensionsOf : % -> List Polynomial Integer +--R construct : (Union(fst: FortranScalarType,void: void),List(Polynomial(Integer)),Boolean) -> % +--R construct : (Union(fst: FortranScalarType,void: void),List(Symbol),Boolean) -> % +--R dimensionsOf : % -> List(Polynomial(Integer)) --R scalarTypeOf : % -> Union(fst: FortranScalarType,void: void) --R --E 1 @@ -46228,7 +46350,8 @@ FortranType() : exports == implementation where --S 1 of 1 )show FourierComponent ---R FourierComponent E: OrderedSet is a domain constructor +--R +--R FourierComponent(E: OrderedSet) is a domain constructor --R Abbreviation for FourierComponent is FCOMP --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for FCOMP @@ -46345,7 +46468,8 @@ FourierComponent(E:OrderedSet): --S 1 of 1 )show FourierSeries ---R FourierSeries(R: Join(CommutativeRing,Algebra Fraction Integer),E: Join(OrderedSet,AbelianGroup)) is a domain constructor +--R +--R FourierSeries(R: Join(CommutativeRing,Algebra(Fraction(Integer))),E: Join(OrderedSet,AbelianGroup)) is a domain constructor --R Abbreviation for FourierSeries is FSERIES --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for FSERIES @@ -46357,7 +46481,7 @@ FourierComponent(E:OrderedSet): --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coerce : FourierComponent E -> % +--R ?^? : (%,PositiveInteger) -> % coerce : FourierComponent(E) -> % --R coerce : R -> % coerce : Integer -> % --R coerce : % -> OutputForm hash : % -> SingleInteger --R latex : % -> String makeCos : (E,R) -> % @@ -46514,7 +46638,7 @@ a := 11/12 --R 11 --R (1) -- --R 12 ---R Type: Fraction Integer +--R Type: Fraction(Integer) --E 1 --S 2 of 12 @@ -46524,7 +46648,7 @@ b := 23/24 --R 23 --R (2) -- --R 24 ---R Type: Fraction Integer +--R Type: Fraction(Integer) --E 2 --S 3 of 12 @@ -46534,7 +46658,7 @@ b := 23/24 --R 313271 --R (3) ------ --R 76032 ---R Type: Fraction Integer +--R Type: Fraction(Integer) --E 3 --S 4 of 12 @@ -46562,7 +46686,7 @@ r := (x**2 + 2*x + 1)/(x**2 - 2*x + 1) --R (6) ----------- --R 2 --R x - 2x + 1 ---R Type: Fraction Polynomial Integer +--R Type: Fraction(Polynomial(Integer)) --E 6 --S 7 of 12 @@ -46574,7 +46698,7 @@ factor(r) --R (7) ----------- --R 2 --R x - 2x + 1 ---R Type: Factored Fraction Polynomial Integer +--R Type: Factored(Fraction(Polynomial(Integer))) --E 7 --S 8 of 12 @@ -46586,7 +46710,7 @@ map(factor,r) --R (8) -------- --R 2 --R (x - 1) ---R Type: Fraction Factored Polynomial Integer +--R Type: Fraction(Factored(Polynomial(Integer))) --E 8 --S 9 of 12 @@ -46596,7 +46720,7 @@ continuedFraction(7/12) --R 1 | 1 | 1 | 1 | --R (9) +---+ + +---+ + +---+ + +---+ --R | 1 | 1 | 2 | 2 ---R Type: ContinuedFraction Integer +--R Type: ContinuedFraction(Integer) --E 9 --S 10 of 12 @@ -46607,7 +46731,7 @@ partialFraction(7,12) --R (10) 1 - -- + - --R 2 3 --R 2 ---R Type: PartialFraction Integer +--R Type: PartialFraction(Integer) --E 10 --S 11 of 12 @@ -46617,7 +46741,7 @@ g := 2/3 + 4/5*%i --R 2 4 --R (11) - + - %i --R 3 5 ---R Type: Complex Fraction Integer +--R Type: Complex(Fraction(Integer)) --E 11 --S 12 of 12 @@ -46627,7 +46751,7 @@ g :: FRAC COMPLEX INT --R 10 + 12%i --R (12) --------- --R 15 ---R Type: Fraction Complex Integer +--R Type: Fraction(Complex(Integer)) --E 12 )spool @@ -47193,7 +47317,8 @@ Fraction(S: IntegralDomain): QuotientFieldCategory S with --S 1 of 1 )show FractionalIdeal ---R FractionalIdeal(R: EuclideanDomain,F: QuotientFieldCategory R,UP: UnivariatePolynomialCategory F,A: Join(FramedAlgebra(F,UP),RetractableTo F)) is a domain constructor +--R +--R FractionalIdeal(R: EuclideanDomain,F: QuotientFieldCategory(R),UP: UnivariatePolynomialCategory(F),A: Join(FramedAlgebra(F,UP),RetractableTo(F))) is a domain constructor --R Abbreviation for FractionalIdeal is FRIDEAL --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for FRIDEAL @@ -47203,17 +47328,17 @@ Fraction(S: IntegralDomain): QuotientFieldCategory S with --R ?**? : (%,PositiveInteger) -> % ?/? : (%,%) -> % --R ?=? : (%,%) -> Boolean 1 : () -> % --R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % ---R basis : % -> Vector A coerce : % -> OutputForm +--R basis : % -> Vector(A) coerce : % -> OutputForm --R commutator : (%,%) -> % conjugate : (%,%) -> % --R denom : % -> R hash : % -> SingleInteger ---R ideal : Vector A -> % inv : % -> % +--R ideal : Vector(A) -> % inv : % -> % --R latex : % -> String minimize : % -> % ---R norm : % -> F numer : % -> Vector A +--R norm : % -> F numer : % -> Vector(A) --R one? : % -> Boolean recip : % -> Union(%,"failed") --R sample : () -> % ?~=? : (%,%) -> Boolean --R ?**? : (%,NonNegativeInteger) -> % --R ?^? : (%,NonNegativeInteger) -> % ---R randomLC : (NonNegativeInteger,Vector A) -> A +--R randomLC : (NonNegativeInteger,Vector(A)) -> A --R --E 1 @@ -47455,7 +47580,8 @@ FractionalIdeal(R, F, UP, A): Exports == Implementation where --S 1 of 1 )show FramedModule ---R FramedModule(R: EuclideanDomain,F: QuotientFieldCategory R,UP: UnivariatePolynomialCategory F,A: FramedAlgebra(F,UP),ibasis: Vector A) is a domain constructor +--R +--R FramedModule(R: EuclideanDomain,F: QuotientFieldCategory(R),UP: UnivariatePolynomialCategory(F),A: FramedAlgebra(F,UP),ibasis: Vector(A)) is a domain constructor --R Abbreviation for FramedModule is FRMOD --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for FRMOD @@ -47463,15 +47589,15 @@ FractionalIdeal(R, F, UP, A): Exports == Implementation where --R------------------------------- Operations -------------------------------- --R ?*? : (%,%) -> % ?**? : (%,PositiveInteger) -> % --R ?=? : (%,%) -> Boolean 1 : () -> % ---R ?^? : (%,PositiveInteger) -> % basis : % -> Vector A +--R ?^? : (%,PositiveInteger) -> % basis : % -> Vector(A) --R coerce : % -> OutputForm hash : % -> SingleInteger ---R latex : % -> String module : Vector A -> % +--R latex : % -> String module : Vector(A) -> % --R norm : % -> F one? : % -> Boolean --R recip : % -> Union(%,"failed") sample : () -> % --R ?~=? : (%,%) -> Boolean --R ?**? : (%,NonNegativeInteger) -> % --R ?^? : (%,NonNegativeInteger) -> % ---R module : FractionalIdeal(R,F,UP,A) -> % if A has RETRACT F +--R module : FractionalIdeal(R,F,UP,A) -> % if A has RETRACT(F) --R --E 1 @@ -47640,7 +47766,8 @@ FramedModule(R, F, UP, A, ibasis): Exports == Implementation where --S 1 of 1 )show FreeAbelianGroup ---R FreeAbelianGroup S: SetCategory is a domain constructor +--R +--R FreeAbelianGroup(S: SetCategory) is a domain constructor --R Abbreviation for FreeAbelianGroup is FAGROUP --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for FAGROUP @@ -47669,7 +47796,7 @@ FramedModule(R, F, UP, A, ibasis): Exports == Implementation where --R min : (%,%) -> % if S has ORDSET --R retractIfCan : % -> Union(S,"failed") --R subtractIfCan : (%,%) -> Union(%,"failed") ---R terms : % -> List Record(gen: S,exp: Integer) +--R terms : % -> List(Record(gen: S,exp: Integer)) --R --E 1 @@ -47793,7 +47920,8 @@ FreeAbelianGroup(S:SetCategory): Exports == Implementation where --S 1 of 1 )show FreeAbelianMonoid ---R FreeAbelianMonoid S: SetCategory is a domain constructor +--R +--R FreeAbelianMonoid(S: SetCategory) is a domain constructor --R Abbreviation for FreeAbelianMonoid is FAMONOID --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for FAMONOID @@ -47815,7 +47943,7 @@ FreeAbelianGroup(S:SetCategory): Exports == Implementation where --R nthCoef : (%,Integer) -> NonNegativeInteger --R retractIfCan : % -> Union(S,"failed") --R subtractIfCan : (%,%) -> Union(%,"failed") ---R terms : % -> List Record(gen: S,exp: NonNegativeInteger) +--R terms : % -> List(Record(gen: S,exp: NonNegativeInteger)) --R --E 1 @@ -47901,7 +48029,8 @@ FreeAbelianMonoid(S: SetCategory): --S 1 of 1 )show FreeGroup ---R FreeGroup S: SetCategory is a domain constructor +--R +--R FreeGroup(S: SetCategory) is a domain constructor --R Abbreviation for FreeGroup is FGROUP --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for FGROUP @@ -47923,7 +48052,7 @@ FreeAbelianMonoid(S: SetCategory): --R ?~=? : (%,%) -> Boolean --R ?**? : (%,NonNegativeInteger) -> % --R ?^? : (%,NonNegativeInteger) -> % ---R factors : % -> List Record(gen: S,exp: Integer) +--R factors : % -> List(Record(gen: S,exp: Integer)) --R mapExpon : ((Integer -> Integer),%) -> % --R retractIfCan : % -> Union(S,"failed") --R @@ -48215,6 +48344,7 @@ FreeModule(R:Ring,S:OrderedSet): --S 1 of 1 )show FreeModule1 +--R --R FreeModule1(R: Ring,S: OrderedSet) is a domain constructor --R Abbreviation for FreeModule1 is FM1 --R This constructor is not exposed in this frame. @@ -48227,17 +48357,17 @@ FreeModule(R:Ring,S:OrderedSet): --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 0 : () -> % coefficient : (%,S) -> R ---R coefficients : % -> List R coerce : S -> % +--R coefficients : % -> List(R) coerce : S -> % --R coerce : % -> OutputForm hash : % -> SingleInteger --R latex : % -> String leadingCoefficient : % -> R --R leadingMonomial : % -> S map : ((R -> R),%) -> % --R monom : (S,R) -> % monomial? : % -> Boolean ---R monomials : % -> List % reductum : % -> % +--R monomials : % -> List(%) reductum : % -> % --R retract : % -> S sample : () -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (NonNegativeInteger,%) -> % --R leadingTerm : % -> Record(k: S,c: R) ---R listOfTerms : % -> List Record(k: S,c: R) +--R listOfTerms : % -> List(Record(k: S,c: R)) --R numberOfMonomials : % -> NonNegativeInteger --R retractIfCan : % -> Union(S,"failed") --R subtractIfCan : (%,%) -> Union(%,"failed") @@ -48409,7 +48539,8 @@ FreeModule1(R:Ring,S:OrderedSet): FMcat == FMdef where --S 1 of 1 )show FreeMonoid ---R FreeMonoid S: SetCategory is a domain constructor +--R +--R FreeMonoid(S: SetCategory) is a domain constructor --R Abbreviation for FreeMonoid is FMONOID --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for FMONOID @@ -48434,7 +48565,7 @@ FreeModule1(R:Ring,S:OrderedSet): FMcat == FMdef where --R ?>=? : (%,%) -> Boolean if S has ORDSET --R ?^? : (%,NonNegativeInteger) -> % --R divide : (%,%) -> Union(Record(lm: %,rm: %),"failed") ---R factors : % -> List Record(gen: S,exp: NonNegativeInteger) +--R factors : % -> List(Record(gen: S,exp: NonNegativeInteger)) --R lquo : (%,%) -> Union(%,"failed") --R mapExpon : ((NonNegativeInteger -> NonNegativeInteger),%) -> % --R max : (%,%) -> % if S has ORDSET @@ -48932,7 +49063,7 @@ f : Fx := 36 / (x**5-2*x**4-2*x**3+4*x**2+x-2) --R (2) ---------------------------- --R 5 4 3 2 --R x - 2x - 2x + 4x + x - 2 ---R Type: Fraction UnivariatePolynomial(x,Fraction Integer) +--R Type: Fraction(UnivariatePolynomial(x,Fraction(Integer))) --E 2 --S 3 of 16 @@ -48944,7 +49075,7 @@ g := fullPartialFraction f --R x - 2 x + 1 --+ 2 --R 2 (x - %A) --R %A - 1= 0 ---RType: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer)) +--RType: FullPartialFractionExpansion(Fraction(Integer),UnivariatePolynomial(x,Fraction(Integer))) --E 3 --S 4 of 16 @@ -48955,7 +49086,7 @@ g :: Fx --R (4) ---------------------------- --R 5 4 3 2 --R x - 2x - 2x + 4x + x - 2 ---R Type: Fraction UnivariatePolynomial(x,Fraction Integer) +--R Type: Fraction(UnivariatePolynomial(x,Fraction(Integer))) --E 4 --S 5 of 16 @@ -48967,7 +49098,7 @@ g5 := D(g, 5) --R 6 6 --+ 7 --R (x - 2) (x + 1) 2 (x - %A) --R %A - 1= 0 ---RType: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer)) +--RType: FullPartialFractionExpansion(Fraction(Integer),UnivariatePolynomial(x,Fraction(Integer))) --E 5 --S 6 of 16 @@ -48989,7 +49120,7 @@ f5 := D(f, 5) --R + --R 4 3 2 --R 276x - 1184x + 208x + 192x - 64 ---R Type: Fraction UnivariatePolynomial(x,Fraction Integer) +--R Type: Fraction(UnivariatePolynomial(x,Fraction(Integer))) --E 6 --S 7 of 16 @@ -48997,7 +49128,7 @@ g5::Fx - f5 --R --R --R (7) 0 ---R Type: Fraction UnivariatePolynomial(x,Fraction Integer) +--R Type: Fraction(UnivariatePolynomial(x,Fraction(Integer))) --E 7 --S 8 of 16 @@ -49009,7 +49140,7 @@ f : Fx := (x**5 * (x-1)) / ((x**2 + x + 1)**2 * (x-2)**3) --R (8) ----------------------------------- --R 7 6 5 3 2 --R x - 4x + 3x + 9x - 6x - 4x - 8 ---R Type: Fraction UnivariatePolynomial(x,Fraction Integer) +--R Type: Fraction(UnivariatePolynomial(x,Fraction(Integer))) --E 8 --S 9 of 16 @@ -49032,7 +49163,7 @@ g := fullPartialFraction f --R --+ 2 --R 2 (x - %A) --R %A + %A + 1= 0 ---RType: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer)) +--RType: FullPartialFractionExpansion(Fraction(Integer),UnivariatePolynomial(x,Fraction(Integer))) --E 9 --S 10 of 16 @@ -49040,7 +49171,7 @@ g :: Fx - f --R --R --R (10) 0 ---R Type: Fraction UnivariatePolynomial(x,Fraction Integer) +--R Type: Fraction(UnivariatePolynomial(x,Fraction(Integer))) --E 10 --S 11 of 16 @@ -49052,7 +49183,7 @@ f : Fx := (2*x**7-7*x**5+26*x**3+8*x) / (x**8-5*x**6+6*x**4+4*x**2-8) --R (11) ------------------------ --R 8 6 4 2 --R x - 5x + 6x + 4x - 8 ---R Type: Fraction UnivariatePolynomial(x,Fraction Integer) +--R Type: Fraction(UnivariatePolynomial(x,Fraction(Integer))) --E 11 --S 12 of 16 @@ -49066,7 +49197,7 @@ g := fullPartialFraction f --R --+ x - %A --+ 3 --+ x - %A --R 2 2 (x - %A) 2 --R %A - 2= 0 %A - 2= 0 %A + 1= 0 ---RType: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer)) +--RType: FullPartialFractionExpansion(Fraction(Integer),UnivariatePolynomial(x,Fraction(Integer))) --E 12 --S 13 of 16 @@ -49074,7 +49205,7 @@ g :: Fx - f --R --R --R (13) 0 ---R Type: Fraction UnivariatePolynomial(x,Fraction Integer) +--R Type: Fraction(UnivariatePolynomial(x,Fraction(Integer))) --E 13 --S 14 of 16 @@ -49092,7 +49223,7 @@ f:Fx := x**3 / (x**21 + 2*x**20 + 4*x**19 + 7*x**18 + 10*x**17 + 17*x**16 + 22*x --R 47x + 46x + 49x + 43x + 38x + 32x + 23x + 19x + 10x + 7x + 2x --R + --R 1 ---R Type: Fraction UnivariatePolynomial(x,Fraction Integer) +--R Type: Fraction(UnivariatePolynomial(x,Fraction(Integer))) --E 14 --S 15 of 16 @@ -49151,7 +49282,7 @@ g := fullPartialFraction f --R ------------------------------------------------------------------- --R 3 --R (x - %A) ---RType: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer)) +--RType: FullPartialFractionExpansion(Fraction(Integer),UnivariatePolynomial(x,Fraction(Integer))) --E 15 --S 16 of 16 @@ -49159,7 +49290,7 @@ g :: Fx - f --R --R --R (16) 0 ---R Type: Fraction UnivariatePolynomial(x,Fraction Integer) +--R Type: Fraction(UnivariatePolynomial(x,Fraction(Integer))) --E 16 )spool )lisp (bye) @@ -49601,7 +49732,8 @@ FullPartialFractionExpansion(F, UP): Exports == Implementation where --S 1 of 1 )show FunctionCalled ---R FunctionCalled f: Symbol is a domain constructor +--R +--R FunctionCalled(f: Symbol) is a domain constructor --R Abbreviation for FunctionCalled is FUNCTION --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for FUNCTION @@ -49685,7 +49817,7 @@ d1 := -4*z + 4*y**2*x + 16*x**2 + 1 --R --R 2 2 --R (2) - 4z + 4y x + 16x + 1 ---R Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer) +--R Type: DistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 2 --S 3 of 10 @@ -49694,7 +49826,7 @@ d2 := 2*z*y**2 + 4*x + 1 --R --R 2 --R (3) 2z y + 4x + 1 ---R Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer) +--R Type: DistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 3 --S 4 of 10 @@ -49703,7 +49835,7 @@ d3 := 2*z*x**2 - 2*y**2 - x --R --R 2 2 --R (4) 2z x - 2y - x ---R Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer) +--R Type: DistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 4 --S 5 of 10 @@ -49720,7 +49852,7 @@ groebner [d1,d2,d3] --R 7 29 6 17 4 11 3 1 2 15 1 --R x + -- x - -- x - -- x + -- x + -- x + -] --R 4 16 8 32 16 4 ---R Type: List DistributedMultivariatePolynomial([z,y,x],Fraction Integer) +--R Type: List(DistributedMultivariatePolynomial([z,y,x],Fraction(Integer))) --E 5 --S 6 of 10 @@ -49735,7 +49867,7 @@ n1 := d1 --R --R 2 2 --R (7) 4y x + 16x - 4z + 1 ---R Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer) +--RType: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 7 --S 8 of 10 @@ -49744,7 +49876,7 @@ n2 := d2 --R --R 2 --R (8) 2z y + 4x + 1 ---R Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer) +--RType: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 8 --S 9 of 10 @@ -49753,7 +49885,7 @@ n3 := d3 --R --R 2 2 --R (9) 2z x - 2y - x ---R Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer) +--RType: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 9 --S 10 of 10 @@ -49770,7 +49902,7 @@ groebner [n1,n2,n3] --R 2 2 2 1 3 --R z - 4y + 2x - - z - - x] --R 4 2 ---RType: List HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer) +--RType: List(HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction(Integer))) --E 10 )spool )lisp (bye) @@ -50239,7 +50371,8 @@ GeneralDistributedMultivariatePolynomial(vl,R,E): public == private where --S 1 of 1 )show GeneralModulePolynomial ---R GeneralModulePolynomial(vl: List Symbol,R: CommutativeRing,IS: OrderedSet,E: DirectProductCategory(# vl,NonNegativeInteger),ff: ((Record(index: IS,exponent: E),Record(index: IS,exponent: E)) -> Boolean),P: PolynomialCategory(R,E,OrderedVariableList vl)) is a domain constructor +--R +--R GeneralModulePolynomial(vl: List(Symbol),R: CommutativeRing,IS: OrderedSet,E: DirectProductCategory(#(vl),NonNegativeInteger),ff: ((Record(index: IS,exponent: E),Record(index: IS,exponent: E)) -> Boolean),P: PolynomialCategory(R,E,OrderedVariableList(vl))) is a domain constructor --R Abbreviation for GeneralModulePolynomial is GMODPOL --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for GMODPOL @@ -50401,7 +50534,8 @@ GeneralModulePolynomial(vl, R, IS, E, ff, P): public == private where --S 1 of 1 )show GenericNonAssociativeAlgebra ---R GenericNonAssociativeAlgebra(R: CommutativeRing,n: PositiveInteger,ls: List Symbol,gamma: Vector Matrix R) is a domain constructor +--R +--R GenericNonAssociativeAlgebra(R: CommutativeRing,n: PositiveInteger,ls: List(Symbol),gamma: Vector(Matrix(R))) is a domain constructor --R Abbreviation for GenericNonAssociativeAlgebra is GCNAALG --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for GCNAALG @@ -50414,89 +50548,90 @@ GeneralModulePolynomial(vl, R, IS, E, ff, P): public == private where --R 0 : () -> % alternative? : () -> Boolean --R antiAssociative? : () -> Boolean antiCommutative? : () -> Boolean --R antiCommutator : (%,%) -> % associative? : () -> Boolean ---R associator : (%,%,%) -> % basis : () -> Vector % +--R associator : (%,%,%) -> % basis : () -> Vector(%) --R coerce : % -> OutputForm commutative? : () -> Boolean --R commutator : (%,%) -> % flexible? : () -> Boolean ---R generic : (Symbol,Vector %) -> % generic : Vector % -> % ---R generic : Vector Symbol -> % generic : Symbol -> % ---R generic : () -> % hash : % -> SingleInteger ---R jacobiIdentity? : () -> Boolean jordanAdmissible? : () -> Boolean ---R jordanAlgebra? : () -> Boolean latex : % -> String ---R leftAlternative? : () -> Boolean lieAdmissible? : () -> Boolean ---R lieAlgebra? : () -> Boolean powerAssociative? : () -> Boolean ---R rank : () -> PositiveInteger rightAlternative? : () -> Boolean ---R sample : () -> % someBasis : () -> Vector % ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (SquareMatrix(n,Fraction Polynomial R),%) -> % ---R ?*? : (Fraction Polynomial R,%) -> % ---R ?*? : (%,Fraction Polynomial R) -> % +--R generic : Vector(%) -> % generic : Vector(Symbol) -> % +--R generic : Symbol -> % generic : () -> % +--R hash : % -> SingleInteger jacobiIdentity? : () -> Boolean +--R jordanAdmissible? : () -> Boolean jordanAlgebra? : () -> Boolean +--R latex : % -> String leftAlternative? : () -> Boolean +--R lieAdmissible? : () -> Boolean lieAlgebra? : () -> Boolean +--R powerAssociative? : () -> Boolean rank : () -> PositiveInteger +--R rightAlternative? : () -> Boolean sample : () -> % +--R someBasis : () -> Vector(%) zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (SquareMatrix(n,Fraction(Polynomial(R))),%) -> % +--R ?*? : (Fraction(Polynomial(R)),%) -> % +--R ?*? : (%,Fraction(Polynomial(R))) -> % --R ?*? : (NonNegativeInteger,%) -> % ---R apply : (Matrix Fraction Polynomial R,%) -> % ---R associatorDependence : () -> List Vector Fraction Polynomial R if Fraction Polynomial R has INTDOM ---R coerce : Vector Fraction Polynomial R -> % ---R conditionsForIdempotents : () -> List Polynomial R if R has INTDOM ---R conditionsForIdempotents : Vector % -> List Polynomial R if R has INTDOM ---R conditionsForIdempotents : () -> List Polynomial Fraction Polynomial R ---R conditionsForIdempotents : Vector % -> List Polynomial Fraction Polynomial R ---R convert : Vector Fraction Polynomial R -> % ---R convert : % -> Vector Fraction Polynomial R ---R coordinates : Vector % -> Matrix Fraction Polynomial R ---R coordinates : % -> Vector Fraction Polynomial R ---R coordinates : (Vector %,Vector %) -> Matrix Fraction Polynomial R ---R coordinates : (%,Vector %) -> Vector Fraction Polynomial R ---R ?.? : (%,Integer) -> Fraction Polynomial R ---R generic : (Vector Symbol,Vector %) -> % ---R genericLeftDiscriminant : () -> Fraction Polynomial R if R has INTDOM ---R genericLeftMinimalPolynomial : % -> SparseUnivariatePolynomial Fraction Polynomial R if R has INTDOM ---R genericLeftNorm : % -> Fraction Polynomial R if R has INTDOM ---R genericLeftTrace : % -> Fraction Polynomial R if R has INTDOM ---R genericLeftTraceForm : (%,%) -> Fraction Polynomial R if R has INTDOM ---R genericRightDiscriminant : () -> Fraction Polynomial R if R has INTDOM ---R genericRightMinimalPolynomial : % -> SparseUnivariatePolynomial Fraction Polynomial R if R has INTDOM ---R genericRightNorm : % -> Fraction Polynomial R if R has INTDOM ---R genericRightTrace : % -> Fraction Polynomial R if R has INTDOM ---R genericRightTraceForm : (%,%) -> Fraction Polynomial R if R has INTDOM ---R leftCharacteristicPolynomial : % -> SparseUnivariatePolynomial Fraction Polynomial R ---R leftDiscriminant : () -> Fraction Polynomial R ---R leftDiscriminant : Vector % -> Fraction Polynomial R ---R leftMinimalPolynomial : % -> SparseUnivariatePolynomial Fraction Polynomial R if Fraction Polynomial R has INTDOM ---R leftNorm : % -> Fraction Polynomial R +--R apply : (Matrix(Fraction(Polynomial(R))),%) -> % +--R associatorDependence : () -> List(Vector(Fraction(Polynomial(R)))) if Fraction(Polynomial(R)) has INTDOM +--R coerce : Vector(Fraction(Polynomial(R))) -> % +--R conditionsForIdempotents : () -> List(Polynomial(R)) if R has INTDOM +--R conditionsForIdempotents : Vector(%) -> List(Polynomial(R)) if R has INTDOM +--R conditionsForIdempotents : () -> List(Polynomial(Fraction(Polynomial(R)))) +--R conditionsForIdempotents : Vector(%) -> List(Polynomial(Fraction(Polynomial(R)))) +--R convert : Vector(Fraction(Polynomial(R))) -> % +--R convert : % -> Vector(Fraction(Polynomial(R))) +--R coordinates : Vector(%) -> Matrix(Fraction(Polynomial(R))) +--R coordinates : % -> Vector(Fraction(Polynomial(R))) +--R coordinates : (Vector(%),Vector(%)) -> Matrix(Fraction(Polynomial(R))) +--R coordinates : (%,Vector(%)) -> Vector(Fraction(Polynomial(R))) +--R ?.? : (%,Integer) -> Fraction(Polynomial(R)) +--R generic : (Vector(Symbol),Vector(%)) -> % +--R generic : (Symbol,Vector(%)) -> % +--R genericLeftDiscriminant : () -> Fraction(Polynomial(R)) if R has INTDOM +--R genericLeftMinimalPolynomial : % -> SparseUnivariatePolynomial(Fraction(Polynomial(R))) if R has INTDOM +--R genericLeftNorm : % -> Fraction(Polynomial(R)) if R has INTDOM +--R genericLeftTrace : % -> Fraction(Polynomial(R)) if R has INTDOM +--R genericLeftTraceForm : (%,%) -> Fraction(Polynomial(R)) if R has INTDOM +--R genericRightDiscriminant : () -> Fraction(Polynomial(R)) if R has INTDOM +--R genericRightMinimalPolynomial : % -> SparseUnivariatePolynomial(Fraction(Polynomial(R))) if R has INTDOM +--R genericRightNorm : % -> Fraction(Polynomial(R)) if R has INTDOM +--R genericRightTrace : % -> Fraction(Polynomial(R)) if R has INTDOM +--R genericRightTraceForm : (%,%) -> Fraction(Polynomial(R)) if R has INTDOM +--R leftCharacteristicPolynomial : % -> SparseUnivariatePolynomial(Fraction(Polynomial(R))) +--R leftDiscriminant : () -> Fraction(Polynomial(R)) +--R leftDiscriminant : Vector(%) -> Fraction(Polynomial(R)) +--R leftMinimalPolynomial : % -> SparseUnivariatePolynomial(Fraction(Polynomial(R))) if Fraction(Polynomial(R)) has INTDOM +--R leftNorm : % -> Fraction(Polynomial(R)) --R leftPower : (%,PositiveInteger) -> % ---R leftRankPolynomial : () -> SparseUnivariatePolynomial Fraction Polynomial R if R has INTDOM ---R leftRankPolynomial : () -> SparseUnivariatePolynomial Polynomial Fraction Polynomial R if Fraction Polynomial R has FIELD ---R leftRecip : % -> Union(%,"failed") if Fraction Polynomial R has INTDOM ---R leftRegularRepresentation : % -> Matrix Fraction Polynomial R ---R leftRegularRepresentation : (%,Vector %) -> Matrix Fraction Polynomial R ---R leftTrace : % -> Fraction Polynomial R ---R leftTraceMatrix : () -> Matrix Fraction Polynomial R ---R leftTraceMatrix : Vector % -> Matrix Fraction Polynomial R ---R leftUnit : () -> Union(%,"failed") if Fraction Polynomial R has INTDOM ---R leftUnits : () -> Union(Record(particular: %,basis: List %),"failed") +--R leftRankPolynomial : () -> SparseUnivariatePolynomial(Fraction(Polynomial(R))) if R has INTDOM +--R leftRankPolynomial : () -> SparseUnivariatePolynomial(Polynomial(Fraction(Polynomial(R)))) if Fraction(Polynomial(R)) has FIELD +--R leftRecip : % -> Union(%,"failed") if Fraction(Polynomial(R)) has INTDOM +--R leftRegularRepresentation : % -> Matrix(Fraction(Polynomial(R))) +--R leftRegularRepresentation : (%,Vector(%)) -> Matrix(Fraction(Polynomial(R))) +--R leftTrace : % -> Fraction(Polynomial(R)) +--R leftTraceMatrix : () -> Matrix(Fraction(Polynomial(R))) +--R leftTraceMatrix : Vector(%) -> Matrix(Fraction(Polynomial(R))) +--R leftUnit : () -> Union(%,"failed") if Fraction(Polynomial(R)) has INTDOM +--R leftUnits : () -> Union(Record(particular: %,basis: List(%)),"failed") --R noncommutativeJordanAlgebra? : () -> Boolean --R plenaryPower : (%,PositiveInteger) -> % ---R recip : % -> Union(%,"failed") if Fraction Polynomial R has INTDOM ---R represents : Vector Fraction Polynomial R -> % ---R represents : (Vector Fraction Polynomial R,Vector %) -> % ---R rightCharacteristicPolynomial : % -> SparseUnivariatePolynomial Fraction Polynomial R ---R rightDiscriminant : () -> Fraction Polynomial R ---R rightDiscriminant : Vector % -> Fraction Polynomial R ---R rightMinimalPolynomial : % -> SparseUnivariatePolynomial Fraction Polynomial R if Fraction Polynomial R has INTDOM ---R rightNorm : % -> Fraction Polynomial R +--R recip : % -> Union(%,"failed") if Fraction(Polynomial(R)) has INTDOM +--R represents : Vector(Fraction(Polynomial(R))) -> % +--R represents : (Vector(Fraction(Polynomial(R))),Vector(%)) -> % +--R rightCharacteristicPolynomial : % -> SparseUnivariatePolynomial(Fraction(Polynomial(R))) +--R rightDiscriminant : () -> Fraction(Polynomial(R)) +--R rightDiscriminant : Vector(%) -> Fraction(Polynomial(R)) +--R rightMinimalPolynomial : % -> SparseUnivariatePolynomial(Fraction(Polynomial(R))) if Fraction(Polynomial(R)) has INTDOM +--R rightNorm : % -> Fraction(Polynomial(R)) --R rightPower : (%,PositiveInteger) -> % ---R rightRankPolynomial : () -> SparseUnivariatePolynomial Fraction Polynomial R if R has INTDOM ---R rightRankPolynomial : () -> SparseUnivariatePolynomial Polynomial Fraction Polynomial R if Fraction Polynomial R has FIELD ---R rightRecip : % -> Union(%,"failed") if Fraction Polynomial R has INTDOM ---R rightRegularRepresentation : % -> Matrix Fraction Polynomial R ---R rightRegularRepresentation : (%,Vector %) -> Matrix Fraction Polynomial R ---R rightTrace : % -> Fraction Polynomial R ---R rightTraceMatrix : () -> Matrix Fraction Polynomial R ---R rightTraceMatrix : Vector % -> Matrix Fraction Polynomial R ---R rightUnit : () -> Union(%,"failed") if Fraction Polynomial R has INTDOM ---R rightUnits : () -> Union(Record(particular: %,basis: List %),"failed") ---R structuralConstants : () -> Vector Matrix Fraction Polynomial R ---R structuralConstants : Vector % -> Vector Matrix Fraction Polynomial R +--R rightRankPolynomial : () -> SparseUnivariatePolynomial(Fraction(Polynomial(R))) if R has INTDOM +--R rightRankPolynomial : () -> SparseUnivariatePolynomial(Polynomial(Fraction(Polynomial(R)))) if Fraction(Polynomial(R)) has FIELD +--R rightRecip : % -> Union(%,"failed") if Fraction(Polynomial(R)) has INTDOM +--R rightRegularRepresentation : % -> Matrix(Fraction(Polynomial(R))) +--R rightRegularRepresentation : (%,Vector(%)) -> Matrix(Fraction(Polynomial(R))) +--R rightTrace : % -> Fraction(Polynomial(R)) +--R rightTraceMatrix : () -> Matrix(Fraction(Polynomial(R))) +--R rightTraceMatrix : Vector(%) -> Matrix(Fraction(Polynomial(R))) +--R rightUnit : () -> Union(%,"failed") if Fraction(Polynomial(R)) has INTDOM +--R rightUnits : () -> Union(Record(particular: %,basis: List(%)),"failed") +--R structuralConstants : () -> Vector(Matrix(Fraction(Polynomial(R)))) +--R structuralConstants : Vector(%) -> Vector(Matrix(Fraction(Polynomial(R)))) --R subtractIfCan : (%,%) -> Union(%,"failed") ---R unit : () -> Union(%,"failed") if Fraction Polynomial R has INTDOM +--R unit : () -> Union(%,"failed") if Fraction(Polynomial(R)) has INTDOM --R --E 1 @@ -50928,32 +51063,33 @@ GenericNonAssociativeAlgebra(R : CommutativeRing, n : PositiveInteger,_ --S 1 of 1 )show GeneralPolynomialSet +--R --R GeneralPolynomialSet(R: Ring,E: OrderedAbelianMonoidSup,VarSet: OrderedSet,P: RecursivePolynomialCategory(R,E,VarSet)) is a domain constructor --R Abbreviation for GeneralPolynomialSet is GPOLSET --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for GPOLSET --R --R------------------------------- Operations -------------------------------- ---R ?=? : (%,%) -> Boolean coerce : % -> List P +--R ?=? : (%,%) -> Boolean coerce : % -> List(P) --R coerce : % -> OutputForm collect : (%,VarSet) -> % --R collectUnder : (%,VarSet) -> % collectUpper : (%,VarSet) -> % ---R construct : List P -> % convert : List P -> % +--R construct : List(P) -> % convert : List(P) -> % --R copy : % -> % empty : () -> % --R empty? : % -> Boolean eq? : (%,%) -> Boolean --R hash : % -> SingleInteger latex : % -> String ---R mainVariables : % -> List VarSet map : ((P -> P),%) -> % ---R mvar : % -> VarSet retract : List P -> % +--R mainVariables : % -> List(VarSet) map : ((P -> P),%) -> % +--R mvar : % -> VarSet retract : List(P) -> % --R sample : () -> % trivialIdeal? : % -> Boolean ---R variables : % -> List VarSet ?~=? : (%,%) -> Boolean +--R variables : % -> List(VarSet) ?~=? : (%,%) -> Boolean --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R any? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate ---R convert : % -> InputForm if P has KONVERT INFORM +--R convert : % -> InputForm if P has KONVERT(INFORM) --R count : ((P -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate --R count : (P,%) -> NonNegativeInteger if $ has finiteAggregate and P has SETCAT ---R eval : (%,List Equation P) -> % if P has EVALAB P and P has SETCAT ---R eval : (%,Equation P) -> % if P has EVALAB P and P has SETCAT ---R eval : (%,P,P) -> % if P has EVALAB P and P has SETCAT ---R eval : (%,List P,List P) -> % if P has EVALAB P and P has SETCAT +--R eval : (%,List(Equation(P))) -> % if P has EVALAB(P) and P has SETCAT +--R eval : (%,Equation(P)) -> % if P has EVALAB(P) and P has SETCAT +--R eval : (%,P,P) -> % if P has EVALAB(P) and P has SETCAT +--R eval : (%,List(P),List(P)) -> % if P has EVALAB(P) and P has SETCAT --R every? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate --R find : ((P -> Boolean),%) -> Union(P,"failed") --R headRemainder : (P,%) -> Record(num: P,den: R) if R has INTDOM @@ -50961,9 +51097,9 @@ GenericNonAssociativeAlgebra(R : CommutativeRing, n : PositiveInteger,_ --R mainVariable? : (VarSet,%) -> Boolean --R map! : ((P -> P),%) -> % if $ has shallowlyMutable --R member? : (P,%) -> Boolean if $ has finiteAggregate and P has SETCAT ---R members : % -> List P if $ has finiteAggregate +--R members : % -> List(P) if $ has finiteAggregate --R more? : (%,NonNegativeInteger) -> Boolean ---R parts : % -> List P if $ has finiteAggregate +--R parts : % -> List(P) if $ has finiteAggregate --R reduce : (((P,P) -> P),%) -> P if $ has finiteAggregate --R reduce : (((P,P) -> P),%,P) -> P if $ has finiteAggregate --R reduce : (((P,P) -> P),%,P,P) -> P if $ has finiteAggregate and P has SETCAT @@ -50971,9 +51107,9 @@ GenericNonAssociativeAlgebra(R : CommutativeRing, n : PositiveInteger,_ --R remove : ((P -> Boolean),%) -> % if $ has finiteAggregate --R remove : (P,%) -> % if $ has finiteAggregate and P has SETCAT --R removeDuplicates : % -> % if $ has finiteAggregate and P has SETCAT ---R retractIfCan : List P -> Union(%,"failed") ---R rewriteIdealWithHeadRemainder : (List P,%) -> List P if R has INTDOM ---R rewriteIdealWithRemainder : (List P,%) -> List P if R has INTDOM +--R retractIfCan : List(P) -> Union(%,"failed") +--R rewriteIdealWithHeadRemainder : (List(P),%) -> List(P) if R has INTDOM +--R rewriteIdealWithRemainder : (List(P),%) -> List(P) if R has INTDOM --R roughBase? : % -> Boolean if R has INTDOM --R roughEqualIdeals? : (%,%) -> Boolean if R has INTDOM --R roughSubIdeal? : (%,%) -> Boolean if R has INTDOM @@ -51354,6 +51490,7 @@ GeneralSparseTable(Key, Entry, Tbl, dent): TableAggregate(Key, Entry) == Impl --S 1 of 1 )show GeneralTriangularSet +--R --R GeneralTriangularSet(R: IntegralDomain,E: OrderedAbelianMonoidSup,V: OrderedSet,P: RecursivePolynomialCategory(R,E,V)) is a domain constructor --R Abbreviation for GeneralTriangularSet is GTSET --R This constructor is not exposed in this frame. @@ -51361,10 +51498,10 @@ GeneralSparseTable(Key, Entry, Tbl, dent): TableAggregate(Key, Entry) == Impl --R --R------------------------------- Operations -------------------------------- --R ?=? : (%,%) -> Boolean algebraic? : (V,%) -> Boolean ---R algebraicVariables : % -> List V coerce : % -> List P +--R algebraicVariables : % -> List(V) coerce : % -> List(P) --R coerce : % -> OutputForm collect : (%,V) -> % --R collectQuasiMonic : % -> % collectUnder : (%,V) -> % ---R collectUpper : (%,V) -> % construct : List P -> % +--R collectUpper : (%,V) -> % construct : List(P) -> % --R copy : % -> % degree : % -> NonNegativeInteger --R empty : () -> % empty? : % -> Boolean --R eq? : (%,%) -> Boolean extend : (%,P) -> % @@ -51372,29 +51509,29 @@ GeneralSparseTable(Key, Entry, Tbl, dent): TableAggregate(Key, Entry) == Impl --R headReduce : (P,%) -> P headReduced? : % -> Boolean --R headReduced? : (P,%) -> Boolean infRittWu? : (%,%) -> Boolean --R initiallyReduce : (P,%) -> P initiallyReduced? : % -> Boolean ---R initials : % -> List P last : % -> Union(P,"failed") +--R initials : % -> List(P) last : % -> Union(P,"failed") --R latex : % -> String mainVariable? : (V,%) -> Boolean ---R mainVariables : % -> List V map : ((P -> P),%) -> % +--R mainVariables : % -> List(V) map : ((P -> P),%) -> % --R mvar : % -> V normalized? : % -> Boolean --R normalized? : (P,%) -> Boolean reduceByQuasiMonic : (P,%) -> P --R removeZero : (P,%) -> P rest : % -> Union(%,"failed") ---R retract : List P -> % sample : () -> % +--R retract : List(P) -> % sample : () -> % --R stronglyReduce : (P,%) -> P stronglyReduced? : % -> Boolean ---R trivialIdeal? : % -> Boolean variables : % -> List V ---R zeroSetSplit : List P -> List % ?~=? : (%,%) -> Boolean +--R trivialIdeal? : % -> Boolean variables : % -> List(V) +--R zeroSetSplit : List(P) -> List(%) ?~=? : (%,%) -> Boolean --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R any? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate ---R autoReduced? : (%,((P,List P) -> Boolean)) -> Boolean ---R basicSet : (List P,(P -> Boolean),((P,P) -> Boolean)) -> Union(Record(bas: %,top: List P),"failed") ---R basicSet : (List P,((P,P) -> Boolean)) -> Union(Record(bas: %,top: List P),"failed") +--R autoReduced? : (%,((P,List(P)) -> Boolean)) -> Boolean +--R basicSet : (List(P),(P -> Boolean),((P,P) -> Boolean)) -> Union(Record(bas: %,top: List(P)),"failed") +--R basicSet : (List(P),((P,P) -> Boolean)) -> Union(Record(bas: %,top: List(P)),"failed") --R coHeight : % -> NonNegativeInteger if V has FINITE ---R convert : % -> InputForm if P has KONVERT INFORM +--R convert : % -> InputForm if P has KONVERT(INFORM) --R count : ((P -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate --R count : (P,%) -> NonNegativeInteger if $ has finiteAggregate and P has SETCAT ---R eval : (%,List Equation P) -> % if P has EVALAB P and P has SETCAT ---R eval : (%,Equation P) -> % if P has EVALAB P and P has SETCAT ---R eval : (%,P,P) -> % if P has EVALAB P and P has SETCAT ---R eval : (%,List P,List P) -> % if P has EVALAB P and P has SETCAT +--R eval : (%,List(Equation(P))) -> % if P has EVALAB(P) and P has SETCAT +--R eval : (%,Equation(P)) -> % if P has EVALAB(P) and P has SETCAT +--R eval : (%,P,P) -> % if P has EVALAB(P) and P has SETCAT +--R eval : (%,List(P),List(P)) -> % if P has EVALAB(P) and P has SETCAT --R every? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate --R extendIfCan : (%,P) -> Union(%,"failed") --R find : ((P -> Boolean),%) -> Union(P,"failed") @@ -51403,10 +51540,10 @@ GeneralSparseTable(Key, Entry, Tbl, dent): TableAggregate(Key, Entry) == Impl --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((P -> P),%) -> % if $ has shallowlyMutable --R member? : (P,%) -> Boolean if $ has finiteAggregate and P has SETCAT ---R members : % -> List P if $ has finiteAggregate +--R members : % -> List(P) if $ has finiteAggregate --R more? : (%,NonNegativeInteger) -> Boolean ---R parts : % -> List P if $ has finiteAggregate ---R quasiComponent : % -> Record(close: List P,open: List P) +--R parts : % -> List(P) if $ has finiteAggregate +--R quasiComponent : % -> Record(close: List(P),open: List(P)) --R reduce : (P,%,((P,P) -> P),((P,P) -> Boolean)) -> P --R reduce : (((P,P) -> P),%) -> P if $ has finiteAggregate --R reduce : (((P,P) -> P),%,P) -> P if $ has finiteAggregate @@ -51416,10 +51553,10 @@ GeneralSparseTable(Key, Entry, Tbl, dent): TableAggregate(Key, Entry) == Impl --R remove : ((P -> Boolean),%) -> % if $ has finiteAggregate --R remove : (P,%) -> % if $ has finiteAggregate and P has SETCAT --R removeDuplicates : % -> % if $ has finiteAggregate and P has SETCAT ---R retractIfCan : List P -> Union(%,"failed") ---R rewriteIdealWithHeadRemainder : (List P,%) -> List P if R has INTDOM ---R rewriteIdealWithRemainder : (List P,%) -> List P if R has INTDOM ---R rewriteSetWithReduction : (List P,%,((P,P) -> P),((P,P) -> Boolean)) -> List P +--R retractIfCan : List(P) -> Union(%,"failed") +--R rewriteIdealWithHeadRemainder : (List(P),%) -> List(P) if R has INTDOM +--R rewriteIdealWithRemainder : (List(P),%) -> List(P) if R has INTDOM +--R rewriteSetWithReduction : (List(P),%,((P,P) -> P),((P,P) -> Boolean)) -> List(P) --R roughBase? : % -> Boolean if R has INTDOM --R roughEqualIdeals? : (%,%) -> Boolean if R has INTDOM --R roughSubIdeal? : (%,%) -> Boolean if R has INTDOM @@ -51430,7 +51567,7 @@ GeneralSparseTable(Key, Entry, Tbl, dent): TableAggregate(Key, Entry) == Impl --R sort : (%,V) -> Record(under: %,floor: %,upper: %) --R stronglyReduced? : (P,%) -> Boolean --R triangular? : % -> Boolean if R has INTDOM ---R zeroSetSplitIntoTriangularSystems : List P -> List Record(close: %,open: List P) +--R zeroSetSplitIntoTriangularSystems : List(P) -> List(Record(close: %,open: List(P))) --R --E 1 @@ -51663,6 +51800,7 @@ GeneralTriangularSet(R,E,V,P) : Exports == Implementation where --S 1 of 1 )show GeneralUnivariatePowerSeries +--R --R GeneralUnivariatePowerSeries(Coef: Ring,var: Symbol,cen: Coef) is a domain constructor --R Abbreviation for GeneralUnivariatePowerSeries is GSERIES --R This constructor is exposed in this frame. @@ -51676,121 +51814,121 @@ GeneralTriangularSet(R,E,V,P) : Exports == Implementation where --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % --R ?^? : (%,PositiveInteger) -> % center : % -> Coef ---R coerce : Variable var -> % coerce : Integer -> % +--R coerce : Variable(var) -> % coerce : Integer -> % --R coerce : % -> OutputForm complete : % -> % ---R degree : % -> Fraction Integer hash : % -> SingleInteger +--R degree : % -> Fraction(Integer) hash : % -> SingleInteger --R latex : % -> String leadingCoefficient : % -> Coef --R leadingMonomial : % -> % map : ((Coef -> Coef),%) -> % --R monomial? : % -> Boolean one? : % -> Boolean ---R order : % -> Fraction Integer pole? : % -> Boolean +--R order : % -> Fraction(Integer) pole? : % -> Boolean --R recip : % -> Union(%,"failed") reductum : % -> % --R sample : () -> % variable : % -> Symbol --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT ---R ?*? : (Fraction Integer,%) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) +--R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?*? : (NonNegativeInteger,%) -> % ---R ?**? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT ---R ?**? : (%,%) -> % if Coef has ALGEBRA FRAC INT +--R ?**? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) +--R ?**? : (%,%) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?**? : (%,Integer) -> % if Coef has FIELD --R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,%) -> % if Coef has FIELD --R ?/? : (%,Coef) -> % if Coef has FIELD ---R D : % -> % if Coef has *: (Fraction Integer,Coef) -> Coef ---R D : (%,NonNegativeInteger) -> % if Coef has *: (Fraction Integer,Coef) -> Coef ---R D : (%,Symbol) -> % if Coef has *: (Fraction Integer,Coef) -> Coef and Coef has PDRING SYMBOL ---R D : (%,List Symbol) -> % if Coef has *: (Fraction Integer,Coef) -> Coef and Coef has PDRING SYMBOL ---R D : (%,Symbol,NonNegativeInteger) -> % if Coef has *: (Fraction Integer,Coef) -> Coef and Coef has PDRING SYMBOL ---R D : (%,List Symbol,List NonNegativeInteger) -> % if Coef has *: (Fraction Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R D : % -> % if Coef has *: (Fraction(Integer),Coef) -> Coef +--R D : (%,NonNegativeInteger) -> % if Coef has *: (Fraction(Integer),Coef) -> Coef +--R D : (%,Symbol) -> % if Coef has *: (Fraction(Integer),Coef) -> Coef and Coef has PDRING(SYMBOL) +--R D : (%,List(Symbol)) -> % if Coef has *: (Fraction(Integer),Coef) -> Coef and Coef has PDRING(SYMBOL) +--R D : (%,Symbol,NonNegativeInteger) -> % if Coef has *: (Fraction(Integer),Coef) -> Coef and Coef has PDRING(SYMBOL) +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has *: (Fraction(Integer),Coef) -> Coef and Coef has PDRING(SYMBOL) --R ?^? : (%,Integer) -> % if Coef has FIELD --R ?^? : (%,NonNegativeInteger) -> % ---R acos : % -> % if Coef has ALGEBRA FRAC INT ---R acosh : % -> % if Coef has ALGEBRA FRAC INT ---R acot : % -> % if Coef has ALGEBRA FRAC INT ---R acoth : % -> % if Coef has ALGEBRA FRAC INT ---R acsc : % -> % if Coef has ALGEBRA FRAC INT ---R acsch : % -> % if Coef has ALGEBRA FRAC INT ---R approximate : (%,Fraction Integer) -> Coef if Coef has **: (Coef,Fraction Integer) -> Coef and Coef has coerce: Symbol -> Coef ---R asec : % -> % if Coef has ALGEBRA FRAC INT ---R asech : % -> % if Coef has ALGEBRA FRAC INT ---R asin : % -> % if Coef has ALGEBRA FRAC INT ---R asinh : % -> % if Coef has ALGEBRA FRAC INT +--R acos : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R acosh : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R acot : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R acoth : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R acsc : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R acsch : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R approximate : (%,Fraction(Integer)) -> Coef if Coef has **: (Coef,Fraction(Integer)) -> Coef and Coef has coerce: Symbol -> Coef +--R asec : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R asech : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R asin : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R asinh : % -> % if Coef has ALGEBRA(FRAC(INT)) --R associates? : (%,%) -> Boolean if Coef has INTDOM ---R atan : % -> % if Coef has ALGEBRA FRAC INT ---R atanh : % -> % if Coef has ALGEBRA FRAC INT +--R atan : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R atanh : % -> % if Coef has ALGEBRA(FRAC(INT)) --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ ---R coefficient : (%,Fraction Integer) -> Coef +--R coefficient : (%,Fraction(Integer)) -> Coef --R coerce : % -> % if Coef has INTDOM ---R coerce : Fraction Integer -> % if Coef has ALGEBRA FRAC INT +--R coerce : Fraction(Integer) -> % if Coef has ALGEBRA(FRAC(INT)) --R coerce : UnivariatePuiseuxSeries(Coef,var,cen) -> % --R coerce : Coef -> % if Coef has COMRING ---R cos : % -> % if Coef has ALGEBRA FRAC INT ---R cosh : % -> % if Coef has ALGEBRA FRAC INT ---R cot : % -> % if Coef has ALGEBRA FRAC INT ---R coth : % -> % if Coef has ALGEBRA FRAC INT ---R csc : % -> % if Coef has ALGEBRA FRAC INT ---R csch : % -> % if Coef has ALGEBRA FRAC INT ---R differentiate : (%,Variable var) -> % ---R differentiate : % -> % if Coef has *: (Fraction Integer,Coef) -> Coef ---R differentiate : (%,NonNegativeInteger) -> % if Coef has *: (Fraction Integer,Coef) -> Coef ---R differentiate : (%,Symbol) -> % if Coef has *: (Fraction Integer,Coef) -> Coef and Coef has PDRING SYMBOL ---R differentiate : (%,List Symbol) -> % if Coef has *: (Fraction Integer,Coef) -> Coef and Coef has PDRING SYMBOL ---R differentiate : (%,Symbol,NonNegativeInteger) -> % if Coef has *: (Fraction Integer,Coef) -> Coef and Coef has PDRING SYMBOL ---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if Coef has *: (Fraction Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R cos : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R cosh : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R cot : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R coth : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R csc : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R csch : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R differentiate : (%,Variable(var)) -> % +--R differentiate : % -> % if Coef has *: (Fraction(Integer),Coef) -> Coef +--R differentiate : (%,NonNegativeInteger) -> % if Coef has *: (Fraction(Integer),Coef) -> Coef +--R differentiate : (%,Symbol) -> % if Coef has *: (Fraction(Integer),Coef) -> Coef and Coef has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol)) -> % if Coef has *: (Fraction(Integer),Coef) -> Coef and Coef has PDRING(SYMBOL) +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if Coef has *: (Fraction(Integer),Coef) -> Coef and Coef has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has *: (Fraction(Integer),Coef) -> Coef and Coef has PDRING(SYMBOL) --R divide : (%,%) -> Record(quotient: %,remainder: %) if Coef has FIELD ---R ?.? : (%,%) -> % if Fraction Integer has SGROUP ---R ?.? : (%,Fraction Integer) -> Coef +--R ?.? : (%,%) -> % if Fraction(Integer) has SGROUP +--R ?.? : (%,Fraction(Integer)) -> Coef --R euclideanSize : % -> NonNegativeInteger if Coef has FIELD ---R eval : (%,Coef) -> Stream Coef if Coef has **: (Coef,Fraction Integer) -> Coef ---R exp : % -> % if Coef has ALGEBRA FRAC INT ---R expressIdealMember : (List %,%) -> Union(List %,"failed") if Coef has FIELD +--R eval : (%,Coef) -> Stream(Coef) if Coef has **: (Coef,Fraction(Integer)) -> Coef +--R exp : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if Coef has FIELD --R exquo : (%,%) -> Union(%,"failed") if Coef has INTDOM ---R extend : (%,Fraction Integer) -> % +--R extend : (%,Fraction(Integer)) -> % --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if Coef has FIELD --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if Coef has FIELD ---R factor : % -> Factored % if Coef has FIELD +--R factor : % -> Factored(%) if Coef has FIELD --R gcd : (%,%) -> % if Coef has FIELD ---R gcd : List % -> % if Coef has FIELD ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if Coef has FIELD ---R integrate : (%,Variable var) -> % if Coef has ALGEBRA FRAC INT ---R integrate : (%,Symbol) -> % if Coef has integrate: (Coef,Symbol) -> Coef and Coef has variables: Coef -> List Symbol and Coef has ALGEBRA FRAC INT or Coef has ACFS INT and Coef has ALGEBRA FRAC INT and Coef has PRIMCAT and Coef has TRANFUN ---R integrate : % -> % if Coef has ALGEBRA FRAC INT +--R gcd : List(%) -> % if Coef has FIELD +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if Coef has FIELD +--R integrate : (%,Variable(var)) -> % if Coef has ALGEBRA(FRAC(INT)) +--R integrate : (%,Symbol) -> % if Coef has integrate: (Coef,Symbol) -> Coef and Coef has variables: Coef -> List(Symbol) and Coef has ALGEBRA(FRAC(INT)) or Coef has ACFS(INT) and Coef has ALGEBRA(FRAC(INT)) and Coef has PRIMCAT and Coef has TRANFUN +--R integrate : % -> % if Coef has ALGEBRA(FRAC(INT)) --R inv : % -> % if Coef has FIELD --R lcm : (%,%) -> % if Coef has FIELD ---R lcm : List % -> % if Coef has FIELD ---R log : % -> % if Coef has ALGEBRA FRAC INT ---R monomial : (%,List SingletonAsOrderedSet,List Fraction Integer) -> % ---R monomial : (%,SingletonAsOrderedSet,Fraction Integer) -> % ---R monomial : (Coef,Fraction Integer) -> % ---R multiEuclidean : (List %,%) -> Union(List %,"failed") if Coef has FIELD ---R multiplyExponents : (%,Fraction Integer) -> % +--R lcm : List(%) -> % if Coef has FIELD +--R log : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R monomial : (%,List(SingletonAsOrderedSet),List(Fraction(Integer))) -> % +--R monomial : (%,SingletonAsOrderedSet,Fraction(Integer)) -> % +--R monomial : (Coef,Fraction(Integer)) -> % +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") if Coef has FIELD +--R multiplyExponents : (%,Fraction(Integer)) -> % --R multiplyExponents : (%,PositiveInteger) -> % ---R nthRoot : (%,Integer) -> % if Coef has ALGEBRA FRAC INT ---R order : (%,Fraction Integer) -> Fraction Integer ---R pi : () -> % if Coef has ALGEBRA FRAC INT +--R nthRoot : (%,Integer) -> % if Coef has ALGEBRA(FRAC(INT)) +--R order : (%,Fraction(Integer)) -> Fraction(Integer) +--R pi : () -> % if Coef has ALGEBRA(FRAC(INT)) --R prime? : % -> Boolean if Coef has FIELD ---R principalIdeal : List % -> Record(coef: List %,generator: %) if Coef has FIELD +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if Coef has FIELD --R ?quo? : (%,%) -> % if Coef has FIELD --R ?rem? : (%,%) -> % if Coef has FIELD ---R sec : % -> % if Coef has ALGEBRA FRAC INT ---R sech : % -> % if Coef has ALGEBRA FRAC INT ---R series : (NonNegativeInteger,Stream Record(k: Fraction Integer,c: Coef)) -> % ---R sin : % -> % if Coef has ALGEBRA FRAC INT ---R sinh : % -> % if Coef has ALGEBRA FRAC INT +--R sec : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R sech : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R series : (NonNegativeInteger,Stream(Record(k: Fraction(Integer),c: Coef))) -> % +--R sin : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R sinh : % -> % if Coef has ALGEBRA(FRAC(INT)) --R sizeLess? : (%,%) -> Boolean if Coef has FIELD ---R sqrt : % -> % if Coef has ALGEBRA FRAC INT ---R squareFree : % -> Factored % if Coef has FIELD +--R sqrt : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R squareFree : % -> Factored(%) if Coef has FIELD --R squareFreePart : % -> % if Coef has FIELD --R subtractIfCan : (%,%) -> Union(%,"failed") ---R tan : % -> % if Coef has ALGEBRA FRAC INT ---R tanh : % -> % if Coef has ALGEBRA FRAC INT ---R terms : % -> Stream Record(k: Fraction Integer,c: Coef) ---R truncate : (%,Fraction Integer,Fraction Integer) -> % ---R truncate : (%,Fraction Integer) -> % +--R tan : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R tanh : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R terms : % -> Stream(Record(k: Fraction(Integer),c: Coef)) +--R truncate : (%,Fraction(Integer),Fraction(Integer)) -> % +--R truncate : (%,Fraction(Integer)) -> % --R unit? : % -> Boolean if Coef has INTDOM --R unitCanonical : % -> % if Coef has INTDOM --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Coef has INTDOM ---R variables : % -> List SingletonAsOrderedSet +--R variables : % -> List(SingletonAsOrderedSet) --R --E 1 @@ -52041,6 +52179,7 @@ GeneralUnivariatePowerSeries(Coef,var,cen): Exports == Implementation where --S 1 of 1 )show GraphImage +--R --R GraphImage is a domain constructor --R Abbreviation for GraphImage is GRIMAGE --R This constructor is not exposed in this frame. @@ -52050,22 +52189,23 @@ GeneralUnivariatePowerSeries(Coef,var,cen): Exports == Implementation where --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R graphImage : () -> % hash : % -> SingleInteger --R key : % -> Integer latex : % -> String ---R makeGraphImage : % -> % ranges : % -> List Segment Float ---R units : % -> List Float ?~=? : (%,%) -> Boolean ---R appendPoint : (%,Point DoubleFloat) -> Void ---R coerce : List List Point DoubleFloat -> % ---R component : (%,Point DoubleFloat,Palette,Palette,PositiveInteger) -> Void ---R component : (%,Point DoubleFloat) -> Void ---R component : (%,List Point DoubleFloat,Palette,Palette,PositiveInteger) -> Void ---R figureUnits : List List Point DoubleFloat -> List DoubleFloat ---R makeGraphImage : (List List Point DoubleFloat,List Palette,List Palette,List PositiveInteger,List DrawOption) -> % ---R makeGraphImage : (List List Point DoubleFloat,List Palette,List Palette,List PositiveInteger) -> % ---R makeGraphImage : List List Point DoubleFloat -> % ---R point : (%,Point DoubleFloat,Palette) -> Void ---R pointLists : % -> List List Point DoubleFloat ---R putColorInfo : (List List Point DoubleFloat,List Palette) -> List List Point DoubleFloat ---R ranges : (%,List Segment Float) -> List Segment Float ---R units : (%,List Float) -> List Float +--R makeGraphImage : % -> % units : % -> List(Float) +--R ?~=? : (%,%) -> Boolean +--R appendPoint : (%,Point(DoubleFloat)) -> Void +--R coerce : List(List(Point(DoubleFloat))) -> % +--R component : (%,Point(DoubleFloat),Palette,Palette,PositiveInteger) -> Void +--R component : (%,Point(DoubleFloat)) -> Void +--R component : (%,List(Point(DoubleFloat)),Palette,Palette,PositiveInteger) -> Void +--R figureUnits : List(List(Point(DoubleFloat))) -> List(DoubleFloat) +--R makeGraphImage : (List(List(Point(DoubleFloat))),List(Palette),List(Palette),List(PositiveInteger),List(DrawOption)) -> % +--R makeGraphImage : (List(List(Point(DoubleFloat))),List(Palette),List(Palette),List(PositiveInteger)) -> % +--R makeGraphImage : List(List(Point(DoubleFloat))) -> % +--R point : (%,Point(DoubleFloat),Palette) -> Void +--R pointLists : % -> List(List(Point(DoubleFloat))) +--R putColorInfo : (List(List(Point(DoubleFloat))),List(Palette)) -> List(List(Point(DoubleFloat))) +--R ranges : (%,List(Segment(Float))) -> List(Segment(Float)) +--R ranges : % -> List(Segment(Float)) +--R units : (%,List(Float)) -> List(Float) --R --E 1 @@ -52532,6 +52672,7 @@ GraphImage (): Exports == Implementation where --S 1 of 1 )show GuessOption +--R --R GuessOption is a domain constructor --R Abbreviation for GuessOption is GOPT --R This constructor is exposed in this frame. @@ -52541,7 +52682,7 @@ GraphImage (): Exports == Implementation where --R ?=? : (%,%) -> Boolean allDegrees : Boolean -> % --R checkExtraValues : Boolean -> % coerce : % -> OutputForm --R debug : Boolean -> % displayKind : Symbol -> % ---R functionName : Symbol -> % functionNames : List Symbol -> % +--R functionName : Symbol -> % functionNames : List(Symbol) -> % --R hash : % -> SingleInteger indexName : Symbol -> % --R latex : % -> String one : Boolean -> % --R safety : NonNegativeInteger -> % variableName : Symbol -> % @@ -52556,7 +52697,7 @@ GraphImage (): Exports == Implementation where --R maxPower : Union(PositiveInteger,arbitrary) -> % --R maxShift : Union(NonNegativeInteger,arbitrary) -> % --R maxSubst : Union(PositiveInteger,arbitrary) -> % ---R option : (List %,Symbol) -> Union(Any,"failed") +--R option : (List(%),Symbol) -> Union(Any,"failed") --R --E 1 @@ -52792,17 +52933,20 @@ GuessOption(): Exports == Implementation where --S 1 of 1 )show GuessOptionFunctions0 +--R --R GuessOptionFunctions0 is a domain constructor --R Abbreviation for GuessOptionFunctions0 is GOPT0 --R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for GOPT0 +--R --R------------------------------- Operations -------------------------------- --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R one : List(GuessOption) -> Boolean ?~=? : (%,%) -> Boolean ---R MonteCarlo : List(GuessOption) -> Boolean --R Somos : List(GuessOption) -> Union(PositiveInteger,Boolean) --R allDegrees : List(GuessOption) -> Boolean ---R check : List(GuessOption) -> Boolean +--R check : List(GuessOption) -> Union(skip,MonteCarlo,deterministic) +--R checkExtraValues : List(GuessOption) -> Boolean --R checkOptions : List(GuessOption) -> Void --R debug : List(GuessOption) -> Boolean --R displayAsGF : List(GuessOption) -> Boolean @@ -53151,6 +53295,7 @@ GuessOptionFunctions0(): Exports == Implementation where --S 1 of 1 )show HashTable +--R --R HashTable(Key: SetCategory,Entry: SetCategory,hashfn: String) is a domain constructor --R Abbreviation for HashTable is HASHTBL --R This constructor is not exposed in this frame. @@ -53160,9 +53305,9 @@ GuessOptionFunctions0(): Exports == Implementation where --R copy : % -> % dictionary : () -> % --R elt : (%,Key,Entry) -> Entry ?.? : (%,Key) -> Entry --R empty : () -> % empty? : % -> Boolean ---R entries : % -> List Entry eq? : (%,%) -> Boolean ---R index? : (Key,%) -> Boolean indices : % -> List Key ---R key? : (Key,%) -> Boolean keys : % -> List Key +--R entries : % -> List(Entry) eq? : (%,%) -> Boolean +--R index? : (Key,%) -> Boolean indices : % -> List(Key) +--R key? : (Key,%) -> Boolean keys : % -> List(Key) --R map : ((Entry -> Entry),%) -> % qelt : (%,Key) -> Entry --R sample : () -> % setelt : (%,Key,Entry) -> Entry --R table : () -> % @@ -53170,24 +53315,24 @@ GuessOptionFunctions0(): Exports == Implementation where --R ?=? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT --R any? : ((Entry -> Boolean),%) -> Boolean if $ has finiteAggregate --R any? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate ---R bag : List Record(key: Key,entry: Entry) -> % +--R bag : List(Record(key: Key,entry: Entry)) -> % --R coerce : % -> OutputForm if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT ---R construct : List Record(key: Key,entry: Entry) -> % ---R convert : % -> InputForm if Record(key: Key,entry: Entry) has KONVERT INFORM +--R construct : List(Record(key: Key,entry: Entry)) -> % +--R convert : % -> InputForm if Record(key: Key,entry: Entry) has KONVERT(INFORM) --R count : ((Entry -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate --R count : (Entry,%) -> NonNegativeInteger if $ has finiteAggregate and Entry has SETCAT --R count : (Record(key: Key,entry: Entry),%) -> NonNegativeInteger if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT --R count : ((Record(key: Key,entry: Entry) -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate ---R dictionary : List Record(key: Key,entry: Entry) -> % +--R dictionary : List(Record(key: Key,entry: Entry)) -> % --R entry? : (Entry,%) -> Boolean if $ has finiteAggregate and Entry has SETCAT ---R eval : (%,List Equation Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT ---R eval : (%,Equation Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT ---R eval : (%,Entry,Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT ---R eval : (%,List Entry,List Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT ---R eval : (%,List Record(key: Key,entry: Entry),List Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT ---R eval : (%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT ---R eval : (%,Equation Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT ---R eval : (%,List Equation Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,List(Equation(Entry))) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R eval : (%,Equation(Entry)) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R eval : (%,Entry,Entry) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R eval : (%,List(Entry),List(Entry)) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R eval : (%,List(Record(key: Key,entry: Entry)),List(Record(key: Key,entry: Entry))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,Equation(Record(key: Key,entry: Entry))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,List(Equation(Record(key: Key,entry: Entry)))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT --R every? : ((Entry -> Boolean),%) -> Boolean if $ has finiteAggregate --R every? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate --R extract! : % -> Record(key: Key,entry: Entry) @@ -53206,12 +53351,12 @@ GuessOptionFunctions0(): Exports == Implementation where --R maxIndex : % -> Key if Key has ORDSET --R member? : (Entry,%) -> Boolean if $ has finiteAggregate and Entry has SETCAT --R member? : (Record(key: Key,entry: Entry),%) -> Boolean if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT ---R members : % -> List Entry if $ has finiteAggregate ---R members : % -> List Record(key: Key,entry: Entry) if $ has finiteAggregate +--R members : % -> List(Entry) if $ has finiteAggregate +--R members : % -> List(Record(key: Key,entry: Entry)) if $ has finiteAggregate --R minIndex : % -> Key if Key has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean ---R parts : % -> List Entry if $ has finiteAggregate ---R parts : % -> List Record(key: Key,entry: Entry) if $ has finiteAggregate +--R parts : % -> List(Entry) if $ has finiteAggregate +--R parts : % -> List(Record(key: Key,entry: Entry)) if $ has finiteAggregate --R qsetelt! : (%,Key,Entry) -> Entry if $ has shallowlyMutable --R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%) -> Record(key: Key,entry: Entry) if $ has finiteAggregate --R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has finiteAggregate @@ -53227,7 +53372,7 @@ GuessOptionFunctions0(): Exports == Implementation where --R select! : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate --R size? : (%,NonNegativeInteger) -> Boolean --R swap! : (%,Key,Key) -> Void if $ has shallowlyMutable ---R table : List Record(key: Key,entry: Entry) -> % +--R table : List(Record(key: Key,entry: Entry)) -> % --R ?~=? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT --R --E 1 @@ -53386,7 +53531,7 @@ a:Heap INT:= heap [1,2,3,4,5] --R --R --R (1) [5,4,2,1,3] ---R Type: Heap Integer +--R Type: Heap(Integer) --E 1 --S 2 of 42 @@ -53394,7 +53539,7 @@ bag([1,2,3,4,5])$Heap(INT) --R --R --R (2) [5,4,3,1,2] ---R Type: Heap Integer +--R Type: Heap(Integer) --E 2 --S 3 of 42 @@ -53402,7 +53547,7 @@ c:=copy a --R --R --R (3) [5,4,2,1,3] ---R Type: Heap Integer +--R Type: Heap(Integer) --E 3 --S 4 of 42 @@ -53418,7 +53563,7 @@ b:=empty()$(Heap INT) --R --R --R (5) [] ---R Type: Heap Integer +--R Type: Heap(Integer) --E 5 --S 6 of 42 @@ -53450,7 +53595,7 @@ h:=heap [17,-4,9,-11,2,7,-7] --R --R --R (9) [17,2,9,- 11,- 4,7,- 7] ---R Type: Heap Integer +--R Type: Heap(Integer) --E 8 --S 9 of 42 @@ -53458,7 +53603,7 @@ h:=heap [17,-4,9,-11,2,7,-7] --R --R --R (10) [17,9,7,2,- 4,- 7,- 11] ---R Type: List Integer +--R Type: List(Integer) --E 9 --S 10 of 42 @@ -53470,7 +53615,7 @@ heapsort(x) == (empty? x => []; cons(extract!(x),heapsort x)) --S 11 of 42 h1 := heapsort heap [17,-4,9,-11,2,7,-7] --R ---R Compiling function heapsort with type Heap Integer -> List Integer +--R Compiling function heapsort with type Heap(Integer) -> List(Integer) --R --R (12) [17,9,7,2,- 4,- 7,- 11] --R Type: List Integer @@ -53497,7 +53642,7 @@ a --R --R --R (15) [4,3,2,1] ---R Type: Heap Integer +--R Type: Heap(Integer) --E 14 --S 15 of 42 @@ -53513,7 +53658,7 @@ insert!(9,a) --R --R --R (17) [9,4,2,1,3] ---R Type: Heap Integer +--R Type: Heap(Integer) --E 16 --S 17 of 42 @@ -53521,7 +53666,7 @@ map(x+->x+10,a) --R --R --R (18) [19,14,12,11,13] ---R Type: Heap Integer +--R Type: Heap(Integer) --E 17 --S 18 of 42 @@ -53529,7 +53674,7 @@ a --R --R --R (19) [9,4,2,1,3] ---R Type: Heap Integer +--R Type: Heap(Integer) --E 18 --S 19 of 42 @@ -53537,7 +53682,7 @@ map!(x+->x+10,a) --R --R --R (20) [19,14,12,11,13] ---R Type: Heap Integer +--R Type: Heap(Integer) --E 19 --S 20 of 42 @@ -53545,7 +53690,7 @@ a --R --R --R (21) [19,14,12,11,13] ---R Type: Heap Integer +--R Type: Heap(Integer) --E 20 --S 21 of 42 @@ -53561,7 +53706,7 @@ merge(a,c) --R --R --R (23) [19,14,12,11,13,5,4,2,1,3] ---R Type: Heap Integer +--R Type: Heap(Integer) --E 22 --S 23 of 42 @@ -53569,7 +53714,7 @@ a --R --R --R (24) [19,14,12,11,13] ---R Type: Heap Integer +--R Type: Heap(Integer) --E 23 --S 24 of 42 @@ -53577,7 +53722,7 @@ merge!(a,c) --R --R --R (25) [19,14,12,11,13,5,4,2,1,3] ---R Type: Heap Integer +--R Type: Heap(Integer) --E 24 --S 25 of 42 @@ -53585,7 +53730,7 @@ a --R --R --R (26) [19,14,12,11,13,5,4,2,1,3] ---R Type: Heap Integer +--R Type: Heap(Integer) --E 25 --S 26 of 42 @@ -53593,7 +53738,7 @@ c --R --R --R (27) [5,4,2,1,3] ---R Type: Heap Integer +--R Type: Heap(Integer) --E 26 --S 27 of 42 @@ -53601,7 +53746,7 @@ sample()$Heap(INT) --R --R --R (28) [] ---R Type: Heap Integer +--R Type: Heap(Integer) --E 27 --S 28 of 42 @@ -53633,7 +53778,7 @@ parts a --R --R --R (32) [19,14,12,11,13,5,4,2,1,3] ---R Type: List Integer +--R Type: List(Integer) --E 31 --S 32 of 42 @@ -53665,7 +53810,7 @@ members a --R --R --R (36) [19,14,12,11,13,5,4,2,1,3] ---R Type: List Integer +--R Type: List(Integer) --E 35 --S 36 of 42 @@ -53719,16 +53864,16 @@ coerce a --S 42 of 42 )show Heap --R ---R Heap S: OrderedSet is a domain constructor +--R Heap(S: OrderedSet) is a domain constructor --R Abbreviation for Heap is HEAP --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for HEAP --R --R------------------------------- Operations -------------------------------- ---R bag : List S -> % copy : % -> % +--R bag : List(S) -> % copy : % -> % --R empty : () -> % empty? : % -> Boolean --R eq? : (%,%) -> Boolean extract! : % -> S ---R heap : List S -> % insert! : (S,%) -> % +--R heap : List(S) -> % insert! : (S,%) -> % --R inspect : % -> S map : ((S -> S),%) -> % --R max : % -> S merge : (%,%) -> % --R merge! : (%,%) -> % sample : () -> % @@ -53738,19 +53883,19 @@ coerce a --R coerce : % -> OutputForm if S has SETCAT --R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT --R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate ---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if S has SETCAT --R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT ---R members : % -> List S if $ has finiteAggregate +--R members : % -> List(S) if $ has finiteAggregate --R more? : (%,NonNegativeInteger) -> Boolean ---R parts : % -> List S if $ has finiteAggregate +--R parts : % -> List(S) if $ has finiteAggregate --R size? : (%,NonNegativeInteger) -> Boolean --R ?~=? : (%,%) -> Boolean if S has SETCAT --R @@ -54279,7 +54424,7 @@ r + hex(6/7) --R [0.00BB3EE721A54D88, 0.00BAB6561, 0.00BA2E8, 0.00B9A7862A0FF465879D5F, --R _____________________________ --R 0.00B92143FA36F5E02E4850FE8DBD78] ---R Type: List HexadecimalExpansion +--R Type: List(HexadecimalExpansion) --E 3 --S 4 of 7 @@ -54300,7 +54445,7 @@ p := hex(1/4)*x**2 + hex(2/3)*x + hex(4/9) --R --R 2 _ ___ --R (5) 0.4x + 0.Ax + 0.71C ---R Type: Polynomial HexadecimalExpansion +--R Type: Polynomial(HexadecimalExpansion) --E 5 --S 6 of 7 @@ -54309,7 +54454,7 @@ q := D(p, x) --R --R _ --R (6) 0.8x + 0.A ---R Type: Polynomial HexadecimalExpansion +--R Type: Polynomial(HexadecimalExpansion) --E 6 --S 7 of 7 @@ -54318,7 +54463,7 @@ g := gcd(p, q) --R --R _ --R (7) x + 1.5 ---R Type: Polynomial HexadecimalExpansion +--R Type: Polynomial(HexadecimalExpansion) --E 7 )spool )lisp (bye) @@ -55748,6 +55893,7 @@ HTMLFormat(): public == private where --S 1 of 1 )show HomogeneousDirectProduct +--R --R HomogeneousDirectProduct(dim: NonNegativeInteger,S: OrderedAbelianMonoidSup) is a domain constructor --R Abbreviation for HomogeneousDirectProduct is HDP --R This constructor is not exposed in this frame. @@ -55755,12 +55901,12 @@ HTMLFormat(): public == private where --R --R------------------------------- Operations -------------------------------- --R -? : % -> % if S has RING 1 : () -> % if S has MONOID ---R 0 : () -> % if S has CABMON coerce : % -> Vector S ---R copy : % -> % directProduct : Vector S -> % +--R 0 : () -> % if S has CABMON coerce : % -> Vector(S) +--R copy : % -> % directProduct : Vector(S) -> % --R ?.? : (%,Integer) -> S elt : (%,Integer,S) -> S --R empty : () -> % empty? : % -> Boolean ---R entries : % -> List S eq? : (%,%) -> Boolean ---R index? : (Integer,%) -> Boolean indices : % -> List Integer +--R entries : % -> List(S) eq? : (%,%) -> Boolean +--R index? : (Integer,%) -> Boolean indices : % -> List(Integer) --R map : ((S -> S),%) -> % qelt : (%,Integer) -> S --R sample : () -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate @@ -55782,10 +55928,10 @@ HTMLFormat(): public == private where --R ?>=? : (%,%) -> Boolean if S has OAMONS or S has ORDRING --R D : (%,(S -> S)) -> % if S has RING --R D : (%,(S -> S),NonNegativeInteger) -> % if S has RING ---R D : (%,List Symbol,List NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING ---R D : (%,Symbol,NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING ---R D : (%,List Symbol) -> % if S has PDRING SYMBOL and S has RING ---R D : (%,Symbol) -> % if S has PDRING SYMBOL and S has RING +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if S has PDRING(SYMBOL) and S has RING +--R D : (%,Symbol,NonNegativeInteger) -> % if S has PDRING(SYMBOL) and S has RING +--R D : (%,List(Symbol)) -> % if S has PDRING(SYMBOL) and S has RING +--R D : (%,Symbol) -> % if S has PDRING(SYMBOL) and S has RING --R D : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING --R D : % -> % if S has DIFRING and S has RING --R ?^? : (%,PositiveInteger) -> % if S has MONOID @@ -55794,26 +55940,26 @@ HTMLFormat(): public == private where --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R characteristic : () -> NonNegativeInteger if S has RING --R coerce : S -> % if S has SETCAT ---R coerce : Fraction Integer -> % if S has RETRACT FRAC INT and S has SETCAT ---R coerce : Integer -> % if S has RETRACT INT and S has SETCAT or S has RING +--R coerce : Fraction(Integer) -> % if S has RETRACT(FRAC(INT)) and S has SETCAT +--R coerce : Integer -> % if S has RETRACT(INT) and S has SETCAT or S has RING --R coerce : % -> OutputForm if S has SETCAT --R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT --R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate --R differentiate : (%,(S -> S)) -> % if S has RING --R differentiate : (%,(S -> S),NonNegativeInteger) -> % if S has RING ---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING ---R differentiate : (%,Symbol,NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING ---R differentiate : (%,List Symbol) -> % if S has PDRING SYMBOL and S has RING ---R differentiate : (%,Symbol) -> % if S has PDRING SYMBOL and S has RING +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if S has PDRING(SYMBOL) and S has RING +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if S has PDRING(SYMBOL) and S has RING +--R differentiate : (%,List(Symbol)) -> % if S has PDRING(SYMBOL) and S has RING +--R differentiate : (%,Symbol) -> % if S has PDRING(SYMBOL) and S has RING --R differentiate : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING --R differentiate : % -> % if S has DIFRING and S has RING --R dimension : () -> CardinalNumber if S has FIELD --R dot : (%,%) -> S if S has RING --R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT ---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R fill! : (%,S) -> % if $ has shallowlyMutable --R first : % -> S if Integer has ORDSET @@ -55826,27 +55972,27 @@ HTMLFormat(): public == private where --R max : (%,%) -> % if S has OAMONS or S has ORDRING --R maxIndex : % -> Integer if Integer has ORDSET --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT ---R members : % -> List S if $ has finiteAggregate +--R members : % -> List(S) if $ has finiteAggregate --R min : (%,%) -> % if S has OAMONS or S has ORDRING --R minIndex : % -> Integer if Integer has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean --R negative? : % -> Boolean if S has ORDRING --R one? : % -> Boolean if S has MONOID ---R parts : % -> List S if $ has finiteAggregate +--R parts : % -> List(S) if $ has finiteAggregate --R positive? : % -> Boolean if S has ORDRING --R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable --R random : () -> % if S has FINITE --R recip : % -> Union(%,"failed") if S has MONOID ---R reducedSystem : Matrix % -> Matrix S if S has RING ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix S,vec: Vector S) if S has RING ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if S has LINEXP INT and S has RING ---R reducedSystem : Matrix % -> Matrix Integer if S has LINEXP INT and S has RING +--R reducedSystem : Matrix(%) -> Matrix(S) if S has RING +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(S),vec: Vector(S)) if S has RING +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if S has LINEXP(INT) and S has RING +--R reducedSystem : Matrix(%) -> Matrix(Integer) if S has LINEXP(INT) and S has RING --R retract : % -> S if S has SETCAT ---R retract : % -> Fraction Integer if S has RETRACT FRAC INT and S has SETCAT ---R retract : % -> Integer if S has RETRACT INT and S has SETCAT +--R retract : % -> Fraction(Integer) if S has RETRACT(FRAC(INT)) and S has SETCAT +--R retract : % -> Integer if S has RETRACT(INT) and S has SETCAT --R retractIfCan : % -> Union(S,"failed") if S has SETCAT ---R retractIfCan : % -> Union(Fraction Integer,"failed") if S has RETRACT FRAC INT and S has SETCAT ---R retractIfCan : % -> Union(Integer,"failed") if S has RETRACT INT and S has SETCAT +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if S has RETRACT(FRAC(INT)) and S has SETCAT +--R retractIfCan : % -> Union(Integer,"failed") if S has RETRACT(INT) and S has SETCAT --R setelt : (%,Integer,S) -> S if $ has shallowlyMutable --R sign : % -> Integer if S has ORDRING --R size : () -> NonNegativeInteger if S has FINITE @@ -56026,7 +56172,7 @@ d1 := -4*z + 4*y**2*x + 16*x**2 + 1 --R --R 2 2 --R (2) - 4z + 4y x + 16x + 1 ---R Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer) +--R Type: DistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 2 --S 3 of 10 @@ -56035,7 +56181,7 @@ d2 := 2*z*y**2 + 4*x + 1 --R --R 2 --R (3) 2z y + 4x + 1 ---R Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer) +--R Type: DistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 3 --S 4 of 10 @@ -56044,7 +56190,7 @@ d3 := 2*z*x**2 - 2*y**2 - x --R --R 2 2 --R (4) 2z x - 2y - x ---R Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer) +--R Type: DistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 4 --S 5 of 10 @@ -56061,7 +56207,7 @@ groebner [d1,d2,d3] --R 7 29 6 17 4 11 3 1 2 15 1 --R x + -- x - -- x - -- x + -- x + -- x + -] --R 4 16 8 32 16 4 ---R Type: List DistributedMultivariatePolynomial([z,y,x],Fraction Integer) +--R Type: List(DistributedMultivariatePolynomial([z,y,x],Fraction(Integer))) --E 5 --S 6 of 10 @@ -56076,7 +56222,7 @@ n1 := d1 --R --R 2 2 --R (7) 4y x + 16x - 4z + 1 ---R Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer) +--RType: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 7 --S 8 of 10 @@ -56085,7 +56231,7 @@ n2 := d2 --R --R 2 --R (8) 2z y + 4x + 1 ---R Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer) +--RType: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 8 --S 9 of 10 @@ -56094,7 +56240,7 @@ n3 := d3 --R --R 2 2 --R (9) 2z x - 2y - x ---R Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer) +--RType: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction(Integer)) --E 9 --S 10 of 10 @@ -56111,7 +56257,7 @@ groebner [n1,n2,n3] --R 2 2 2 1 3 --R z - 4y + 2x - - z - - x] --R 4 2 ---RType: List HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer) +--RType: List(HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction(Integer))) --E 10 )spool )lisp (bye) @@ -56368,7 +56514,8 @@ HomogeneousDistributedMultivariatePolynomial(vl,R): public == private where --S 1 of 1 )show HyperellipticFiniteDivisor ---R HyperellipticFiniteDivisor(F: Field,UP: UnivariatePolynomialCategory F,UPUP: UnivariatePolynomialCategory Fraction UP,R: FunctionFieldCategory(F,UP,UPUP)) is a domain constructor +--R +--R HyperellipticFiniteDivisor(F: Field,UP: UnivariatePolynomialCategory(F),UPUP: UnivariatePolynomialCategory(Fraction(UP)),R: FunctionFieldCategory(F,UP,UPUP)) is a domain constructor --R Abbreviation for HyperellipticFiniteDivisor is HELLFDIV --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for HELLFDIV @@ -56385,10 +56532,10 @@ HomogeneousDistributedMultivariatePolynomial(vl,R): public == private where --R sample : () -> % zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean --R ?*? : (NonNegativeInteger,%) -> % ---R decompose : % -> Record(id: FractionalIdeal(UP,Fraction UP,UPUP,R),principalPart: R) ---R divisor : FractionalIdeal(UP,Fraction UP,UPUP,R) -> % +--R decompose : % -> Record(id: FractionalIdeal(UP,Fraction(UP),UPUP,R),principalPart: R) +--R divisor : FractionalIdeal(UP,Fraction(UP),UPUP,R) -> % --R generator : % -> Union(R,"failed") ---R ideal : % -> FractionalIdeal(UP,Fraction UP,UPUP,R) +--R ideal : % -> FractionalIdeal(UP,Fraction(UP),UPUP,R) --R subtractIfCan : (%,%) -> Union(%,"failed") --R --E 1 @@ -56897,7 +57044,7 @@ a:IBITS(32):=new(32,false) --R --R --R (1) "00000000000000000000000000000000" ---R Type: IndexedBits 32 +--R Type: IndexedBits(32) --E 1 --S 2 of 13 @@ -56905,7 +57052,7 @@ b:IBITS(32):=new(32,true) --R --R --R (2) "11111111111111111111111111111111" ---R Type: IndexedBits 32 +--R Type: IndexedBits(32) --E 2 --S 3 of 13 @@ -56929,7 +57076,7 @@ a --R --R --R (5) "00000000000000000000000000000100" ---R Type: IndexedBits 32 +--R Type: IndexedBits(32) --E 5 --S 6 of 13 @@ -56969,7 +57116,7 @@ Or(a,b) --R --R --R (10) "11111111111111111111111111111111" ---R Type: IndexedBits 32 +--R Type: IndexedBits(32) --E 10 --S 11 of 13 @@ -56977,7 +57124,7 @@ And(a,b) --R --R --R (11) "00000000000000000000000000000100" ---R Type: IndexedBits 32 +--R Type: IndexedBits(32) --E 11 --S 12 of 13 @@ -56985,7 +57132,7 @@ Not(a) --R --R --R (12) "11111111111111111111111111111011" ---R Type: IndexedBits 32 +--R Type: IndexedBits(32) --E 12 --S 13 of 13 @@ -56993,7 +57140,7 @@ c:=copy a --R --R --R (13) "00000000000000000000000000000100" ---R Type: IndexedBits 32 +--R Type: IndexedBits(32) --E 13 )spool )lisp (bye) @@ -57883,7 +58030,8 @@ IndexedDirectProductOrderedAbelianMonoidSup(A:OrderedAbelianMonoidSup,S:OrderedS --S 1 of 1 )show IndexedExponents ---R IndexedExponents Varset: OrderedSet is a domain constructor +--R +--R IndexedExponents(Varset: OrderedSet) is a domain constructor --R Abbreviation for IndexedExponents is INDE --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for INDE @@ -58006,22 +58154,23 @@ IndexedExponents(Varset:OrderedSet): C == T where --S 1 of 1 )show IndexedFlexibleArray +--R --R IndexedFlexibleArray(S: Type,mn: Integer) is a domain constructor --R Abbreviation for IndexedFlexibleArray is IFARRAY --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for IFARRAY --R --R------------------------------- Operations -------------------------------- ---R concat : List % -> % concat : (%,%) -> % +--R concat : List(%) -> % concat : (%,%) -> % --R concat : (S,%) -> % concat : (%,S) -> % --R concat! : (%,S) -> % concat! : (%,%) -> % ---R construct : List S -> % copy : % -> % +--R construct : List(S) -> % copy : % -> % --R delete : (%,Integer) -> % delete! : (%,Integer) -> % --R ?.? : (%,Integer) -> S elt : (%,Integer,S) -> S --R empty : () -> % empty? : % -> Boolean ---R entries : % -> List S eq? : (%,%) -> Boolean ---R flexibleArray : List S -> % index? : (Integer,%) -> Boolean ---R indices : % -> List Integer insert : (%,%,Integer) -> % +--R entries : % -> List(S) eq? : (%,%) -> Boolean +--R flexibleArray : List(S) -> % index? : (Integer,%) -> Boolean +--R indices : % -> List(Integer) insert : (%,%,Integer) -> % --R insert : (S,%,Integer) -> % insert! : (S,%,Integer) -> % --R insert! : (%,%,Integer) -> % map : (((S,S) -> S),%,%) -> % --R map : ((S -> S),%) -> % new : (NonNegativeInteger,S) -> % @@ -58035,18 +58184,18 @@ IndexedExponents(Varset:OrderedSet): C == T where --R ?>=? : (%,%) -> Boolean if S has ORDSET --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R coerce : % -> OutputForm if S has SETCAT ---R convert : % -> InputForm if S has KONVERT INFORM +--R convert : % -> InputForm if S has KONVERT(INFORM) --R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable --R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT --R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate ---R delete : (%,UniversalSegment Integer) -> % ---R delete! : (%,UniversalSegment Integer) -> % ---R ?.? : (%,UniversalSegment Integer) -> % +--R delete : (%,UniversalSegment(Integer)) -> % +--R delete! : (%,UniversalSegment(Integer)) -> % +--R ?.? : (%,UniversalSegment(Integer)) -> % --R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT ---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R fill! : (%,S) -> % if $ has shallowlyMutable --R find : ((S -> Boolean),%) -> Union(S,"failed") @@ -58058,7 +58207,7 @@ IndexedExponents(Varset:OrderedSet): C == T where --R max : (%,%) -> % if S has ORDSET --R maxIndex : % -> Integer if Integer has ORDSET --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT ---R members : % -> List S if $ has finiteAggregate +--R members : % -> List(S) if $ has finiteAggregate --R merge : (%,%) -> % if S has ORDSET --R merge : (((S,S) -> Boolean),%,%) -> % --R merge! : (((S,S) -> Boolean),%,%) -> % @@ -58066,7 +58215,7 @@ IndexedExponents(Varset:OrderedSet): C == T where --R min : (%,%) -> % if S has ORDSET --R minIndex : % -> Integer if Integer has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean ---R parts : % -> List S if $ has finiteAggregate +--R parts : % -> List(S) if $ has finiteAggregate --R physicalLength : % -> NonNegativeInteger --R physicalLength! : (%,Integer) -> % --R position : (S,%,Integer) -> Integer if S has SETCAT @@ -58085,7 +58234,7 @@ IndexedExponents(Varset:OrderedSet): C == T where --R reverse! : % -> % if $ has shallowlyMutable --R select : ((S -> Boolean),%) -> % if $ has finiteAggregate --R select! : ((S -> Boolean),%) -> % ---R setelt : (%,UniversalSegment Integer,S) -> S if $ has shallowlyMutable +--R setelt : (%,UniversalSegment(Integer),S) -> S if $ has shallowlyMutable --R setelt : (%,Integer,S) -> S if $ has shallowlyMutable --R size? : (%,NonNegativeInteger) -> Boolean --R sort : % -> % if S has ORDSET @@ -58454,16 +58603,17 @@ IndexedFlexibleArray(S:Type, mn: Integer): Exports == Implementation where --S 1 of 1 )show IndexedList +--R --R IndexedList(S: Type,mn: Integer) is a domain constructor --R Abbreviation for IndexedList is ILIST --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ILIST --R --R------------------------------- Operations -------------------------------- ---R children : % -> List % concat : (%,S) -> % ---R concat : List % -> % concat : (S,%) -> % +--R children : % -> List(%) concat : (%,S) -> % +--R concat : List(%) -> % concat : (S,%) -> % --R concat : (%,%) -> % concat! : (%,S) -> % ---R concat! : (%,%) -> % construct : List S -> % +--R concat! : (%,%) -> % construct : List(S) -> % --R copy : % -> % cycleEntry : % -> % --R cycleTail : % -> % cyclic? : % -> Boolean --R delete : (%,Integer) -> % delete! : (%,Integer) -> % @@ -58471,16 +58621,16 @@ IndexedFlexibleArray(S:Type, mn: Integer): Exports == Implementation where --R ?.? : (%,Integer) -> S ?.last : (%,last) -> S --R ?.rest : (%,rest) -> % ?.first : (%,first) -> S --R ?.value : (%,value) -> S empty : () -> % ---R empty? : % -> Boolean entries : % -> List S +--R empty? : % -> Boolean entries : % -> List(S) --R eq? : (%,%) -> Boolean explicitlyFinite? : % -> Boolean --R first : % -> S index? : (Integer,%) -> Boolean ---R indices : % -> List Integer insert : (S,%,Integer) -> % +--R indices : % -> List(Integer) insert : (S,%,Integer) -> % --R insert : (%,%,Integer) -> % insert! : (S,%,Integer) -> % --R insert! : (%,%,Integer) -> % last : % -> S ---R leaf? : % -> Boolean leaves : % -> List S +--R leaf? : % -> Boolean leaves : % -> List(S) --R list : S -> % map : (((S,S) -> S),%,%) -> % --R map : ((S -> S),%) -> % new : (NonNegativeInteger,S) -> % ---R nodes : % -> List % possiblyInfinite? : % -> Boolean +--R nodes : % -> List(%) possiblyInfinite? : % -> Boolean --R qelt : (%,Integer) -> S rest : % -> % --R reverse : % -> % sample : () -> % --R second : % -> S tail : % -> % @@ -58494,20 +58644,20 @@ IndexedFlexibleArray(S:Type, mn: Integer): Exports == Implementation where --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R child? : (%,%) -> Boolean if S has SETCAT --R coerce : % -> OutputForm if S has SETCAT ---R convert : % -> InputForm if S has KONVERT INFORM +--R convert : % -> InputForm if S has KONVERT(INFORM) --R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable --R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT --R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate --R cycleLength : % -> NonNegativeInteger --R cycleSplit! : % -> % if $ has shallowlyMutable ---R delete : (%,UniversalSegment Integer) -> % ---R delete! : (%,UniversalSegment Integer) -> % ---R ?.? : (%,UniversalSegment Integer) -> % +--R delete : (%,UniversalSegment(Integer)) -> % +--R delete! : (%,UniversalSegment(Integer)) -> % +--R ?.? : (%,UniversalSegment(Integer)) -> % --R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT ---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R fill! : (%,S) -> % if $ has shallowlyMutable --R find : ((S -> Boolean),%) -> Union(S,"failed") @@ -58520,7 +58670,7 @@ IndexedFlexibleArray(S:Type, mn: Integer): Exports == Implementation where --R max : (%,%) -> % if S has ORDSET --R maxIndex : % -> Integer if Integer has ORDSET --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT ---R members : % -> List S if $ has finiteAggregate +--R members : % -> List(S) if $ has finiteAggregate --R merge : (((S,S) -> Boolean),%,%) -> % --R merge : (%,%) -> % if S has ORDSET --R merge! : (((S,S) -> Boolean),%,%) -> % @@ -58529,7 +58679,7 @@ IndexedFlexibleArray(S:Type, mn: Integer): Exports == Implementation where --R minIndex : % -> Integer if Integer has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean --R node? : (%,%) -> Boolean if S has SETCAT ---R parts : % -> List S if $ has finiteAggregate +--R parts : % -> List(S) if $ has finiteAggregate --R position : ((S -> Boolean),%) -> Integer --R position : (S,%) -> Integer if S has SETCAT --R position : (S,%,Integer) -> Integer if S has SETCAT @@ -58547,9 +58697,9 @@ IndexedFlexibleArray(S:Type, mn: Integer): Exports == Implementation where --R reverse! : % -> % if $ has shallowlyMutable --R select : ((S -> Boolean),%) -> % if $ has finiteAggregate --R select! : ((S -> Boolean),%) -> % ---R setchildren! : (%,List %) -> % if $ has shallowlyMutable +--R setchildren! : (%,List(%)) -> % if $ has shallowlyMutable --R setelt : (%,Integer,S) -> S if $ has shallowlyMutable ---R setelt : (%,UniversalSegment Integer,S) -> S if $ has shallowlyMutable +--R setelt : (%,UniversalSegment(Integer),S) -> S if $ has shallowlyMutable --R setelt : (%,last,S) -> S if $ has shallowlyMutable --R setelt : (%,rest,%) -> % if $ has shallowlyMutable --R setelt : (%,first,S) -> S if $ has shallowlyMutable @@ -58905,6 +59055,7 @@ IndexedList(S:Type, mn:Integer): Exports == Implementation where --S 1 of 1 )show IndexedMatrix +--R --R IndexedMatrix(R: Ring,mnRow: Integer,mnCol: Integer) is a domain constructor --R Abbreviation for IndexedMatrix is IMATRIX --R This constructor is not exposed in this frame. @@ -58916,17 +59067,17 @@ IndexedList(S:Type, mn:Integer): Exports == Implementation where --R ?+? : (%,%) -> % -? : % -> % --R ?-? : (%,%) -> % antisymmetric? : % -> Boolean --R copy : % -> % diagonal? : % -> Boolean ---R diagonalMatrix : List % -> % diagonalMatrix : List R -> % +--R diagonalMatrix : List(%) -> % diagonalMatrix : List(R) -> % --R elt : (%,Integer,Integer,R) -> R elt : (%,Integer,Integer) -> R --R empty : () -> % empty? : % -> Boolean --R eq? : (%,%) -> Boolean fill! : (%,R) -> % ---R horizConcat : (%,%) -> % listOfLists : % -> List List R +--R horizConcat : (%,%) -> % listOfLists : % -> List(List(R)) --R map : (((R,R) -> R),%,%,R) -> % map : (((R,R) -> R),%,%) -> % --R map : ((R -> R),%) -> % map! : ((R -> R),%) -> % ---R matrix : List List R -> % maxColIndex : % -> Integer +--R matrix : List(List(R)) -> % maxColIndex : % -> Integer --R maxRowIndex : % -> Integer minColIndex : % -> Integer --R minRowIndex : % -> Integer ncols : % -> NonNegativeInteger ---R nrows : % -> NonNegativeInteger parts : % -> List R +--R nrows : % -> NonNegativeInteger parts : % -> List(R) --R qelt : (%,Integer,Integer) -> R sample : () -> % --R square? : % -> Boolean squareTop : % -> % --R symmetric? : % -> Boolean transpose : % -> % @@ -58942,15 +59093,15 @@ IndexedList(S:Type, mn:Integer): Exports == Implementation where --R coerce : IndexedVector(R,mnRow) -> % --R coerce : % -> OutputForm if R has SETCAT --R column : (%,Integer) -> IndexedVector(R,mnRow) ---R columnSpace : % -> List IndexedVector(R,mnRow) if R has EUCDOM +--R columnSpace : % -> List(IndexedVector(R,mnRow)) if R has EUCDOM --R count : (R,%) -> NonNegativeInteger if $ has finiteAggregate and R has SETCAT --R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate ---R determinant : % -> R if R has commutative * ---R elt : (%,List Integer,List Integer) -> % ---R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT ---R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT ---R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT ---R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT +--R determinant : % -> R if R has commutative(*) +--R elt : (%,List(Integer),List(Integer)) -> % +--R eval : (%,List(R),List(R)) -> % if R has EVALAB(R) and R has SETCAT +--R eval : (%,R,R) -> % if R has EVALAB(R) and R has SETCAT +--R eval : (%,Equation(R)) -> % if R has EVALAB(R) and R has SETCAT +--R eval : (%,List(Equation(R))) -> % if R has EVALAB(R) and R has SETCAT --R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate --R exquo : (%,R) -> Union(%,"failed") if R has INTDOM --R hash : % -> SingleInteger if R has SETCAT @@ -58958,11 +59109,11 @@ IndexedList(S:Type, mn:Integer): Exports == Implementation where --R latex : % -> String if R has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R member? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT ---R members : % -> List R if $ has finiteAggregate ---R minordet : % -> R if R has commutative * +--R members : % -> List(R) if $ has finiteAggregate +--R minordet : % -> R if R has commutative(*) --R more? : (%,NonNegativeInteger) -> Boolean --R new : (NonNegativeInteger,NonNegativeInteger,R) -> % ---R nullSpace : % -> List IndexedVector(R,mnRow) if R has INTDOM +--R nullSpace : % -> List(IndexedVector(R,mnRow)) if R has INTDOM --R nullity : % -> NonNegativeInteger if R has INTDOM --R pfaffian : % -> R if R has COMRING --R qsetelt! : (%,Integer,Integer,R) -> R @@ -58972,7 +59123,7 @@ IndexedList(S:Type, mn:Integer): Exports == Implementation where --R scalarMatrix : (NonNegativeInteger,R) -> % --R setColumn! : (%,Integer,IndexedVector(R,mnRow)) -> % --R setRow! : (%,Integer,IndexedVector(R,mnCol)) -> % ---R setelt : (%,List Integer,List Integer,%) -> % +--R setelt : (%,List(Integer),List(Integer),%) -> % --R setelt : (%,Integer,Integer,R) -> R --R setsubMatrix! : (%,Integer,Integer,%) -> % --R size? : (%,NonNegativeInteger) -> Boolean @@ -59168,20 +59319,21 @@ IndexedMatrix(R,mnRow,mnCol): Exports == Implementation where --S 1 of 1 )show IndexedOneDimensionalArray +--R --R IndexedOneDimensionalArray(S: Type,mn: Integer) is a domain constructor --R Abbreviation for IndexedOneDimensionalArray is IARRAY1 --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for IARRAY1 --R --R------------------------------- Operations -------------------------------- ---R concat : List % -> % concat : (%,%) -> % +--R concat : List(%) -> % concat : (%,%) -> % --R concat : (S,%) -> % concat : (%,S) -> % ---R construct : List S -> % copy : % -> % +--R construct : List(S) -> % copy : % -> % --R delete : (%,Integer) -> % ?.? : (%,Integer) -> S --R elt : (%,Integer,S) -> S empty : () -> % ---R empty? : % -> Boolean entries : % -> List S +--R empty? : % -> Boolean entries : % -> List(S) --R eq? : (%,%) -> Boolean index? : (Integer,%) -> Boolean ---R indices : % -> List Integer insert : (%,%,Integer) -> % +--R indices : % -> List(Integer) insert : (%,%,Integer) -> % --R insert : (S,%,Integer) -> % map : (((S,S) -> S),%,%) -> % --R map : ((S -> S),%) -> % new : (NonNegativeInteger,S) -> % --R qelt : (%,Integer) -> S reverse : % -> % @@ -59194,17 +59346,17 @@ IndexedMatrix(R,mnRow,mnCol): Exports == Implementation where --R ?>=? : (%,%) -> Boolean if S has ORDSET --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R coerce : % -> OutputForm if S has SETCAT ---R convert : % -> InputForm if S has KONVERT INFORM +--R convert : % -> InputForm if S has KONVERT(INFORM) --R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable --R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT --R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate ---R delete : (%,UniversalSegment Integer) -> % ---R ?.? : (%,UniversalSegment Integer) -> % +--R delete : (%,UniversalSegment(Integer)) -> % +--R ?.? : (%,UniversalSegment(Integer)) -> % --R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT ---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R fill! : (%,S) -> % if $ has shallowlyMutable --R find : ((S -> Boolean),%) -> Union(S,"failed") @@ -59216,13 +59368,13 @@ IndexedMatrix(R,mnRow,mnCol): Exports == Implementation where --R max : (%,%) -> % if S has ORDSET --R maxIndex : % -> Integer if Integer has ORDSET --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT ---R members : % -> List S if $ has finiteAggregate +--R members : % -> List(S) if $ has finiteAggregate --R merge : (%,%) -> % if S has ORDSET --R merge : (((S,S) -> Boolean),%,%) -> % --R min : (%,%) -> % if S has ORDSET --R minIndex : % -> Integer if Integer has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean ---R parts : % -> List S if $ has finiteAggregate +--R parts : % -> List(S) if $ has finiteAggregate --R position : (S,%,Integer) -> Integer if S has SETCAT --R position : (S,%) -> Integer if S has SETCAT --R position : ((S -> Boolean),%) -> Integer @@ -59235,7 +59387,7 @@ IndexedMatrix(R,mnRow,mnCol): Exports == Implementation where --R removeDuplicates : % -> % if $ has finiteAggregate and S has SETCAT --R reverse! : % -> % if $ has shallowlyMutable --R select : ((S -> Boolean),%) -> % if $ has finiteAggregate ---R setelt : (%,UniversalSegment Integer,S) -> S if $ has shallowlyMutable +--R setelt : (%,UniversalSegment(Integer),S) -> S if $ has shallowlyMutable --R setelt : (%,Integer,S) -> S if $ has shallowlyMutable --R size? : (%,NonNegativeInteger) -> Boolean --R sort : % -> % if S has ORDSET @@ -59461,26 +59613,27 @@ IndexedOneDimensionalArray(S:Type, mn:Integer): --S 1 of 1 )show IndexedString ---R IndexedString mn: Integer is a domain constructor +--R +--R IndexedString(mn: Integer) is a domain constructor --R Abbreviation for IndexedString is ISTRING --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ISTRING --R --R------------------------------- Operations -------------------------------- ---R coerce : Character -> % concat : List % -> % +--R coerce : Character -> % concat : List(%) -> % --R concat : (%,%) -> % concat : (Character,%) -> % ---R concat : (%,Character) -> % construct : List Character -> % +--R concat : (%,Character) -> % construct : List(Character) -> % --R copy : % -> % delete : (%,Integer) -> % --R ?.? : (%,%) -> % ?.? : (%,Integer) -> Character --R empty : () -> % empty? : % -> Boolean ---R entries : % -> List Character eq? : (%,%) -> Boolean +--R entries : % -> List(Character) eq? : (%,%) -> Boolean --R hash : % -> Integer index? : (Integer,%) -> Boolean ---R indices : % -> List Integer insert : (%,%,Integer) -> % +--R indices : % -> List(Integer) insert : (%,%,Integer) -> % --R leftTrim : (%,Character) -> % lowerCase : % -> % --R lowerCase! : % -> % prefix? : (%,%) -> Boolean --R qelt : (%,Integer) -> Character reverse : % -> % --R rightTrim : (%,Character) -> % sample : () -> % ---R split : (%,Character) -> List % suffix? : (%,%) -> Boolean +--R split : (%,Character) -> List(%) suffix? : (%,%) -> Boolean --R trim : (%,CharacterClass) -> % trim : (%,Character) -> % --R upperCase : % -> % upperCase! : % -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate @@ -59491,18 +59644,18 @@ IndexedOneDimensionalArray(S:Type, mn:Integer): --R ?>=? : (%,%) -> Boolean if Character has ORDSET --R any? : ((Character -> Boolean),%) -> Boolean if $ has finiteAggregate --R coerce : % -> OutputForm if Character has SETCAT ---R convert : % -> InputForm if Character has KONVERT INFORM +--R convert : % -> InputForm if Character has KONVERT(INFORM) --R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable --R count : (Character,%) -> NonNegativeInteger if $ has finiteAggregate and Character has SETCAT --R count : ((Character -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate ---R delete : (%,UniversalSegment Integer) -> % ---R ?.? : (%,UniversalSegment Integer) -> % +--R delete : (%,UniversalSegment(Integer)) -> % +--R ?.? : (%,UniversalSegment(Integer)) -> % --R elt : (%,Integer,Character) -> Character --R entry? : (Character,%) -> Boolean if $ has finiteAggregate and Character has SETCAT ---R eval : (%,List Character,List Character) -> % if Character has EVALAB CHAR and Character has SETCAT ---R eval : (%,Character,Character) -> % if Character has EVALAB CHAR and Character has SETCAT ---R eval : (%,Equation Character) -> % if Character has EVALAB CHAR and Character has SETCAT ---R eval : (%,List Equation Character) -> % if Character has EVALAB CHAR and Character has SETCAT +--R eval : (%,List(Character),List(Character)) -> % if Character has EVALAB(CHAR) and Character has SETCAT +--R eval : (%,Character,Character) -> % if Character has EVALAB(CHAR) and Character has SETCAT +--R eval : (%,Equation(Character)) -> % if Character has EVALAB(CHAR) and Character has SETCAT +--R eval : (%,List(Equation(Character))) -> % if Character has EVALAB(CHAR) and Character has SETCAT --R every? : ((Character -> Boolean),%) -> Boolean if $ has finiteAggregate --R fill! : (%,Character) -> % if $ has shallowlyMutable --R find : ((Character -> Boolean),%) -> Union(Character,"failed") @@ -59520,14 +59673,14 @@ IndexedOneDimensionalArray(S:Type, mn:Integer): --R max : (%,%) -> % if Character has ORDSET --R maxIndex : % -> Integer if Integer has ORDSET --R member? : (Character,%) -> Boolean if $ has finiteAggregate and Character has SETCAT ---R members : % -> List Character if $ has finiteAggregate +--R members : % -> List(Character) if $ has finiteAggregate --R merge : (%,%) -> % if Character has ORDSET --R merge : (((Character,Character) -> Boolean),%,%) -> % --R min : (%,%) -> % if Character has ORDSET --R minIndex : % -> Integer if Integer has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean --R new : (NonNegativeInteger,Character) -> % ---R parts : % -> List Character if $ has finiteAggregate +--R parts : % -> List(Character) if $ has finiteAggregate --R position : (CharacterClass,%,Integer) -> Integer --R position : (%,%,Integer) -> Integer --R position : (Character,%,Integer) -> Integer if Character has SETCAT @@ -59540,11 +59693,11 @@ IndexedOneDimensionalArray(S:Type, mn:Integer): --R remove : ((Character -> Boolean),%) -> % if $ has finiteAggregate --R remove : (Character,%) -> % if $ has finiteAggregate and Character has SETCAT --R removeDuplicates : % -> % if $ has finiteAggregate and Character has SETCAT ---R replace : (%,UniversalSegment Integer,%) -> % +--R replace : (%,UniversalSegment(Integer),%) -> % --R reverse! : % -> % if $ has shallowlyMutable --R rightTrim : (%,CharacterClass) -> % --R select : ((Character -> Boolean),%) -> % if $ has finiteAggregate ---R setelt : (%,UniversalSegment Integer,Character) -> Character if $ has shallowlyMutable +--R setelt : (%,UniversalSegment(Integer),Character) -> Character if $ has shallowlyMutable --R setelt : (%,Integer,Character) -> Character if $ has shallowlyMutable --R size? : (%,NonNegativeInteger) -> Boolean --R sort : % -> % if Character has ORDSET @@ -59553,7 +59706,7 @@ IndexedOneDimensionalArray(S:Type, mn:Integer): --R sort! : (((Character,Character) -> Boolean),%) -> % if $ has shallowlyMutable --R sorted? : % -> Boolean if Character has ORDSET --R sorted? : (((Character,Character) -> Boolean),%) -> Boolean ---R split : (%,CharacterClass) -> List % +--R split : (%,CharacterClass) -> List(%) --R substring? : (%,%,Integer) -> Boolean --R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable --R ?~=? : (%,%) -> Boolean if Character has SETCAT @@ -59887,6 +60040,7 @@ first column in an array and vice versa. --S 1 of 1 )show IndexedTwoDimensionalArray +--R --R IndexedTwoDimensionalArray(R: Type,mnRow: Integer,mnCol: Integer) is a domain constructor --R Abbreviation for IndexedTwoDimensionalArray is IARRAY2 --R This constructor is not exposed in this frame. @@ -59901,7 +60055,7 @@ first column in an array and vice versa. --R map! : ((R -> R),%) -> % maxColIndex : % -> Integer --R maxRowIndex : % -> Integer minColIndex : % -> Integer --R minRowIndex : % -> Integer ncols : % -> NonNegativeInteger ---R nrows : % -> NonNegativeInteger parts : % -> List R +--R nrows : % -> NonNegativeInteger parts : % -> List(R) --R qelt : (%,Integer,Integer) -> R sample : () -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?=? : (%,%) -> Boolean if R has SETCAT @@ -59910,16 +60064,16 @@ first column in an array and vice versa. --R column : (%,Integer) -> IndexedOneDimensionalArray(R,mnRow) --R count : (R,%) -> NonNegativeInteger if $ has finiteAggregate and R has SETCAT --R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate ---R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT ---R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT ---R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT ---R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,List(R),List(R)) -> % if R has EVALAB(R) and R has SETCAT +--R eval : (%,R,R) -> % if R has EVALAB(R) and R has SETCAT +--R eval : (%,Equation(R)) -> % if R has EVALAB(R) and R has SETCAT +--R eval : (%,List(Equation(R))) -> % if R has EVALAB(R) and R has SETCAT --R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if R has SETCAT --R latex : % -> String if R has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R member? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT ---R members : % -> List R if $ has finiteAggregate +--R members : % -> List(R) if $ has finiteAggregate --R more? : (%,NonNegativeInteger) -> Boolean --R new : (NonNegativeInteger,NonNegativeInteger,R) -> % --R qsetelt! : (%,Integer,Integer,R) -> R @@ -60034,20 +60188,21 @@ IndexedTwoDimensionalArray(R,mnRow,mnCol):Exports == Implementation where --S 1 of 1 )show IndexedVector +--R --R IndexedVector(R: Type,mn: Integer) is a domain constructor --R Abbreviation for IndexedVector is IVECTOR --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for IVECTOR --R --R------------------------------- Operations -------------------------------- ---R -? : % -> % if R has ABELGRP concat : List % -> % +--R -? : % -> % if R has ABELGRP concat : List(%) -> % --R concat : (%,%) -> % concat : (R,%) -> % ---R concat : (%,R) -> % construct : List R -> % +--R concat : (%,R) -> % construct : List(R) -> % --R copy : % -> % delete : (%,Integer) -> % --R ?.? : (%,Integer) -> R elt : (%,Integer,R) -> R --R empty : () -> % empty? : % -> Boolean ---R entries : % -> List R eq? : (%,%) -> Boolean ---R index? : (Integer,%) -> Boolean indices : % -> List Integer +--R entries : % -> List(R) eq? : (%,%) -> Boolean +--R index? : (Integer,%) -> Boolean indices : % -> List(Integer) --R insert : (%,%,Integer) -> % insert : (R,%,Integer) -> % --R map : (((R,R) -> R),%,%) -> % map : ((R -> R),%) -> % --R new : (NonNegativeInteger,R) -> % qelt : (%,Integer) -> R @@ -60065,19 +60220,19 @@ IndexedTwoDimensionalArray(R,mnRow,mnCol):Exports == Implementation where --R ?>=? : (%,%) -> Boolean if R has ORDSET --R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate --R coerce : % -> OutputForm if R has SETCAT ---R convert : % -> InputForm if R has KONVERT INFORM +--R convert : % -> InputForm if R has KONVERT(INFORM) --R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable --R count : (R,%) -> NonNegativeInteger if $ has finiteAggregate and R has SETCAT --R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate --R cross : (%,%) -> % if R has RING ---R delete : (%,UniversalSegment Integer) -> % +--R delete : (%,UniversalSegment(Integer)) -> % --R dot : (%,%) -> R if R has RING ---R ?.? : (%,UniversalSegment Integer) -> % +--R ?.? : (%,UniversalSegment(Integer)) -> % --R entry? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT ---R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT ---R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT ---R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT ---R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,List(R),List(R)) -> % if R has EVALAB(R) and R has SETCAT +--R eval : (%,R,R) -> % if R has EVALAB(R) and R has SETCAT +--R eval : (%,Equation(R)) -> % if R has EVALAB(R) and R has SETCAT +--R eval : (%,List(Equation(R))) -> % if R has EVALAB(R) and R has SETCAT --R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate --R fill! : (%,R) -> % if $ has shallowlyMutable --R find : ((R -> Boolean),%) -> Union(R,"failed") @@ -60091,14 +60246,14 @@ IndexedTwoDimensionalArray(R,mnRow,mnCol):Exports == Implementation where --R max : (%,%) -> % if R has ORDSET --R maxIndex : % -> Integer if Integer has ORDSET --R member? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT ---R members : % -> List R if $ has finiteAggregate +--R members : % -> List(R) if $ has finiteAggregate --R merge : (%,%) -> % if R has ORDSET --R merge : (((R,R) -> Boolean),%,%) -> % --R min : (%,%) -> % if R has ORDSET --R minIndex : % -> Integer if Integer has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean ---R outerProduct : (%,%) -> Matrix R if R has RING ---R parts : % -> List R if $ has finiteAggregate +--R outerProduct : (%,%) -> Matrix(R) if R has RING +--R parts : % -> List(R) if $ has finiteAggregate --R position : (R,%,Integer) -> Integer if R has SETCAT --R position : (R,%) -> Integer if R has SETCAT --R position : ((R -> Boolean),%) -> Integer @@ -60111,7 +60266,7 @@ IndexedTwoDimensionalArray(R,mnRow,mnCol):Exports == Implementation where --R removeDuplicates : % -> % if $ has finiteAggregate and R has SETCAT --R reverse! : % -> % if $ has shallowlyMutable --R select : ((R -> Boolean),%) -> % if $ has finiteAggregate ---R setelt : (%,UniversalSegment Integer,R) -> R if $ has shallowlyMutable +--R setelt : (%,UniversalSegment(Integer),R) -> R if $ has shallowlyMutable --R setelt : (%,Integer,R) -> R if $ has shallowlyMutable --R size? : (%,NonNegativeInteger) -> Boolean --R sort : % -> % if R has ORDSET @@ -60255,13 +60410,14 @@ IndexedVector(R:Type, mn:Integer): --S 1 of 1 )show InfiniteTuple ---R InfiniteTuple S: Type is a domain constructor +--R +--R InfiniteTuple(S: Type) is a domain constructor --R Abbreviation for InfiniteTuple is ITUPLE --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ITUPLE --R --R------------------------------- Operations -------------------------------- ---R coerce : % -> OutputForm construct : % -> Stream S +--R coerce : % -> OutputForm construct : % -> Stream(S) --R generate : ((S -> S),S) -> % map : ((S -> S),%) -> % --R select : ((S -> Boolean),%) -> % --R filterUntil : ((S -> Boolean),%) -> % @@ -60763,6 +60919,7 @@ InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField(K,symb,BLMET):_ --S 1 of 1 )show InnerAlgebraicNumber +--R --R InnerAlgebraicNumber is a domain constructor --R Abbreviation for InnerAlgebraicNumber is IAN --R This constructor is not exposed in this frame. @@ -60770,110 +60927,113 @@ InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField(K,symb,BLMET):_ --R --R------------------------------- Operations -------------------------------- --R ?*? : (PositiveInteger,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (%,%) -> % ?*? : (%,Fraction Integer) -> % ---R ?*? : (Fraction Integer,%) -> % ?**? : (%,PositiveInteger) -> % ---R ?**? : (%,Integer) -> % ?**? : (%,Fraction Integer) -> % ---R ?+? : (%,%) -> % -? : % -> % ---R ?-? : (%,%) -> % ?/? : (%,%) -> % ---R ? Boolean ?<=? : (%,%) -> Boolean ---R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean ---R ?>=? : (%,%) -> Boolean D : % -> % ---R D : (%,NonNegativeInteger) -> % 1 : () -> % ---R 0 : () -> % ?^? : (%,PositiveInteger) -> % ---R ?^? : (%,Integer) -> % associates? : (%,%) -> Boolean ---R belong? : BasicOperator -> Boolean box : List % -> % ---R box : % -> % coerce : Integer -> % ---R coerce : % -> % coerce : Fraction Integer -> % ---R coerce : Kernel % -> % coerce : % -> OutputForm ---R convert : % -> Complex Float convert : % -> DoubleFloat ---R convert : % -> Float differentiate : % -> % ---R distribute : (%,%) -> % distribute : % -> % ---R elt : (BasicOperator,%,%) -> % elt : (BasicOperator,%) -> % ---R eval : (%,List %,List %) -> % eval : (%,%,%) -> % ---R eval : (%,Equation %) -> % eval : (%,List Equation %) -> % ---R eval : (%,Kernel %,%) -> % factor : % -> Factored % ---R freeOf? : (%,Symbol) -> Boolean freeOf? : (%,%) -> Boolean ---R gcd : (%,%) -> % gcd : List % -> % ---R hash : % -> SingleInteger height : % -> NonNegativeInteger ---R inv : % -> % is? : (%,Symbol) -> Boolean ---R kernel : (BasicOperator,%) -> % kernels : % -> List Kernel % ---R latex : % -> String lcm : (%,%) -> % ---R lcm : List % -> % map : ((% -> %),Kernel %) -> % +--R ?*? : (%,%) -> % ?*? : (%,Fraction(Integer)) -> % +--R ?*? : (Fraction(Integer),%) -> % ?**? : (%,PositiveInteger) -> % +--R ?**? : (%,Integer) -> % ?+? : (%,%) -> % +--R -? : % -> % ?-? : (%,%) -> % +--R ?/? : (%,%) -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R D : % -> % D : (%,NonNegativeInteger) -> % +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % ?^? : (%,Integer) -> % +--R associates? : (%,%) -> Boolean belong? : BasicOperator -> Boolean +--R box : List(%) -> % box : % -> % +--R coerce : Integer -> % coerce : % -> % +--R coerce : Fraction(Integer) -> % coerce : Kernel(%) -> % +--R coerce : % -> OutputForm convert : % -> Complex(Float) +--R convert : % -> DoubleFloat convert : % -> Float +--R differentiate : % -> % distribute : (%,%) -> % +--R distribute : % -> % elt : (BasicOperator,%,%) -> % +--R elt : (BasicOperator,%) -> % eval : (%,%,%) -> % +--R eval : (%,Equation(%)) -> % eval : (%,Kernel(%),%) -> % +--R factor : % -> Factored(%) freeOf? : (%,Symbol) -> Boolean +--R freeOf? : (%,%) -> Boolean gcd : (%,%) -> % +--R gcd : List(%) -> % hash : % -> SingleInteger +--R height : % -> NonNegativeInteger inv : % -> % +--R is? : (%,Symbol) -> Boolean kernel : (BasicOperator,%) -> % +--R kernels : % -> List(Kernel(%)) latex : % -> String +--R lcm : (%,%) -> % lcm : List(%) -> % --R max : (%,%) -> % min : (%,%) -> % ---R norm : (%,List Kernel %) -> % norm : (%,Kernel %) -> % +--R norm : (%,List(Kernel(%))) -> % norm : (%,Kernel(%)) -> % --R nthRoot : (%,Integer) -> % one? : % -> Boolean ---R paren : List % -> % paren : % -> % +--R paren : List(%) -> % paren : % -> % --R prime? : % -> Boolean ?quo? : (%,%) -> % --R recip : % -> Union(%,"failed") reduce : % -> % ---R ?rem? : (%,%) -> % retract : % -> Fraction Integer ---R retract : % -> Integer retract : % -> Kernel % ---R rootOf : Polynomial % -> % rootsOf : Polynomial % -> List % ---R sample : () -> % sizeLess? : (%,%) -> Boolean ---R sqrt : % -> % squareFree : % -> Factored % ---R squareFreePart : % -> % subst : (%,Equation %) -> % ---R tower : % -> List Kernel % trueEqual : (%,%) -> Boolean ---R unit? : % -> Boolean unitCanonical : % -> % ---R zero? : % -> Boolean zeroOf : Polynomial % -> % ---R zerosOf : Polynomial % -> List % ?~=? : (%,%) -> Boolean +--R ?rem? : (%,%) -> % retract : % -> Fraction(Integer) +--R retract : % -> Integer retract : % -> Kernel(%) +--R rootOf : Polynomial(%) -> % sample : () -> % +--R sizeLess? : (%,%) -> Boolean sqrt : % -> % +--R squareFree : % -> Factored(%) squareFreePart : % -> % +--R subst : (%,Equation(%)) -> % tower : % -> List(Kernel(%)) +--R trueEqual : (%,%) -> Boolean unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R zeroOf : Polynomial(%) -> % ?~=? : (%,%) -> Boolean --R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,NonNegativeInteger) -> % +--R ?**? : (%,Fraction(Integer)) -> % --R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger ---R coerce : SparseMultivariatePolynomial(Integer,Kernel %) -> % +--R coerce : SparseMultivariatePolynomial(Integer,Kernel(%)) -> % --R definingPolynomial : % -> % if $ has RING ---R denom : % -> SparseMultivariatePolynomial(Integer,Kernel %) +--R denom : % -> SparseMultivariatePolynomial(Integer,Kernel(%)) --R differentiate : (%,NonNegativeInteger) -> % --R divide : (%,%) -> Record(quotient: %,remainder: %) ---R elt : (BasicOperator,List %) -> % +--R elt : (BasicOperator,List(%)) -> % --R elt : (BasicOperator,%,%,%,%) -> % --R elt : (BasicOperator,%,%,%) -> % --R euclideanSize : % -> NonNegativeInteger --R eval : (%,BasicOperator,(% -> %)) -> % ---R eval : (%,BasicOperator,(List % -> %)) -> % ---R eval : (%,List BasicOperator,List (List % -> %)) -> % ---R eval : (%,List BasicOperator,List (% -> %)) -> % +--R eval : (%,BasicOperator,(List(%) -> %)) -> % +--R eval : (%,List(BasicOperator),List((List(%) -> %))) -> % +--R eval : (%,List(BasicOperator),List((% -> %))) -> % --R eval : (%,Symbol,(% -> %)) -> % ---R eval : (%,Symbol,(List % -> %)) -> % ---R eval : (%,List Symbol,List (List % -> %)) -> % ---R eval : (%,List Symbol,List (% -> %)) -> % ---R eval : (%,List Kernel %,List %) -> % ---R even? : % -> Boolean if $ has RETRACT INT ---R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R eval : (%,Symbol,(List(%) -> %)) -> % +--R eval : (%,List(Symbol),List((List(%) -> %))) -> % +--R eval : (%,List(Symbol),List((% -> %))) -> % +--R eval : (%,List(%),List(%)) -> % +--R eval : (%,List(Equation(%))) -> % +--R eval : (%,List(Kernel(%)),List(%)) -> % +--R even? : % -> Boolean if $ has RETRACT(INT) +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") --R exquo : (%,%) -> Union(%,"failed") --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) --R is? : (%,BasicOperator) -> Boolean ---R kernel : (BasicOperator,List %) -> % ---R mainKernel : % -> Union(Kernel %,"failed") ---R minPoly : Kernel % -> SparseUnivariatePolynomial % if $ has RING ---R multiEuclidean : (List %,%) -> Union(List %,"failed") ---R norm : (SparseUnivariatePolynomial %,List Kernel %) -> SparseUnivariatePolynomial % ---R norm : (SparseUnivariatePolynomial %,Kernel %) -> SparseUnivariatePolynomial % ---R numer : % -> SparseMultivariatePolynomial(Integer,Kernel %) ---R odd? : % -> Boolean if $ has RETRACT INT +--R kernel : (BasicOperator,List(%)) -> % +--R mainKernel : % -> Union(Kernel(%),"failed") +--R map : ((% -> %),Kernel(%)) -> % +--R minPoly : Kernel(%) -> SparseUnivariatePolynomial(%) if $ has RING +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") +--R norm : (SparseUnivariatePolynomial(%),List(Kernel(%))) -> SparseUnivariatePolynomial(%) +--R norm : (SparseUnivariatePolynomial(%),Kernel(%)) -> SparseUnivariatePolynomial(%) +--R numer : % -> SparseMultivariatePolynomial(Integer,Kernel(%)) +--R odd? : % -> Boolean if $ has RETRACT(INT) --R operator : BasicOperator -> BasicOperator ---R operators : % -> List BasicOperator ---R principalIdeal : List % -> Record(coef: List %,generator: %) ---R reducedSystem : Matrix % -> Matrix Fraction Integer ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Fraction Integer,vec: Vector Fraction Integer) ---R reducedSystem : Matrix % -> Matrix Integer ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) ---R retractIfCan : % -> Union(Fraction Integer,"failed") +--R operators : % -> List(BasicOperator) +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) +--R reducedSystem : Matrix(%) -> Matrix(Fraction(Integer)) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Fraction(Integer)),vec: Vector(Fraction(Integer))) +--R reducedSystem : Matrix(%) -> Matrix(Integer) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) +--R retractIfCan : % -> Union(Fraction(Integer),"failed") --R retractIfCan : % -> Union(Integer,"failed") ---R retractIfCan : % -> Union(Kernel %,"failed") ---R rootOf : SparseUnivariatePolynomial % -> % ---R rootOf : (SparseUnivariatePolynomial %,Symbol) -> % ---R rootsOf : SparseUnivariatePolynomial % -> List % ---R rootsOf : (SparseUnivariatePolynomial %,Symbol) -> List % ---R subst : (%,List Kernel %,List %) -> % ---R subst : (%,List Equation %) -> % +--R retractIfCan : % -> Union(Kernel(%),"failed") +--R rootOf : SparseUnivariatePolynomial(%) -> % +--R rootOf : (SparseUnivariatePolynomial(%),Symbol) -> % +--R rootsOf : Polynomial(%) -> List(%) +--R rootsOf : SparseUnivariatePolynomial(%) -> List(%) +--R rootsOf : (SparseUnivariatePolynomial(%),Symbol) -> List(%) +--R subst : (%,List(Kernel(%)),List(%)) -> % +--R subst : (%,List(Equation(%))) -> % --R subtractIfCan : (%,%) -> Union(%,"failed") --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) ---R zeroOf : SparseUnivariatePolynomial % -> % ---R zeroOf : (SparseUnivariatePolynomial %,Symbol) -> % ---R zerosOf : SparseUnivariatePolynomial % -> List % ---R zerosOf : (SparseUnivariatePolynomial %,Symbol) -> List % +--R zeroOf : SparseUnivariatePolynomial(%) -> % +--R zeroOf : (SparseUnivariatePolynomial(%),Symbol) -> % +--R zerosOf : Polynomial(%) -> List(%) +--R zerosOf : SparseUnivariatePolynomial(%) -> List(%) +--R zerosOf : (SparseUnivariatePolynomial(%),Symbol) -> List(%) --R --E 1 @@ -61152,102 +61312,104 @@ InnerAlgebraicNumber(): Exports == Implementation where --S 1 of 1 )show InnerFiniteField +--R --R InnerFiniteField(p: PositiveInteger,n: PositiveInteger) is a domain constructor --R Abbreviation for InnerFiniteField is IFF --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for IFF --R --R------------------------------- Operations -------------------------------- ---R ?*? : (InnerPrimeField p,%) -> % ?*? : (%,InnerPrimeField p) -> % ---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % --R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % --R ?-? : (%,%) -> % -? : % -> % ---R ?/? : (%,InnerPrimeField p) -> % ?/? : (%,%) -> % ---R ?=? : (%,%) -> Boolean 1 : () -> % ---R 0 : () -> % ?^? : (%,Integer) -> % ---R ?^? : (%,PositiveInteger) -> % algebraic? : % -> Boolean ---R associates? : (%,%) -> Boolean basis : () -> Vector % ---R coerce : InnerPrimeField p -> % coerce : Fraction Integer -> % ---R coerce : % -> % coerce : Integer -> % ---R coerce : % -> OutputForm degree : % -> PositiveInteger ---R dimension : () -> CardinalNumber factor : % -> Factored % ---R gcd : List % -> % gcd : (%,%) -> % ---R hash : % -> SingleInteger inGroundField? : % -> Boolean ---R inv : % -> % latex : % -> String ---R lcm : List % -> % lcm : (%,%) -> % ---R norm : % -> InnerPrimeField p one? : % -> Boolean ---R prime? : % -> Boolean ?quo? : (%,%) -> % ---R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % ---R retract : % -> InnerPrimeField p sample : () -> % ---R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored % ---R squareFreePart : % -> % trace : % -> InnerPrimeField p ---R transcendent? : % -> Boolean unit? : % -> Boolean ---R unitCanonical : % -> % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean +--R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R algebraic? : % -> Boolean associates? : (%,%) -> Boolean +--R basis : () -> Vector(%) coerce : InnerPrimeField(p) -> % +--R coerce : Fraction(Integer) -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R degree : % -> PositiveInteger dimension : () -> CardinalNumber +--R factor : % -> Factored(%) gcd : List(%) -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R inGroundField? : % -> Boolean inv : % -> % +--R latex : % -> String lcm : List(%) -> % +--R lcm : (%,%) -> % norm : % -> InnerPrimeField(p) +--R one? : % -> Boolean prime? : % -> Boolean +--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % retract : % -> InnerPrimeField(p) +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored(%) squareFreePart : % -> % +--R trace : % -> InnerPrimeField(p) transcendent? : % -> Boolean +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (InnerPrimeField(p),%) -> % +--R ?*? : (%,InnerPrimeField(p)) -> % --R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,NonNegativeInteger) -> % ---R D : (%,NonNegativeInteger) -> % if InnerPrimeField p has FINITE ---R D : % -> % if InnerPrimeField p has FINITE ---R Frobenius : (%,NonNegativeInteger) -> % if InnerPrimeField p has FINITE ---R Frobenius : % -> % if InnerPrimeField p has FINITE +--R ?/? : (%,InnerPrimeField(p)) -> % +--R D : (%,NonNegativeInteger) -> % if InnerPrimeField(p) has FINITE +--R D : % -> % if InnerPrimeField(p) has FINITE +--R Frobenius : (%,NonNegativeInteger) -> % if InnerPrimeField(p) has FINITE +--R Frobenius : % -> % if InnerPrimeField(p) has FINITE --R ?^? : (%,NonNegativeInteger) -> % ---R basis : PositiveInteger -> Vector % +--R basis : PositiveInteger -> Vector(%) --R characteristic : () -> NonNegativeInteger ---R charthRoot : % -> Union(%,"failed") if InnerPrimeField p has CHARNZ or InnerPrimeField p has FINITE ---R charthRoot : % -> % if InnerPrimeField p has FINITE ---R conditionP : Matrix % -> Union(Vector %,"failed") if InnerPrimeField p has FINITE ---R coordinates : Vector % -> Matrix InnerPrimeField p ---R coordinates : % -> Vector InnerPrimeField p ---R createNormalElement : () -> % if InnerPrimeField p has FINITE ---R createPrimitiveElement : () -> % if InnerPrimeField p has FINITE ---R definingPolynomial : () -> SparseUnivariatePolynomial InnerPrimeField p ---R degree : % -> OnePointCompletion PositiveInteger ---R differentiate : (%,NonNegativeInteger) -> % if InnerPrimeField p has FINITE ---R differentiate : % -> % if InnerPrimeField p has FINITE ---R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if InnerPrimeField p has CHARNZ or InnerPrimeField p has FINITE ---R discreteLog : % -> NonNegativeInteger if InnerPrimeField p has FINITE +--R charthRoot : % -> Union(%,"failed") if InnerPrimeField(p) has CHARNZ or InnerPrimeField(p) has FINITE +--R charthRoot : % -> % if InnerPrimeField(p) has FINITE +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if InnerPrimeField(p) has FINITE +--R coordinates : Vector(%) -> Matrix(InnerPrimeField(p)) +--R coordinates : % -> Vector(InnerPrimeField(p)) +--R createNormalElement : () -> % if InnerPrimeField(p) has FINITE +--R createPrimitiveElement : () -> % if InnerPrimeField(p) has FINITE +--R definingPolynomial : () -> SparseUnivariatePolynomial(InnerPrimeField(p)) +--R degree : % -> OnePointCompletion(PositiveInteger) +--R differentiate : (%,NonNegativeInteger) -> % if InnerPrimeField(p) has FINITE +--R differentiate : % -> % if InnerPrimeField(p) has FINITE +--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if InnerPrimeField(p) has CHARNZ or InnerPrimeField(p) has FINITE +--R discreteLog : % -> NonNegativeInteger if InnerPrimeField(p) has FINITE --R divide : (%,%) -> Record(quotient: %,remainder: %) --R euclideanSize : % -> NonNegativeInteger ---R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") --R exquo : (%,%) -> Union(%,"failed") --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) --R extensionDegree : () -> PositiveInteger ---R extensionDegree : () -> OnePointCompletion PositiveInteger ---R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if InnerPrimeField p has FINITE ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % ---R generator : () -> % if InnerPrimeField p has FINITE ---R index : PositiveInteger -> % if InnerPrimeField p has FINITE ---R init : () -> % if InnerPrimeField p has FINITE ---R linearAssociatedExp : (%,SparseUnivariatePolynomial InnerPrimeField p) -> % if InnerPrimeField p has FINITE ---R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial InnerPrimeField p,"failed") if InnerPrimeField p has FINITE ---R linearAssociatedLog : % -> SparseUnivariatePolynomial InnerPrimeField p if InnerPrimeField p has FINITE ---R linearAssociatedOrder : % -> SparseUnivariatePolynomial InnerPrimeField p if InnerPrimeField p has FINITE ---R lookup : % -> PositiveInteger if InnerPrimeField p has FINITE ---R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial % if InnerPrimeField p has FINITE ---R minimalPolynomial : % -> SparseUnivariatePolynomial InnerPrimeField p ---R multiEuclidean : (List %,%) -> Union(List %,"failed") ---R nextItem : % -> Union(%,"failed") if InnerPrimeField p has FINITE ---R norm : (%,PositiveInteger) -> % if InnerPrimeField p has FINITE ---R normal? : % -> Boolean if InnerPrimeField p has FINITE ---R normalElement : () -> % if InnerPrimeField p has FINITE ---R order : % -> OnePointCompletion PositiveInteger if InnerPrimeField p has CHARNZ or InnerPrimeField p has FINITE ---R order : % -> PositiveInteger if InnerPrimeField p has FINITE ---R primeFrobenius : % -> % if InnerPrimeField p has CHARNZ or InnerPrimeField p has FINITE ---R primeFrobenius : (%,NonNegativeInteger) -> % if InnerPrimeField p has CHARNZ or InnerPrimeField p has FINITE ---R primitive? : % -> Boolean if InnerPrimeField p has FINITE ---R primitiveElement : () -> % if InnerPrimeField p has FINITE ---R principalIdeal : List % -> Record(coef: List %,generator: %) ---R random : () -> % if InnerPrimeField p has FINITE ---R representationType : () -> Union("prime",polynomial,normal,cyclic) if InnerPrimeField p has FINITE ---R represents : Vector InnerPrimeField p -> % ---R retractIfCan : % -> Union(InnerPrimeField p,"failed") ---R size : () -> NonNegativeInteger if InnerPrimeField p has FINITE +--R extensionDegree : () -> OnePointCompletion(PositiveInteger) +--R factorsOfCyclicGroupSize : () -> List(Record(factor: Integer,exponent: Integer)) if InnerPrimeField(p) has FINITE +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) +--R generator : () -> % if InnerPrimeField(p) has FINITE +--R index : PositiveInteger -> % if InnerPrimeField(p) has FINITE +--R init : () -> % if InnerPrimeField(p) has FINITE +--R linearAssociatedExp : (%,SparseUnivariatePolynomial(InnerPrimeField(p))) -> % if InnerPrimeField(p) has FINITE +--R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial(InnerPrimeField(p)),"failed") if InnerPrimeField(p) has FINITE +--R linearAssociatedLog : % -> SparseUnivariatePolynomial(InnerPrimeField(p)) if InnerPrimeField(p) has FINITE +--R linearAssociatedOrder : % -> SparseUnivariatePolynomial(InnerPrimeField(p)) if InnerPrimeField(p) has FINITE +--R lookup : % -> PositiveInteger if InnerPrimeField(p) has FINITE +--R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial(%) if InnerPrimeField(p) has FINITE +--R minimalPolynomial : % -> SparseUnivariatePolynomial(InnerPrimeField(p)) +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") +--R nextItem : % -> Union(%,"failed") if InnerPrimeField(p) has FINITE +--R norm : (%,PositiveInteger) -> % if InnerPrimeField(p) has FINITE +--R normal? : % -> Boolean if InnerPrimeField(p) has FINITE +--R normalElement : () -> % if InnerPrimeField(p) has FINITE +--R order : % -> OnePointCompletion(PositiveInteger) if InnerPrimeField(p) has CHARNZ or InnerPrimeField(p) has FINITE +--R order : % -> PositiveInteger if InnerPrimeField(p) has FINITE +--R primeFrobenius : % -> % if InnerPrimeField(p) has CHARNZ or InnerPrimeField(p) has FINITE +--R primeFrobenius : (%,NonNegativeInteger) -> % if InnerPrimeField(p) has CHARNZ or InnerPrimeField(p) has FINITE +--R primitive? : % -> Boolean if InnerPrimeField(p) has FINITE +--R primitiveElement : () -> % if InnerPrimeField(p) has FINITE +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) +--R random : () -> % if InnerPrimeField(p) has FINITE +--R representationType : () -> Union("prime",polynomial,normal,cyclic) if InnerPrimeField(p) has FINITE +--R represents : Vector(InnerPrimeField(p)) -> % +--R retractIfCan : % -> Union(InnerPrimeField(p),"failed") +--R size : () -> NonNegativeInteger if InnerPrimeField(p) has FINITE --R subtractIfCan : (%,%) -> Union(%,"failed") ---R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if InnerPrimeField p has FINITE ---R trace : (%,PositiveInteger) -> % if InnerPrimeField p has FINITE +--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if InnerPrimeField(p) has FINITE +--R trace : (%,PositiveInteger) -> % if InnerPrimeField(p) has FINITE --R transcendenceDegree : () -> NonNegativeInteger --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) --R @@ -61407,6 +61569,7 @@ InnerFiniteField(p:PositiveInteger, n:PositiveInteger) == --S 1 of 1 )show InnerFreeAbelianMonoid +--R --R InnerFreeAbelianMonoid(S: SetCategory,E: CancellationAbelianMonoid,un: E) is a domain constructor --R Abbreviation for InnerFreeAbelianMonoid is IFAMON --R This constructor is not exposed in this frame. @@ -61427,7 +61590,7 @@ InnerFiniteField(p:PositiveInteger, n:PositiveInteger) == --R highCommonTerms : (%,%) -> % if E has OAMON --R retractIfCan : % -> Union(S,"failed") --R subtractIfCan : (%,%) -> Union(%,"failed") ---R terms : % -> List Record(gen: S,exp: E) +--R terms : % -> List(Record(gen: S,exp: E)) --R --E 1 @@ -61537,7 +61700,8 @@ This is an internal type which provides an implementation of --S 1 of 1 )show InnerIndexedTwoDimensionalArray ---R InnerIndexedTwoDimensionalArray(R: Type,mnRow: Integer,mnCol: Integer,Row: FiniteLinearAggregate R,Col: FiniteLinearAggregate R) is a domain constructor +--R +--R InnerIndexedTwoDimensionalArray(R: Type,mnRow: Integer,mnCol: Integer,Row: FiniteLinearAggregate(R),Col: FiniteLinearAggregate(R)) is a domain constructor --R Abbreviation for InnerIndexedTwoDimensionalArray is IIARRAY2 --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for IIARRAY2 @@ -61552,7 +61716,7 @@ This is an internal type which provides an implementation of --R maxColIndex : % -> Integer maxRowIndex : % -> Integer --R minColIndex : % -> Integer minRowIndex : % -> Integer --R ncols : % -> NonNegativeInteger nrows : % -> NonNegativeInteger ---R parts : % -> List R qelt : (%,Integer,Integer) -> R +--R parts : % -> List(R) qelt : (%,Integer,Integer) -> R --R row : (%,Integer) -> Row sample : () -> % --R setRow! : (%,Integer,Row) -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate @@ -61561,16 +61725,16 @@ This is an internal type which provides an implementation of --R coerce : % -> OutputForm if R has SETCAT --R count : (R,%) -> NonNegativeInteger if $ has finiteAggregate and R has SETCAT --R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate ---R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT ---R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT ---R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT ---R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,List(R),List(R)) -> % if R has EVALAB(R) and R has SETCAT +--R eval : (%,R,R) -> % if R has EVALAB(R) and R has SETCAT +--R eval : (%,Equation(R)) -> % if R has EVALAB(R) and R has SETCAT +--R eval : (%,List(Equation(R))) -> % if R has EVALAB(R) and R has SETCAT --R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if R has SETCAT --R latex : % -> String if R has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R member? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT ---R members : % -> List R if $ has finiteAggregate +--R members : % -> List(R) if $ has finiteAggregate --R more? : (%,NonNegativeInteger) -> Boolean --R new : (NonNegativeInteger,NonNegativeInteger,R) -> % --R qsetelt! : (%,Integer,Integer,R) -> R @@ -61750,6 +61914,7 @@ InnerIndexedTwoDimensionalArray(R,mnRow,mnCol,Row,Col):_ --S 1 of 1 )show InnerPAdicInteger +--R --R InnerPAdicInteger(p: Integer,unBalanced?: Boolean) is a domain constructor --R Abbreviation for InnerPAdicInteger is IPADIC --R This constructor is not exposed in this frame. @@ -61764,10 +61929,10 @@ InnerIndexedTwoDimensionalArray(R,mnRow,mnCol,Row,Col):_ --R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean --R coerce : % -> % coerce : Integer -> % --R coerce : % -> OutputForm complete : % -> % ---R digits : % -> Stream Integer extend : (%,Integer) -> % ---R gcd : List % -> % gcd : (%,%) -> % +--R digits : % -> Stream(Integer) extend : (%,Integer) -> % +--R gcd : List(%) -> % gcd : (%,%) -> % --R hash : % -> SingleInteger latex : % -> String ---R lcm : List % -> % lcm : (%,%) -> % +--R lcm : List(%) -> % lcm : (%,%) -> % --R moduloP : % -> Integer modulus : () -> Integer --R one? : % -> Boolean order : % -> NonNegativeInteger --R ?quo? : (%,%) -> % quotientByP : % -> % @@ -61783,14 +61948,14 @@ InnerIndexedTwoDimensionalArray(R,mnRow,mnCol,Row,Col):_ --R characteristic : () -> NonNegativeInteger --R divide : (%,%) -> Record(quotient: %,remainder: %) --R euclideanSize : % -> NonNegativeInteger ---R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") --R exquo : (%,%) -> Union(%,"failed") --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % ---R multiEuclidean : (List %,%) -> Union(List %,"failed") ---R principalIdeal : List % -> Record(coef: List %,generator: %) ---R root : (SparseUnivariatePolynomial Integer,Integer) -> % +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) +--R root : (SparseUnivariatePolynomial(Integer),Integer) -> % --R subtractIfCan : (%,%) -> Union(%,"failed") --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) --R @@ -62140,13 +62305,14 @@ InnerPAdicInteger(p,unBalanced?): Exports == Implementation where --S 1 of 1 )show InnerPrimeField ---R InnerPrimeField p: PositiveInteger is a domain constructor +--R +--R InnerPrimeField(p: PositiveInteger) is a domain constructor --R Abbreviation for InnerPrimeField is IPF --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for IPF --R --R------------------------------- Operations -------------------------------- ---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % --R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % @@ -62156,27 +62322,27 @@ InnerPAdicInteger(p,unBalanced?): Exports == Implementation where --R 1 : () -> % 0 : () -> % --R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % --R algebraic? : % -> Boolean associates? : (%,%) -> Boolean ---R basis : () -> Vector % charthRoot : % -> % ---R coerce : Fraction Integer -> % coerce : % -> % +--R basis : () -> Vector(%) charthRoot : % -> % +--R coerce : Fraction(Integer) -> % coerce : % -> % --R coerce : Integer -> % coerce : % -> OutputForm ---R convert : % -> Integer coordinates : % -> Vector % +--R convert : % -> Integer coordinates : % -> Vector(%) --R createPrimitiveElement : () -> % degree : % -> PositiveInteger --R differentiate : % -> % dimension : () -> CardinalNumber ---R factor : % -> Factored % gcd : List % -> % +--R factor : % -> Factored(%) gcd : List(%) -> % --R gcd : (%,%) -> % hash : % -> SingleInteger --R inGroundField? : % -> Boolean index : PositiveInteger -> % --R init : () -> % inv : % -> % ---R latex : % -> String lcm : List % -> % +--R latex : % -> String lcm : List(%) -> % --R lcm : (%,%) -> % lookup : % -> PositiveInteger --R norm : % -> % one? : % -> Boolean --R order : % -> PositiveInteger prime? : % -> Boolean --R primeFrobenius : % -> % primitive? : % -> Boolean --R primitiveElement : () -> % ?quo? : (%,%) -> % --R random : () -> % recip : % -> Union(%,"failed") ---R ?rem? : (%,%) -> % represents : Vector % -> % +--R ?rem? : (%,%) -> % represents : Vector(%) -> % --R retract : % -> % sample : () -> % --R size : () -> NonNegativeInteger sizeLess? : (%,%) -> Boolean ---R squareFree : % -> Factored % squareFreePart : % -> % +--R squareFree : % -> Factored(%) squareFreePart : % -> % --R trace : % -> % transcendent? : % -> Boolean --R unit? : % -> Boolean unitCanonical : % -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean @@ -62185,42 +62351,42 @@ InnerPAdicInteger(p,unBalanced?): Exports == Implementation where --R Frobenius : % -> % if $ has FINITE --R Frobenius : (%,NonNegativeInteger) -> % if $ has FINITE --R ?^? : (%,NonNegativeInteger) -> % ---R basis : PositiveInteger -> Vector % +--R basis : PositiveInteger -> Vector(%) --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") ---R conditionP : Matrix % -> Union(Vector %,"failed") ---R coordinates : Vector % -> Matrix % +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") +--R coordinates : Vector(%) -> Matrix(%) --R createNormalElement : () -> % if $ has FINITE ---R definingPolynomial : () -> SparseUnivariatePolynomial % ---R degree : % -> OnePointCompletion PositiveInteger +--R definingPolynomial : () -> SparseUnivariatePolynomial(%) +--R degree : % -> OnePointCompletion(PositiveInteger) --R differentiate : (%,NonNegativeInteger) -> % --R discreteLog : % -> NonNegativeInteger --R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") --R divide : (%,%) -> Record(quotient: %,remainder: %) --R euclideanSize : % -> NonNegativeInteger ---R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") --R exquo : (%,%) -> Union(%,"failed") --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) ---R extensionDegree : () -> OnePointCompletion PositiveInteger +--R extensionDegree : () -> OnePointCompletion(PositiveInteger) --R extensionDegree : () -> PositiveInteger ---R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R factorsOfCyclicGroupSize : () -> List(Record(factor: Integer,exponent: Integer)) +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) --R generator : () -> % if $ has FINITE ---R linearAssociatedExp : (%,SparseUnivariatePolynomial %) -> % if $ has FINITE ---R linearAssociatedLog : % -> SparseUnivariatePolynomial % if $ has FINITE ---R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial %,"failed") if $ has FINITE ---R linearAssociatedOrder : % -> SparseUnivariatePolynomial % if $ has FINITE ---R minimalPolynomial : % -> SparseUnivariatePolynomial % ---R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial % if $ has FINITE ---R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R linearAssociatedExp : (%,SparseUnivariatePolynomial(%)) -> % if $ has FINITE +--R linearAssociatedLog : % -> SparseUnivariatePolynomial(%) if $ has FINITE +--R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial(%),"failed") if $ has FINITE +--R linearAssociatedOrder : % -> SparseUnivariatePolynomial(%) if $ has FINITE +--R minimalPolynomial : % -> SparseUnivariatePolynomial(%) +--R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial(%) if $ has FINITE +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") --R nextItem : % -> Union(%,"failed") --R norm : (%,PositiveInteger) -> % if $ has FINITE --R normal? : % -> Boolean if $ has FINITE --R normalElement : () -> % if $ has FINITE ---R order : % -> OnePointCompletion PositiveInteger +--R order : % -> OnePointCompletion(PositiveInteger) --R primeFrobenius : (%,NonNegativeInteger) -> % ---R principalIdeal : List % -> Record(coef: List %,generator: %) +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) --R representationType : () -> Union("prime",polynomial,normal,cyclic) --R retractIfCan : % -> Union(%,"failed") --R subtractIfCan : (%,%) -> Union(%,"failed") @@ -62537,7 +62703,8 @@ InnerPrimeField(p:PositiveInteger): Exports == Implementation where --S 1 of 1 )show InnerSparseUnivariatePowerSeries ---R InnerSparseUnivariatePowerSeries Coef: Ring is a domain constructor +--R +--R InnerSparseUnivariatePowerSeries(Coef: Ring) is a domain constructor --R Abbreviation for InnerSparseUnivariatePowerSeries is ISUPS --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ISUPS @@ -62564,80 +62731,80 @@ InnerPrimeField(p:PositiveInteger): Exports == Implementation where --R taylorQuoByVar : % -> % truncate : (%,Integer) -> % --R variable : % -> Symbol zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean ---R ?*? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT ---R ?*? : (Fraction Integer,%) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) +--R ?*? : (Fraction(Integer),%) -> % if Coef has ALGEBRA(FRAC(INT)) --R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,Coef) -> % if Coef has FIELD --R D : % -> % if Coef has *: (Integer,Coef) -> Coef --R D : (%,NonNegativeInteger) -> % if Coef has *: (Integer,Coef) -> Coef ---R D : (%,Symbol) -> % if Coef has *: (Integer,Coef) -> Coef and Coef has PDRING SYMBOL ---R D : (%,List Symbol) -> % if Coef has *: (Integer,Coef) -> Coef and Coef has PDRING SYMBOL ---R D : (%,Symbol,NonNegativeInteger) -> % if Coef has *: (Integer,Coef) -> Coef and Coef has PDRING SYMBOL ---R D : (%,List Symbol,List NonNegativeInteger) -> % if Coef has *: (Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R D : (%,Symbol) -> % if Coef has *: (Integer,Coef) -> Coef and Coef has PDRING(SYMBOL) +--R D : (%,List(Symbol)) -> % if Coef has *: (Integer,Coef) -> Coef and Coef has PDRING(SYMBOL) +--R D : (%,Symbol,NonNegativeInteger) -> % if Coef has *: (Integer,Coef) -> Coef and Coef has PDRING(SYMBOL) +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has *: (Integer,Coef) -> Coef and Coef has PDRING(SYMBOL) --R ?^? : (%,NonNegativeInteger) -> % --R approximate : (%,Integer) -> Coef if Coef has **: (Coef,Integer) -> Coef and Coef has coerce: Symbol -> Coef --R associates? : (%,%) -> Boolean if Coef has INTDOM ---R cAcos : % -> % if Coef has ALGEBRA FRAC INT ---R cAcosh : % -> % if Coef has ALGEBRA FRAC INT ---R cAcot : % -> % if Coef has ALGEBRA FRAC INT ---R cAcoth : % -> % if Coef has ALGEBRA FRAC INT ---R cAcsc : % -> % if Coef has ALGEBRA FRAC INT ---R cAcsch : % -> % if Coef has ALGEBRA FRAC INT ---R cAsec : % -> % if Coef has ALGEBRA FRAC INT ---R cAsech : % -> % if Coef has ALGEBRA FRAC INT ---R cAsin : % -> % if Coef has ALGEBRA FRAC INT ---R cAsinh : % -> % if Coef has ALGEBRA FRAC INT ---R cAtan : % -> % if Coef has ALGEBRA FRAC INT ---R cAtanh : % -> % if Coef has ALGEBRA FRAC INT ---R cCos : % -> % if Coef has ALGEBRA FRAC INT ---R cCosh : % -> % if Coef has ALGEBRA FRAC INT ---R cCot : % -> % if Coef has ALGEBRA FRAC INT ---R cCoth : % -> % if Coef has ALGEBRA FRAC INT ---R cCsc : % -> % if Coef has ALGEBRA FRAC INT ---R cCsch : % -> % if Coef has ALGEBRA FRAC INT ---R cExp : % -> % if Coef has ALGEBRA FRAC INT ---R cLog : % -> % if Coef has ALGEBRA FRAC INT ---R cPower : (%,Coef) -> % if Coef has ALGEBRA FRAC INT ---R cRationalPower : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT ---R cSec : % -> % if Coef has ALGEBRA FRAC INT ---R cSech : % -> % if Coef has ALGEBRA FRAC INT ---R cSin : % -> % if Coef has ALGEBRA FRAC INT ---R cSinh : % -> % if Coef has ALGEBRA FRAC INT ---R cTan : % -> % if Coef has ALGEBRA FRAC INT ---R cTanh : % -> % if Coef has ALGEBRA FRAC INT +--R cAcos : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R cAcosh : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R cAcot : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R cAcoth : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R cAcsc : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R cAcsch : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R cAsec : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R cAsech : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R cAsin : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R cAsinh : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R cAtan : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R cAtanh : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R cCos : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R cCosh : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R cCot : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R cCoth : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R cCsc : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R cCsch : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R cExp : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R cLog : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R cPower : (%,Coef) -> % if Coef has ALGEBRA(FRAC(INT)) +--R cRationalPower : (%,Fraction(Integer)) -> % if Coef has ALGEBRA(FRAC(INT)) +--R cSec : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R cSech : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R cSin : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R cSinh : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R cTan : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R cTanh : % -> % if Coef has ALGEBRA(FRAC(INT)) --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ --R coerce : Coef -> % if Coef has COMRING --R coerce : % -> % if Coef has INTDOM ---R coerce : Fraction Integer -> % if Coef has ALGEBRA FRAC INT +--R coerce : Fraction(Integer) -> % if Coef has ALGEBRA(FRAC(INT)) --R differentiate : % -> % if Coef has *: (Integer,Coef) -> Coef --R differentiate : (%,NonNegativeInteger) -> % if Coef has *: (Integer,Coef) -> Coef ---R differentiate : (%,Symbol) -> % if Coef has *: (Integer,Coef) -> Coef and Coef has PDRING SYMBOL ---R differentiate : (%,List Symbol) -> % if Coef has *: (Integer,Coef) -> Coef and Coef has PDRING SYMBOL ---R differentiate : (%,Symbol,NonNegativeInteger) -> % if Coef has *: (Integer,Coef) -> Coef and Coef has PDRING SYMBOL ---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if Coef has *: (Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R differentiate : (%,Symbol) -> % if Coef has *: (Integer,Coef) -> Coef and Coef has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol)) -> % if Coef has *: (Integer,Coef) -> Coef and Coef has PDRING(SYMBOL) +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if Coef has *: (Integer,Coef) -> Coef and Coef has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if Coef has *: (Integer,Coef) -> Coef and Coef has PDRING(SYMBOL) --R ?.? : (%,%) -> % if Integer has SGROUP ---R eval : (%,Coef) -> Stream Coef if Coef has **: (Coef,Integer) -> Coef +--R eval : (%,Coef) -> Stream(Coef) if Coef has **: (Coef,Integer) -> Coef --R exquo : (%,%) -> Union(%,"failed") if Coef has INTDOM ---R getRef : % -> Reference OrderedCompletion Integer ---R getStream : % -> Stream Record(k: Integer,c: Coef) +--R getRef : % -> Reference(OrderedCompletion(Integer)) +--R getStream : % -> Stream(Record(k: Integer,c: Coef)) --R iExquo : (%,%,Boolean) -> Union(%,"failed") ---R integrate : % -> % if Coef has ALGEBRA FRAC INT ---R makeSeries : (Reference OrderedCompletion Integer,Stream Record(k: Integer,c: Coef)) -> % ---R monomial : (%,List SingletonAsOrderedSet,List Integer) -> % +--R integrate : % -> % if Coef has ALGEBRA(FRAC(INT)) +--R makeSeries : (Reference(OrderedCompletion(Integer)),Stream(Record(k: Integer,c: Coef))) -> % +--R monomial : (%,List(SingletonAsOrderedSet),List(Integer)) -> % --R monomial : (%,SingletonAsOrderedSet,Integer) -> % --R multiplyCoefficients : ((Integer -> Coef),%) -> % --R multiplyExponents : (%,PositiveInteger) -> % ---R series : Stream Record(k: Integer,c: Coef) -> % ---R seriesToOutputForm : (Stream Record(k: Integer,c: Coef),Reference OrderedCompletion Integer,Symbol,Coef,Fraction Integer) -> OutputForm +--R series : Stream(Record(k: Integer,c: Coef)) -> % +--R seriesToOutputForm : (Stream(Record(k: Integer,c: Coef)),Reference(OrderedCompletion(Integer)),Symbol,Coef,Fraction(Integer)) -> OutputForm --R subtractIfCan : (%,%) -> Union(%,"failed") ---R terms : % -> Stream Record(k: Integer,c: Coef) +--R terms : % -> Stream(Record(k: Integer,c: Coef)) --R truncate : (%,Integer,Integer) -> % --R unit? : % -> Boolean if Coef has INTDOM --R unitCanonical : % -> % if Coef has INTDOM --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Coef has INTDOM ---R variables : % -> List SingletonAsOrderedSet +--R variables : % -> List(SingletonAsOrderedSet) --R --E 1 @@ -63835,6 +64002,7 @@ InnerSparseUnivariatePowerSeries(Coef): Exports == Implementation where --S 1 of 1 )show InnerTable +--R --R InnerTable(Key: SetCategory,Entry: SetCategory,addDom) where --R addDom: TableAggregate(Key,Entry) with --R finiteAggregate is a domain constructor @@ -63846,9 +64014,9 @@ InnerSparseUnivariatePowerSeries(Coef): Exports == Implementation where --R copy : % -> % dictionary : () -> % --R elt : (%,Key,Entry) -> Entry ?.? : (%,Key) -> Entry --R empty : () -> % empty? : % -> Boolean ---R entries : % -> List Entry eq? : (%,%) -> Boolean ---R index? : (Key,%) -> Boolean indices : % -> List Key ---R key? : (Key,%) -> Boolean keys : % -> List Key +--R entries : % -> List(Entry) eq? : (%,%) -> Boolean +--R index? : (Key,%) -> Boolean indices : % -> List(Key) +--R key? : (Key,%) -> Boolean keys : % -> List(Key) --R map : ((Entry -> Entry),%) -> % qelt : (%,Key) -> Entry --R sample : () -> % setelt : (%,Key,Entry) -> Entry --R table : () -> % @@ -63856,24 +64024,24 @@ InnerSparseUnivariatePowerSeries(Coef): Exports == Implementation where --R ?=? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT --R any? : ((Entry -> Boolean),%) -> Boolean if $ has finiteAggregate --R any? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate ---R bag : List Record(key: Key,entry: Entry) -> % +--R bag : List(Record(key: Key,entry: Entry)) -> % --R coerce : % -> OutputForm if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT ---R construct : List Record(key: Key,entry: Entry) -> % ---R convert : % -> InputForm if Record(key: Key,entry: Entry) has KONVERT INFORM +--R construct : List(Record(key: Key,entry: Entry)) -> % +--R convert : % -> InputForm if Record(key: Key,entry: Entry) has KONVERT(INFORM) --R count : ((Entry -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate --R count : (Entry,%) -> NonNegativeInteger if $ has finiteAggregate and Entry has SETCAT --R count : (Record(key: Key,entry: Entry),%) -> NonNegativeInteger if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT --R count : ((Record(key: Key,entry: Entry) -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate ---R dictionary : List Record(key: Key,entry: Entry) -> % +--R dictionary : List(Record(key: Key,entry: Entry)) -> % --R entry? : (Entry,%) -> Boolean if $ has finiteAggregate and Entry has SETCAT ---R eval : (%,List Equation Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT ---R eval : (%,Equation Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT ---R eval : (%,Entry,Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT ---R eval : (%,List Entry,List Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT ---R eval : (%,List Record(key: Key,entry: Entry),List Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT ---R eval : (%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT ---R eval : (%,Equation Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT ---R eval : (%,List Equation Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,List(Equation(Entry))) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R eval : (%,Equation(Entry)) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R eval : (%,Entry,Entry) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R eval : (%,List(Entry),List(Entry)) -> % if Entry has EVALAB(Entry) and Entry has SETCAT +--R eval : (%,List(Record(key: Key,entry: Entry)),List(Record(key: Key,entry: Entry))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,Equation(Record(key: Key,entry: Entry))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,List(Equation(Record(key: Key,entry: Entry)))) -> % if Record(key: Key,entry: Entry) has EVALAB(Record(key: Key,entry: Entry)) and Record(key: Key,entry: Entry) has SETCAT --R every? : ((Entry -> Boolean),%) -> Boolean if $ has finiteAggregate --R every? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate --R extract! : % -> Record(key: Key,entry: Entry) @@ -63892,12 +64060,12 @@ InnerSparseUnivariatePowerSeries(Coef): Exports == Implementation where --R maxIndex : % -> Key if Key has ORDSET --R member? : (Entry,%) -> Boolean if $ has finiteAggregate and Entry has SETCAT --R member? : (Record(key: Key,entry: Entry),%) -> Boolean if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT ---R members : % -> List Entry if $ has finiteAggregate ---R members : % -> List Record(key: Key,entry: Entry) if $ has finiteAggregate +--R members : % -> List(Entry) if $ has finiteAggregate +--R members : % -> List(Record(key: Key,entry: Entry)) if $ has finiteAggregate --R minIndex : % -> Key if Key has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean ---R parts : % -> List Entry if $ has finiteAggregate ---R parts : % -> List Record(key: Key,entry: Entry) if $ has finiteAggregate +--R parts : % -> List(Entry) if $ has finiteAggregate +--R parts : % -> List(Record(key: Key,entry: Entry)) if $ has finiteAggregate --R qsetelt! : (%,Key,Entry) -> Entry if $ has shallowlyMutable --R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%) -> Record(key: Key,entry: Entry) if $ has finiteAggregate --R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has finiteAggregate @@ -63913,7 +64081,7 @@ InnerSparseUnivariatePowerSeries(Coef): Exports == Implementation where --R select! : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate --R size? : (%,NonNegativeInteger) -> Boolean --R swap! : (%,Key,Key) -> Void if $ has shallowlyMutable ---R table : List Record(key: Key,entry: Entry) -> % +--R table : List(Record(key: Key,entry: Entry)) -> % --R ?~=? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT --R --E 1 @@ -64044,7 +64212,8 @@ InnerTable(Key: SetCategory, Entry: SetCategory, addDom):Exports == Implementati --S 1 of 1 )show InnerTaylorSeries ---R InnerTaylorSeries Coef: Ring is a domain constructor +--R +--R InnerTaylorSeries(Coef: Ring) is a domain constructor --R Abbreviation for InnerTaylorSeries is ITAYLOR --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ITAYLOR @@ -64057,12 +64226,12 @@ InnerTable(Key: SetCategory, Entry: SetCategory, addDom):Exports == Implementati --R ?-? : (%,%) -> % -? : % -> % --R ?=? : (%,%) -> Boolean 1 : () -> % --R 0 : () -> % ?^? : (%,PositiveInteger) -> % ---R coefficients : % -> Stream Coef coerce : Integer -> % +--R coefficients : % -> Stream(Coef) coerce : Integer -> % --R coerce : % -> OutputForm hash : % -> SingleInteger --R latex : % -> String one? : % -> Boolean --R order : % -> NonNegativeInteger pole? : % -> Boolean --R recip : % -> Union(%,"failed") sample : () -> % ---R series : Stream Coef -> % zero? : % -> Boolean +--R series : Stream(Coef) -> % zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean --R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,NonNegativeInteger) -> % @@ -64286,6 +64455,7 @@ InnerTaylorSeries(Coef): Exports == Implementation where --S 1 of 1 )show InputForm +--R --R InputForm is a domain constructor --R Abbreviation for InputForm is INFORM --R This constructor is not exposed in this frame. @@ -64296,28 +64466,28 @@ InnerTaylorSeries(Coef): Exports == Implementation where --R ?**? : (%,Integer) -> % ?+? : (%,%) -> % --R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R atom? : % -> Boolean binary : (%,List %) -> % +--R atom? : % -> Boolean binary : (%,List(%)) -> % --R car : % -> % cdr : % -> % --R coerce : % -> OutputForm convert : SExpression -> % --R convert : % -> SExpression convert : OutputForm -> % --R convert : DoubleFloat -> % convert : Integer -> % --R convert : Symbol -> % convert : String -> % ---R convert : List % -> % declare : List % -> Symbol ---R destruct : % -> List % ?.? : (%,List Integer) -> % +--R convert : List(%) -> % declare : List(%) -> Symbol +--R destruct : % -> List(%) ?.? : (%,List(Integer)) -> % --R ?.? : (%,Integer) -> % eq : (%,%) -> Boolean --R expr : % -> OutputForm flatten : % -> % --R float : % -> DoubleFloat float? : % -> Boolean --R hash : % -> SingleInteger integer : % -> Integer --R integer? : % -> Boolean interpret : % -> Any ---R lambda : (%,List Symbol) -> % latex : % -> String +--R lambda : (%,List(Symbol)) -> % latex : % -> String --R list? : % -> Boolean null? : % -> Boolean --R pair? : % -> Boolean parse : String -> % --R string : % -> String string? : % -> Boolean --R symbol : % -> Symbol symbol? : % -> Boolean --R unparse : % -> String ?~=? : (%,%) -> Boolean --R ?**? : (%,NonNegativeInteger) -> % ---R compile : (Symbol,List %) -> Symbol ---R function : (%,List Symbol,Symbol) -> % +--R compile : (Symbol,List(%)) -> Symbol +--R function : (%,List(Symbol),Symbol) -> % --R --E 1 @@ -64783,7 +64953,7 @@ reduce(lcm,[2,45,-89,78,100,-45]) --R 13 --R (24) -- --R 4 ---R Type: Fraction Integer +--R Type: Fraction(Integer) --E 24 --S 25 of 42 @@ -64840,7 +65010,7 @@ factor 102400 --R --R 12 2 --R (31) 2 5 ---R Type: Factored Integer +--R Type: Factored(Integer) --E 31 --S 32 of 42 @@ -64880,7 +65050,7 @@ primes(100,175) --R --R --R (36) [173,167,163,157,151,149,139,137,131,127,113,109,107,103,101] ---R Type: List Integer +--R Type: List(Integer) --E 36 --S 37 of 42 @@ -64889,7 +65059,7 @@ factor(2 :: Complex Integer) --R --R 2 --R (37) - %i (1 + %i) ---R Type: Factored Complex Integer +--R Type: Factored(Complex(Integer)) --E 37 --S 38 of 42 @@ -64897,7 +65067,7 @@ factor(2 :: Complex Integer) --R --R --R (38) [0,1,1,2,3,5,8,13,21,34,...] ---R Type: Stream Integer +--R Type: Stream(Integer) --E 38 --S 39 of 42 @@ -64905,7 +65075,7 @@ factor(2 :: Complex Integer) --R --R --R (39) [0,1,- 1,1,1,1,- 1,- 1,- 1,1,- 1] ---R Type: List Integer +--R Type: List(Integer) --E 39 --S 40 of 42 @@ -64913,7 +65083,7 @@ factor(2 :: Complex Integer) --R --R --R (40) [0,1,1,0,1,0,0,- 1,1,0] ---R Type: List Integer +--R Type: List(Integer) --E 40 --S 41 of 42 @@ -64921,7 +65091,7 @@ factor(2 :: Complex Integer) --R --R --R (41) [1,1,2,2,4,2,6,4,6,4,...] ---R Type: Stream Integer +--R Type: Stream(Integer) --E 41 --S 42 of 42 @@ -64929,7 +65099,7 @@ factor(2 :: Complex Integer) --R --R --R (42) [1,- 1,- 1,0,- 1,1,- 1,0,0,1,...] ---R Type: Stream Integer +--R Type: Stream(Integer) --E 42 )spool )lisp (bye) @@ -65539,7 +65709,8 @@ Integer: Join(IntegerNumberSystem, ConvertibleTo String, OpenMath) with --S 1 of 1 )show IntegerMod ---R IntegerMod p: PositiveInteger is a domain constructor +--R +--R IntegerMod(p: PositiveInteger) is a domain constructor --R Abbreviation for IntegerMod is ZMOD --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ZMOD @@ -65719,6 +65890,7 @@ IntegerMod(p:PositiveInteger): --S 1 of 1 )show IntegrationFunctionsTable +--R --R IntegrationFunctionsTable is a domain constructor --R Abbreviation for IntegrationFunctionsTable is INTFTBL --R This constructor is exposed in this frame. @@ -65726,12 +65898,12 @@ IntegerMod(p:PositiveInteger): --R --R------------------------------- Operations -------------------------------- --R clearTheFTable : () -> Void showTheFTable : () -> % ---R entries : % -> List Record(key: Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),entry: Record(endPointContinuity: Union(continuous: Continuous at the end points,lowerSingular: There is a singularity at the lower end point,upperSingular: There is a singularity at the upper end point,bothSingular: There are singularities at both end points,notEvaluated: End point continuity not yet evaluated),singularitiesStream: Union(str: Stream DoubleFloat,notEvaluated: Internal singularities not yet evaluated),range: Union(finite: The range is finite,lowerInfinite: The bottom of range is infinite,upperInfinite: The top of range is infinite,bothInfinite: Both top and bottom points are infinite,notEvaluated: Range not yet evaluated))) ---R entry : Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat) -> Record(endPointContinuity: Union(continuous: Continuous at the end points,lowerSingular: There is a singularity at the lower end point,upperSingular: There is a singularity at the upper end point,bothSingular: There are singularities at both end points,notEvaluated: End point continuity not yet evaluated),singularitiesStream: Union(str: Stream DoubleFloat,notEvaluated: Internal singularities not yet evaluated),range: Union(finite: The range is finite,lowerInfinite: The bottom of range is infinite,upperInfinite: The top of range is infinite,bothInfinite: Both top and bottom points are infinite,notEvaluated: Range not yet evaluated)) ---R fTable : List Record(key: Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),entry: Record(endPointContinuity: Union(continuous: Continuous at the end points,lowerSingular: There is a singularity at the lower end point,upperSingular: There is a singularity at the upper end point,bothSingular: There are singularities at both end points,notEvaluated: End point continuity not yet evaluated),singularitiesStream: Union(str: Stream DoubleFloat,notEvaluated: Internal singularities not yet evaluated),range: Union(finite: The range is finite,lowerInfinite: The bottom of range is infinite,upperInfinite: The top of range is infinite,bothInfinite: Both top and bottom points are infinite,notEvaluated: Range not yet evaluated))) -> % ---R insert! : Record(key: Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),entry: Record(endPointContinuity: Union(continuous: Continuous at the end points,lowerSingular: There is a singularity at the lower end point,upperSingular: There is a singularity at the upper end point,bothSingular: There are singularities at both end points,notEvaluated: End point continuity not yet evaluated),singularitiesStream: Union(str: Stream DoubleFloat,notEvaluated: Internal singularities not yet evaluated),range: Union(finite: The range is finite,lowerInfinite: The bottom of range is infinite,upperInfinite: The top of range is infinite,bothInfinite: Both top and bottom points are infinite,notEvaluated: Range not yet evaluated))) -> % ---R keys : % -> List Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat) ---R showAttributes : Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat) -> Union(Record(endPointContinuity: Union(continuous: Continuous at the end points,lowerSingular: There is a singularity at the lower end point,upperSingular: There is a singularity at the upper end point,bothSingular: There are singularities at both end points,notEvaluated: End point continuity not yet evaluated),singularitiesStream: Union(str: Stream DoubleFloat,notEvaluated: Internal singularities not yet evaluated),range: Union(finite: The range is finite,lowerInfinite: The bottom of range is infinite,upperInfinite: The top of range is infinite,bothInfinite: Both top and bottom points are infinite,notEvaluated: Range not yet evaluated)),"failed") +--R entries : % -> List(Record(key: Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat),entry: Record(endPointContinuity: Union(continuous: Continuous at the end points,lowerSingular: There is a singularity at the lower end point,upperSingular: There is a singularity at the upper end point,bothSingular: There are singularities at both end points,notEvaluated: End point continuity not yet evaluated),singularitiesStream: Union(str: Stream(DoubleFloat),notEvaluated: Internal singularities not yet evaluated),range: Union(finite: The range is finite,lowerInfinite: The bottom of range is infinite,upperInfinite: The top of range is infinite,bothInfinite: Both top and bottom points are infinite,notEvaluated: Range not yet evaluated)))) +--R entry : Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat) -> Record(endPointContinuity: Union(continuous: Continuous at the end points,lowerSingular: There is a singularity at the lower end point,upperSingular: There is a singularity at the upper end point,bothSingular: There are singularities at both end points,notEvaluated: End point continuity not yet evaluated),singularitiesStream: Union(str: Stream(DoubleFloat),notEvaluated: Internal singularities not yet evaluated),range: Union(finite: The range is finite,lowerInfinite: The bottom of range is infinite,upperInfinite: The top of range is infinite,bothInfinite: Both top and bottom points are infinite,notEvaluated: Range not yet evaluated)) +--R fTable : List(Record(key: Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat),entry: Record(endPointContinuity: Union(continuous: Continuous at the end points,lowerSingular: There is a singularity at the lower end point,upperSingular: There is a singularity at the upper end point,bothSingular: There are singularities at both end points,notEvaluated: End point continuity not yet evaluated),singularitiesStream: Union(str: Stream(DoubleFloat),notEvaluated: Internal singularities not yet evaluated),range: Union(finite: The range is finite,lowerInfinite: The bottom of range is infinite,upperInfinite: The top of range is infinite,bothInfinite: Both top and bottom points are infinite,notEvaluated: Range not yet evaluated)))) -> % +--R insert! : Record(key: Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat),entry: Record(endPointContinuity: Union(continuous: Continuous at the end points,lowerSingular: There is a singularity at the lower end point,upperSingular: There is a singularity at the upper end point,bothSingular: There are singularities at both end points,notEvaluated: End point continuity not yet evaluated),singularitiesStream: Union(str: Stream(DoubleFloat),notEvaluated: Internal singularities not yet evaluated),range: Union(finite: The range is finite,lowerInfinite: The bottom of range is infinite,upperInfinite: The top of range is infinite,bothInfinite: Both top and bottom points are infinite,notEvaluated: Range not yet evaluated))) -> % +--R keys : % -> List(Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat)) +--R showAttributes : Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat) -> Union(Record(endPointContinuity: Union(continuous: Continuous at the end points,lowerSingular: There is a singularity at the lower end point,upperSingular: There is a singularity at the upper end point,bothSingular: There are singularities at both end points,notEvaluated: End point continuity not yet evaluated),singularitiesStream: Union(str: Stream(DoubleFloat),notEvaluated: Internal singularities not yet evaluated),range: Union(finite: The range is finite,lowerInfinite: The bottom of range is infinite,upperInfinite: The top of range is infinite,bothInfinite: Both top and bottom points are infinite,notEvaluated: Range not yet evaluated)),"failed") --R --E 1 @@ -65881,13 +66053,14 @@ IntegrationFunctionsTable(): E == I where --S 1 of 1 )show IntegrationResult ---R IntegrationResult F: Field is a domain constructor +--R +--R IntegrationResult(F: Field) is a domain constructor --R Abbreviation for IntegrationResult is IR --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for IR --R --R------------------------------- Operations -------------------------------- ---R ?*? : (%,Fraction Integer) -> % ?*? : (Fraction Integer,%) -> % +--R ?*? : (%,Fraction(Integer)) -> % ?*? : (Fraction(Integer),%) -> % --R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean @@ -65899,11 +66072,11 @@ IntegrationFunctionsTable(): E == I where --R sample : () -> % zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean --R ?*? : (NonNegativeInteger,%) -> % ---R differentiate : (%,Symbol) -> F if F has PDRING SYMBOL ---R integral : (F,Symbol) -> % if F has RETRACT SYMBOL ---R logpart : % -> List Record(scalar: Fraction Integer,coeff: SparseUnivariatePolynomial F,logand: SparseUnivariatePolynomial F) ---R mkAnswer : (F,List Record(scalar: Fraction Integer,coeff: SparseUnivariatePolynomial F,logand: SparseUnivariatePolynomial F),List Record(integrand: F,intvar: F)) -> % ---R notelem : % -> List Record(integrand: F,intvar: F) +--R differentiate : (%,Symbol) -> F if F has PDRING(SYMBOL) +--R integral : (F,Symbol) -> % if F has RETRACT(SYMBOL) +--R logpart : % -> List(Record(scalar: Fraction(Integer),coeff: SparseUnivariatePolynomial(F),logand: SparseUnivariatePolynomial(F))) +--R mkAnswer : (F,List(Record(scalar: Fraction(Integer),coeff: SparseUnivariatePolynomial(F),logand: SparseUnivariatePolynomial(F))),List(Record(integrand: F,intvar: F))) -> % +--R notelem : % -> List(Record(integrand: F,intvar: F)) --R retractIfCan : % -> Union(F,"failed") --R subtractIfCan : (%,%) -> Union(%,"failed") --R @@ -66900,7 +67073,7 @@ x :: Expression Integer --R --R --R (1) x ---R Type: Expression Integer +--R Type: Expression(Integer) --E 1 --S 2 of 19 @@ -66908,7 +67081,7 @@ kernel x --R --R --R (2) x ---R Type: Kernel Expression Integer +--R Type: Kernel(Expression(Integer)) --E 2 --S 3 of 19 @@ -66916,7 +67089,7 @@ sin(x) + cos(x) --R --R --R (3) sin(x) + cos(x) ---R Type: Expression Integer +--R Type: Expression(Integer) --E 3 --S 4 of 19 @@ -66924,7 +67097,7 @@ kernels % --R --R --R (4) [sin(x),cos(x)] ---R Type: List Kernel Expression Integer +--R Type: List(Kernel(Expression(Integer))) --E 4 --S 5 of 19 @@ -66933,7 +67106,7 @@ sin(x)**2 + sin(x) + cos(x) --R --R 2 --R (5) sin(x) + sin(x) + cos(x) ---R Type: Expression Integer +--R Type: Expression(Integer) --E 5 --S 6 of 19 @@ -66941,7 +67114,7 @@ kernels % --R --R --R (6) [sin(x),cos(x)] ---R Type: List Kernel Expression Integer +--R Type: List(Kernel(Expression(Integer))) --E 6 --S 7 of 19 @@ -66949,7 +67122,7 @@ kernels(1 :: Expression Integer) --R --R --R (7) [] ---R Type: List Kernel Expression Integer +--R Type: List(Kernel(Expression(Integer))) --E 7 --S 8 of 19 @@ -66957,7 +67130,7 @@ mainKernel(cos(x) + tan(x)) --R --R --R (8) tan(x) ---R Type: Union(Kernel Expression Integer,...) +--R Type: Union(Kernel(Expression(Integer)),...) --E 8 --S 9 of 19 @@ -67021,7 +67194,7 @@ e := f(x, y, 10) --R --R --R (16) f(x,y,10) ---R Type: Expression Integer +--R Type: Expression(Integer) --E 16 --S 17 of 19 @@ -67045,7 +67218,7 @@ argument mainKernel e --R --R --R (19) [x,y,10] ---R Type: List Expression Integer +--R Type: List(Expression(Integer)) --E 19 )spool )lisp (bye) @@ -67391,7 +67564,7 @@ ey: KeyedAccessFile(Integer) := open("editor.year", "output") --R --R --R (1) "editor.year" ---R Type: KeyedAccessFile Integer +--R Type: KeyedAccessFile(Integer) --E 1 --S 2 of 20 @@ -67471,7 +67644,7 @@ keys ey --R --R --R (11) ["Fitch","Caviness"] ---R Type: List String +--R Type: List(String) --E 11 --S 12 of 20 @@ -67495,7 +67668,7 @@ reopen!(ey, "output") --R --R --R (14) "editor.year" ---R Type: KeyedAccessFile Integer +--R Type: KeyedAccessFile(Integer) --E 14 --S 15 of 20 @@ -67527,7 +67700,7 @@ close! ey --R --R --R (18) "editor.year" ---R Type: KeyedAccessFile Integer +--R Type: KeyedAccessFile(Integer) --E 18 --S 19 of 20 @@ -67535,7 +67708,7 @@ keys ey --R --R --R (19) ["Wang","Calmet","van Hulzen","Fitch","Caviness"] ---R Type: List String +--R Type: List(String) --E 19 --S 20 of 20 @@ -67543,7 +67716,7 @@ members ey --R --R --R (20) [1981,1982,1983,1984,1985] ---R Type: List Integer +--R Type: List(Integer) --E 20 )system rm -r editor.year @@ -67884,7 +68057,8 @@ KeyedAccessFile(Entry): KAFcategory == KAFcapsule where --S 1 of 1 )show LaurentPolynomial ---R LaurentPolynomial(R: IntegralDomain,UP: UnivariatePolynomialCategory R) is a domain constructor +--R +--R LaurentPolynomial(R: IntegralDomain,UP: UnivariatePolynomialCategory(R)) is a domain constructor --R Abbreviation for LaurentPolynomial is LAUPOL --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for LAUPOL @@ -67900,7 +68074,7 @@ KeyedAccessFile(Entry): KAFcategory == KAFcapsule where --R coefficient : (%,Integer) -> R coerce : UP -> % --R coerce : R -> % coerce : % -> % --R coerce : Integer -> % coerce : % -> OutputForm ---R convert : % -> Fraction UP degree : % -> Integer +--R convert : % -> Fraction(UP) degree : % -> Integer --R hash : % -> SingleInteger latex : % -> String --R leadingCoefficient : % -> R monomial : (R,Integer) -> % --R monomial? : % -> Boolean one? : % -> Boolean @@ -67913,45 +68087,45 @@ KeyedAccessFile(Entry): KAFcategory == KAFcapsule where --R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,NonNegativeInteger) -> % --R D : (%,NonNegativeInteger) -> % if UP has DIFRING ---R D : (%,Symbol) -> % if UP has PDRING SYMBOL ---R D : (%,List Symbol) -> % if UP has PDRING SYMBOL ---R D : (%,Symbol,NonNegativeInteger) -> % if UP has PDRING SYMBOL ---R D : (%,List Symbol,List NonNegativeInteger) -> % if UP has PDRING SYMBOL +--R D : (%,Symbol) -> % if UP has PDRING(SYMBOL) +--R D : (%,List(Symbol)) -> % if UP has PDRING(SYMBOL) +--R D : (%,Symbol,NonNegativeInteger) -> % if UP has PDRING(SYMBOL) +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if UP has PDRING(SYMBOL) --R D : (%,(UP -> UP),NonNegativeInteger) -> % --R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if R has CHARNZ ---R coerce : Fraction Integer -> % if R has RETRACT FRAC INT +--R coerce : Fraction(Integer) -> % if R has RETRACT(FRAC(INT)) --R differentiate : % -> % if UP has DIFRING --R differentiate : (%,NonNegativeInteger) -> % if UP has DIFRING ---R differentiate : (%,Symbol) -> % if UP has PDRING SYMBOL ---R differentiate : (%,List Symbol) -> % if UP has PDRING SYMBOL ---R differentiate : (%,Symbol,NonNegativeInteger) -> % if UP has PDRING SYMBOL ---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if UP has PDRING SYMBOL +--R differentiate : (%,Symbol) -> % if UP has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol)) -> % if UP has PDRING(SYMBOL) +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if UP has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if UP has PDRING(SYMBOL) --R differentiate : (%,(UP -> UP),NonNegativeInteger) -> % --R differentiate : (%,(UP -> UP)) -> % --R divide : (%,%) -> Record(quotient: %,remainder: %) if R has FIELD --R euclideanSize : % -> NonNegativeInteger if R has FIELD ---R expressIdealMember : (List %,%) -> Union(List %,"failed") if R has FIELD +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if R has FIELD --R exquo : (%,%) -> Union(%,"failed") --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has FIELD --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if R has FIELD --R gcd : (%,%) -> % if R has FIELD ---R gcd : List % -> % if R has FIELD ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has FIELD +--R gcd : List(%) -> % if R has FIELD +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has FIELD --R lcm : (%,%) -> % if R has FIELD ---R lcm : List % -> % if R has FIELD ---R multiEuclidean : (List %,%) -> Union(List %,"failed") if R has FIELD ---R principalIdeal : List % -> Record(coef: List %,generator: %) if R has FIELD +--R lcm : List(%) -> % if R has FIELD +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") if R has FIELD +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if R has FIELD --R ?quo? : (%,%) -> % if R has FIELD --R ?rem? : (%,%) -> % if R has FIELD ---R retract : % -> Fraction Integer if R has RETRACT FRAC INT ---R retract : % -> Integer if R has RETRACT INT +--R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT)) +--R retract : % -> Integer if R has RETRACT(INT) --R retractIfCan : % -> Union(UP,"failed") --R retractIfCan : % -> Union(R,"failed") ---R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT ---R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT ---R separate : Fraction UP -> Record(polyPart: %,fracPart: Fraction UP) if R has FIELD +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT)) +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT) +--R separate : Fraction(UP) -> Record(polyPart: %,fracPart: Fraction(UP)) if R has FIELD --R sizeLess? : (%,%) -> Boolean if R has FIELD --R subtractIfCan : (%,%) -> Union(%,"failed") --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) @@ -68229,7 +68403,7 @@ stuff."poly" := x**2 + 1 --R --R 2 --R (3) x + 1 ---R Type: Polynomial Integer +--R Type: Polynomial(Integer) --E 3 --S 4 of 7 @@ -68245,7 +68419,7 @@ keys stuff --R --R --R (5) ["str","poly","int"] ---R Type: List String +--R Type: List(String) --E 5 --S 6 of 7 @@ -68254,7 +68428,7 @@ stuff.poly --R --R 2 --R (6) x + 1 ---R Type: Polynomial Integer +--R Type: Polynomial(Integer) --E 6 --S 7 of 7 @@ -68263,7 +68437,7 @@ stuff("poly") --R --R 2 --R (7) x + 1 ---R Type: Polynomial Integer +--R Type: Polynomial(Integer) --E 7 )system rm -rf Neat.stuff @@ -68464,7 +68638,7 @@ b: Symbol := 'b coef := Fraction(Integer) --R --R ---R (3) Fraction Integer +--R (3) Fraction(Integer) --R Type: Domain --E 3 @@ -68472,7 +68646,7 @@ coef := Fraction(Integer) group := LieExponentials(Symbol, coef, 3) --R --R ---R (4) LieExponentials(Symbol,Fraction Integer,3) +--R (4) LieExponentials(Symbol,Fraction(Integer),3) --R Type: Domain --E 4 @@ -68480,7 +68654,7 @@ group := LieExponentials(Symbol, coef, 3) lpoly := LiePolynomial(Symbol, coef) --R --R ---R (5) LiePolynomial(Symbol,Fraction Integer) +--R (5) LiePolynomial(Symbol,Fraction(Integer)) --R Type: Domain --E 5 @@ -68488,7 +68662,7 @@ lpoly := LiePolynomial(Symbol, coef) poly := XPBWPolynomial(Symbol, coef) --R --R ---R (6) XPBWPolynomial(Symbol,Fraction Integer) +--R (6) XPBWPolynomial(Symbol,Fraction(Integer)) --R Type: Domain --E 6 @@ -68498,7 +68672,7 @@ ea := exp(a::lpoly)$group --R --R [a] --R (7) e ---R Type: LieExponentials(Symbol,Fraction Integer,3) +--R Type: LieExponentials(Symbol,Fraction(Integer),3) --E 7 --S 8 of 13 @@ -68507,7 +68681,7 @@ eb := exp(b::lpoly)$group --R --R [b] --R (8) e ---R Type: LieExponentials(Symbol,Fraction Integer,3) +--R Type: LieExponentials(Symbol,Fraction(Integer),3) --E 8 --S 9 of 13 @@ -68518,7 +68692,7 @@ g: group := ea*eb --R - [a b ] - [a b] --R [b] 2 [a b] 2 [a] --R (9) e e e e e ---R Type: LieExponentials(Symbol,Fraction Integer,3) +--R Type: LieExponentials(Symbol,Fraction(Integer),3) --E 9 --S 10 of 13 @@ -68537,7 +68711,7 @@ g :: poly --R 1 --R - [b][b][b] --R 6 ---R Type: XPBWPolynomial(Symbol,Fraction Integer) +--R Type: XPBWPolynomial(Symbol,Fraction(Integer)) --E 10 --S 11 of 13 @@ -68547,7 +68721,7 @@ log(g)$group --R 1 1 2 1 2 --R (11) [a] + [b] + - [a b] + -- [a b] + -- [a b ] --R 2 12 12 ---R Type: LiePolynomial(Symbol,Fraction Integer) +--R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 11 --S 12 of 13 @@ -68556,7 +68730,7 @@ g1: group := inv(g) --R --R - [b] - [a] --R (12) e e ---R Type: LieExponentials(Symbol,Fraction Integer,3) +--R Type: LieExponentials(Symbol,Fraction(Integer),3) --E 12 --S 13 of 13 @@ -68564,7 +68738,7 @@ g*g1 --R --R --R (13) 1 ---R Type: LieExponentials(Symbol,Fraction Integer,3) +--R Type: LieExponentials(Symbol,Fraction(Integer),3) --E 13 )spool )lisp (bye) @@ -68842,7 +69016,7 @@ LieExponentials(VarSet, R, Order): XDPcat == XDPdef where RN := Fraction Integer --R --R ---R (1) Fraction Integer +--R (1) Fraction(Integer) --R Type: Domain --E 1 @@ -68850,7 +69024,7 @@ RN := Fraction Integer Lpoly := LiePolynomial(Symbol,RN) --R --R ---R (2) LiePolynomial(Symbol,Fraction Integer) +--R (2) LiePolynomial(Symbol,Fraction(Integer)) --R Type: Domain --E 2 @@ -68858,7 +69032,7 @@ Lpoly := LiePolynomial(Symbol,RN) Dpoly := XDPOLY(Symbol,RN) --R --R ---R (3) XDistributedPolynomial(Symbol,Fraction Integer) +--R (3) XDistributedPolynomial(Symbol,Fraction(Integer)) --R Type: Domain --E 3 @@ -68866,7 +69040,7 @@ Dpoly := XDPOLY(Symbol,RN) Lword := LyndonWord Symbol --R --R ---R (4) LyndonWord Symbol +--R (4) LyndonWord(Symbol) --R Type: Domain --E 4 @@ -68899,7 +69073,7 @@ aa: Lpoly := a --R --R --R (8) [a] ---R Type: LiePolynomial(Symbol,Fraction Integer) +--R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 8 --S 9 of 28 @@ -68907,7 +69081,7 @@ bb: Lpoly := b --R --R --R (9) [b] ---R Type: LiePolynomial(Symbol,Fraction Integer) +--R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 9 --S 10 of 28 @@ -68915,7 +69089,7 @@ cc: Lpoly := c --R --R --R (10) [c] ---R Type: LiePolynomial(Symbol,Fraction Integer) +--R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 10 --S 11 of 28 @@ -68923,7 +69097,7 @@ p : Lpoly := [aa,bb] --R --R --R (11) [a b] ---R Type: LiePolynomial(Symbol,Fraction Integer) +--R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 11 --S 12 of 28 @@ -68932,7 +69106,7 @@ q : Lpoly := [p,bb] --R --R 2 --R (12) [a b ] ---R Type: LiePolynomial(Symbol,Fraction Integer) +--R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 12 --S 13 of 28 @@ -68941,7 +69115,7 @@ liste : List Lword := LyndonWordsList([a,b], 4) --R --R 2 2 3 2 2 3 --R (13) [[a],[b],[a b],[a b],[a b ],[a b],[a b ],[a b ]] ---R Type: List LyndonWord Symbol +--R Type: List(LyndonWord(Symbol)) --E 13 --S 14 of 28 @@ -68950,7 +69124,7 @@ r: Lpoly := p + q + 3*LiePoly(liste.4)$Lpoly --R --R 2 2 --R (14) [a b] + 3[a b] + [a b ] ---R Type: LiePolynomial(Symbol,Fraction Integer) +--R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 14 --S 15 of 28 @@ -68959,7 +69133,7 @@ s:Lpoly := [p,r] --R --R 2 2 --R (15) - 3[a b a b] + [a b a b ] ---R Type: LiePolynomial(Symbol,Fraction Integer) +--R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 15 --S 16 of 28 @@ -68968,7 +69142,7 @@ t:Lpoly := s + 2*LiePoly(liste.3) - 5*LiePoly(liste.5) --R --R 2 2 2 --R (16) 2[a b] - 5[a b ] - 3[a b a b] + [a b a b ] ---R Type: LiePolynomial(Symbol,Fraction Integer) +--R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 16 --S 17 of 28 @@ -68985,30 +69159,30 @@ mirror t --R --R 2 2 2 --R (18) - 2[a b] - 5[a b ] - 3[a b a b] + [a b a b ] ---R Type: LiePolynomial(Symbol,Fraction Integer) +--R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 18 --S 19 of 28 Jacobi(p: Lpoly, q: Lpoly, r: Lpoly): Lpoly == _ [ [p,q]$Lpoly, r] + [ [q,r]$Lpoly, p] + [ [r,p]$Lpoly, q] --R ---R Function declaration Jacobi : (LiePolynomial(Symbol,Fraction Integer ---R ),LiePolynomial(Symbol,Fraction Integer),LiePolynomial(Symbol, ---R Fraction Integer)) -> LiePolynomial(Symbol,Fraction Integer) has ---R been added to workspace. +--R Function declaration Jacobi : (LiePolynomial(Symbol,Fraction(Integer +--R )),LiePolynomial(Symbol,Fraction(Integer)),LiePolynomial(Symbol, +--R Fraction(Integer))) -> LiePolynomial(Symbol,Fraction(Integer)) +--R has been added to workspace. --R Type: Void --E 19 --S 20 of 28 test: Lpoly := Jacobi(a,b,b) --R ---R Compiling function Jacobi with type (LiePolynomial(Symbol,Fraction ---R Integer),LiePolynomial(Symbol,Fraction Integer),LiePolynomial( ---R Symbol,Fraction Integer)) -> LiePolynomial(Symbol,Fraction ---R Integer) +--R Compiling function Jacobi with type (LiePolynomial(Symbol,Fraction( +--R Integer)),LiePolynomial(Symbol,Fraction(Integer)),LiePolynomial( +--R Symbol,Fraction(Integer))) -> LiePolynomial(Symbol,Fraction( +--R Integer)) --R --R (20) 0 ---R Type: LiePolynomial(Symbol,Fraction Integer) +--R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 20 --S 21 of 28 @@ -69016,7 +69190,7 @@ test: Lpoly := Jacobi(p,q,r) --R --R --R (21) 0 ---R Type: LiePolynomial(Symbol,Fraction Integer) +--R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 21 --S 22 of 28 @@ -69024,7 +69198,7 @@ test: Lpoly := Jacobi(r,s,t) --R --R --R (22) 0 ---R Type: LiePolynomial(Symbol,Fraction Integer) +--R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 22 --S 23 of 28 @@ -69033,7 +69207,7 @@ eval(p, a, p)$Lpoly --R --R 2 --R (23) [a b ] ---R Type: LiePolynomial(Symbol,Fraction Integer) +--R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 23 --S 24 of 28 @@ -69041,7 +69215,7 @@ eval(p, [a,b], [2*bb, 3*aa])$Lpoly --R --R --R (24) - 6[a b] ---R Type: LiePolynomial(Symbol,Fraction Integer) +--R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 24 --S 25 of 28 @@ -69049,7 +69223,7 @@ r: Lpoly := [p,c] --R --R --R (25) [a b c] + [a c b] ---R Type: LiePolynomial(Symbol,Fraction Integer) +--R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 25 --S 26 of 28 @@ -69057,7 +69231,7 @@ r1: Lpoly := eval(r, [a,b,c], [bb, cc, aa])$Lpoly --R --R --R (26) - [a b c] ---R Type: LiePolynomial(Symbol,Fraction Integer) +--R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 26 --S 27 of 28 @@ -69065,7 +69239,7 @@ r2: Lpoly := eval(r, [a,b,c], [cc, aa, bb])$Lpoly --R --R --R (27) - [a c b] ---R Type: LiePolynomial(Symbol,Fraction Integer) +--R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 27 --S 28 of 28 @@ -69073,7 +69247,7 @@ r + r1 + r2 --R --R --R (28) 0 ---R Type: LiePolynomial(Symbol,Fraction Integer) +--R Type: LiePolynomial(Symbol,Fraction(Integer)) --E 28 )spool @@ -69491,6 +69665,7 @@ LiePolynomial(VarSet:OrderedSet, R:CommutativeRing) : Public == Private where --S 1 of 1 )show LieSquareMatrix +--R --R LieSquareMatrix(n: PositiveInteger,R: CommutativeRing) is a domain constructor --R Abbreviation for LieSquareMatrix is LSQM --R This constructor is exposed in this frame. @@ -69507,14 +69682,14 @@ LiePolynomial(VarSet:OrderedSet, R:CommutativeRing) : Public == Private where --R ?^? : (%,PositiveInteger) -> % alternative? : () -> Boolean --R antiAssociative? : () -> Boolean antiCommutative? : () -> Boolean --R antiCommutator : (%,%) -> % antisymmetric? : % -> Boolean ---R apply : (Matrix R,%) -> % associative? : () -> Boolean ---R associator : (%,%,%) -> % basis : () -> Vector % ---R coerce : % -> Matrix R coerce : R -> % +--R apply : (Matrix(R),%) -> % associative? : () -> Boolean +--R associator : (%,%,%) -> % basis : () -> Vector(%) +--R coerce : % -> Matrix(R) coerce : R -> % --R coerce : Integer -> % coerce : % -> OutputForm --R commutative? : () -> Boolean commutator : (%,%) -> % ---R convert : % -> Vector R convert : Vector R -> % ---R coordinates : % -> Vector R copy : % -> % ---R diagonal? : % -> Boolean diagonalMatrix : List R -> % +--R convert : % -> Vector(R) convert : Vector(R) -> % +--R coordinates : % -> Vector(R) copy : % -> % +--R diagonal? : % -> Boolean diagonalMatrix : List(R) -> % --R diagonalProduct : % -> R ?.? : (%,Integer) -> R --R elt : (%,Integer,Integer) -> R elt : (%,Integer,Integer,R) -> R --R empty : () -> % empty? : % -> Boolean @@ -69522,25 +69697,25 @@ LiePolynomial(VarSet:OrderedSet, R:CommutativeRing) : Public == Private where --R hash : % -> SingleInteger jacobiIdentity? : () -> Boolean --R jordanAdmissible? : () -> Boolean jordanAlgebra? : () -> Boolean --R latex : % -> String leftAlternative? : () -> Boolean ---R leftDiscriminant : Vector % -> R leftDiscriminant : () -> R +--R leftDiscriminant : Vector(%) -> R leftDiscriminant : () -> R --R leftNorm : % -> R leftTrace : % -> R ---R leftTraceMatrix : () -> Matrix R lieAdmissible? : () -> Boolean ---R lieAlgebra? : () -> Boolean listOfLists : % -> List List R +--R leftTraceMatrix : () -> Matrix(R) lieAdmissible? : () -> Boolean +--R lieAlgebra? : () -> Boolean listOfLists : % -> List(List(R)) --R map : ((R -> R),%) -> % map : (((R,R) -> R),%,%) -> % ---R matrix : List List R -> % maxColIndex : % -> Integer +--R matrix : List(List(R)) -> % maxColIndex : % -> Integer --R maxRowIndex : % -> Integer minColIndex : % -> Integer --R minRowIndex : % -> Integer ncols : % -> NonNegativeInteger --R nrows : % -> NonNegativeInteger one? : % -> Boolean --R powerAssociative? : () -> Boolean qelt : (%,Integer,Integer) -> R --R rank : () -> PositiveInteger recip : % -> Union(%,"failed") ---R represents : Vector R -> % retract : % -> R ---R rightAlternative? : () -> Boolean rightDiscriminant : Vector % -> R ---R rightDiscriminant : () -> R rightNorm : % -> R ---R rightTrace : % -> R rightTraceMatrix : () -> Matrix R ---R sample : () -> % scalarMatrix : R -> % ---R someBasis : () -> Vector % square? : % -> Boolean ---R symmetric? : % -> Boolean trace : % -> R ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R represents : Vector(R) -> % retract : % -> R +--R rightAlternative? : () -> Boolean rightDiscriminant : () -> R +--R rightNorm : % -> R rightTrace : % -> R +--R rightTraceMatrix : () -> Matrix(R) sample : () -> % +--R scalarMatrix : R -> % someBasis : () -> Vector(%) +--R square? : % -> Boolean symmetric? : % -> Boolean +--R trace : % -> R zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean --R #? : % -> NonNegativeInteger if $ has finiteAggregate --R ?*? : (DirectProduct(n,R),%) -> DirectProduct(n,R) --R ?*? : (%,DirectProduct(n,R)) -> DirectProduct(n,R) @@ -69549,88 +69724,89 @@ LiePolynomial(VarSet:OrderedSet, R:CommutativeRing) : Public == Private where --R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,R) -> % if R has FIELD --R D : (%,NonNegativeInteger) -> % if R has DIFRING ---R D : (%,Symbol) -> % if R has PDRING SYMBOL ---R D : (%,List Symbol) -> % if R has PDRING SYMBOL ---R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL ---R D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL +--R D : (%,Symbol) -> % if R has PDRING(SYMBOL) +--R D : (%,List(Symbol)) -> % if R has PDRING(SYMBOL) +--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) --R D : (%,(R -> R),NonNegativeInteger) -> % --R ?^? : (%,NonNegativeInteger) -> % --R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate ---R associatorDependence : () -> List Vector R if R has INTDOM +--R associatorDependence : () -> List(Vector(R)) if R has INTDOM --R characteristic : () -> NonNegativeInteger ---R coerce : Fraction Integer -> % if R has RETRACT FRAC INT +--R coerce : Fraction(Integer) -> % if R has RETRACT(FRAC(INT)) --R column : (%,Integer) -> DirectProduct(n,R) ---R conditionsForIdempotents : Vector % -> List Polynomial R ---R conditionsForIdempotents : () -> List Polynomial R ---R coordinates : (%,Vector %) -> Vector R ---R coordinates : (Vector %,Vector %) -> Matrix R ---R coordinates : Vector % -> Matrix R +--R conditionsForIdempotents : Vector(%) -> List(Polynomial(R)) +--R conditionsForIdempotents : () -> List(Polynomial(R)) +--R coordinates : (%,Vector(%)) -> Vector(R) +--R coordinates : (Vector(%),Vector(%)) -> Matrix(R) +--R coordinates : Vector(%) -> Matrix(R) --R count : (R,%) -> NonNegativeInteger if $ has finiteAggregate and R has SETCAT --R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate ---R determinant : % -> R if R has commutative * +--R determinant : % -> R if R has commutative(*) --R diagonal : % -> DirectProduct(n,R) --R differentiate : % -> % if R has DIFRING --R differentiate : (%,NonNegativeInteger) -> % if R has DIFRING ---R differentiate : (%,Symbol) -> % if R has PDRING SYMBOL ---R differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL ---R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL ---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL +--R differentiate : (%,Symbol) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol)) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) --R differentiate : (%,(R -> R),NonNegativeInteger) -> % --R differentiate : (%,(R -> R)) -> % ---R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT ---R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT ---R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT ---R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,List(R),List(R)) -> % if R has EVALAB(R) and R has SETCAT +--R eval : (%,R,R) -> % if R has EVALAB(R) and R has SETCAT +--R eval : (%,Equation(R)) -> % if R has EVALAB(R) and R has SETCAT +--R eval : (%,List(Equation(R))) -> % if R has EVALAB(R) and R has SETCAT --R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate --R exquo : (%,R) -> Union(%,"failed") if R has INTDOM --R inverse : % -> Union(%,"failed") if R has FIELD ---R leftCharacteristicPolynomial : % -> SparseUnivariatePolynomial R ---R leftMinimalPolynomial : % -> SparseUnivariatePolynomial R if R has INTDOM +--R leftCharacteristicPolynomial : % -> SparseUnivariatePolynomial(R) +--R leftMinimalPolynomial : % -> SparseUnivariatePolynomial(R) if R has INTDOM --R leftPower : (%,PositiveInteger) -> % ---R leftRankPolynomial : () -> SparseUnivariatePolynomial Polynomial R if R has FIELD +--R leftRankPolynomial : () -> SparseUnivariatePolynomial(Polynomial(R)) if R has FIELD --R leftRecip : % -> Union(%,"failed") if R has INTDOM ---R leftRegularRepresentation : (%,Vector %) -> Matrix R ---R leftRegularRepresentation : % -> Matrix R ---R leftTraceMatrix : Vector % -> Matrix R +--R leftRegularRepresentation : (%,Vector(%)) -> Matrix(R) +--R leftRegularRepresentation : % -> Matrix(R) +--R leftTraceMatrix : Vector(%) -> Matrix(R) --R leftUnit : () -> Union(%,"failed") if R has INTDOM ---R leftUnits : () -> Union(Record(particular: %,basis: List %),"failed") if R has INTDOM +--R leftUnits : () -> Union(Record(particular: %,basis: List(%)),"failed") if R has INTDOM --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((R -> R),%) -> % if $ has shallowlyMutable --R member? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT ---R members : % -> List R if $ has finiteAggregate ---R minordet : % -> R if R has commutative * +--R members : % -> List(R) if $ has finiteAggregate +--R minordet : % -> R if R has commutative(*) --R more? : (%,NonNegativeInteger) -> Boolean --R noncommutativeJordanAlgebra? : () -> Boolean ---R nullSpace : % -> List DirectProduct(n,R) if R has INTDOM +--R nullSpace : % -> List(DirectProduct(n,R)) if R has INTDOM --R nullity : % -> NonNegativeInteger if R has INTDOM ---R parts : % -> List R if $ has finiteAggregate +--R parts : % -> List(R) if $ has finiteAggregate --R plenaryPower : (%,PositiveInteger) -> % --R rank : % -> NonNegativeInteger if R has INTDOM ---R reducedSystem : Matrix % -> Matrix R ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT ---R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT ---R represents : (Vector R,Vector %) -> % ---R retract : % -> Fraction Integer if R has RETRACT FRAC INT ---R retract : % -> Integer if R has RETRACT INT +--R reducedSystem : Matrix(%) -> Matrix(R) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT) +--R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT) +--R represents : (Vector(R),Vector(%)) -> % +--R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT)) +--R retract : % -> Integer if R has RETRACT(INT) --R retractIfCan : % -> Union(R,"failed") ---R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT ---R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT ---R rightCharacteristicPolynomial : % -> SparseUnivariatePolynomial R ---R rightMinimalPolynomial : % -> SparseUnivariatePolynomial R if R has INTDOM +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT)) +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT) +--R rightCharacteristicPolynomial : % -> SparseUnivariatePolynomial(R) +--R rightDiscriminant : Vector(%) -> R +--R rightMinimalPolynomial : % -> SparseUnivariatePolynomial(R) if R has INTDOM --R rightPower : (%,PositiveInteger) -> % ---R rightRankPolynomial : () -> SparseUnivariatePolynomial Polynomial R if R has FIELD +--R rightRankPolynomial : () -> SparseUnivariatePolynomial(Polynomial(R)) if R has FIELD --R rightRecip : % -> Union(%,"failed") if R has INTDOM ---R rightRegularRepresentation : (%,Vector %) -> Matrix R ---R rightRegularRepresentation : % -> Matrix R ---R rightTraceMatrix : Vector % -> Matrix R +--R rightRegularRepresentation : (%,Vector(%)) -> Matrix(R) +--R rightRegularRepresentation : % -> Matrix(R) +--R rightTraceMatrix : Vector(%) -> Matrix(R) --R rightUnit : () -> Union(%,"failed") if R has INTDOM ---R rightUnits : () -> Union(Record(particular: %,basis: List %),"failed") if R has INTDOM +--R rightUnits : () -> Union(Record(particular: %,basis: List(%)),"failed") if R has INTDOM --R row : (%,Integer) -> DirectProduct(n,R) --R rowEchelon : % -> % if R has EUCDOM --R size? : (%,NonNegativeInteger) -> Boolean ---R structuralConstants : Vector % -> Vector Matrix R ---R structuralConstants : () -> Vector Matrix R +--R structuralConstants : Vector(%) -> Vector(Matrix(R)) +--R structuralConstants : () -> Vector(Matrix(R)) --R subtractIfCan : (%,%) -> Union(%,"failed") --R unit : () -> Union(%,"failed") if R has INTDOM --R @@ -69900,7 +70076,7 @@ Dx := D() --R --R --R (2) D ---IType: LinearOrdinaryDifferentialOperator(Expression Integer,theMap LAMBDA-CLOSURE(NIL,NIL,NIL,G1404 envArg,SPADCALL(G1404,QUOTE x,ELT(*1;anonymousFunction;0;frame0;internal;MV,0)))) +--IType: LinearOrdinaryDifferentialOperator(Expression(Integer),... --E 2 --S 3 of 16 @@ -69912,7 +70088,7 @@ Dop:= Dx^3 + G/x^2*Dx + H/x^3 - 1 --R (3) D + -- D + -------- --R 2 3 --R x x ---IType: LinearOrdinaryDifferentialOperator(Expression Integer,theMap LAMBDA-CLOSURE(NIL,NIL,NIL,G1404 envArg,SPADCALL(G1404,QUOTE x,ELT(*1;anonymousFunction;0;frame0;internal;MV,0)))) +--IType: LinearOrdinaryDifferentialOperator(Expression(Integer),... --E 3 --S 4 of 16 @@ -69967,21 +70143,21 @@ leq == solve(pans1,[subscript(s,[i]) for i in 1..n]) leq --R --R Compiling body of rule n to compute value of type PositiveInteger ---R Compiling body of rule phi to compute value of type Expression ---R Integer ---R Compiling body of rule phi1 to compute value of type Expression ---R Integer ---R Compiling body of rule phi2 to compute value of type Expression ---R Integer ---R Compiling body of rule phi3 to compute value of type Polynomial ---R Integer +--R Compiling body of rule phi to compute value of type Expression( +--R Integer) +--R Compiling body of rule phi1 to compute value of type Expression( +--R Integer) +--R Compiling body of rule phi2 to compute value of type Expression( +--R Integer) +--R Compiling body of rule phi3 to compute value of type Polynomial( +--R Integer) --R Compiling body of rule pans to compute value of type ---R UnivariatePolynomial(x,Polynomial Integer) ---R Compiling body of rule pans1 to compute value of type List ---R Polynomial Integer ---R Compiling body of rule leq to compute value of type List List ---R Equation Fraction Polynomial Integer ---I Compiling function G3349 with type Integer -> Boolean +--R UnivariatePolynomial(x,Polynomial(Integer)) +--R Compiling body of rule pans1 to compute value of type List( +--R Polynomial(Integer)) +--R Compiling body of rule leq to compute value of type List(List( +--R Equation(Fraction(Polynomial(Integer))))) +--I Compiling function G3491 with type Integer -> Boolean --R --R (12) --R 2 3 2 @@ -70011,20 +70187,20 @@ n==4 leq --R --R Compiling body of rule n to compute value of type PositiveInteger ---R Compiling body of rule phi to compute value of type Expression ---R Integer ---R Compiling body of rule phi1 to compute value of type Expression ---R Integer ---R Compiling body of rule phi2 to compute value of type Expression ---R Integer ---R Compiling body of rule phi3 to compute value of type Polynomial ---R Integer +--R Compiling body of rule phi to compute value of type Expression( +--R Integer) +--R Compiling body of rule phi1 to compute value of type Expression( +--R Integer) +--R Compiling body of rule phi2 to compute value of type Expression( +--R Integer) +--R Compiling body of rule phi3 to compute value of type Polynomial( +--R Integer) --R Compiling body of rule pans to compute value of type ---R UnivariatePolynomial(x,Polynomial Integer) ---R Compiling body of rule pans1 to compute value of type List ---R Polynomial Integer ---R Compiling body of rule leq to compute value of type List List ---R Equation Fraction Polynomial Integer +--R UnivariatePolynomial(x,Polynomial(Integer)) +--R Compiling body of rule pans1 to compute value of type List( +--R Polynomial(Integer)) +--R Compiling body of rule leq to compute value of type List(List( +--R Equation(Fraction(Polynomial(Integer))))) --R --R (14) --R [ @@ -70051,7 +70227,7 @@ leq --R 1944 --R ] --R ] ---R Type: List List Equation Fraction Polynomial Integer +--R Type: List(List(Equation(Fraction(Polynomial(Integer))))) --E 14 --S 15 of 16 @@ -70073,20 +70249,20 @@ n==7 leq --R --R Compiling body of rule n to compute value of type PositiveInteger ---R Compiling body of rule phi to compute value of type Expression ---R Integer ---R Compiling body of rule phi1 to compute value of type Expression ---R Integer ---R Compiling body of rule phi2 to compute value of type Expression ---R Integer ---R Compiling body of rule phi3 to compute value of type Polynomial ---R Integer +--R Compiling body of rule phi to compute value of type Expression( +--R Integer) +--R Compiling body of rule phi1 to compute value of type Expression( +--R Integer) +--R Compiling body of rule phi2 to compute value of type Expression( +--R Integer) +--R Compiling body of rule phi3 to compute value of type Polynomial( +--R Integer) --R Compiling body of rule pans to compute value of type ---R UnivariatePolynomial(x,Polynomial Integer) ---R Compiling body of rule pans1 to compute value of type List ---R Polynomial Integer ---R Compiling body of rule leq to compute value of type List List ---R Equation Fraction Polynomial Integer +--R UnivariatePolynomial(x,Polynomial(Integer)) +--R Compiling body of rule pans1 to compute value of type List( +--R Polynomial(Integer)) +--R Compiling body of rule leq to compute value of type List(List( +--R Equation(Fraction(Polynomial(Integer))))) --R --R (16) --R [ @@ -70486,7 +70662,7 @@ LinearOrdinaryDifferentialOperator(A:Ring, diff: A -> A): RFZ := Fraction UnivariatePolynomial('x, Integer) --R --R ---R (1) Fraction UnivariatePolynomial(x,Integer) +--R (1) Fraction(UnivariatePolynomial(x,Integer)) --R Type: Domain --E 1 @@ -70495,7 +70671,7 @@ x : RFZ := 'x --R --R --R (2) x ---R Type: Fraction UnivariatePolynomial(x,Integer) +--R Type: Fraction(UnivariatePolynomial(x,Integer)) --E 2 --S 3 of 20 @@ -70503,7 +70679,7 @@ Dx : LODO1 RFZ := D() --R --R --R (3) D ---RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer) +--RType: LinearOrdinaryDifferentialOperator1(Fraction(UnivariatePolynomial(x,Integer))) --E 3 --S 4 of 20 @@ -70513,7 +70689,7 @@ b : LODO1 RFZ := 3*x**2*Dx**2 + 2*Dx + 1/x --R 2 2 1 --R (4) 3x D + 2D + - --R x ---RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer) +--RType: LinearOrdinaryDifferentialOperator1(Fraction(UnivariatePolynomial(x,Integer))) --E 4 --S 5 of 20 @@ -70523,7 +70699,7 @@ a : LODO1 RFZ := b*(5*x*Dx + 7) --R 3 3 2 2 7 --R (5) 15x D + (51x + 10x)D + 29D + - --R x ---RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer) +--RType: LinearOrdinaryDifferentialOperator1(Fraction(UnivariatePolynomial(x,Integer))) --E 5 --S 6 of 20 @@ -70535,7 +70711,7 @@ p := x**2 + 1/x**2 --R (6) ------ --R 2 --R x ---R Type: Fraction UnivariatePolynomial(x,Integer) +--R Type: Fraction(UnivariatePolynomial(x,Integer)) --E 6 --S 7 of 20 @@ -70547,7 +70723,7 @@ p := x**2 + 1/x**2 --R (7) ------------------ --R 4 --R x ---R Type: Fraction UnivariatePolynomial(x,Integer) +--R Type: Fraction(UnivariatePolynomial(x,Integer)) --E 7 --S 8 of 20 @@ -70555,7 +70731,7 @@ ld := leftDivide(a,b) --R --R --R (8) [quotient= 5x D + 7,remainder= 0] ---RType: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)) +--IType: Record(quotient: LinearOrdinaryDifferentialOperator1(Fraction(... --E 8 --S 9 of 20 @@ -70565,7 +70741,7 @@ a = b * ld.quotient + ld.remainder --R 3 3 2 2 7 3 3 2 2 7 --R (9) 15x D + (51x + 10x)D + 29D + -= 15x D + (51x + 10x)D + 29D + - --R x x ---RType: Equation LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer) +--RType: Equation(LinearOrdinaryDifferentialOperator1(Fraction(UnivariatePolynomial(x,Integer)))) --E 9 --S 10 of 20 @@ -70575,7 +70751,7 @@ rd := rightDivide(a,b) --R 5 --R (10) [quotient= 5x D + 7,remainder= 10D + -] --R x ---RType: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)) +--IType: Record(quotient: LinearOrdinaryDifferentialOperator1(... --E 10 --S 11 of 20 @@ -70585,7 +70761,7 @@ a = rd.quotient * b + rd.remainder --R 3 3 2 2 7 3 3 2 2 7 --R (11) 15x D + (51x + 10x)D + 29D + -= 15x D + (51x + 10x)D + 29D + - --R x x ---RType: Equation LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer) +--RType: Equation(LinearOrdinaryDifferentialOperator1(Fraction(UnivariatePolynomial(x,Integer)))) --E 11 --S 12 of 20 @@ -70593,7 +70769,7 @@ rightQuotient(a,b) --R --R --R (12) 5x D + 7 ---RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer) +--RType: LinearOrdinaryDifferentialOperator1(Fraction(UnivariatePolynomial(x,Integer))) --E 12 --S 13 of 20 @@ -70603,7 +70779,7 @@ rightRemainder(a,b) --R 5 --R (13) 10D + - --R x ---RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer) +--RType: LinearOrdinaryDifferentialOperator1(Fraction(UnivariatePolynomial(x,Integer))) --E 13 --S 14 of 20 @@ -70611,7 +70787,7 @@ leftExactQuotient(a,b) --R --R --R (14) 5x D + 7 ---RType: Union(LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),...) +--RType: Union(LinearOrdinaryDifferentialOperator1(Fraction(UnivariatePolynomial(x,Integer))),...) --E 14 --S 15 of 20 @@ -70621,7 +70797,7 @@ e := leftGcd(a,b) --R 2 2 1 --R (15) 3x D + 2D + - --R x ---RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer) +--RType: LinearOrdinaryDifferentialOperator1(Fraction(UnivariatePolynomial(x,Integer))) --E 15 --S 16 of 20 @@ -70629,7 +70805,7 @@ leftRemainder(a, e) --R --R --R (16) 0 ---RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer) +--RType: LinearOrdinaryDifferentialOperator1(Fraction(UnivariatePolynomial(x,Integer))) --E 16 --S 17 of 20 @@ -70639,7 +70815,7 @@ rightRemainder(a, e) --R 5 --R (17) 10D + - --R x ---RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer) +--RType: LinearOrdinaryDifferentialOperator1(Fraction(UnivariatePolynomial(x,Integer))) --E 17 --S 18 of 20 @@ -70649,7 +70825,7 @@ f := rightLcm(a,b) --R 3 3 2 2 7 --R (18) 15x D + (51x + 10x)D + 29D + - --R x ---RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer) +--RType: LinearOrdinaryDifferentialOperator1(Fraction(UnivariatePolynomial(x,Integer))) --E 18 --S 19 of 20 @@ -70659,7 +70835,7 @@ rightRemainder(f, b) --R 5 --R (19) 10D + - --R x ---RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer) +--RType: LinearOrdinaryDifferentialOperator1(Fraction(UnivariatePolynomial(x,Integer))) --E 19 --S 20 of 20 @@ -70667,7 +70843,7 @@ leftRemainder(f, b) --R --R --R (20) 0 ---RType: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer) +--RType: LinearOrdinaryDifferentialOperator1(Fraction(UnivariatePolynomial(x,Integer))) --E 20 )spool )lisp (bye) @@ -70968,7 +71144,7 @@ LinearOrdinaryDifferentialOperator1(A:DifferentialRing) == Q := Fraction Integer --R --R ---R (1) Fraction Integer +--R (1) Fraction(Integer) --R Type: Domain --E 1 @@ -70976,7 +71152,7 @@ Q := Fraction Integer PQ := UnivariatePolynomial('x, Q) --R --R ---R (2) UnivariatePolynomial(x,Fraction Integer) +--R (2) UnivariatePolynomial(x,Fraction(Integer)) --R Type: Domain --E 2 @@ -70985,7 +71161,7 @@ x: PQ := 'x --R --R --R (3) x ---R Type: UnivariatePolynomial(x,Fraction Integer) +--R Type: UnivariatePolynomial(x,Fraction(Integer)) --E 3 --S 4 of 26 @@ -70993,7 +71169,7 @@ Dx: LODO2(Q, PQ) := D() --R --R --R (4) D ---RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer)) +--RType: LinearOrdinaryDifferentialOperator2(Fraction(Integer),UnivariatePolynomial(x,Fraction(Integer))) --E 4 --S 5 of 26 @@ -71001,7 +71177,7 @@ a := Dx + 1 --R --R --R (5) D + 1 ---RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer)) +--RType: LinearOrdinaryDifferentialOperator2(Fraction(Integer),UnivariatePolynomial(x,Fraction(Integer))) --E 5 --S 6 of 26 @@ -71011,7 +71187,7 @@ b := a + 1/2*Dx**2 - 1/2 --R 1 2 1 --R (6) - D + D + - --R 2 2 ---RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer)) +--RType: LinearOrdinaryDifferentialOperator2(Fraction(Integer),UnivariatePolynomial(x,Fraction(Integer))) --E 6 --S 7 of 26 @@ -71021,7 +71197,7 @@ p := 4*x**2 + 2/3 --R 2 2 --R (7) 4x + - --R 3 ---R Type: UnivariatePolynomial(x,Fraction Integer) +--R Type: UnivariatePolynomial(x,Fraction(Integer)) --E 7 --S 8 of 26 @@ -71031,7 +71207,7 @@ a p --R 2 2 --R (8) 4x + 8x + - --R 3 ---R Type: UnivariatePolynomial(x,Fraction Integer) +--R Type: UnivariatePolynomial(x,Fraction(Integer)) --E 8 --S 9 of 26 @@ -71041,7 +71217,7 @@ a p --R 2 37 2 37 --R (9) 2x + 12x + --= 2x + 12x + -- --R 3 3 ---R Type: Equation UnivariatePolynomial(x,Fraction Integer) +--R Type: Equation(UnivariatePolynomial(x,Fraction(Integer))) --E 9 --S 10 of 26 @@ -71051,7 +71227,7 @@ c := (1/9)*b*(a + b)^2 --R 1 6 5 5 13 4 19 3 79 2 7 1 --R (10) -- D + -- D + -- D + -- D + -- D + -- D + - --R 72 36 24 18 72 12 8 ---RType: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer)) +--RType: LinearOrdinaryDifferentialOperator2(Fraction(Integer),UnivariatePolynomial(x,Fraction(Integer))) --E 10 --S 11 of 26 @@ -71061,7 +71237,7 @@ c := (1/9)*b*(a + b)^2 --R 2 44 541 --R (11) 3x + -- x + --- --R 3 36 ---R Type: UnivariatePolynomial(x,Fraction Integer) +--R Type: UnivariatePolynomial(x,Fraction(Integer)) --E 11 )clear all --S 12 of 26 @@ -71130,7 +71306,7 @@ p:Vect := directProduct [3*x^2+1,2*x,7*x^3+2*x] --R --R 2 3 --R (7) [3x + 1,2x,7x + 2x] ---RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)) +--IType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),... --E 18 --S 19 of 26 @@ -71139,7 +71315,7 @@ q: Vect := m * p --R --R 4 2 5 2 5 3 --R (8) [3x + x + 2x,2x + 3x + 1,28x + 8x ] ---RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)) +--IType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),... --E 19 --S 20 of 26 @@ -71147,7 +71323,7 @@ Dx : Modo := D() --R --R --R (9) D ---RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))) +--IType: LinearOrdinaryDifferentialOperator2(SquareMatrix(... --E 20 --S 21 of 26 @@ -71162,7 +71338,7 @@ a : Modo := Dx + m --R | | --R | 2| --R +0 0 4x + ---RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))) +--IType: LinearOrdinaryDifferentialOperator2(SquareMatrix(... --E 21 --S 22 of 26 @@ -71177,7 +71353,7 @@ b : Modo := m*Dx + 1 --R | | +0 0 1+ --R | 2| --R +0 0 4x + ---RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))) +--IType: LinearOrdinaryDifferentialOperator2(SquareMatrix(... --E 22 --S 23 of 26 @@ -71193,7 +71369,7 @@ c := a*b --R | | | | | | --R | 2| | 4 | | 2| --R +0 0 4x + + 0 0 16x + 8x + 1+ +0 0 4x + ---RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))) +--IType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,... --E 23 --S 24 of 26 @@ -71202,7 +71378,7 @@ a p --R --R 4 2 5 2 5 3 2 --R (13) [3x + x + 8x,2x + 3x + 3,28x + 8x + 21x + 2] ---RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)) +--IType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),... --E 24 --S 25 of 26 @@ -71211,7 +71387,7 @@ b p --R --R 3 2 4 4 3 2 --R (14) [6x + 3x + 3,2x + 8x,84x + 7x + 8x + 2x] ---RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)) +--IType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),... --E 25 --S 26 of 26 @@ -71225,7 +71401,7 @@ b p --R 10x + 10x + 12x + 92x + 6x + 32x + 72x + 28x + 49x + 32x + 19, --R 8 7 6 5 4 3 2 --R 2240x + 224x + 1280x + 3508x + 492x + 751x + 98x + 18x + 4] ---RType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)) +--IType: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),... --E 26 )spool )lisp (bye) @@ -71590,7 +71766,7 @@ LinearOrdinaryDifferentialOperator2(A, M): Exports == Implementation where --R --R --R (1) [2,4,5,6] ---R Type: List PositiveInteger +--R Type: List(PositiveInteger) --E 1 --S 2 of 34 @@ -71598,7 +71774,7 @@ LinearOrdinaryDifferentialOperator2(A, M): Exports == Implementation where --R --R --R (2) [1] ---R Type: List PositiveInteger +--R Type: List(PositiveInteger) --E 2 --S 3 of 34 @@ -71606,7 +71782,7 @@ list(1) --R --R --R (3) [1] ---R Type: List PositiveInteger +--R Type: List(PositiveInteger) --E 3 --S 4 of 34 @@ -71614,7 +71790,7 @@ append([1,2,3],[5,6,7]) --R --R --R (4) [1,2,3,5,6,7] ---R Type: List PositiveInteger +--R Type: List(PositiveInteger) --E 4 --S 5 of 34 @@ -71622,7 +71798,7 @@ cons(10,[9,8,7]) --R --R --R (5) [10,9,8,7] ---R Type: List PositiveInteger +--R Type: List(PositiveInteger) --E 5 --S 6 of 34 @@ -71646,7 +71822,7 @@ k := [4,3,7,3,8,5,9,2] --R --R --R (8) [4,3,7,3,8,5,9,2] ---R Type: List PositiveInteger +--R Type: List(PositiveInteger) --E 8 --S 9 of 34 @@ -71718,7 +71894,7 @@ k := [4,3,7,3,8,5,9,2] --R --R --R (17) [4,3,7,3,8,5,9,2] ---R Type: List PositiveInteger +--R Type: List(PositiveInteger) --E 17 --S 18 of 34 @@ -71734,7 +71910,7 @@ k --R --R --R (19) [999,3,7,3,8,5,9,2] ---R Type: List PositiveInteger +--R Type: List(PositiveInteger) --E 19 --S 20 of 34 @@ -71742,7 +71918,7 @@ k := [1,2] --R --R --R (20) [1,2] ---R Type: List PositiveInteger +--R Type: List(PositiveInteger) --E 20 --S 21 of 34 @@ -71750,7 +71926,7 @@ m := cons(0,k) --R --R --R (21) [0,1,2] ---R Type: List Integer +--R Type: List(Integer) --E 21 --S 22 of 34 @@ -71766,7 +71942,7 @@ m --R --R --R (23) [0,99,2] ---R Type: List Integer +--R Type: List(Integer) --E 23 --S 24 of 34 @@ -71774,7 +71950,7 @@ k --R --R --R (24) [99,2] ---R Type: List PositiveInteger +--R Type: List(PositiveInteger) --E 24 --S 25 of 34 @@ -71782,7 +71958,7 @@ k := [1,2,3] --R --R --R (25) [1,2,3] ---R Type: List PositiveInteger +--R Type: List(PositiveInteger) --E 25 --S 26 of 34 @@ -71790,7 +71966,7 @@ rest k --R --R --R (26) [2,3] ---R Type: List PositiveInteger +--R Type: List(PositiveInteger) --E 26 --S 27 of 34 @@ -71798,7 +71974,7 @@ removeDuplicates [4,3,4,3,5,3,4] --R --R --R (27) [4,3,5] ---R Type: List PositiveInteger +--R Type: List(PositiveInteger) --E 27 --S 28 of 34 @@ -71806,7 +71982,7 @@ reverse [1,2,3,4,5,6] --R --R --R (28) [6,5,4,3,2,1] ---R Type: List PositiveInteger +--R Type: List(PositiveInteger) --E 28 --S 29 of 34 @@ -71830,7 +72006,7 @@ reverse(rest(reverse(k))) --R --R --R (31) [1,2] ---R Type: List PositiveInteger +--R Type: List(PositiveInteger) --E 31 --S 32 of 34 @@ -71838,7 +72014,7 @@ reverse(rest(reverse(k))) --R --R --R (32) [1..3,10..10,20..23] ---R Type: List Segment PositiveInteger +--R Type: List(Segment(PositiveInteger)) --E 32 --S 33 of 34 @@ -71846,7 +72022,7 @@ expand [1..3,10,20..23] --R --R --R (33) [1,2,3,10,20,21,22,23] ---R Type: List Integer +--R Type: List(Integer) --E 33 --S 34 of 34 @@ -71854,7 +72030,7 @@ expand [1..] --R --R --R (34) [1,2,3,4,5,6,7,8,9,10,...] ---R Type: Stream Integer +--R Type: Stream(Integer) --E 34 )spool )lisp (bye) @@ -72406,6 +72582,7 @@ List(S:Type): Exports == Implementation where --S 1 of 1 )show ListMonoidOps +--R --R ListMonoidOps(S: SetCategory,E: AbelianMonoid,un: E) is a domain constructor --R Abbreviation for ListMonoidOps is LMOPS --R This constructor is not exposed in this frame. @@ -72423,8 +72600,8 @@ List(S:Type): Exports == Implementation where --R reverse! : % -> % rightMult : (%,S) -> % --R size : % -> NonNegativeInteger ?~=? : (%,%) -> Boolean --R commutativeEquality : (%,%) -> Boolean ---R listOfMonoms : % -> List Record(gen: S,exp: E) ---R makeMulti : List Record(gen: S,exp: E) -> % +--R listOfMonoms : % -> List(Record(gen: S,exp: E)) +--R makeMulti : List(Record(gen: S,exp: E)) -> % --R outputForm : (%,((OutputForm,OutputForm) -> OutputForm),((OutputForm,OutputForm) -> OutputForm),Integer) -> OutputForm --R retractIfCan : % -> Union(S,"failed") --R @@ -72654,14 +72831,15 @@ ListMonoidOps(S, E, un): Exports == Implementation where --S 1 of 1 )show ListMultiDictionary ---R ListMultiDictionary S: SetCategory is a domain constructor +--R +--R ListMultiDictionary(S: SetCategory) is a domain constructor --R Abbreviation for ListMultiDictionary is LMDICT --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for LMDICT --R --R------------------------------- Operations -------------------------------- ---R bag : List S -> % construct : List S -> % ---R copy : % -> % dictionary : List S -> % +--R bag : List(S) -> % construct : List(S) -> % +--R copy : % -> % dictionary : List(S) -> % --R dictionary : () -> % duplicates? : % -> Boolean --R empty : () -> % empty? : % -> Boolean --R eq? : (%,%) -> Boolean extract! : % -> S @@ -72672,14 +72850,14 @@ ListMonoidOps(S, E, un): Exports == Implementation where --R ?=? : (%,%) -> Boolean if S has SETCAT --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R coerce : % -> OutputForm if S has SETCAT ---R convert : % -> InputForm if S has KONVERT INFORM +--R convert : % -> InputForm if S has KONVERT(INFORM) --R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT --R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate ---R duplicates : % -> List Record(entry: S,count: NonNegativeInteger) ---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R duplicates : % -> List(Record(entry: S,count: NonNegativeInteger)) +--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R find : ((S -> Boolean),%) -> Union(S,"failed") --R hash : % -> SingleInteger if S has SETCAT @@ -72688,9 +72866,9 @@ ListMonoidOps(S, E, un): Exports == Implementation where --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT ---R members : % -> List S if $ has finiteAggregate +--R members : % -> List(S) if $ has finiteAggregate --R more? : (%,NonNegativeInteger) -> Boolean ---R parts : % -> List S if $ has finiteAggregate +--R parts : % -> List(S) if $ has finiteAggregate --R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate --R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate --R reduce : (((S,S) -> S),%,S,S) -> S if $ has finiteAggregate and S has SETCAT @@ -72931,7 +73109,8 @@ ListMultiDictionary(S:SetCategory): EE == II where --S 1 of 1 )show LocalAlgebra ---R LocalAlgebra(A: Algebra R,R: CommutativeRing,S: SubsetCategory(Monoid,R)) is a domain constructor +--R +--R LocalAlgebra(A: Algebra(R),R: CommutativeRing,S: SubsetCategory(Monoid,R)) is a domain constructor --R Abbreviation for LocalAlgebra is LA --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for LA @@ -73076,7 +73255,8 @@ LocalAlgebra(A: Algebra R, --S 1 of 1 )show Localize ---R Localize(M: Module R,R: CommutativeRing,S: SubsetCategory(Monoid,R)) is a domain constructor +--R +--R Localize(M: Module(R),R: CommutativeRing,S: SubsetCategory(Monoid,R)) is a domain constructor --R Abbreviation for Localize is LO --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for LO @@ -73260,7 +73440,7 @@ c:Symbol :='c lword:= LyndonWord(Symbol) --R --R ---R (4) LyndonWord Symbol +--R (4) LyndonWord(Symbol) --R Type: Domain --E 4 @@ -73268,7 +73448,7 @@ lword:= LyndonWord(Symbol) magma := Magma(Symbol) --R --R ---R (5) Magma Symbol +--R (5) Magma(Symbol) --R Type: Domain --E 5 @@ -73276,7 +73456,7 @@ magma := Magma(Symbol) word := OrderedFreeMonoid(Symbol) --R --R ---R (6) OrderedFreeMonoid Symbol +--R (6) OrderedFreeMonoid(Symbol) --R Type: Domain --E 6 @@ -73288,7 +73468,7 @@ LyndonWordsList1([a,b,c],3)$lword --R [[[a],[b],[c]], [[a b],[a c],[b c]], --R 2 2 2 2 2 2 --R [[a b],[a c],[a b ],[a b c],[a c b],[a c ],[b c],[b c ]]] ---R Type: OneDimensionalArray List LyndonWord Symbol +--R Type: OneDimensionalArray(List(LyndonWord(Symbol))) --E 7 --S 8 of 22 @@ -73300,7 +73480,7 @@ LyndonWordsList([a,b,c],3)$lword --R [[a], [b], [c], [a b], [a c], [b c], [a b], [a c], [a b ], [a b c], [a c b], --R 2 2 2 --R [a c ], [b c], [b c ]] ---R Type: List LyndonWord Symbol +--R Type: List(LyndonWord(Symbol)) --E 8 --S 9 of 22 @@ -73312,7 +73492,7 @@ lw := LyndonWordsList([a,b],5)$lword --R [[a], [b], [a b], [a b], [a b ], [a b], [a b ], [a b ], [a b], [a b ], --R 2 2 3 2 4 --R [a b a b], [a b ], [a b a b ], [a b ]] ---R Type: List LyndonWord Symbol +--R Type: List(LyndonWord(Symbol)) --E 9 --S 10 of 22 @@ -73321,7 +73501,7 @@ w1 : word := lw.4 :: word --R --R 2 --R (10) a b ---R Type: OrderedFreeMonoid Symbol +--R Type: OrderedFreeMonoid(Symbol) --E 10 --S 11 of 22 @@ -73330,7 +73510,7 @@ w2 : word := lw.5 :: word --R --R 2 --R (11) a b ---R Type: OrderedFreeMonoid Symbol +--R Type: OrderedFreeMonoid(Symbol) --E 11 --S 12 of 22 @@ -73338,7 +73518,7 @@ factor(a::word)$lword --R --R --R (12) [[a]] ---R Type: List LyndonWord Symbol +--R Type: List(LyndonWord(Symbol)) --E 12 --S 13 of 22 @@ -73347,7 +73527,7 @@ factor(w1*w2)$lword --R --R 2 2 --R (13) [[a b a b ]] ---R Type: List LyndonWord Symbol +--R Type: List(LyndonWord(Symbol)) --E 13 --S 14 of 22 @@ -73356,7 +73536,7 @@ factor(w2*w2)$lword --R --R 2 2 --R (14) [[a b ],[a b ]] ---R Type: List LyndonWord Symbol +--R Type: List(LyndonWord(Symbol)) --E 14 --S 15 of 22 @@ -73365,7 +73545,7 @@ factor(w2*w1)$lword --R --R 2 2 --R (15) [[a b ],[a b]] ---R Type: List LyndonWord Symbol +--R Type: List(LyndonWord(Symbol)) --E 15 --S 16 of 22 @@ -73398,7 +73578,7 @@ lyndonIfCan(w1)$lword --R --R 2 --R (19) [a b] ---R Type: Union(LyndonWord Symbol,...) +--R Type: Union(LyndonWord(Symbol),...) --E 19 --S 20 of 22 @@ -73415,7 +73595,7 @@ lyndon(w1)$lword --R --R 2 --R (21) [a b] ---R Type: LyndonWord Symbol +--R Type: LyndonWord(Symbol) --E 21 --S 22 of 22 @@ -73424,7 +73604,7 @@ lyndon(w1*w2)$lword --R --R 2 2 --R (22) [a b a b ] ---R Type: LyndonWord Symbol +--R Type: LyndonWord(Symbol) --E 22 )spool )lisp (bye) @@ -73780,6 +73960,7 @@ LyndonWord(VarSet:OrderedSet):Public == Private where --S 1 of 1 )show MachineComplex +--R --R MachineComplex is a domain constructor --R Abbreviation for MachineComplex is MCMPLX --R This constructor is exposed in this frame. @@ -73795,8 +73976,8 @@ LyndonWord(VarSet:OrderedSet):Public == Private where --R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % --R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean ---R basis : () -> Vector % coerce : % -> Complex Float ---R coerce : Complex Integer -> % coerce : Complex Float -> % +--R basis : () -> Vector(%) coerce : % -> Complex(Float) +--R coerce : Complex(Integer) -> % coerce : Complex(Float) -> % --R coerce : MachineFloat -> % coerce : Integer -> % --R coerce : % -> % coerce : Integer -> % --R coerce : % -> OutputForm conjugate : % -> % @@ -73811,20 +73992,20 @@ LyndonWord(VarSet:OrderedSet):Public == Private where --R trace : % -> MachineFloat unit? : % -> Boolean --R unitCanonical : % -> % zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean ---R ?*? : (%,Fraction Integer) -> % if MachineFloat has FIELD ---R ?*? : (Fraction Integer,%) -> % if MachineFloat has FIELD +--R ?*? : (%,Fraction(Integer)) -> % if MachineFloat has FIELD +--R ?*? : (Fraction(Integer),%) -> % if MachineFloat has FIELD --R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Integer) -> % if MachineFloat has FIELD ---R ?**? : (%,Fraction Integer) -> % if MachineFloat has RADCAT and MachineFloat has TRANFUN +--R ?**? : (%,Fraction(Integer)) -> % if MachineFloat has RADCAT and MachineFloat has TRANFUN --R ?**? : (%,%) -> % if MachineFloat has TRANFUN --R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,%) -> % if MachineFloat has FIELD --R D : % -> % if MachineFloat has DIFRING --R D : (%,NonNegativeInteger) -> % if MachineFloat has DIFRING ---R D : (%,Symbol) -> % if MachineFloat has PDRING SYMBOL ---R D : (%,List Symbol) -> % if MachineFloat has PDRING SYMBOL ---R D : (%,Symbol,NonNegativeInteger) -> % if MachineFloat has PDRING SYMBOL ---R D : (%,List Symbol,List NonNegativeInteger) -> % if MachineFloat has PDRING SYMBOL +--R D : (%,Symbol) -> % if MachineFloat has PDRING(SYMBOL) +--R D : (%,List(Symbol)) -> % if MachineFloat has PDRING(SYMBOL) +--R D : (%,Symbol,NonNegativeInteger) -> % if MachineFloat has PDRING(SYMBOL) +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if MachineFloat has PDRING(SYMBOL) --R D : (%,(MachineFloat -> MachineFloat),NonNegativeInteger) -> % --R D : (%,(MachineFloat -> MachineFloat)) -> % --R ?^? : (%,Integer) -> % if MachineFloat has FIELD @@ -73844,27 +74025,27 @@ LyndonWord(VarSet:OrderedSet):Public == Private where --R atan : % -> % if MachineFloat has TRANFUN --R atanh : % -> % if MachineFloat has TRANFUN --R characteristic : () -> NonNegativeInteger ---R characteristicPolynomial : % -> SparseUnivariatePolynomial MachineFloat +--R characteristicPolynomial : % -> SparseUnivariatePolynomial(MachineFloat) --R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and MachineFloat has EUCDOM and MachineFloat has PFECAT or MachineFloat has CHARNZ --R charthRoot : % -> % if MachineFloat has FFIELDC ---R coerce : Fraction Integer -> % if MachineFloat has FIELD or MachineFloat has RETRACT FRAC INT ---R coerce : Complex MachineInteger -> % ---R coerce : Complex MachineFloat -> % +--R coerce : Fraction(Integer) -> % if MachineFloat has FIELD or MachineFloat has RETRACT(FRAC(INT)) +--R coerce : Complex(MachineInteger) -> % +--R coerce : Complex(MachineFloat) -> % --R complex : (MachineFloat,MachineFloat) -> % ---R conditionP : Matrix % -> Union(Vector %,"failed") if $ has CHARNZ and MachineFloat has EUCDOM and MachineFloat has PFECAT or MachineFloat has FFIELDC ---R convert : % -> Vector MachineFloat ---R convert : Vector MachineFloat -> % ---R convert : % -> SparseUnivariatePolynomial MachineFloat ---R convert : SparseUnivariatePolynomial MachineFloat -> % ---R convert : % -> Pattern Integer if MachineFloat has KONVERT PATTERN INT ---R convert : % -> Pattern Float if MachineFloat has KONVERT PATTERN FLOAT ---R convert : % -> Complex Float if MachineFloat has REAL ---R convert : % -> Complex DoubleFloat if MachineFloat has REAL ---R convert : % -> InputForm if MachineFloat has KONVERT INFORM ---R coordinates : (%,Vector %) -> Vector MachineFloat ---R coordinates : (Vector %,Vector %) -> Matrix MachineFloat ---R coordinates : % -> Vector MachineFloat ---R coordinates : Vector % -> Matrix MachineFloat +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and MachineFloat has EUCDOM and MachineFloat has PFECAT or MachineFloat has FFIELDC +--R convert : % -> Vector(MachineFloat) +--R convert : Vector(MachineFloat) -> % +--R convert : % -> SparseUnivariatePolynomial(MachineFloat) +--R convert : SparseUnivariatePolynomial(MachineFloat) -> % +--R convert : % -> Pattern(Integer) if MachineFloat has KONVERT(PATTERN(INT)) +--R convert : % -> Pattern(Float) if MachineFloat has KONVERT(PATTERN(FLOAT)) +--R convert : % -> Complex(Float) if MachineFloat has REAL +--R convert : % -> Complex(DoubleFloat) if MachineFloat has REAL +--R convert : % -> InputForm if MachineFloat has KONVERT(INFORM) +--R coordinates : (%,Vector(%)) -> Vector(MachineFloat) +--R coordinates : (Vector(%),Vector(%)) -> Matrix(MachineFloat) +--R coordinates : % -> Vector(MachineFloat) +--R coordinates : Vector(%) -> Matrix(MachineFloat) --R cos : % -> % if MachineFloat has TRANFUN --R cosh : % -> % if MachineFloat has TRANFUN --R cot : % -> % if MachineFloat has TRANFUN @@ -73872,58 +74053,58 @@ LyndonWord(VarSet:OrderedSet):Public == Private where --R createPrimitiveElement : () -> % if MachineFloat has FFIELDC --R csc : % -> % if MachineFloat has TRANFUN --R csch : % -> % if MachineFloat has TRANFUN ---R definingPolynomial : () -> SparseUnivariatePolynomial MachineFloat ---R derivationCoordinates : (Vector %,(MachineFloat -> MachineFloat)) -> Matrix MachineFloat if MachineFloat has FIELD +--R definingPolynomial : () -> SparseUnivariatePolynomial(MachineFloat) +--R derivationCoordinates : (Vector(%),(MachineFloat -> MachineFloat)) -> Matrix(MachineFloat) if MachineFloat has FIELD --R differentiate : % -> % if MachineFloat has DIFRING --R differentiate : (%,NonNegativeInteger) -> % if MachineFloat has DIFRING ---R differentiate : (%,Symbol) -> % if MachineFloat has PDRING SYMBOL ---R differentiate : (%,List Symbol) -> % if MachineFloat has PDRING SYMBOL ---R differentiate : (%,Symbol,NonNegativeInteger) -> % if MachineFloat has PDRING SYMBOL ---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if MachineFloat has PDRING SYMBOL +--R differentiate : (%,Symbol) -> % if MachineFloat has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol)) -> % if MachineFloat has PDRING(SYMBOL) +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if MachineFloat has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if MachineFloat has PDRING(SYMBOL) --R differentiate : (%,(MachineFloat -> MachineFloat),NonNegativeInteger) -> % --R differentiate : (%,(MachineFloat -> MachineFloat)) -> % --R discreteLog : % -> NonNegativeInteger if MachineFloat has FFIELDC --R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if MachineFloat has FFIELDC ---R discriminant : Vector % -> MachineFloat +--R discriminant : Vector(%) -> MachineFloat --R divide : (%,%) -> Record(quotient: %,remainder: %) if MachineFloat has EUCDOM --R ?.? : (%,MachineFloat) -> % if MachineFloat has ELTAB(MFLOAT,MFLOAT) --R euclideanSize : % -> NonNegativeInteger if MachineFloat has EUCDOM ---R eval : (%,List MachineFloat,List MachineFloat) -> % if MachineFloat has EVALAB MFLOAT ---R eval : (%,MachineFloat,MachineFloat) -> % if MachineFloat has EVALAB MFLOAT ---R eval : (%,Equation MachineFloat) -> % if MachineFloat has EVALAB MFLOAT ---R eval : (%,List Equation MachineFloat) -> % if MachineFloat has EVALAB MFLOAT ---R eval : (%,List Symbol,List MachineFloat) -> % if MachineFloat has IEVALAB(SYMBOL,MFLOAT) +--R eval : (%,List(MachineFloat),List(MachineFloat)) -> % if MachineFloat has EVALAB(MFLOAT) +--R eval : (%,MachineFloat,MachineFloat) -> % if MachineFloat has EVALAB(MFLOAT) +--R eval : (%,Equation(MachineFloat)) -> % if MachineFloat has EVALAB(MFLOAT) +--R eval : (%,List(Equation(MachineFloat))) -> % if MachineFloat has EVALAB(MFLOAT) +--R eval : (%,List(Symbol),List(MachineFloat)) -> % if MachineFloat has IEVALAB(SYMBOL,MFLOAT) --R eval : (%,Symbol,MachineFloat) -> % if MachineFloat has IEVALAB(SYMBOL,MFLOAT) --R exp : % -> % if MachineFloat has TRANFUN ---R expressIdealMember : (List %,%) -> Union(List %,"failed") if MachineFloat has EUCDOM +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if MachineFloat has EUCDOM --R exquo : (%,MachineFloat) -> Union(%,"failed") if MachineFloat has INTDOM --R exquo : (%,%) -> Union(%,"failed") --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if MachineFloat has EUCDOM --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if MachineFloat has EUCDOM ---R factor : % -> Factored % if MachineFloat has EUCDOM and MachineFloat has PFECAT or MachineFloat has FIELD ---R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if MachineFloat has EUCDOM and MachineFloat has PFECAT ---R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if MachineFloat has EUCDOM and MachineFloat has PFECAT ---R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if MachineFloat has FFIELDC +--R factor : % -> Factored(%) if MachineFloat has EUCDOM and MachineFloat has PFECAT or MachineFloat has FIELD +--R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if MachineFloat has EUCDOM and MachineFloat has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if MachineFloat has EUCDOM and MachineFloat has PFECAT +--R factorsOfCyclicGroupSize : () -> List(Record(factor: Integer,exponent: Integer)) if MachineFloat has FFIELDC --R gcd : (%,%) -> % if MachineFloat has EUCDOM ---R gcd : List % -> % if MachineFloat has EUCDOM ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if MachineFloat has EUCDOM +--R gcd : List(%) -> % if MachineFloat has EUCDOM +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if MachineFloat has EUCDOM --R index : PositiveInteger -> % if MachineFloat has FINITE --R init : () -> % if MachineFloat has FFIELDC --R inv : % -> % if MachineFloat has FIELD --R lcm : (%,%) -> % if MachineFloat has EUCDOM ---R lcm : List % -> % if MachineFloat has EUCDOM ---R lift : % -> SparseUnivariatePolynomial MachineFloat +--R lcm : List(%) -> % if MachineFloat has EUCDOM +--R lift : % -> SparseUnivariatePolynomial(MachineFloat) --R log : % -> % if MachineFloat has TRANFUN --R lookup : % -> PositiveInteger if MachineFloat has FINITE --R map : ((MachineFloat -> MachineFloat),%) -> % ---R minimalPolynomial : % -> SparseUnivariatePolynomial MachineFloat if MachineFloat has FIELD ---R multiEuclidean : (List %,%) -> Union(List %,"failed") if MachineFloat has EUCDOM +--R minimalPolynomial : % -> SparseUnivariatePolynomial(MachineFloat) if MachineFloat has FIELD +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") if MachineFloat has EUCDOM --R nextItem : % -> Union(%,"failed") if MachineFloat has FFIELDC --R nthRoot : (%,Integer) -> % if MachineFloat has RADCAT and MachineFloat has TRANFUN --R order : % -> PositiveInteger if MachineFloat has FFIELDC ---R order : % -> OnePointCompletion PositiveInteger if MachineFloat has FFIELDC ---R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if MachineFloat has PATMAB INT ---R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if MachineFloat has PATMAB FLOAT +--R order : % -> OnePointCompletion(PositiveInteger) if MachineFloat has FFIELDC +--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if MachineFloat has PATMAB(INT) +--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if MachineFloat has PATMAB(FLOAT) --R pi : () -> % if MachineFloat has TRANFUN --R polarCoordinates : % -> Record(r: MachineFloat,phi: MachineFloat) if MachineFloat has RNS and MachineFloat has TRANFUN --R prime? : % -> Boolean if MachineFloat has EUCDOM and MachineFloat has PFECAT or MachineFloat has FIELD @@ -73931,26 +74112,26 @@ LyndonWord(VarSet:OrderedSet):Public == Private where --R primeFrobenius : % -> % if MachineFloat has FFIELDC --R primitive? : % -> Boolean if MachineFloat has FFIELDC --R primitiveElement : () -> % if MachineFloat has FFIELDC ---R principalIdeal : List % -> Record(coef: List %,generator: %) if MachineFloat has EUCDOM +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if MachineFloat has EUCDOM --R ?quo? : (%,%) -> % if MachineFloat has EUCDOM --R random : () -> % if MachineFloat has FINITE ---R rational : % -> Fraction Integer if MachineFloat has INS +--R rational : % -> Fraction(Integer) if MachineFloat has INS --R rational? : % -> Boolean if MachineFloat has INS ---R rationalIfCan : % -> Union(Fraction Integer,"failed") if MachineFloat has INS ---R reduce : SparseUnivariatePolynomial MachineFloat -> % ---R reduce : Fraction SparseUnivariatePolynomial MachineFloat -> Union(%,"failed") if MachineFloat has FIELD ---R reducedSystem : Matrix % -> Matrix Integer if MachineFloat has LINEXP INT ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if MachineFloat has LINEXP INT ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix MachineFloat,vec: Vector MachineFloat) ---R reducedSystem : Matrix % -> Matrix MachineFloat ---R regularRepresentation : (%,Vector %) -> Matrix MachineFloat ---R regularRepresentation : % -> Matrix MachineFloat +--R rationalIfCan : % -> Union(Fraction(Integer),"failed") if MachineFloat has INS +--R reduce : SparseUnivariatePolynomial(MachineFloat) -> % +--R reduce : Fraction(SparseUnivariatePolynomial(MachineFloat)) -> Union(%,"failed") if MachineFloat has FIELD +--R reducedSystem : Matrix(%) -> Matrix(Integer) if MachineFloat has LINEXP(INT) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if MachineFloat has LINEXP(INT) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(MachineFloat),vec: Vector(MachineFloat)) +--R reducedSystem : Matrix(%) -> Matrix(MachineFloat) +--R regularRepresentation : (%,Vector(%)) -> Matrix(MachineFloat) +--R regularRepresentation : % -> Matrix(MachineFloat) --R ?rem? : (%,%) -> % if MachineFloat has EUCDOM --R representationType : () -> Union("prime",polynomial,normal,cyclic) if MachineFloat has FFIELDC ---R represents : (Vector MachineFloat,Vector %) -> % ---R represents : Vector MachineFloat -> % ---R retract : % -> Fraction Integer if MachineFloat has RETRACT FRAC INT ---R retractIfCan : % -> Union(Fraction Integer,"failed") if MachineFloat has RETRACT FRAC INT +--R represents : (Vector(MachineFloat),Vector(%)) -> % +--R represents : Vector(MachineFloat) -> % +--R retract : % -> Fraction(Integer) if MachineFloat has RETRACT(FRAC(INT)) +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if MachineFloat has RETRACT(FRAC(INT)) --R retractIfCan : % -> Union(MachineFloat,"failed") --R retractIfCan : % -> Union(Integer,"failed") --R sec : % -> % if MachineFloat has TRANFUN @@ -73959,17 +74140,17 @@ LyndonWord(VarSet:OrderedSet):Public == Private where --R sinh : % -> % if MachineFloat has TRANFUN --R size : () -> NonNegativeInteger if MachineFloat has FINITE --R sizeLess? : (%,%) -> Boolean if MachineFloat has EUCDOM ---R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if MachineFloat has EUCDOM and MachineFloat has PFECAT +--R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if MachineFloat has EUCDOM and MachineFloat has PFECAT --R sqrt : % -> % if MachineFloat has RADCAT and MachineFloat has TRANFUN ---R squareFree : % -> Factored % if MachineFloat has EUCDOM and MachineFloat has PFECAT or MachineFloat has FIELD +--R squareFree : % -> Factored(%) if MachineFloat has EUCDOM and MachineFloat has PFECAT or MachineFloat has FIELD --R squareFreePart : % -> % if MachineFloat has EUCDOM and MachineFloat has PFECAT or MachineFloat has FIELD ---R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if MachineFloat has EUCDOM and MachineFloat has PFECAT +--R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if MachineFloat has EUCDOM and MachineFloat has PFECAT --R subtractIfCan : (%,%) -> Union(%,"failed") --R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if MachineFloat has FFIELDC --R tan : % -> % if MachineFloat has TRANFUN --R tanh : % -> % if MachineFloat has TRANFUN ---R traceMatrix : Vector % -> Matrix MachineFloat ---R traceMatrix : () -> Matrix MachineFloat +--R traceMatrix : Vector(%) -> Matrix(MachineFloat) +--R traceMatrix : () -> Matrix(MachineFloat) --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) --R --E 1 @@ -74201,55 +74382,56 @@ MachineComplex():Exports == Implementation where --S 1 of 1 )show MachineFloat +--R --R MachineFloat is a domain constructor --R Abbreviation for MachineFloat is MFLOAT --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for MFLOAT --R --R------------------------------- Operations -------------------------------- ---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % ---R ?*? : (PositiveInteger,%) -> % ?**? : (%,Fraction Integer) -> % ---R ?**? : (%,Integer) -> % ?**? : (%,PositiveInteger) -> % ---R ?+? : (%,%) -> % ?-? : (%,%) -> % ---R -? : % -> % ?/? : (%,%) -> % ---R ? Boolean ?<=? : (%,%) -> Boolean ---R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean ---R ?>=? : (%,%) -> Boolean 1 : () -> % ---R 0 : () -> % ?^? : (%,Integer) -> % ---R ?^? : (%,PositiveInteger) -> % abs : % -> % ---R associates? : (%,%) -> Boolean base : () -> PositiveInteger ---R bits : () -> PositiveInteger ceiling : % -> % ---R coerce : MachineInteger -> % coerce : % -> Float ---R coerce : Float -> % coerce : Fraction Integer -> % ---R coerce : Integer -> % coerce : Fraction Integer -> % ---R coerce : % -> % coerce : Integer -> % ---R coerce : % -> OutputForm convert : % -> Pattern Float ---R convert : % -> DoubleFloat convert : % -> Float ---R digits : () -> PositiveInteger exponent : % -> Integer ---R factor : % -> Factored % float : (Integer,Integer) -> % ---R floor : % -> % fractionPart : % -> % ---R gcd : List % -> % gcd : (%,%) -> % ---R hash : % -> SingleInteger inv : % -> % ---R latex : % -> String lcm : List % -> % ---R lcm : (%,%) -> % mantissa : % -> Integer ---R max : (%,%) -> % maximumExponent : () -> Integer ---R min : (%,%) -> % minimumExponent : () -> Integer ---R negative? : % -> Boolean norm : % -> % ---R nthRoot : (%,Integer) -> % one? : % -> Boolean ---R order : % -> Integer positive? : % -> Boolean ---R precision : () -> PositiveInteger prime? : % -> Boolean ---R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") ---R ?rem? : (%,%) -> % retract : % -> Float ---R retract : % -> Fraction Integer retract : % -> Integer ---R round : % -> % sample : () -> % ---R sign : % -> Integer sizeLess? : (%,%) -> Boolean ---R sqrt : % -> % squareFree : % -> Factored % ---R squareFreePart : % -> % truncate : % -> % ---R unit? : % -> Boolean unitCanonical : % -> % ---R wholePart : % -> Integer zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,%) -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R abs : % -> % associates? : (%,%) -> Boolean +--R base : () -> PositiveInteger bits : () -> PositiveInteger +--R ceiling : % -> % coerce : MachineInteger -> % +--R coerce : % -> Float coerce : Float -> % +--R coerce : Fraction(Integer) -> % coerce : Integer -> % +--R coerce : Fraction(Integer) -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R convert : % -> Pattern(Float) convert : % -> DoubleFloat +--R convert : % -> Float digits : () -> PositiveInteger +--R exponent : % -> Integer factor : % -> Factored(%) +--R float : (Integer,Integer) -> % floor : % -> % +--R fractionPart : % -> % gcd : List(%) -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R inv : % -> % latex : % -> String +--R lcm : List(%) -> % lcm : (%,%) -> % +--R mantissa : % -> Integer max : (%,%) -> % +--R maximumExponent : () -> Integer min : (%,%) -> % +--R minimumExponent : () -> Integer negative? : % -> Boolean +--R norm : % -> % nthRoot : (%,Integer) -> % +--R one? : % -> Boolean order : % -> Integer +--R positive? : % -> Boolean precision : () -> PositiveInteger +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R retract : % -> Float retract : % -> Fraction(Integer) +--R retract : % -> Integer round : % -> % +--R sample : () -> % sign : % -> Integer +--R sizeLess? : (%,%) -> Boolean sqrt : % -> % +--R squareFree : % -> Factored(%) squareFreePart : % -> % +--R truncate : % -> % unit? : % -> Boolean +--R unitCanonical : % -> % wholePart : % -> Integer +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,Fraction(Integer)) -> % --R ?**? : (%,NonNegativeInteger) -> % --R ?^? : (%,NonNegativeInteger) -> % --R base : PositiveInteger -> PositiveInteger @@ -74260,23 +74442,23 @@ MachineComplex():Exports == Implementation where --R digits : PositiveInteger -> PositiveInteger if $ has arbitraryPrecision --R divide : (%,%) -> Record(quotient: %,remainder: %) --R euclideanSize : % -> NonNegativeInteger ---R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") --R exquo : (%,%) -> Union(%,"failed") --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) --R float : (Integer,Integer,PositiveInteger) -> % ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) --R increasePrecision : Integer -> PositiveInteger if $ has arbitraryPrecision ---R max : () -> % if not has($,arbitraryExponent) and not has($,arbitraryPrecision) +--R max : () -> % if not(has($,arbitraryExponent)) and not(has($,arbitraryPrecision)) --R maximumExponent : Integer -> Integer ---R min : () -> % if not has($,arbitraryExponent) and not has($,arbitraryPrecision) +--R min : () -> % if not(has($,arbitraryExponent)) and not(has($,arbitraryPrecision)) --R minimumExponent : Integer -> Integer ---R multiEuclidean : (List %,%) -> Union(List %,"failed") ---R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") +--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) --R precision : PositiveInteger -> PositiveInteger ---R principalIdeal : List % -> Record(coef: List %,generator: %) +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) --R retractIfCan : % -> Union(Float,"failed") ---R retractIfCan : % -> Union(Fraction Integer,"failed") +--R retractIfCan : % -> Union(Fraction(Integer),"failed") --R retractIfCan : % -> Union(Integer,"failed") --R subtractIfCan : (%,%) -> Union(%,"failed") --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) @@ -74707,6 +74889,7 @@ MachineFloat(): Exports == Implementation where --S 1 of 1 )show MachineInteger +--R --R MachineInteger is a domain constructor --R Abbreviation for MachineInteger is MINT --R This constructor is exposed in this frame. @@ -74727,16 +74910,16 @@ MachineFloat(): Exports == Implementation where --R bit? : (%,%) -> Boolean coerce : Integer -> % --R coerce : % -> % coerce : Integer -> % --R coerce : % -> OutputForm convert : % -> Integer ---R convert : % -> InputForm convert : % -> Pattern Integer +--R convert : % -> InputForm convert : % -> Pattern(Integer) --R convert : % -> Float convert : % -> DoubleFloat --R copy : % -> % dec : % -> % --R differentiate : % -> % even? : % -> Boolean ---R factor : % -> Factored % factorial : % -> % ---R gcd : (%,%) -> % gcd : List % -> % +--R factor : % -> Factored(%) factorial : % -> % +--R gcd : (%,%) -> % gcd : List(%) -> % --R hash : % -> % hash : % -> SingleInteger --R inc : % -> % init : () -> % --R invmod : (%,%) -> % latex : % -> String ---R lcm : (%,%) -> % lcm : List % -> % +--R lcm : (%,%) -> % lcm : List(%) -> % --R length : % -> % mask : % -> % --R max : (%,%) -> % maxint : () -> PositiveInteger --R min : (%,%) -> % mulmod : (%,%,%) -> % @@ -74745,12 +74928,12 @@ MachineFloat(): Exports == Implementation where --R positive? : % -> Boolean positiveRemainder : (%,%) -> % --R powmod : (%,%,%) -> % prime? : % -> Boolean --R ?quo? : (%,%) -> % random : () -> % ---R random : % -> % rational : % -> Fraction Integer +--R random : % -> % rational : % -> Fraction(Integer) --R rational? : % -> Boolean recip : % -> Union(%,"failed") --R ?rem? : (%,%) -> % retract : % -> Integer --R sample : () -> % shift : (%,%) -> % --R sign : % -> Integer sizeLess? : (%,%) -> Boolean ---R squareFree : % -> Factored % squareFreePart : % -> % +--R squareFree : % -> Factored(%) squareFreePart : % -> % --R submod : (%,%,%) -> % symmetricRemainder : (%,%) -> % --R unit? : % -> Boolean unitCanonical : % -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean @@ -74758,23 +74941,23 @@ MachineFloat(): Exports == Implementation where --R ?**? : (%,NonNegativeInteger) -> % --R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger ---R coerce : Expression Integer -> Expression % +--R coerce : Expression(Integer) -> Expression(%) --R differentiate : (%,NonNegativeInteger) -> % --R divide : (%,%) -> Record(quotient: %,remainder: %) --R euclideanSize : % -> NonNegativeInteger ---R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") --R exquo : (%,%) -> Union(%,"failed") --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) --R maxint : PositiveInteger -> PositiveInteger ---R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") --R nextItem : % -> Union(%,"failed") ---R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) ---R principalIdeal : List % -> Record(coef: List %,generator: %) ---R rationalIfCan : % -> Union(Fraction Integer,"failed") ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) ---R reducedSystem : Matrix % -> Matrix Integer +--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) +--R rationalIfCan : % -> Union(Fraction(Integer),"failed") +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) +--R reducedSystem : Matrix(%) -> Matrix(Integer) --R retractIfCan : % -> Union(Integer,"failed") --R subtractIfCan : (%,%) -> Union(%,"failed") --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) @@ -74987,7 +75170,7 @@ z:Symbol :='z word := OrderedFreeMonoid(Symbol) --R --R ---R (4) OrderedFreeMonoid Symbol +--R (4) OrderedFreeMonoid(Symbol) --R Type: Domain --E 4 @@ -74995,7 +75178,7 @@ word := OrderedFreeMonoid(Symbol) tree := Magma(Symbol) --R --R ---R (5) Magma Symbol +--R (5) Magma(Symbol) --R Type: Domain --E 5 @@ -75004,7 +75187,7 @@ a:tree := x*x --R --R --R (6) [x,x] ---R Type: Magma Symbol +--R Type: Magma(Symbol) --E 6 --S 7 of 22 @@ -75012,7 +75195,7 @@ b:tree := y*y --R --R --R (7) [y,y] ---R Type: Magma Symbol +--R Type: Magma(Symbol) --E 7 --S 8 of 22 @@ -75020,7 +75203,7 @@ c:tree := a*b --R --R --R (8) [[x,x],[y,y]] ---R Type: Magma Symbol +--R Type: Magma(Symbol) --E 8 --S 9 of 22 @@ -75028,7 +75211,7 @@ left c --R --R --R (9) [x,x] ---R Type: Magma Symbol +--R Type: Magma(Symbol) --E 9 --S 10 of 22 @@ -75036,7 +75219,7 @@ right c --R --R --R (10) [y,y] ---R Type: Magma Symbol +--R Type: Magma(Symbol) --E 10 --S 11 of 22 @@ -75053,7 +75236,7 @@ c::word --R --R 2 2 --R (12) x y ---R Type: OrderedFreeMonoid Symbol +--R Type: OrderedFreeMonoid(Symbol) --E 12 --S 13 of 22 @@ -75093,7 +75276,7 @@ rest c --R --R --R (17) [x,[y,y]] ---R Type: Magma Symbol +--R Type: Magma(Symbol) --E 17 --S 18 of 22 @@ -75101,7 +75284,7 @@ rest rest c --R --R --R (18) [y,y] ---R Type: Magma Symbol +--R Type: Magma(Symbol) --E 18 --S 19 of 22 @@ -75109,7 +75292,7 @@ ax:tree := a*x --R --R --R (19) [[x,x],x] ---R Type: Magma Symbol +--R Type: Magma(Symbol) --E 19 --S 20 of 22 @@ -75117,7 +75300,7 @@ xa:tree := x*a --R --R --R (20) [x,[x,x]] ---R Type: Magma Symbol +--R Type: Magma(Symbol) --E 20 --S 21 of 22 @@ -75446,7 +75629,8 @@ Magma(VarSet:OrderedSet):Public == Private where --S 1 of 1 )show MakeCachableSet ---R MakeCachableSet S: SetCategory is a domain constructor +--R +--R MakeCachableSet(S: SetCategory) is a domain constructor --R Abbreviation for MakeCachableSet is MKCHSET --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for MKCHSET @@ -77220,7 +77404,7 @@ m : Matrix(Integer) := new(3,3,0) --R (1) |0 0 0| --R | | --R +0 0 0+ ---R Type: Matrix Integer +--R Type: Matrix(Integer) --E 1 --S 2 of 38 @@ -77248,7 +77432,7 @@ m --R (4) |0 0 5| --R | | --R +0 0 0+ ---R Type: Matrix Integer +--R Type: Matrix(Integer) --E 4 --S 5 of 38 @@ -77258,7 +77442,7 @@ matrix [ [1,2,3,4],[0,9,8,7] ] --R +1 2 3 4+ --R (5) | | --R +0 9 8 7+ ---R Type: Matrix Integer +--R Type: Matrix(Integer) --E 5 --S 6 of 38 @@ -77278,7 +77462,7 @@ dm := diagonalMatrix [1,x**2,x**3,x**4,x**5] --R | | --R | 5| --R +0 0 0 0 x + ---R Type: Matrix Polynomial Integer +--R Type: Matrix(Polynomial(Integer)) --E 6 --S 7 of 38 @@ -77297,7 +77481,7 @@ setRow!(dm,5,vector [1,1,1,1,1]) --R |0 0 0 x 0| --R | | --R +1 1 1 1 1+ ---R Type: Matrix Polynomial Integer +--R Type: Matrix(Polynomial(Integer)) --E 7 --S 8 of 38 @@ -77315,7 +77499,7 @@ setColumn!(dm,2,vector [y,y,y,y,y]) --R |0 y 0 x 0| --R | | --R +1 y 1 1 1+ ---R Type: Matrix Polynomial Integer +--R Type: Matrix(Polynomial(Integer)) --E 8 --S 9 of 38 @@ -77333,7 +77517,7 @@ cdm := copy(dm) --R |0 y 0 x 0| --R | | --R +1 y 1 1 1+ ---R Type: Matrix Polynomial Integer +--R Type: Matrix(Polynomial(Integer)) --E 9 --S 10 of 38 @@ -77342,7 +77526,7 @@ setelt(dm,4,1,1-x**7) --R --R 7 --R (10) - x + 1 ---R Type: Polynomial Integer +--R Type: Polynomial(Integer) --E 10 --S 11 of 38 @@ -77360,7 +77544,7 @@ setelt(dm,4,1,1-x**7) --R |- x + 1 y 0 x 0| |0 y 0 x 0| --R | | | | --R + 1 y 1 1 1+ +1 y 1 1 1+ ---R Type: List Matrix Polynomial Integer +--R Type: List(Matrix(Polynomial(Integer))) --E 11 --S 12 of 38 @@ -77371,7 +77555,7 @@ subMatrix(dm,2,3,2,4) --R (12) | | --R | 3 | --R +y x 0+ ---R Type: Matrix Polynomial Integer +--R Type: Matrix(Polynomial(Integer)) --E 12 --S 13 of 38 @@ -77385,7 +77569,7 @@ d := diagonalMatrix [1.2,-1.3,1.4,-1.5] --R |0.0 0.0 1.4 0.0 | --R | | --R +0.0 0.0 0.0 - 1.5+ ---R Type: Matrix Float +--R Type: Matrix(Float) --E 13 --S 14 of 38 @@ -77395,7 +77579,7 @@ e := matrix [ [6.7,9.11],[-31.33,67.19] ] --R + 6.7 9.11 + --R (14) | | --R +- 31.33 67.19+ ---R Type: Matrix Float +--R Type: Matrix(Float) --E 14 --S 15 of 38 @@ -77409,7 +77593,7 @@ setsubMatrix!(d,1,2,e) --R |0.0 0.0 1.4 0.0 | --R | | --R +0.0 0.0 0.0 - 1.5+ ---R Type: Matrix Float +--R Type: Matrix(Float) --E 15 --S 16 of 38 @@ -77423,7 +77607,7 @@ d --R |0.0 0.0 1.4 0.0 | --R | | --R +0.0 0.0 0.0 - 1.5+ ---R Type: Matrix Float +--R Type: Matrix(Float) --E 16 --S 17 of 38 @@ -77437,7 +77621,7 @@ a := matrix [ [1/2,1/3,1/4],[1/5,1/6,1/7] ] --R |1 1 1| --R |- - -| --R +5 6 7+ ---R Type: Matrix Fraction Integer +--R Type: Matrix(Fraction(Integer)) --E 17 --S 18 of 38 @@ -77451,7 +77635,7 @@ b := matrix [ [3/5,3/7,3/11],[3/13,3/17,3/19] ] --R | 3 3 3| --R |-- -- --| --R +13 17 19+ ---R Type: Matrix Fraction Integer +--R Type: Matrix(Fraction(Integer)) --E 18 --S 19 of 38 @@ -77465,7 +77649,7 @@ horizConcat(a,b) --R |1 1 1 3 3 3| --R |- - - -- -- --| --R +5 6 7 13 17 19+ ---R Type: Matrix Fraction Integer +--R Type: Matrix(Fraction(Integer)) --E 19 --S 20 of 38 @@ -77487,7 +77671,7 @@ vab := vertConcat(a,b) --R | 3 3 3| --R |-- -- --| --R +13 17 19+ ---R Type: Matrix Fraction Integer +--R Type: Matrix(Fraction(Integer)) --E 20 --S 21 of 38 @@ -77505,7 +77689,7 @@ transpose vab --R |1 1 3 3| --R |- - -- --| --R +4 7 11 19+ ---R Type: Matrix Fraction Integer +--R Type: Matrix(Fraction(Integer)) --E 21 --S 22 of 38 @@ -77515,7 +77699,7 @@ m := matrix [ [1,2],[3,4] ] --R +1 2+ --R (22) | | --R +3 4+ ---R Type: Matrix Integer +--R Type: Matrix(Integer) --E 22 --S 23 of 38 @@ -77525,7 +77709,7 @@ m := matrix [ [1,2],[3,4] ] --R +- 20 - 40+ --R (23) | | --R +- 60 - 80+ ---R Type: Matrix Integer +--R Type: Matrix(Integer) --E 23 --S 24 of 38 @@ -77535,7 +77719,7 @@ n := matrix([ [1,0,-2],[-3,5,1] ]) --R + 1 0 - 2+ --R (24) | | --R +- 3 5 1 + ---R Type: Matrix Integer +--R Type: Matrix(Integer) --E 24 --S 25 of 38 @@ -77545,7 +77729,7 @@ m * n --R +- 5 10 0 + --R (25) | | --R +- 9 20 - 2+ ---R Type: Matrix Integer +--R Type: Matrix(Integer) --E 25 --S 26 of 38 @@ -77553,7 +77737,7 @@ vec := column(n,3) --R --R --R (26) [- 2,1] ---R Type: Vector Integer +--R Type: Vector(Integer) --E 26 --S 27 of 38 @@ -77561,7 +77745,7 @@ vec * m --R --R --R (27) [1,0] ---R Type: Vector Integer +--R Type: Vector(Integer) --E 27 --S 28 of 38 @@ -77569,7 +77753,7 @@ m * vec --R --R --R (28) [0,- 2] ---R Type: Vector Integer +--R Type: Vector(Integer) --E 28 --S 29 of 38 @@ -77587,7 +77771,7 @@ hilb := matrix([ [1/(i + j) for i in 1..3] for j in 1..3]) --R |1 1 1| --R |- - -| --R +4 5 6+ ---R Type: Matrix Fraction Integer +--R Type: Matrix(Fraction(Integer)) --E 29 --S 30 of 38 @@ -77599,7 +77783,7 @@ inverse(hilb) --R (30) |- 240 900 - 720| --R | | --R + 180 - 720 600 + ---R Type: Union(Matrix Fraction Integer,...) +--R Type: Union(Matrix(Fraction(Integer)),...) --E 30 --S 31 of 38 @@ -77613,7 +77797,7 @@ mm := matrix([ [1,2,3,4], [5,6,7,8], [9,10,11,12], [13,14,15,16] ]) --R |9 10 11 12| --R | | --R +13 14 15 16+ ---R Type: Matrix Integer +--R Type: Matrix(Integer) --E 31 --S 32 of 38 @@ -77661,7 +77845,7 @@ nullSpace(mm) --R --R --R (37) [[1,- 2,1,0],[2,- 3,0,1]] ---R Type: List Vector Integer +--R Type: List(Vector(Integer)) --E 37 --S 38 of 38 @@ -77675,7 +77859,7 @@ rowEchelon(mm) --R |0 0 0 0 | --R | | --R +0 0 0 0 + ---R Type: Matrix Integer +--R Type: Matrix(Integer) --E 38 )spool )lisp (bye) @@ -78394,7 +78578,8 @@ Matrix(R): Exports == Implementation where --S 1 of 1 )show ModMonic ---R ModMonic(R: Ring,Rep: UnivariatePolynomialCategory R) is a domain constructor +--R +--R ModMonic(R: Ring,Rep: UnivariatePolynomialCategory(R)) is a domain constructor --R Abbreviation for ModMonic is MODMON --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for MODMON @@ -78405,31 +78590,30 @@ Matrix(R): Exports == Implementation where --R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean ---R An : % -> Vector R D : (%,(R -> R)) -> % +--R An : % -> Vector(R) D : (%,(R -> R)) -> % --R D : % -> % D : (%,NonNegativeInteger) -> % ---R 1 : () -> % UnVectorise : Vector R -> % ---R Vectorise : % -> Vector R 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coefficients : % -> List R +--R 1 : () -> % UnVectorise : Vector(R) -> % +--R Vectorise : % -> Vector(R) 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coefficients : % -> List(R) --R coerce : Rep -> % coerce : R -> % --R coerce : Integer -> % coerce : % -> OutputForm --R degree : % -> NonNegativeInteger differentiate : % -> % --R ?.? : (%,%) -> % ?.? : (%,R) -> R ---R eval : (%,List %,List %) -> % eval : (%,%,%) -> % ---R eval : (%,Equation %) -> % eval : (%,List Equation %) -> % +--R eval : (%,%,%) -> % eval : (%,Equation(%)) -> % --R ground : % -> R ground? : % -> Boolean --R hash : % -> SingleInteger init : () -> % if R has STEP --R latex : % -> String leadingCoefficient : % -> R --R leadingMonomial : % -> % lift : % -> Rep --R map : ((R -> R),%) -> % modulus : () -> Rep ---R monomial? : % -> Boolean monomials : % -> List % ---R one? : % -> Boolean pow : () -> PrimitiveArray % ---R primitiveMonomials : % -> List % pseudoRemainder : (%,%) -> % ---R recip : % -> Union(%,"failed") reduce : Rep -> % ---R reductum : % -> % retract : % -> R ---R sample : () -> % setPoly : Rep -> Rep ---R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (Fraction Integer,%) -> % if R has ALGEBRA FRAC INT ---R ?*? : (%,Fraction Integer) -> % if R has ALGEBRA FRAC INT +--R monomial? : % -> Boolean monomials : % -> List(%) +--R one? : % -> Boolean pow : () -> PrimitiveArray(%) +--R pseudoRemainder : (%,%) -> % recip : % -> Union(%,"failed") +--R reduce : Rep -> % reductum : % -> % +--R retract : % -> R sample : () -> % +--R setPoly : Rep -> Rep zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT)) +--R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) --R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,R) -> % if R has FIELD @@ -78438,147 +78622,150 @@ Matrix(R): Exports == Implementation where --R ?>? : (%,%) -> Boolean if R has ORDSET --R ?>=? : (%,%) -> Boolean if R has ORDSET --R D : (%,(R -> R),NonNegativeInteger) -> % ---R D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL ---R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL ---R D : (%,List Symbol) -> % if R has PDRING SYMBOL ---R D : (%,Symbol) -> % if R has PDRING SYMBOL ---R D : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) +--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) +--R D : (%,List(Symbol)) -> % if R has PDRING(SYMBOL) +--R D : (%,Symbol) -> % if R has PDRING(SYMBOL) +--R D : (%,List(SingletonAsOrderedSet),List(NonNegativeInteger)) -> % --R D : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % ---R D : (%,List SingletonAsOrderedSet) -> % +--R D : (%,List(SingletonAsOrderedSet)) -> % --R D : (%,SingletonAsOrderedSet) -> % --R ?^? : (%,NonNegativeInteger) -> % --R associates? : (%,%) -> Boolean if R has INTDOM --R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and R has PFECAT or R has CHARNZ ---R coefficient : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R coefficient : (%,List(SingletonAsOrderedSet),List(NonNegativeInteger)) -> % --R coefficient : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % --R coefficient : (%,NonNegativeInteger) -> R --R coerce : % -> % if R has INTDOM ---R coerce : Fraction Integer -> % if R has ALGEBRA FRAC INT or R has RETRACT FRAC INT +--R coerce : Fraction(Integer) -> % if R has ALGEBRA(FRAC(INT)) or R has RETRACT(FRAC(INT)) --R coerce : SingletonAsOrderedSet -> % ---R composite : (Fraction %,%) -> Union(Fraction %,"failed") if R has INTDOM +--R composite : (Fraction(%),%) -> Union(Fraction(%),"failed") if R has INTDOM --R composite : (%,%) -> Union(%,"failed") if R has INTDOM ---R computePowers : () -> PrimitiveArray % ---R conditionP : Matrix % -> Union(Vector %,"failed") if $ has CHARNZ and R has PFECAT +--R computePowers : () -> PrimitiveArray(%) +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and R has PFECAT --R content : (%,SingletonAsOrderedSet) -> % if R has GCDDOM --R content : % -> R if R has GCDDOM ---R convert : % -> InputForm if SingletonAsOrderedSet has KONVERT INFORM and R has KONVERT INFORM ---R convert : % -> Pattern Integer if SingletonAsOrderedSet has KONVERT PATTERN INT and R has KONVERT PATTERN INT ---R convert : % -> Pattern Float if SingletonAsOrderedSet has KONVERT PATTERN FLOAT and R has KONVERT PATTERN FLOAT ---R degree : (%,List SingletonAsOrderedSet) -> List NonNegativeInteger +--R convert : % -> InputForm if SingletonAsOrderedSet has KONVERT(INFORM) and R has KONVERT(INFORM) +--R convert : % -> Pattern(Integer) if SingletonAsOrderedSet has KONVERT(PATTERN(INT)) and R has KONVERT(PATTERN(INT)) +--R convert : % -> Pattern(Float) if SingletonAsOrderedSet has KONVERT(PATTERN(FLOAT)) and R has KONVERT(PATTERN(FLOAT)) +--R degree : (%,List(SingletonAsOrderedSet)) -> List(NonNegativeInteger) --R degree : (%,SingletonAsOrderedSet) -> NonNegativeInteger --R differentiate : (%,(R -> R),%) -> % --R differentiate : (%,(R -> R)) -> % --R differentiate : (%,(R -> R),NonNegativeInteger) -> % ---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL ---R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL ---R differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL ---R differentiate : (%,Symbol) -> % if R has PDRING SYMBOL +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol)) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,Symbol) -> % if R has PDRING(SYMBOL) --R differentiate : (%,NonNegativeInteger) -> % ---R differentiate : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R differentiate : (%,List(SingletonAsOrderedSet),List(NonNegativeInteger)) -> % --R differentiate : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % ---R differentiate : (%,List SingletonAsOrderedSet) -> % +--R differentiate : (%,List(SingletonAsOrderedSet)) -> % --R differentiate : (%,SingletonAsOrderedSet) -> % --R discriminant : % -> R if R has COMRING --R discriminant : (%,SingletonAsOrderedSet) -> % if R has COMRING --R divide : (%,%) -> Record(quotient: %,remainder: %) if R has FIELD --R divideExponents : (%,NonNegativeInteger) -> Union(%,"failed") ---R ?.? : (%,Fraction %) -> Fraction % if R has INTDOM ---R elt : (Fraction %,R) -> R if R has FIELD ---R elt : (Fraction %,Fraction %) -> Fraction % if R has INTDOM +--R ?.? : (%,Fraction(%)) -> Fraction(%) if R has INTDOM +--R elt : (Fraction(%),R) -> R if R has FIELD +--R elt : (Fraction(%),Fraction(%)) -> Fraction(%) if R has INTDOM --R euclideanSize : % -> NonNegativeInteger if R has FIELD ---R eval : (%,List SingletonAsOrderedSet,List %) -> % +--R eval : (%,List(SingletonAsOrderedSet),List(%)) -> % --R eval : (%,SingletonAsOrderedSet,%) -> % ---R eval : (%,List SingletonAsOrderedSet,List R) -> % +--R eval : (%,List(SingletonAsOrderedSet),List(R)) -> % --R eval : (%,SingletonAsOrderedSet,R) -> % ---R expressIdealMember : (List %,%) -> Union(List %,"failed") if R has FIELD +--R eval : (%,List(%),List(%)) -> % +--R eval : (%,List(Equation(%))) -> % +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if R has FIELD --R exquo : (%,%) -> Union(%,"failed") if R has INTDOM --R exquo : (%,R) -> Union(%,"failed") if R has INTDOM --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has FIELD --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if R has FIELD ---R factor : % -> Factored % if R has PFECAT ---R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT ---R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R factor : % -> Factored(%) if R has PFECAT +--R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT --R frobenius : % -> % if R has FFIELDC --R gcd : (%,%) -> % if R has GCDDOM ---R gcd : List % -> % if R has GCDDOM ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has GCDDOM +--R gcd : List(%) -> % if R has GCDDOM +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has GCDDOM --R index : PositiveInteger -> % if R has FINITE ---R integrate : % -> % if R has ALGEBRA FRAC INT +--R integrate : % -> % if R has ALGEBRA(FRAC(INT)) --R isExpt : % -> Union(Record(var: SingletonAsOrderedSet,exponent: NonNegativeInteger),"failed") ---R isPlus : % -> Union(List %,"failed") ---R isTimes : % -> Union(List %,"failed") +--R isPlus : % -> Union(List(%),"failed") +--R isTimes : % -> Union(List(%),"failed") --R karatsubaDivide : (%,NonNegativeInteger) -> Record(quotient: %,remainder: %) --R lcm : (%,%) -> % if R has GCDDOM ---R lcm : List % -> % if R has GCDDOM +--R lcm : List(%) -> % if R has GCDDOM --R lookup : % -> PositiveInteger if R has FINITE --R mainVariable : % -> Union(SingletonAsOrderedSet,"failed") ---R makeSUP : % -> SparseUnivariatePolynomial R +--R makeSUP : % -> SparseUnivariatePolynomial(R) --R mapExponents : ((NonNegativeInteger -> NonNegativeInteger),%) -> % --R max : (%,%) -> % if R has ORDSET --R min : (%,%) -> % if R has ORDSET ---R minimumDegree : (%,List SingletonAsOrderedSet) -> List NonNegativeInteger +--R minimumDegree : (%,List(SingletonAsOrderedSet)) -> List(NonNegativeInteger) --R minimumDegree : (%,SingletonAsOrderedSet) -> NonNegativeInteger --R minimumDegree : % -> NonNegativeInteger --R monicDivide : (%,%) -> Record(quotient: %,remainder: %) --R monicDivide : (%,%,SingletonAsOrderedSet) -> Record(quotient: %,remainder: %) ---R monomial : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R monomial : (%,List(SingletonAsOrderedSet),List(NonNegativeInteger)) -> % --R monomial : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % --R monomial : (R,NonNegativeInteger) -> % ---R multiEuclidean : (List %,%) -> Union(List %,"failed") if R has FIELD +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") if R has FIELD --R multiplyExponents : (%,NonNegativeInteger) -> % ---R multivariate : (SparseUnivariatePolynomial %,SingletonAsOrderedSet) -> % ---R multivariate : (SparseUnivariatePolynomial R,SingletonAsOrderedSet) -> % +--R multivariate : (SparseUnivariatePolynomial(%),SingletonAsOrderedSet) -> % +--R multivariate : (SparseUnivariatePolynomial(R),SingletonAsOrderedSet) -> % --R nextItem : % -> Union(%,"failed") if R has STEP --R numberOfMonomials : % -> NonNegativeInteger --R order : (%,%) -> NonNegativeInteger if R has INTDOM ---R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if SingletonAsOrderedSet has PATMAB INT and R has PATMAB INT ---R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if SingletonAsOrderedSet has PATMAB FLOAT and R has PATMAB FLOAT +--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if SingletonAsOrderedSet has PATMAB(INT) and R has PATMAB(INT) +--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if SingletonAsOrderedSet has PATMAB(FLOAT) and R has PATMAB(FLOAT) --R pomopo! : (%,R,NonNegativeInteger,%) -> % --R prime? : % -> Boolean if R has PFECAT +--R primitiveMonomials : % -> List(%) --R primitivePart : (%,SingletonAsOrderedSet) -> % if R has GCDDOM --R primitivePart : % -> % if R has GCDDOM ---R principalIdeal : List % -> Record(coef: List %,generator: %) if R has FIELD +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if R has FIELD --R pseudoDivide : (%,%) -> Record(coef: R,quotient: %,remainder: %) if R has INTDOM --R pseudoQuotient : (%,%) -> % if R has INTDOM --R ?quo? : (%,%) -> % if R has FIELD --R random : () -> % if R has FINITE ---R reducedSystem : Matrix % -> Matrix R ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT ---R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT +--R reducedSystem : Matrix(%) -> Matrix(R) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT) +--R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT) --R ?rem? : (%,%) -> % if R has FIELD --R resultant : (%,%) -> R if R has COMRING --R resultant : (%,%,SingletonAsOrderedSet) -> % if R has COMRING --R retract : % -> SingletonAsOrderedSet ---R retract : % -> Integer if R has RETRACT INT ---R retract : % -> Fraction Integer if R has RETRACT FRAC INT +--R retract : % -> Integer if R has RETRACT(INT) +--R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT)) --R retractIfCan : % -> Union(SingletonAsOrderedSet,"failed") ---R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT ---R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT) +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT)) --R retractIfCan : % -> Union(R,"failed") --R separate : (%,%) -> Record(primePart: %,commonPart: %) if R has GCDDOM --R shiftLeft : (%,NonNegativeInteger) -> % --R shiftRight : (%,NonNegativeInteger) -> % --R size : () -> NonNegativeInteger if R has FINITE --R sizeLess? : (%,%) -> Boolean if R has FIELD ---R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if R has PFECAT ---R squareFree : % -> Factored % if R has GCDDOM +--R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if R has PFECAT +--R squareFree : % -> Factored(%) if R has GCDDOM --R squareFreePart : % -> % if R has GCDDOM ---R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT --R subResultantGcd : (%,%) -> % if R has INTDOM --R subtractIfCan : (%,%) -> Union(%,"failed") ---R totalDegree : (%,List SingletonAsOrderedSet) -> NonNegativeInteger +--R totalDegree : (%,List(SingletonAsOrderedSet)) -> NonNegativeInteger --R totalDegree : % -> NonNegativeInteger --R unit? : % -> Boolean if R has INTDOM --R unitCanonical : % -> % if R has INTDOM --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM ---R univariate : % -> SparseUnivariatePolynomial R ---R univariate : (%,SingletonAsOrderedSet) -> SparseUnivariatePolynomial % ---R unmakeSUP : SparseUnivariatePolynomial R -> % ---R variables : % -> List SingletonAsOrderedSet ---R vectorise : (%,NonNegativeInteger) -> Vector R +--R univariate : % -> SparseUnivariatePolynomial(R) +--R univariate : (%,SingletonAsOrderedSet) -> SparseUnivariatePolynomial(%) +--R unmakeSUP : SparseUnivariatePolynomial(R) -> % +--R variables : % -> List(SingletonAsOrderedSet) +--R vectorise : (%,NonNegativeInteger) -> Vector(R) --R --E 1 @@ -78917,13 +79104,14 @@ ModMonic(R,Rep): C == T --S 1 of 1 )show ModularField +--R --R ModularField(R: CommutativeRing,Mod: AbelianMonoid,reduction: ((R,Mod) -> R),merge: ((Mod,Mod) -> Union(Mod,"failed")),exactQuo: ((R,R,Mod) -> Union(R,"failed"))) is a domain constructor --R Abbreviation for ModularField is MODFIELD --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for MODFIELD --R --R------------------------------- Operations -------------------------------- ---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % --R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % @@ -78932,17 +79120,17 @@ ModMonic(R,Rep): C == T --R 1 : () -> % 0 : () -> % --R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % --R associates? : (%,%) -> Boolean coerce : % -> R ---R coerce : Fraction Integer -> % coerce : % -> % +--R coerce : Fraction(Integer) -> % coerce : % -> % --R coerce : Integer -> % coerce : % -> OutputForm ---R factor : % -> Factored % gcd : List % -> % +--R factor : % -> Factored(%) gcd : List(%) -> % --R gcd : (%,%) -> % hash : % -> SingleInteger --R inv : % -> % latex : % -> String ---R lcm : List % -> % lcm : (%,%) -> % +--R lcm : List(%) -> % lcm : (%,%) -> % --R modulus : % -> Mod one? : % -> Boolean --R prime? : % -> Boolean ?quo? : (%,%) -> % --R recip : % -> Union(%,"failed") reduce : (R,Mod) -> % --R ?rem? : (%,%) -> % sample : () -> % ---R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored % +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) --R squareFreePart : % -> % unit? : % -> Boolean --R unitCanonical : % -> % zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean @@ -78953,13 +79141,13 @@ ModMonic(R,Rep): C == T --R divide : (%,%) -> Record(quotient: %,remainder: %) --R euclideanSize : % -> NonNegativeInteger --R exQuo : (%,%) -> Union(%,"failed") ---R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") --R exquo : (%,%) -> Union(%,"failed") --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % ---R multiEuclidean : (List %,%) -> Union(List %,"failed") ---R principalIdeal : List % -> Record(coef: List %,generator: %) +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) --R subtractIfCan : (%,%) -> Union(%,"failed") --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) --R @@ -79370,7 +79558,8 @@ ModuleMonomial(IS: OrderedSet, --S 1 of 1 )show ModuleOperator ---R ModuleOperator(R: Ring,M: LeftModule R) is a domain constructor +--R +--R ModuleOperator(R: Ring,M: LeftModule(R)) is a domain constructor --R Abbreviation for ModuleOperator is MODOP --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for MODOP @@ -79402,7 +79591,7 @@ ModuleMonomial(IS: OrderedSet, --R charthRoot : % -> Union(%,"failed") if R has CHARNZ --R conjug : R -> R if R has COMRING --R evaluateInverse : (%,(M -> M)) -> % ---R makeop : (R,FreeGroup BasicOperator) -> % +--R makeop : (R,FreeGroup(BasicOperator)) -> % --R retractIfCan : % -> Union(BasicOperator,"failed") --R retractIfCan : % -> Union(R,"failed") --R subtractIfCan : (%,%) -> Union(%,"failed") @@ -79709,7 +79898,8 @@ ModuleOperator(R: Ring, M:LeftModule(R)): Exports == Implementation where --S 1 of 1 )show MoebiusTransform ---R MoebiusTransform F: Field is a domain constructor +--R +--R MoebiusTransform(F: Field) is a domain constructor --R Abbreviation for MoebiusTransform is MOEBIUS --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for MOEBIUS @@ -79730,7 +79920,7 @@ ModuleOperator(R: Ring, M:LeftModule(R)): Exports == Implementation where --R shift : F -> % ?~=? : (%,%) -> Boolean --R ?**? : (%,NonNegativeInteger) -> % --R ?^? : (%,NonNegativeInteger) -> % ---R eval : (%,OnePointCompletion F) -> OnePointCompletion F +--R eval : (%,OnePointCompletion(F)) -> OnePointCompletion(F) --R --E 1 @@ -79896,6 +80086,7 @@ MoebiusTransform(F): Exports == Implementation where --S 1 of 1 )show MonoidRing +--R --R MonoidRing(R: Ring,M: Monoid) is a domain constructor --R Abbreviation for MonoidRing is MRING --R This constructor is not exposed in this frame. @@ -79908,12 +80099,12 @@ MoebiusTransform(F): Exports == Implementation where --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % --R ?^? : (%,PositiveInteger) -> % coefficient : (%,M) -> R ---R coefficients : % -> List R coerce : R -> % +--R coefficients : % -> List(R) coerce : R -> % --R coerce : M -> % coerce : Integer -> % --R coerce : % -> OutputForm hash : % -> SingleInteger --R latex : % -> String map : ((R -> R),%) -> % --R monomial : (R,M) -> % monomial? : % -> Boolean ---R monomials : % -> List % one? : % -> Boolean +--R monomials : % -> List(%) one? : % -> Boolean --R recip : % -> Union(%,"failed") retract : % -> R --R retract : % -> M sample : () -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean @@ -79924,7 +80115,7 @@ MoebiusTransform(F): Exports == Implementation where --R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if R has CHARNZ ---R coerce : List Record(coef: R,monom: M) -> % +--R coerce : List(Record(coef: R,monom: M)) -> % --R index : PositiveInteger -> % if M has FINITE and R has FINITE --R leadingCoefficient : % -> R if M has ORDSET --R leadingMonomial : % -> M if M has ORDSET @@ -79936,7 +80127,7 @@ MoebiusTransform(F): Exports == Implementation where --R retractIfCan : % -> Union(M,"failed") --R size : () -> NonNegativeInteger if M has FINITE and R has FINITE --R subtractIfCan : (%,%) -> Union(%,"failed") ---R terms : % -> List Record(coef: R,monom: M) +--R terms : % -> List(Record(coef: R,monom: M)) --R --E 1 @@ -80338,7 +80529,7 @@ s := multiset [1,2,3,4,5,4,3,2,3,4,5,6,7,4,10] --R --R --R (1) {1,2: 2,3: 3,4: 4,2: 5,6,7,10} ---R Type: Multiset PositiveInteger +--R Type: Multiset(PositiveInteger) --E 1 --S 2 of 14 @@ -80346,7 +80537,7 @@ insert!(3,s) --R --R --R (2) {1,2: 2,4: 3,4: 4,2: 5,6,7,10} ---R Type: Multiset PositiveInteger +--R Type: Multiset(PositiveInteger) --E 2 --S 3 of 14 @@ -80354,7 +80545,7 @@ remove!(3,s,1) --R --R --R (3) {1,2: 2,3: 3,4: 4,2: 5,6,7,10} ---R Type: Multiset PositiveInteger +--R Type: Multiset(PositiveInteger) --E 3 --S 4 of 14 @@ -80362,7 +80553,7 @@ s --R --R --R (4) {1,2: 2,3: 3,4: 4,2: 5,6,7,10} ---R Type: Multiset PositiveInteger +--R Type: Multiset(PositiveInteger) --E 4 --S 5 of 14 @@ -80370,7 +80561,7 @@ remove!(5,s) --R --R --R (5) {1,2: 2,3: 3,4: 4,6,7,10} ---R Type: Multiset PositiveInteger +--R Type: Multiset(PositiveInteger) --E 5 --S 6 of 14 @@ -80378,7 +80569,7 @@ s --R --R --R (6) {1,2: 2,3: 3,4: 4,6,7,10} ---R Type: Multiset PositiveInteger +--R Type: Multiset(PositiveInteger) --E 6 --S 7 of 14 @@ -80394,7 +80585,7 @@ t := multiset [2,2,2,-9] --R --R --R (8) {3: 2,- 9} ---R Type: Multiset Integer +--R Type: Multiset(Integer) --E 8 --S 9 of 14 @@ -80402,7 +80593,7 @@ U := union(s,t) --R --R --R (9) {1,5: 2,3: 3,4: 4,6,7,10,- 9} ---R Type: Multiset Integer +--R Type: Multiset(Integer) --E 9 --S 10 of 14 @@ -80410,7 +80601,7 @@ I := intersect(s,t) --R --R --R (10) {5: 2} ---R Type: Multiset Integer +--R Type: Multiset(Integer) --E 10 --S 11 of 14 @@ -80418,7 +80609,7 @@ difference(s,t) --R --R --R (11) {1,3: 3,4: 4,6,7,10} ---R Type: Multiset Integer +--R Type: Multiset(Integer) --E 11 --S 12 of 14 @@ -80426,7 +80617,7 @@ S := symmetricDifference(s,t) --R --R --R (12) {1,3: 3,4: 4,6,7,10,- 9} ---R Type: Multiset Integer +--R Type: Multiset(Integer) --E 12 --S 13 of 14 @@ -80442,7 +80633,7 @@ t1 := multiset [1,2,2,3]; [t1 < t, t1 < s, t < s, t1 <= s] --R --R --R (14) [false,true,false,true] ---R Type: List Boolean +--R Type: List(Boolean) --E 14 )spool )lisp (bye) @@ -80926,7 +81117,7 @@ p :: POLY INT --R --R --R (4) p ---R Type: Polynomial Integer +--R Type: Polynomial(Integer) --E 4 --S 5 of 9 @@ -80934,7 +81125,7 @@ p :: POLY INT --R --R --R (5) p ---R Type: MultivariatePolynomial([a,b],Polynomial Integer) +--R Type: MultivariatePolynomial([a,b],Polynomial(Integer)) --E 5 --S 6 of 9 @@ -80952,7 +81143,7 @@ q := (x^2 - x*(z+1)/y +2)^2 --R (7) x + -------- x + ----------------- x + -------- x + 4 --R y 2 y --R y ---R Type: UnivariatePolynomial(x,Fraction MultivariatePolynomial([y,z],Integer)) +--RType: UnivariatePolynomial(x,Fraction(MultivariatePolynomial([y,z],Integer))) --E 7 --S 8 of 9 @@ -80965,7 +81156,7 @@ q :: UP(z, FRAC MPOLY([x,y],INT)) --R -- z + -------------------- z + --------------------------------------- --R 2 2 2 --R y y y ---R Type: UnivariatePolynomial(z,Fraction MultivariatePolynomial([x,y],Integer)) +--RType: UnivariatePolynomial(z,Fraction(MultivariatePolynomial([x,y],Integer))) --E 8 --S 9 of 9 @@ -80977,7 +81168,7 @@ q :: MPOLY([x,z], FRAC UP(y,INT)) --R (9) x + (- - z - -)x + (-- z + -- z + -------)x + (- - z - -)x + 4 --R y y 2 2 2 y y --R y y y ---R Type: MultivariatePolynomial([x,z],Fraction UnivariatePolynomial(y,Integer)) +--RType: MultivariatePolynomial([x,z],Fraction(UnivariatePolynomial(y,Integer))) --E 9 )spool )lisp (bye) @@ -81966,14 +82157,15 @@ MyUnivariatePolynomial(x:Symbol, R:Ring): --S 1 of 1 )show NeitherSparseOrDensePowerSeries ---R NeitherSparseOrDensePowerSeries K: Field is a domain constructor +--R +--R NeitherSparseOrDensePowerSeries(K: Field) is a domain constructor --R Abbreviation for NeitherSparseOrDensePowerSeries is NSDPS --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for NSDPS --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,K) -> % ?*? : (K,%) -> % ---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % --R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % @@ -81982,11 +82174,11 @@ MyUnivariatePolynomial(x:Symbol, R:Ring): --R 1 : () -> % 0 : () -> % --R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % --R associates? : (%,%) -> Boolean center : % -> K ---R children : % -> List % coefOfFirstNonZeroTerm : % -> K ---R coefficient : (%,Integer) -> K coerce : Fraction Integer -> % +--R children : % -> List(%) coefOfFirstNonZeroTerm : % -> K +--R coefficient : (%,Integer) -> K coerce : Fraction(Integer) -> % --R coerce : % -> % coerce : Integer -> % --R coerce : % -> OutputForm complete : % -> % ---R concat : (%,%) -> % concat : List % -> % +--R concat : (%,%) -> % concat : List(%) -> % --R copy : % -> % cycleEntry : % -> % --R cycleTail : % -> % cyclic? : % -> Boolean --R degree : % -> Integer delay : (() -> %) -> % @@ -81995,18 +82187,18 @@ MyUnivariatePolynomial(x:Symbol, R:Ring): --R empty : () -> % empty? : % -> Boolean --R eq? : (%,%) -> Boolean explicitEntries? : % -> Boolean --R explicitlyEmpty? : % -> Boolean explicitlyFinite? : % -> Boolean ---R extend : (%,Integer) -> % factor : % -> Factored % +--R extend : (%,Integer) -> % factor : % -> Factored(%) --R filterUpTo : (%,Integer) -> % findCoef : (%,Integer) -> K ---R gcd : List % -> % gcd : (%,%) -> % +--R gcd : List(%) -> % gcd : (%,%) -> % --R hash : % -> SingleInteger index? : (Integer,%) -> Boolean ---R indices : % -> List Integer insert : (%,%,Integer) -> % +--R indices : % -> List(Integer) insert : (%,%,Integer) -> % --R inv : % -> % latex : % -> String --R lazy? : % -> Boolean lazyEvaluate : % -> % ---R lcm : List % -> % lcm : (%,%) -> % +--R lcm : List(%) -> % lcm : (%,%) -> % --R leadingCoefficient : % -> K leadingMonomial : % -> % --R leaf? : % -> Boolean map : ((K -> K),%) -> % --R monomial : (K,Integer) -> % monomial? : % -> Boolean ---R nodes : % -> List % one? : % -> Boolean +--R nodes : % -> List(%) one? : % -> Boolean --R order : % -> Integer order : % -> Integer --R order : (%,Integer) -> Integer pole? : % -> Boolean --R posExpnPart : % -> % possiblyInfinite? : % -> Boolean @@ -82018,7 +82210,7 @@ MyUnivariatePolynomial(x:Symbol, R:Ring): --R rest : % -> % rst : % -> % --R sample : () -> % sbt : (%,%) -> % --R series : (Integer,K,%) -> % shift : (%,Integer) -> % ---R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored % +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) --R squareFreePart : % -> % tail : % -> % --R truncate : (%,Integer) -> % unit? : % -> Boolean --R unitCanonical : % -> % variable : % -> Symbol @@ -82027,10 +82219,10 @@ MyUnivariatePolynomial(x:Symbol, R:Ring): --R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,K) -> % if K has FIELD ---R D : (%,List Symbol,List NonNegativeInteger) -> % if K has *: (Integer,K) -> K and K has PDRING SYMBOL ---R D : (%,Symbol,NonNegativeInteger) -> % if K has *: (Integer,K) -> K and K has PDRING SYMBOL ---R D : (%,List Symbol) -> % if K has *: (Integer,K) -> K and K has PDRING SYMBOL ---R D : (%,Symbol) -> % if K has *: (Integer,K) -> K and K has PDRING SYMBOL +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if K has *: (Integer,K) -> K and K has PDRING(SYMBOL) +--R D : (%,Symbol,NonNegativeInteger) -> % if K has *: (Integer,K) -> K and K has PDRING(SYMBOL) +--R D : (%,List(Symbol)) -> % if K has *: (Integer,K) -> K and K has PDRING(SYMBOL) +--R D : (%,Symbol) -> % if K has *: (Integer,K) -> K and K has PDRING(SYMBOL) --R D : (%,NonNegativeInteger) -> % if K has *: (Integer,K) -> K --R D : % -> % if K has *: (Integer,K) -> K --R ?^? : (%,NonNegativeInteger) -> % @@ -82039,44 +82231,44 @@ MyUnivariatePolynomial(x:Symbol, R:Ring): --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if K has CHARNZ --R child? : (%,%) -> Boolean if Record(k: Integer,c: K) has SETCAT ---R coerce : % -> Stream Record(k: Integer,c: K) ---R coerce : Stream Record(k: Integer,c: K) -> % +--R coerce : % -> Stream(Record(k: Integer,c: K)) +--R coerce : Stream(Record(k: Integer,c: K)) -> % --R coerce : K -> % if K has COMRING --R concat : (Record(k: Integer,c: K),%) -> % --R concat : (%,Record(k: Integer,c: K)) -> % --R concat! : (%,%) -> % if $ has shallowlyMutable --R concat! : (%,Record(k: Integer,c: K)) -> % if $ has shallowlyMutable ---R construct : List Record(k: Integer,c: K) -> % ---R convert : % -> InputForm if Record(k: Integer,c: K) has KONVERT INFORM +--R construct : List(Record(k: Integer,c: K)) -> % +--R convert : % -> InputForm if Record(k: Integer,c: K) has KONVERT(INFORM) --R count : ((Record(k: Integer,c: K) -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate --R count : (Record(k: Integer,c: K),%) -> NonNegativeInteger if $ has finiteAggregate and Record(k: Integer,c: K) has SETCAT --R cycleLength : % -> NonNegativeInteger --R cycleSplit! : % -> % if $ has shallowlyMutable ---R delete : (%,UniversalSegment Integer) -> % ---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if K has *: (Integer,K) -> K and K has PDRING SYMBOL ---R differentiate : (%,Symbol,NonNegativeInteger) -> % if K has *: (Integer,K) -> K and K has PDRING SYMBOL ---R differentiate : (%,List Symbol) -> % if K has *: (Integer,K) -> K and K has PDRING SYMBOL ---R differentiate : (%,Symbol) -> % if K has *: (Integer,K) -> K and K has PDRING SYMBOL +--R delete : (%,UniversalSegment(Integer)) -> % +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if K has *: (Integer,K) -> K and K has PDRING(SYMBOL) +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if K has *: (Integer,K) -> K and K has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol)) -> % if K has *: (Integer,K) -> K and K has PDRING(SYMBOL) +--R differentiate : (%,Symbol) -> % if K has *: (Integer,K) -> K and K has PDRING(SYMBOL) --R differentiate : (%,NonNegativeInteger) -> % if K has *: (Integer,K) -> K --R differentiate : % -> % if K has *: (Integer,K) -> K --R divide : (%,%) -> Record(quotient: %,remainder: %) --R ?.value : (%,value) -> Record(k: Integer,c: K) --R ?.first : (%,first) -> Record(k: Integer,c: K) --R ?.last : (%,last) -> Record(k: Integer,c: K) ---R ?.? : (%,UniversalSegment Integer) -> % +--R ?.? : (%,UniversalSegment(Integer)) -> % --R ?.? : (%,Integer) -> Record(k: Integer,c: K) --R elt : (%,Integer,Record(k: Integer,c: K)) -> Record(k: Integer,c: K) --R ?.? : (%,%) -> % if Integer has SGROUP ---R entries : % -> List Record(k: Integer,c: K) +--R entries : % -> List(Record(k: Integer,c: K)) --R entry? : (Record(k: Integer,c: K),%) -> Boolean if $ has finiteAggregate and Record(k: Integer,c: K) has SETCAT --R euclideanSize : % -> NonNegativeInteger ---R eval : (%,List Equation Record(k: Integer,c: K)) -> % if Record(k: Integer,c: K) has EVALAB Record(k: Integer,c: K) and Record(k: Integer,c: K) has SETCAT ---R eval : (%,Equation Record(k: Integer,c: K)) -> % if Record(k: Integer,c: K) has EVALAB Record(k: Integer,c: K) and Record(k: Integer,c: K) has SETCAT ---R eval : (%,Record(k: Integer,c: K),Record(k: Integer,c: K)) -> % if Record(k: Integer,c: K) has EVALAB Record(k: Integer,c: K) and Record(k: Integer,c: K) has SETCAT ---R eval : (%,List Record(k: Integer,c: K),List Record(k: Integer,c: K)) -> % if Record(k: Integer,c: K) has EVALAB Record(k: Integer,c: K) and Record(k: Integer,c: K) has SETCAT ---R eval : (%,K) -> Stream K if K has **: (K,Integer) -> K +--R eval : (%,List(Equation(Record(k: Integer,c: K)))) -> % if Record(k: Integer,c: K) has EVALAB(Record(k: Integer,c: K)) and Record(k: Integer,c: K) has SETCAT +--R eval : (%,Equation(Record(k: Integer,c: K))) -> % if Record(k: Integer,c: K) has EVALAB(Record(k: Integer,c: K)) and Record(k: Integer,c: K) has SETCAT +--R eval : (%,Record(k: Integer,c: K),Record(k: Integer,c: K)) -> % if Record(k: Integer,c: K) has EVALAB(Record(k: Integer,c: K)) and Record(k: Integer,c: K) has SETCAT +--R eval : (%,List(Record(k: Integer,c: K)),List(Record(k: Integer,c: K))) -> % if Record(k: Integer,c: K) has EVALAB(Record(k: Integer,c: K)) and Record(k: Integer,c: K) has SETCAT +--R eval : (%,K) -> Stream(K) if K has **: (K,Integer) -> K --R every? : ((Record(k: Integer,c: K) -> Boolean),%) -> Boolean if $ has finiteAggregate ---R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") --R exquo : (%,%) -> Union(%,"failed") --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) @@ -82086,31 +82278,31 @@ MyUnivariatePolynomial(x:Symbol, R:Ring): --R first : % -> Record(k: Integer,c: K) --R first : (%,NonNegativeInteger) -> % --R frst : % -> Record(k: Integer,c: K) ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) --R insert : (Record(k: Integer,c: K),%,Integer) -> % --R last : % -> Record(k: Integer,c: K) --R last : (%,NonNegativeInteger) -> % ---R leaves : % -> List Record(k: Integer,c: K) +--R leaves : % -> List(Record(k: Integer,c: K)) --R less? : (%,NonNegativeInteger) -> Boolean --R map : ((Record(k: Integer,c: K) -> Record(k: Integer,c: K)),%) -> % --R map : (((Record(k: Integer,c: K),Record(k: Integer,c: K)) -> Record(k: Integer,c: K)),%,%) -> % --R map! : ((Record(k: Integer,c: K) -> Record(k: Integer,c: K)),%) -> % if $ has shallowlyMutable --R maxIndex : % -> Integer if Integer has ORDSET --R member? : (Record(k: Integer,c: K),%) -> Boolean if $ has finiteAggregate and Record(k: Integer,c: K) has SETCAT ---R members : % -> List Record(k: Integer,c: K) if $ has finiteAggregate +--R members : % -> List(Record(k: Integer,c: K)) if $ has finiteAggregate --R minIndex : % -> Integer if Integer has ORDSET --R monomial : (%,SingletonAsOrderedSet,Integer) -> % ---R monomial : (%,List SingletonAsOrderedSet,List Integer) -> % ---R monomial2series : (List %,List NonNegativeInteger,Integer) -> % +--R monomial : (%,List(SingletonAsOrderedSet),List(Integer)) -> % +--R monomial2series : (List(%),List(NonNegativeInteger),Integer) -> % --R more? : (%,NonNegativeInteger) -> Boolean ---R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") --R multiplyExponents : (%,PositiveInteger) -> % --R new : (NonNegativeInteger,Record(k: Integer,c: K)) -> % --R node? : (%,%) -> Boolean if Record(k: Integer,c: K) has SETCAT --R numberOfComputedEntries : % -> NonNegativeInteger --R orderIfNegative : % -> Union(Integer,"failed") ---R parts : % -> List Record(k: Integer,c: K) if $ has finiteAggregate ---R principalIdeal : List % -> Record(coef: List %,generator: %) +--R parts : % -> List(Record(k: Integer,c: K)) if $ has finiteAggregate +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) --R qelt : (%,Integer) -> Record(k: Integer,c: K) --R qsetelt! : (%,Integer,Record(k: Integer,c: K)) -> Record(k: Integer,c: K) if $ has shallowlyMutable --R reduce : (((Record(k: Integer,c: K),Record(k: Integer,c: K)) -> Record(k: Integer,c: K)),%) -> Record(k: Integer,c: K) if $ has finiteAggregate @@ -82122,12 +82314,12 @@ MyUnivariatePolynomial(x:Symbol, R:Ring): --R rest : (%,NonNegativeInteger) -> % --R second : % -> Record(k: Integer,c: K) --R select : ((Record(k: Integer,c: K) -> Boolean),%) -> % ---R setchildren! : (%,List %) -> % if $ has shallowlyMutable +--R setchildren! : (%,List(%)) -> % if $ has shallowlyMutable --R setelt : (%,value,Record(k: Integer,c: K)) -> Record(k: Integer,c: K) if $ has shallowlyMutable --R setelt : (%,first,Record(k: Integer,c: K)) -> Record(k: Integer,c: K) if $ has shallowlyMutable --R setelt : (%,rest,%) -> % if $ has shallowlyMutable --R setelt : (%,last,Record(k: Integer,c: K)) -> Record(k: Integer,c: K) if $ has shallowlyMutable ---R setelt : (%,UniversalSegment Integer,Record(k: Integer,c: K)) -> Record(k: Integer,c: K) if $ has shallowlyMutable +--R setelt : (%,UniversalSegment(Integer),Record(k: Integer,c: K)) -> Record(k: Integer,c: K) if $ has shallowlyMutable --R setelt : (%,Integer,Record(k: Integer,c: K)) -> Record(k: Integer,c: K) if $ has shallowlyMutable --R setfirst! : (%,Record(k: Integer,c: K)) -> Record(k: Integer,c: K) if $ has shallowlyMutable --R setlast! : (%,Record(k: Integer,c: K)) -> Record(k: Integer,c: K) if $ has shallowlyMutable @@ -82137,12 +82329,12 @@ MyUnivariatePolynomial(x:Symbol, R:Ring): --R split! : (%,Integer) -> % if $ has shallowlyMutable --R subtractIfCan : (%,%) -> Union(%,"failed") --R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable ---R terms : % -> Stream Record(k: Integer,c: K) +--R terms : % -> Stream(Record(k: Integer,c: K)) --R third : % -> Record(k: Integer,c: K) --R truncate : (%,Integer,Integer) -> % --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) --R value : % -> Record(k: Integer,c: K) ---R variables : % -> List SingletonAsOrderedSet +--R variables : % -> List(SingletonAsOrderedSet) --R --E 1 @@ -82580,6 +82772,7 @@ by means of triangular sets. --S 1 of 1 )show NewSparseMultivariatePolynomial +--R --R NewSparseMultivariatePolynomial(R: Ring,VarSet: OrderedSet) is a domain constructor --R Abbreviation for NewSparseMultivariatePolynomial is NSMP --R This constructor is not exposed in this frame. @@ -82591,42 +82784,40 @@ by means of triangular sets. --R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean ---R D : (%,List VarSet) -> % D : (%,VarSet) -> % +--R D : (%,List(VarSet)) -> % D : (%,VarSet) -> % --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coefficients : % -> List R +--R ?^? : (%,PositiveInteger) -> % coefficients : % -> List(R) --R coerce : VarSet -> % coerce : R -> % --R coerce : Integer -> % coerce : % -> OutputForm --R deepestInitial : % -> % deepestTail : % -> % --R differentiate : (%,VarSet) -> % eval : (%,VarSet,%) -> % ---R eval : (%,VarSet,R) -> % eval : (%,List %,List %) -> % ---R eval : (%,%,%) -> % eval : (%,Equation %) -> % ---R eval : (%,List Equation %) -> % ground : % -> R +--R eval : (%,VarSet,R) -> % eval : (%,%,%) -> % +--R eval : (%,Equation(%)) -> % ground : % -> R --R ground? : % -> Boolean hash : % -> SingleInteger --R head : % -> % headReduce : (%,%) -> % --R headReduced? : (%,%) -> Boolean infRittWu? : (%,%) -> Boolean --R init : % -> % initiallyReduce : (%,%) -> % ---R iteratedInitials : % -> List % latex : % -> String +--R iteratedInitials : % -> List(%) latex : % -> String --R lazyPquo : (%,%,VarSet) -> % lazyPquo : (%,%) -> % --R lazyPrem : (%,%,VarSet) -> % lazyPrem : (%,%) -> % --R leadingCoefficient : % -> R leadingMonomial : % -> % ---R leastMonomial : % -> % mainCoefficients : % -> List % ---R mainMonomial : % -> % mainMonomials : % -> List % +--R leastMonomial : % -> % mainCoefficients : % -> List(%) +--R mainMonomial : % -> % mainMonomials : % -> List(%) --R map : ((R -> R),%) -> % mdeg : % -> NonNegativeInteger --R monic? : % -> Boolean monicModulo : (%,%) -> % ---R monomial? : % -> Boolean monomials : % -> List % +--R monomial? : % -> Boolean monomials : % -> List(%) --R mvar : % -> VarSet normalized? : (%,%) -> Boolean --R one? : % -> Boolean pquo : (%,%,VarSet) -> % --R pquo : (%,%) -> % prem : (%,%,VarSet) -> % ---R prem : (%,%) -> % primitiveMonomials : % -> List % ---R quasiMonic? : % -> Boolean recip : % -> Union(%,"failed") ---R reduced? : (%,List %) -> Boolean reduced? : (%,%) -> Boolean +--R prem : (%,%) -> % quasiMonic? : % -> Boolean +--R recip : % -> Union(%,"failed") reduced? : (%,%) -> Boolean --R reductum : (%,VarSet) -> % reductum : % -> % --R retract : % -> VarSet retract : % -> R --R sample : () -> % supRittWu? : (%,%) -> Boolean ---R tail : % -> % variables : % -> List VarSet +--R tail : % -> % variables : % -> List(VarSet) --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean ---R ?*? : (Fraction Integer,%) -> % if R has ALGEBRA FRAC INT ---R ?*? : (%,Fraction Integer) -> % if R has ALGEBRA FRAC INT +--R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT)) +--R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) --R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,R) -> % if R has FIELD @@ -82634,7 +82825,7 @@ by means of triangular sets. --R ?<=? : (%,%) -> Boolean if R has ORDSET --R ?>? : (%,%) -> Boolean if R has ORDSET --R ?>=? : (%,%) -> Boolean if R has ORDSET ---R D : (%,List VarSet,List NonNegativeInteger) -> % +--R D : (%,List(VarSet),List(NonNegativeInteger)) -> % --R D : (%,VarSet,NonNegativeInteger) -> % --R LazardQuotient : (%,%,NonNegativeInteger) -> % if R has INTDOM --R LazardQuotient2 : (%,%,%,NonNegativeInteger) -> % if R has INTDOM @@ -82644,34 +82835,36 @@ by means of triangular sets. --R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and R has PFECAT or R has CHARNZ ---R coefficient : (%,List VarSet,List NonNegativeInteger) -> % +--R coefficient : (%,List(VarSet),List(NonNegativeInteger)) -> % --R coefficient : (%,VarSet,NonNegativeInteger) -> % ---R coefficient : (%,IndexedExponents VarSet) -> R +--R coefficient : (%,IndexedExponents(VarSet)) -> R --R coerce : % -> % if R has INTDOM ---R coerce : Fraction Integer -> % if R has ALGEBRA FRAC INT or R has RETRACT FRAC INT +--R coerce : Fraction(Integer) -> % if R has ALGEBRA(FRAC(INT)) or R has RETRACT(FRAC(INT)) --R coerce : SparseMultivariatePolynomial(R,VarSet) -> % --R coerce : % -> SparseMultivariatePolynomial(R,VarSet) ---R coerce : % -> Polynomial R if VarSet has KONVERT SYMBOL ---R conditionP : Matrix % -> Union(Vector %,"failed") if $ has CHARNZ and R has PFECAT +--R coerce : % -> Polynomial(R) if VarSet has KONVERT(SYMBOL) +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and R has PFECAT --R content : (%,VarSet) -> % if R has GCDDOM --R content : % -> R if R has GCDDOM ---R convert : % -> Polynomial R if VarSet has KONVERT SYMBOL ---R convert : % -> String if R has RETRACT INT and VarSet has KONVERT SYMBOL ---R convert : Polynomial R -> % if VarSet has KONVERT SYMBOL ---R convert : Polynomial Integer -> % if R has ALGEBRA INT and VarSet has KONVERT SYMBOL and not has(R,Algebra Fraction Integer) or R has ALGEBRA FRAC INT and VarSet has KONVERT SYMBOL ---R convert : Polynomial Fraction Integer -> % if R has ALGEBRA FRAC INT and VarSet has KONVERT SYMBOL ---R convert : % -> InputForm if R has KONVERT INFORM and VarSet has KONVERT INFORM ---R convert : % -> Pattern Integer if R has KONVERT PATTERN INT and VarSet has KONVERT PATTERN INT ---R convert : % -> Pattern Float if R has KONVERT PATTERN FLOAT and VarSet has KONVERT PATTERN FLOAT ---R degree : (%,List VarSet) -> List NonNegativeInteger +--R convert : % -> Polynomial(R) if VarSet has KONVERT(SYMBOL) +--R convert : % -> String if R has RETRACT(INT) and VarSet has KONVERT(SYMBOL) +--R convert : Polynomial(R) -> % if VarSet has KONVERT(SYMBOL) +--R convert : Polynomial(Integer) -> % if R has ALGEBRA(INT) and VarSet has KONVERT(SYMBOL) and not(has(R,Algebra(Fraction(Integer)))) or R has ALGEBRA(FRAC(INT)) and VarSet has KONVERT(SYMBOL) +--R convert : Polynomial(Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) and VarSet has KONVERT(SYMBOL) +--R convert : % -> InputForm if R has KONVERT(INFORM) and VarSet has KONVERT(INFORM) +--R convert : % -> Pattern(Integer) if R has KONVERT(PATTERN(INT)) and VarSet has KONVERT(PATTERN(INT)) +--R convert : % -> Pattern(Float) if R has KONVERT(PATTERN(FLOAT)) and VarSet has KONVERT(PATTERN(FLOAT)) +--R degree : (%,List(VarSet)) -> List(NonNegativeInteger) --R degree : (%,VarSet) -> NonNegativeInteger ---R degree : % -> IndexedExponents VarSet ---R differentiate : (%,List VarSet,List NonNegativeInteger) -> % +--R degree : % -> IndexedExponents(VarSet) +--R differentiate : (%,List(VarSet),List(NonNegativeInteger)) -> % --R differentiate : (%,VarSet,NonNegativeInteger) -> % ---R differentiate : (%,List VarSet) -> % +--R differentiate : (%,List(VarSet)) -> % --R discriminant : (%,VarSet) -> % if R has COMRING ---R eval : (%,List VarSet,List %) -> % ---R eval : (%,List VarSet,List R) -> % +--R eval : (%,List(VarSet),List(%)) -> % +--R eval : (%,List(VarSet),List(R)) -> % +--R eval : (%,List(%),List(%)) -> % +--R eval : (%,List(Equation(%))) -> % --R exactQuotient : (%,%) -> % if R has INTDOM --R exactQuotient : (%,R) -> % if R has INTDOM --R exactQuotient! : (%,%) -> % if R has INTDOM @@ -82679,21 +82872,21 @@ by means of triangular sets. --R exquo : (%,%) -> Union(%,"failed") if R has INTDOM --R exquo : (%,R) -> Union(%,"failed") if R has INTDOM --R extendedSubResultantGcd : (%,%) -> Record(gcd: %,coef1: %,coef2: %) if R has INTDOM ---R factor : % -> Factored % if R has PFECAT ---R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT ---R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R factor : % -> Factored(%) if R has PFECAT +--R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT --R gcd : (%,%) -> % if R has GCDDOM ---R gcd : List % -> % if R has GCDDOM +--R gcd : List(%) -> % if R has GCDDOM --R gcd : (R,%) -> R if R has GCDDOM ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has GCDDOM +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has GCDDOM --R halfExtendedSubResultantGcd1 : (%,%) -> Record(gcd: %,coef1: %) if R has INTDOM --R halfExtendedSubResultantGcd2 : (%,%) -> Record(gcd: %,coef2: %) if R has INTDOM ---R headReduced? : (%,List %) -> Boolean ---R initiallyReduced? : (%,List %) -> Boolean +--R headReduced? : (%,List(%)) -> Boolean +--R initiallyReduced? : (%,List(%)) -> Boolean --R initiallyReduced? : (%,%) -> Boolean --R isExpt : % -> Union(Record(var: VarSet,exponent: NonNegativeInteger),"failed") ---R isPlus : % -> Union(List %,"failed") ---R isTimes : % -> Union(List %,"failed") +--R isPlus : % -> Union(List(%),"failed") +--R isTimes : % -> Union(List(%),"failed") --R lastSubResultant : (%,%) -> % if R has INTDOM --R lazyPremWithDefault : (%,%,VarSet) -> Record(coef: %,gap: NonNegativeInteger,remainder: %) --R lazyPremWithDefault : (%,%) -> Record(coef: %,gap: NonNegativeInteger,remainder: %) @@ -82701,71 +82894,73 @@ by means of triangular sets. --R lazyPseudoDivide : (%,%) -> Record(coef: %,gap: NonNegativeInteger,quotient: %,remainder: %) --R lazyResidueClass : (%,%) -> Record(polnum: %,polden: %,power: NonNegativeInteger) --R lcm : (%,%) -> % if R has GCDDOM ---R lcm : List % -> % if R has GCDDOM +--R lcm : List(%) -> % if R has GCDDOM --R leadingCoefficient : (%,VarSet) -> % --R mainContent : % -> % if R has GCDDOM --R mainPrimitivePart : % -> % if R has GCDDOM --R mainSquareFreePart : % -> % if R has GCDDOM --R mainVariable : % -> Union(VarSet,"failed") ---R mapExponents : ((IndexedExponents VarSet -> IndexedExponents VarSet),%) -> % +--R mapExponents : ((IndexedExponents(VarSet) -> IndexedExponents(VarSet)),%) -> % --R max : (%,%) -> % if R has ORDSET --R min : (%,%) -> % if R has ORDSET ---R minimumDegree : (%,List VarSet) -> List NonNegativeInteger +--R minimumDegree : (%,List(VarSet)) -> List(NonNegativeInteger) --R minimumDegree : (%,VarSet) -> NonNegativeInteger ---R minimumDegree : % -> IndexedExponents VarSet +--R minimumDegree : % -> IndexedExponents(VarSet) --R monicDivide : (%,%,VarSet) -> Record(quotient: %,remainder: %) ---R monomial : (%,List VarSet,List NonNegativeInteger) -> % +--R monomial : (%,List(VarSet),List(NonNegativeInteger)) -> % --R monomial : (%,VarSet,NonNegativeInteger) -> % ---R monomial : (R,IndexedExponents VarSet) -> % ---R multivariate : (SparseUnivariatePolynomial %,VarSet) -> % ---R multivariate : (SparseUnivariatePolynomial R,VarSet) -> % +--R monomial : (R,IndexedExponents(VarSet)) -> % +--R multivariate : (SparseUnivariatePolynomial(%),VarSet) -> % +--R multivariate : (SparseUnivariatePolynomial(R),VarSet) -> % --R nextsubResultant2 : (%,%,%,%) -> % if R has INTDOM ---R normalized? : (%,List %) -> Boolean +--R normalized? : (%,List(%)) -> Boolean --R numberOfMonomials : % -> NonNegativeInteger ---R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if R has PATMAB INT and VarSet has PATMAB INT ---R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if R has PATMAB FLOAT and VarSet has PATMAB FLOAT ---R pomopo! : (%,R,IndexedExponents VarSet,%) -> % +--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if R has PATMAB(INT) and VarSet has PATMAB(INT) +--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if R has PATMAB(FLOAT) and VarSet has PATMAB(FLOAT) +--R pomopo! : (%,R,IndexedExponents(VarSet),%) -> % --R primPartElseUnitCanonical : % -> % if R has INTDOM --R primPartElseUnitCanonical! : % -> % if R has INTDOM --R prime? : % -> Boolean if R has PFECAT +--R primitiveMonomials : % -> List(%) --R primitivePart : (%,VarSet) -> % if R has GCDDOM --R primitivePart : % -> % if R has GCDDOM --R primitivePart! : % -> % if R has GCDDOM --R pseudoDivide : (%,%) -> Record(quotient: %,remainder: %) ---R reducedSystem : Matrix % -> Matrix R ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT ---R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT +--R reduced? : (%,List(%)) -> Boolean +--R reducedSystem : Matrix(%) -> Matrix(R) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT) +--R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT) --R resultant : (%,%) -> % if R has INTDOM --R resultant : (%,%,VarSet) -> % if R has COMRING --R retract : % -> SparseMultivariatePolynomial(R,VarSet) ---R retract : Polynomial R -> % if VarSet has KONVERT SYMBOL and not has(R,Algebra Fraction Integer) and not has(R,Algebra Integer) or R has ALGEBRA INT and VarSet has KONVERT SYMBOL and not has(R,Algebra Fraction Integer) and not has(R,IntegerNumberSystem) or R has ALGEBRA FRAC INT and VarSet has KONVERT SYMBOL and not has(R,QuotientFieldCategory Integer) ---R retract : Polynomial Integer -> % if R has ALGEBRA INT and VarSet has KONVERT SYMBOL and not has(R,Algebra Fraction Integer) or R has ALGEBRA FRAC INT and VarSet has KONVERT SYMBOL ---R retract : Polynomial Fraction Integer -> % if R has ALGEBRA FRAC INT and VarSet has KONVERT SYMBOL ---R retract : % -> Integer if R has RETRACT INT ---R retract : % -> Fraction Integer if R has RETRACT FRAC INT +--R retract : Polynomial(R) -> % if VarSet has KONVERT(SYMBOL) and not(has(R,Algebra(Fraction(Integer)))) and not(has(R,Algebra(Integer))) or R has ALGEBRA(INT) and VarSet has KONVERT(SYMBOL) and not(has(R,Algebra(Fraction(Integer)))) and not(has(R,IntegerNumberSystem)) or R has ALGEBRA(FRAC(INT)) and VarSet has KONVERT(SYMBOL) and not(has(R,QuotientFieldCategory(Integer))) +--R retract : Polynomial(Integer) -> % if R has ALGEBRA(INT) and VarSet has KONVERT(SYMBOL) and not(has(R,Algebra(Fraction(Integer)))) or R has ALGEBRA(FRAC(INT)) and VarSet has KONVERT(SYMBOL) +--R retract : Polynomial(Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) and VarSet has KONVERT(SYMBOL) +--R retract : % -> Integer if R has RETRACT(INT) +--R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT)) --R retractIfCan : % -> Union(SparseMultivariatePolynomial(R,VarSet),"failed") ---R retractIfCan : Polynomial R -> Union(%,"failed") if VarSet has KONVERT SYMBOL and not has(R,Algebra Fraction Integer) and not has(R,Algebra Integer) or R has ALGEBRA INT and VarSet has KONVERT SYMBOL and not has(R,Algebra Fraction Integer) and not has(R,IntegerNumberSystem) or R has ALGEBRA FRAC INT and VarSet has KONVERT SYMBOL and not has(R,QuotientFieldCategory Integer) ---R retractIfCan : Polynomial Integer -> Union(%,"failed") if R has ALGEBRA INT and VarSet has KONVERT SYMBOL and not has(R,Algebra Fraction Integer) or R has ALGEBRA FRAC INT and VarSet has KONVERT SYMBOL ---R retractIfCan : Polynomial Fraction Integer -> Union(%,"failed") if R has ALGEBRA FRAC INT and VarSet has KONVERT SYMBOL +--R retractIfCan : Polynomial(R) -> Union(%,"failed") if VarSet has KONVERT(SYMBOL) and not(has(R,Algebra(Fraction(Integer)))) and not(has(R,Algebra(Integer))) or R has ALGEBRA(INT) and VarSet has KONVERT(SYMBOL) and not(has(R,Algebra(Fraction(Integer)))) and not(has(R,IntegerNumberSystem)) or R has ALGEBRA(FRAC(INT)) and VarSet has KONVERT(SYMBOL) and not(has(R,QuotientFieldCategory(Integer))) +--R retractIfCan : Polynomial(Integer) -> Union(%,"failed") if R has ALGEBRA(INT) and VarSet has KONVERT(SYMBOL) and not(has(R,Algebra(Fraction(Integer)))) or R has ALGEBRA(FRAC(INT)) and VarSet has KONVERT(SYMBOL) +--R retractIfCan : Polynomial(Fraction(Integer)) -> Union(%,"failed") if R has ALGEBRA(FRAC(INT)) and VarSet has KONVERT(SYMBOL) --R retractIfCan : % -> Union(VarSet,"failed") ---R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT ---R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT) +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT)) --R retractIfCan : % -> Union(R,"failed") ---R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if R has PFECAT ---R squareFree : % -> Factored % if R has GCDDOM +--R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if R has PFECAT +--R squareFree : % -> Factored(%) if R has GCDDOM --R squareFreePart : % -> % if R has GCDDOM ---R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT ---R subResultantChain : (%,%) -> List % if R has INTDOM +--R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT +--R subResultantChain : (%,%) -> List(%) if R has INTDOM --R subResultantGcd : (%,%) -> % if R has INTDOM --R subtractIfCan : (%,%) -> Union(%,"failed") ---R totalDegree : (%,List VarSet) -> NonNegativeInteger +--R totalDegree : (%,List(VarSet)) -> NonNegativeInteger --R totalDegree : % -> NonNegativeInteger --R unit? : % -> Boolean if R has INTDOM --R unitCanonical : % -> % if R has INTDOM --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM ---R univariate : % -> SparseUnivariatePolynomial R ---R univariate : (%,VarSet) -> SparseUnivariatePolynomial % +--R univariate : % -> SparseUnivariatePolynomial(R) +--R univariate : (%,VarSet) -> SparseUnivariatePolynomial(%) --R --E 1 @@ -83351,7 +83546,8 @@ constructur {\bf SparseUnivariatePolynomial}. --S 1 of 1 )show NewSparseUnivariatePolynomial ---R NewSparseUnivariatePolynomial R: Ring is a domain constructor +--R +--R NewSparseUnivariatePolynomial(R: Ring) is a domain constructor --R Abbreviation for NewSparseUnivariatePolynomial is NSUP --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for NSUP @@ -83365,25 +83561,23 @@ constructur {\bf SparseUnivariatePolynomial}. --R D : (%,(R -> R)) -> % D : % -> % --R D : (%,NonNegativeInteger) -> % 1 : () -> % --R 0 : () -> % ?^? : (%,PositiveInteger) -> % ---R coefficients : % -> List R coerce : R -> % +--R coefficients : % -> List(R) coerce : R -> % --R coerce : Integer -> % coerce : % -> OutputForm --R degree : % -> NonNegativeInteger differentiate : % -> % --R ?.? : (%,%) -> % ?.? : (%,R) -> R ---R eval : (%,List %,List %) -> % eval : (%,%,%) -> % ---R eval : (%,Equation %) -> % eval : (%,List Equation %) -> % +--R eval : (%,%,%) -> % eval : (%,Equation(%)) -> % --R ground : % -> R ground? : % -> Boolean --R hash : % -> SingleInteger init : () -> % if R has STEP --R latex : % -> String lazyPseudoQuotient : (%,%) -> % --R leadingCoefficient : % -> R leadingMonomial : % -> % --R map : ((R -> R),%) -> % monicModulo : (%,%) -> % ---R monomial? : % -> Boolean monomials : % -> List % ---R one? : % -> Boolean primitiveMonomials : % -> List % ---R pseudoRemainder : (%,%) -> % recip : % -> Union(%,"failed") ---R reductum : % -> % retract : % -> R ---R sample : () -> % zero? : % -> Boolean ---R ?~=? : (%,%) -> Boolean ---R ?*? : (Fraction Integer,%) -> % if R has ALGEBRA FRAC INT ---R ?*? : (%,Fraction Integer) -> % if R has ALGEBRA FRAC INT +--R monomial? : % -> Boolean monomials : % -> List(%) +--R one? : % -> Boolean pseudoRemainder : (%,%) -> % +--R recip : % -> Union(%,"failed") reductum : % -> % +--R retract : % -> R sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT)) +--R ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) --R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,NonNegativeInteger) -> % --R ?/? : (%,R) -> % if R has FIELD @@ -83392,157 +83586,160 @@ constructur {\bf SparseUnivariatePolynomial}. --R ?>? : (%,%) -> Boolean if R has ORDSET --R ?>=? : (%,%) -> Boolean if R has ORDSET --R D : (%,(R -> R),NonNegativeInteger) -> % ---R D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL ---R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL ---R D : (%,List Symbol) -> % if R has PDRING SYMBOL ---R D : (%,Symbol) -> % if R has PDRING SYMBOL ---R D : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) +--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) +--R D : (%,List(Symbol)) -> % if R has PDRING(SYMBOL) +--R D : (%,Symbol) -> % if R has PDRING(SYMBOL) +--R D : (%,List(SingletonAsOrderedSet),List(NonNegativeInteger)) -> % --R D : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % ---R D : (%,List SingletonAsOrderedSet) -> % +--R D : (%,List(SingletonAsOrderedSet)) -> % --R D : (%,SingletonAsOrderedSet) -> % --R ?^? : (%,NonNegativeInteger) -> % --R associates? : (%,%) -> Boolean if R has INTDOM --R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and R has PFECAT or R has CHARNZ ---R coefficient : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R coefficient : (%,List(SingletonAsOrderedSet),List(NonNegativeInteger)) -> % --R coefficient : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % --R coefficient : (%,NonNegativeInteger) -> R --R coerce : % -> % if R has INTDOM ---R coerce : Fraction Integer -> % if R has ALGEBRA FRAC INT or R has RETRACT FRAC INT ---R coerce : SparseUnivariatePolynomial R -> % ---R coerce : % -> SparseUnivariatePolynomial R +--R coerce : Fraction(Integer) -> % if R has ALGEBRA(FRAC(INT)) or R has RETRACT(FRAC(INT)) +--R coerce : SparseUnivariatePolynomial(R) -> % +--R coerce : % -> SparseUnivariatePolynomial(R) --R coerce : SingletonAsOrderedSet -> % ---R composite : (Fraction %,%) -> Union(Fraction %,"failed") if R has INTDOM +--R composite : (Fraction(%),%) -> Union(Fraction(%),"failed") if R has INTDOM --R composite : (%,%) -> Union(%,"failed") if R has INTDOM ---R conditionP : Matrix % -> Union(Vector %,"failed") if $ has CHARNZ and R has PFECAT +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and R has PFECAT --R content : (%,SingletonAsOrderedSet) -> % if R has GCDDOM --R content : % -> R if R has GCDDOM ---R convert : % -> InputForm if SingletonAsOrderedSet has KONVERT INFORM and R has KONVERT INFORM ---R convert : % -> Pattern Integer if SingletonAsOrderedSet has KONVERT PATTERN INT and R has KONVERT PATTERN INT ---R convert : % -> Pattern Float if SingletonAsOrderedSet has KONVERT PATTERN FLOAT and R has KONVERT PATTERN FLOAT ---R degree : (%,List SingletonAsOrderedSet) -> List NonNegativeInteger +--R convert : % -> InputForm if SingletonAsOrderedSet has KONVERT(INFORM) and R has KONVERT(INFORM) +--R convert : % -> Pattern(Integer) if SingletonAsOrderedSet has KONVERT(PATTERN(INT)) and R has KONVERT(PATTERN(INT)) +--R convert : % -> Pattern(Float) if SingletonAsOrderedSet has KONVERT(PATTERN(FLOAT)) and R has KONVERT(PATTERN(FLOAT)) +--R degree : (%,List(SingletonAsOrderedSet)) -> List(NonNegativeInteger) --R degree : (%,SingletonAsOrderedSet) -> NonNegativeInteger --R differentiate : (%,(R -> R),%) -> % --R differentiate : (%,(R -> R)) -> % --R differentiate : (%,(R -> R),NonNegativeInteger) -> % ---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL ---R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL ---R differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL ---R differentiate : (%,Symbol) -> % if R has PDRING SYMBOL +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol)) -> % if R has PDRING(SYMBOL) +--R differentiate : (%,Symbol) -> % if R has PDRING(SYMBOL) --R differentiate : (%,NonNegativeInteger) -> % ---R differentiate : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R differentiate : (%,List(SingletonAsOrderedSet),List(NonNegativeInteger)) -> % --R differentiate : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % ---R differentiate : (%,List SingletonAsOrderedSet) -> % +--R differentiate : (%,List(SingletonAsOrderedSet)) -> % --R differentiate : (%,SingletonAsOrderedSet) -> % --R discriminant : % -> R if R has COMRING --R discriminant : (%,SingletonAsOrderedSet) -> % if R has COMRING --R divide : (%,%) -> Record(quotient: %,remainder: %) if R has FIELD --R divideExponents : (%,NonNegativeInteger) -> Union(%,"failed") ---R ?.? : (%,Fraction %) -> Fraction % if R has INTDOM ---R elt : (Fraction %,R) -> R if R has FIELD ---R elt : (Fraction %,Fraction %) -> Fraction % if R has INTDOM +--R ?.? : (%,Fraction(%)) -> Fraction(%) if R has INTDOM +--R elt : (Fraction(%),R) -> R if R has FIELD +--R elt : (Fraction(%),Fraction(%)) -> Fraction(%) if R has INTDOM --R euclideanSize : % -> NonNegativeInteger if R has FIELD ---R eval : (%,List SingletonAsOrderedSet,List %) -> % +--R eval : (%,List(SingletonAsOrderedSet),List(%)) -> % --R eval : (%,SingletonAsOrderedSet,%) -> % ---R eval : (%,List SingletonAsOrderedSet,List R) -> % +--R eval : (%,List(SingletonAsOrderedSet),List(R)) -> % --R eval : (%,SingletonAsOrderedSet,R) -> % ---R expressIdealMember : (List %,%) -> Union(List %,"failed") if R has FIELD +--R eval : (%,List(%),List(%)) -> % +--R eval : (%,List(Equation(%))) -> % +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if R has FIELD --R exquo : (%,%) -> Union(%,"failed") if R has INTDOM --R exquo : (%,R) -> Union(%,"failed") if R has INTDOM --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has FIELD --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if R has FIELD --R extendedResultant : (%,%) -> Record(resultant: R,coef1: %,coef2: %) if R has INTDOM --R extendedSubResultantGcd : (%,%) -> Record(gcd: %,coef1: %,coef2: %) if R has INTDOM ---R factor : % -> Factored % if R has PFECAT ---R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT ---R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R factor : % -> Factored(%) if R has PFECAT +--R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT --R fmecg : (%,NonNegativeInteger,R,%) -> % --R gcd : (%,%) -> % if R has GCDDOM ---R gcd : List % -> % if R has GCDDOM ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has GCDDOM +--R gcd : List(%) -> % if R has GCDDOM +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has GCDDOM --R halfExtendedResultant1 : (%,%) -> Record(resultant: R,coef1: %) if R has INTDOM --R halfExtendedResultant2 : (%,%) -> Record(resultant: R,coef2: %) if R has INTDOM --R halfExtendedSubResultantGcd1 : (%,%) -> Record(gcd: %,coef1: %) if R has INTDOM --R halfExtendedSubResultantGcd2 : (%,%) -> Record(gcd: %,coef2: %) if R has INTDOM ---R integrate : % -> % if R has ALGEBRA FRAC INT +--R integrate : % -> % if R has ALGEBRA(FRAC(INT)) --R isExpt : % -> Union(Record(var: SingletonAsOrderedSet,exponent: NonNegativeInteger),"failed") ---R isPlus : % -> Union(List %,"failed") ---R isTimes : % -> Union(List %,"failed") +--R isPlus : % -> Union(List(%),"failed") +--R isTimes : % -> Union(List(%),"failed") --R karatsubaDivide : (%,NonNegativeInteger) -> Record(quotient: %,remainder: %) --R lastSubResultant : (%,%) -> % if R has INTDOM --R lazyPseudoDivide : (%,%) -> Record(coef: R,gap: NonNegativeInteger,quotient: %,remainder: %) --R lazyPseudoRemainder : (%,%) -> % --R lazyResidueClass : (%,%) -> Record(polnum: %,polden: R,power: NonNegativeInteger) --R lcm : (%,%) -> % if R has GCDDOM ---R lcm : List % -> % if R has GCDDOM +--R lcm : List(%) -> % if R has GCDDOM --R mainVariable : % -> Union(SingletonAsOrderedSet,"failed") ---R makeSUP : % -> SparseUnivariatePolynomial R +--R makeSUP : % -> SparseUnivariatePolynomial(R) --R mapExponents : ((NonNegativeInteger -> NonNegativeInteger),%) -> % --R max : (%,%) -> % if R has ORDSET --R min : (%,%) -> % if R has ORDSET ---R minimumDegree : (%,List SingletonAsOrderedSet) -> List NonNegativeInteger +--R minimumDegree : (%,List(SingletonAsOrderedSet)) -> List(NonNegativeInteger) --R minimumDegree : (%,SingletonAsOrderedSet) -> NonNegativeInteger --R minimumDegree : % -> NonNegativeInteger --R monicDivide : (%,%) -> Record(quotient: %,remainder: %) --R monicDivide : (%,%,SingletonAsOrderedSet) -> Record(quotient: %,remainder: %) ---R monomial : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R monomial : (%,List(SingletonAsOrderedSet),List(NonNegativeInteger)) -> % --R monomial : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % --R monomial : (R,NonNegativeInteger) -> % ---R multiEuclidean : (List %,%) -> Union(List %,"failed") if R has FIELD +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") if R has FIELD --R multiplyExponents : (%,NonNegativeInteger) -> % ---R multivariate : (SparseUnivariatePolynomial %,SingletonAsOrderedSet) -> % ---R multivariate : (SparseUnivariatePolynomial R,SingletonAsOrderedSet) -> % +--R multivariate : (SparseUnivariatePolynomial(%),SingletonAsOrderedSet) -> % +--R multivariate : (SparseUnivariatePolynomial(R),SingletonAsOrderedSet) -> % --R nextItem : % -> Union(%,"failed") if R has STEP --R numberOfMonomials : % -> NonNegativeInteger --R order : (%,%) -> NonNegativeInteger if R has INTDOM ---R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if SingletonAsOrderedSet has PATMAB INT and R has PATMAB INT ---R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if SingletonAsOrderedSet has PATMAB FLOAT and R has PATMAB FLOAT +--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if SingletonAsOrderedSet has PATMAB(INT) and R has PATMAB(INT) +--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if SingletonAsOrderedSet has PATMAB(FLOAT) and R has PATMAB(FLOAT) --R pomopo! : (%,R,NonNegativeInteger,%) -> % --R prime? : % -> Boolean if R has PFECAT +--R primitiveMonomials : % -> List(%) --R primitivePart : (%,SingletonAsOrderedSet) -> % if R has GCDDOM --R primitivePart : % -> % if R has GCDDOM ---R principalIdeal : List % -> Record(coef: List %,generator: %) if R has FIELD +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if R has FIELD --R pseudoDivide : (%,%) -> Record(coef: R,quotient: %,remainder: %) if R has INTDOM --R pseudoQuotient : (%,%) -> % if R has INTDOM --R ?quo? : (%,%) -> % if R has FIELD ---R reducedSystem : Matrix % -> Matrix R ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT ---R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT +--R reducedSystem : Matrix(%) -> Matrix(R) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT) +--R reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT) --R ?rem? : (%,%) -> % if R has FIELD --R resultant : (%,%) -> R if R has COMRING --R resultant : (%,%,SingletonAsOrderedSet) -> % if R has COMRING ---R retract : % -> SparseUnivariatePolynomial R +--R retract : % -> SparseUnivariatePolynomial(R) --R retract : % -> SingletonAsOrderedSet ---R retract : % -> Integer if R has RETRACT INT ---R retract : % -> Fraction Integer if R has RETRACT FRAC INT ---R retractIfCan : % -> Union(SparseUnivariatePolynomial R,"failed") +--R retract : % -> Integer if R has RETRACT(INT) +--R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT)) +--R retractIfCan : % -> Union(SparseUnivariatePolynomial(R),"failed") --R retractIfCan : % -> Union(SingletonAsOrderedSet,"failed") ---R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT ---R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT) +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT)) --R retractIfCan : % -> Union(R,"failed") --R separate : (%,%) -> Record(primePart: %,commonPart: %) if R has GCDDOM --R shiftLeft : (%,NonNegativeInteger) -> % --R shiftRight : (%,NonNegativeInteger) -> % --R sizeLess? : (%,%) -> Boolean if R has FIELD ---R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if R has PFECAT ---R squareFree : % -> Factored % if R has GCDDOM +--R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if R has PFECAT +--R squareFree : % -> Factored(%) if R has GCDDOM --R squareFreePart : % -> % if R has GCDDOM ---R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT --R subResultantGcd : (%,%) -> % if R has INTDOM ---R subResultantsChain : (%,%) -> List % if R has INTDOM +--R subResultantsChain : (%,%) -> List(%) if R has INTDOM --R subtractIfCan : (%,%) -> Union(%,"failed") ---R totalDegree : (%,List SingletonAsOrderedSet) -> NonNegativeInteger +--R totalDegree : (%,List(SingletonAsOrderedSet)) -> NonNegativeInteger --R totalDegree : % -> NonNegativeInteger --R unit? : % -> Boolean if R has INTDOM --R unitCanonical : % -> % if R has INTDOM --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM ---R univariate : % -> SparseUnivariatePolynomial R ---R univariate : (%,SingletonAsOrderedSet) -> SparseUnivariatePolynomial % ---R unmakeSUP : SparseUnivariatePolynomial R -> % ---R variables : % -> List SingletonAsOrderedSet ---R vectorise : (%,NonNegativeInteger) -> Vector R +--R univariate : % -> SparseUnivariatePolynomial(R) +--R univariate : (%,SingletonAsOrderedSet) -> SparseUnivariatePolynomial(%) +--R unmakeSUP : SparseUnivariatePolynomial(R) -> % +--R variables : % -> List(SingletonAsOrderedSet) +--R vectorise : (%,NonNegativeInteger) -> Vector(R) --R --E 1 @@ -83978,7 +84175,7 @@ NewSparseUnivariatePolynomial(R): Exports == Implementation where --R --R --R (1) [] ---R Type: List None +--R Type: List(None) --E 1 --S 2 of 3 @@ -83986,7 +84183,7 @@ NewSparseUnivariatePolynomial(R): Exports == Implementation where --R --R --R (2) [] ---R Type: List Float +--R Type: List(Float) --E 2 --S 3 of 3 @@ -83994,7 +84191,7 @@ NewSparseUnivariatePolynomial(R): Exports == Implementation where --R --R --R (3) [] ---R Type: List NonNegativeInteger +--R Type: List(NonNegativeInteger) --E 3 )spool )lisp (bye) @@ -84236,7 +84433,7 @@ x:=monomial(1,1)$UFPS PF 1783 --R --R --R (1) x ---R Type: UnivariateFormalPowerSeries PrimeField 1783 +--R Type: UnivariateFormalPowerSeries(PrimeField(1783)) --E 1 --S 2 of 8 @@ -84245,7 +84442,7 @@ s:=retract(sin x)$NOTTING PF 1783 --R --R 3 5 7 9 11 --R (2) x + 297x + 1679x + 427x + 316x + O(x ) ---R Type: NottinghamGroup PrimeField 1783 +--R Type: NottinghamGroup(PrimeField(1783)) --E 2 --S 3 of 8 @@ -84254,7 +84451,7 @@ s^2 --R --R 3 5 7 9 11 --R (3) x + 594x + 535x + 1166x + 1379x + O(x ) ---R Type: NottinghamGroup PrimeField 1783 +--R Type: NottinghamGroup(PrimeField(1783)) --E 3 --S 4 of 8 @@ -84263,7 +84460,7 @@ s^-1 --R --R 3 5 7 9 11 --R (4) x + 1486x + 847x + 207x + 1701x + O(x ) ---R Type: NottinghamGroup PrimeField 1783 +--R Type: NottinghamGroup(PrimeField(1783)) --E 4 --S 5 of 8 @@ -84272,7 +84469,7 @@ s^-1*s --R --R 11 --R (5) x + O(x ) ---R Type: NottinghamGroup PrimeField 1783 +--R Type: NottinghamGroup(PrimeField(1783)) --E 5 --S 6 of 8 @@ -84281,20 +84478,20 @@ s*s^-1 --R --R 11 --R (6) x + O(x ) ---R Type: NottinghamGroup PrimeField 1783 +--R Type: NottinghamGroup(PrimeField(1783)) --E 6 --S 7 of 8 sample()$NOTTING(PF(1783)) --R --R (7) x ---R Type: NottinghamGroup PrimeField 1783 +--R Type: NottinghamGroup(PrimeField(1783)) --E 7 --S 8 of 8 )show NottinghamGroup --R ---R NottinghamGroup F: FiniteFieldCategory is a domain constructor +--R NottinghamGroup(F: FiniteFieldCategory) is a domain constructor --R Abbreviation for NottinghamGroup is NOTTING --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for NOTTING @@ -84311,7 +84508,7 @@ sample()$NOTTING(PF(1783)) --R sample : () -> % ?~=? : (%,%) -> Boolean --R ?**? : (%,NonNegativeInteger) -> % --R ?^? : (%,NonNegativeInteger) -> % ---R retract : UnivariateFormalPowerSeries F -> % +--R retract : UnivariateFormalPowerSeries(F) -> % --R --E 8 @@ -84431,6 +84628,7 @@ NottinghamGroup(F:FiniteFieldCategory): Group with --S 1 of 1 )show NumericalIntegrationProblem +--R --R NumericalIntegrationProblem is a domain constructor --R Abbreviation for NumericalIntegrationProblem is NIPROB --R This constructor is exposed in this frame. @@ -84440,10 +84638,10 @@ NottinghamGroup(F:FiniteFieldCategory): Group with --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R ?~=? : (%,%) -> Boolean ---R coerce : Union(nia: Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),mdnia: Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> % ---R coerce : Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat) -> % ---R coerce : Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat) -> % ---R retract : % -> Union(nia: Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),mdnia: Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) +--R coerce : Union(nia: Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat),mdnia: Record(fn: Expression(DoubleFloat),range: List(Segment(OrderedCompletion(DoubleFloat))),abserr: DoubleFloat,relerr: DoubleFloat)) -> % +--R coerce : Record(fn: Expression(DoubleFloat),range: List(Segment(OrderedCompletion(DoubleFloat))),abserr: DoubleFloat,relerr: DoubleFloat) -> % +--R coerce : Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat) -> % +--R retract : % -> Union(nia: Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat),mdnia: Record(fn: Expression(DoubleFloat),range: List(Segment(OrderedCompletion(DoubleFloat))),abserr: DoubleFloat,relerr: DoubleFloat)) --R --E 1 @@ -84557,6 +84755,7 @@ NumericalIntegrationProblem(): EE == II where --S 1 of 1 )show NumericalODEProblem +--R --R NumericalODEProblem is a domain constructor --R Abbreviation for NumericalODEProblem is ODEPROB --R This constructor is exposed in this frame. @@ -84566,8 +84765,8 @@ NumericalIntegrationProblem(): EE == II where --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R ?~=? : (%,%) -> Boolean ---R coerce : Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat) -> % ---R retract : % -> Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat) +--R coerce : Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector(Expression(DoubleFloat)),yinit: List(DoubleFloat),intvals: List(DoubleFloat),g: Expression(DoubleFloat),abserr: DoubleFloat,relerr: DoubleFloat) -> % +--R retract : % -> Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector(Expression(DoubleFloat)),yinit: List(DoubleFloat),intvals: List(DoubleFloat),g: Expression(DoubleFloat),abserr: DoubleFloat,relerr: DoubleFloat) --R --E 1 @@ -84665,6 +84864,7 @@ NumericalODEProblem(): EE == II where --S 1 of 1 )show NumericalOptimizationProblem +--R --R NumericalOptimizationProblem is a domain constructor --R Abbreviation for NumericalOptimizationProblem is OPTPROB --R This constructor is exposed in this frame. @@ -84674,10 +84874,10 @@ NumericalODEProblem(): EE == II where --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R ?~=? : (%,%) -> Boolean ---R coerce : Union(noa: Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat),lsa: Record(lfn: List Expression DoubleFloat,init: List DoubleFloat)) -> % ---R coerce : Record(lfn: List Expression DoubleFloat,init: List DoubleFloat) -> % ---R coerce : Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat) -> % ---R retract : % -> Union(noa: Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat),lsa: Record(lfn: List Expression DoubleFloat,init: List DoubleFloat)) +--R coerce : Union(noa: Record(fn: Expression(DoubleFloat),init: List(DoubleFloat),lb: List(OrderedCompletion(DoubleFloat)),cf: List(Expression(DoubleFloat)),ub: List(OrderedCompletion(DoubleFloat))),lsa: Record(lfn: List(Expression(DoubleFloat)),init: List(DoubleFloat))) -> % +--R coerce : Record(lfn: List(Expression(DoubleFloat)),init: List(DoubleFloat)) -> % +--R coerce : Record(fn: Expression(DoubleFloat),init: List(DoubleFloat),lb: List(OrderedCompletion(DoubleFloat)),cf: List(Expression(DoubleFloat)),ub: List(OrderedCompletion(DoubleFloat))) -> % +--R retract : % -> Union(noa: Record(fn: Expression(DoubleFloat),init: List(DoubleFloat),lb: List(OrderedCompletion(DoubleFloat)),cf: List(Expression(DoubleFloat)),ub: List(OrderedCompletion(DoubleFloat))),lsa: Record(lfn: List(Expression(DoubleFloat)),init: List(DoubleFloat))) --R --E 1 @@ -84792,6 +84992,7 @@ NumericalOptimizationProblem(): EE == II where --S 1 of 1 )show NumericalPDEProblem +--R --R NumericalPDEProblem is a domain constructor --R Abbreviation for NumericalPDEProblem is PDEPROB --R This constructor is exposed in this frame. @@ -84801,8 +85002,8 @@ NumericalOptimizationProblem(): EE == II where --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R hash : % -> SingleInteger latex : % -> String --R ?~=? : (%,%) -> Boolean ---R coerce : Record(pde: List Expression DoubleFloat,constraints: List Record(start: DoubleFloat,finish: DoubleFloat,grid: NonNegativeInteger,boundaryType: Integer,dStart: Matrix DoubleFloat,dFinish: Matrix DoubleFloat),f: List List Expression DoubleFloat,st: String,tol: DoubleFloat) -> % ---R retract : % -> Record(pde: List Expression DoubleFloat,constraints: List Record(start: DoubleFloat,finish: DoubleFloat,grid: NonNegativeInteger,boundaryType: Integer,dStart: Matrix DoubleFloat,dFinish: Matrix DoubleFloat),f: List List Expression DoubleFloat,st: String,tol: DoubleFloat) +--R coerce : Record(pde: List(Expression(DoubleFloat)),constraints: List(Record(start: DoubleFloat,finish: DoubleFloat,grid: NonNegativeInteger,boundaryType: Integer,dStart: Matrix(DoubleFloat),dFinish: Matrix(DoubleFloat))),f: List(List(Expression(DoubleFloat))),st: String,tol: DoubleFloat) -> % +--R retract : % -> Record(pde: List(Expression(DoubleFloat)),constraints: List(Record(start: DoubleFloat,finish: DoubleFloat,grid: NonNegativeInteger,boundaryType: Integer,dStart: Matrix(DoubleFloat),dFinish: Matrix(DoubleFloat))),f: List(List(Expression(DoubleFloat))),st: String,tol: DoubleFloat) --R --E 1 @@ -84957,7 +85158,7 @@ oci1 := octon(1,2,3,4,5,6,7,8) --R --R --R (1) 1 + 2i + 3j + 4k + 5E + 6I + 7J + 8K ---R Type: Octonion Integer +--R Type: Octonion(Integer) --E 1 --S 2 of 15 @@ -84965,7 +85166,7 @@ oci2 := octon(7,2,3,-4,5,6,-7,0) --R --R --R (2) 7 + 2i + 3j - 4k + 5E + 6I - 7J ---R Type: Octonion Integer +--R Type: Octonion(Integer) --E 2 --S 3 of 15 @@ -84973,7 +85174,7 @@ oci3 := octon(quatern(-7,-12,3,-10), quatern(5,6,9,0)) --R --R --R (3) - 7 - 12i + 3j - 10k + 5E + 6I + 9J ---R Type: Octonion Integer +--R Type: Octonion(Integer) --E 3 --S 4 of 15 @@ -84981,7 +85182,7 @@ oci3 := octon(quatern(-7,-12,3,-10), quatern(5,6,9,0)) --R --R --R (4) 2696i - 2928j - 4072k + 16E - 1192I + 832J + 2616K ---R Type: Octonion Integer +--R Type: Octonion(Integer) --E 4 --S 5 of 15 @@ -84990,7 +85191,7 @@ oci3 := octon(quatern(-7,-12,3,-10), quatern(5,6,9,0)) --R --R --R (5) [1,2,3,4,5,6,7,8] ---R Type: List PositiveInteger +--R Type: List(PositiveInteger) --E 5 --S 6 of 15 @@ -84998,7 +85199,7 @@ q : Quaternion Polynomial Integer := quatern(q1, qi, qj, qk) --R --R --R (6) q1 + qi i + qj j + qk k ---R Type: Quaternion Polynomial Integer +--R Type: Quaternion(Polynomial(Integer)) --E 6 --S 7 of 15 @@ -85006,7 +85207,7 @@ E : Octonion Polynomial Integer:= octon(0,0,0,0,1,0,0,0) --R --R --R (7) E ---R Type: Octonion Polynomial Integer +--R Type: Octonion(Polynomial(Integer)) --E 7 --S 8 of 15 @@ -85014,7 +85215,7 @@ q * E --R --R --R (8) q1 E + qi I + qj J + qk K ---R Type: Octonion Polynomial Integer +--R Type: Octonion(Polynomial(Integer)) --E 8 --S 9 of 15 @@ -85022,7 +85223,7 @@ E * q --R --R --R (9) q1 E - qi I - qj J - qk K ---R Type: Octonion Polynomial Integer +--R Type: Octonion(Polynomial(Integer)) --E 9 --S 10 of 15 @@ -85030,7 +85231,7 @@ q * 1$(Octonion Polynomial Integer) --R --R --R (10) q1 + qi i + qj j + qk k ---R Type: Octonion Polynomial Integer +--R Type: Octonion(Polynomial(Integer)) --E 10 --S 11 of 15 @@ -85038,7 +85239,7 @@ q * 1$(Octonion Polynomial Integer) --R --R --R (11) q1 + qi i + qj j + qk k ---R Type: Octonion Polynomial Integer +--R Type: Octonion(Polynomial(Integer)) --E 11 --S 12 of 15 @@ -85046,7 +85247,7 @@ o : Octonion Polynomial Integer := octon(o1, oi, oj, ok, oE, oI, oJ, oK) --R --R --R (12) o1 + oi i + oj j + ok k + oE E + oI I + oJ J + oK K ---R Type: Octonion Polynomial Integer +--R Type: Octonion(Polynomial(Integer)) --E 12 --S 13 of 15 @@ -85055,7 +85256,7 @@ norm o --R --R 2 2 2 2 2 2 2 2 --R (13) ok + oj + oi + oK + oJ + oI + oE + o1 ---R Type: Polynomial Integer +--R Type: Polynomial(Integer) --E 13 --S 14 of 15 @@ -85063,7 +85264,7 @@ p : Octonion Polynomial Integer := octon(p1, pi, pj, pk, pE, pI, pJ, pK) --R --R --R (14) p1 + pi i + pj j + pk k + pE E + pI I + pJ J + pK K ---R Type: Octonion Polynomial Integer +--R Type: Octonion(Polynomial(Integer)) --E 14 --S 15 of 15 @@ -85071,7 +85272,7 @@ norm(o*p)-norm(p)*norm(o) --R --R --R (15) 0 ---R Type: Polynomial Integer +--R Type: Polynomial(Integer) --E 15 )spool )lisp (bye) @@ -85327,6 +85528,7 @@ Octonion(R:CommutativeRing): export == impl where --S 1 of 1 )show ODEIntensityFunctionsTable +--R --R ODEIntensityFunctionsTable is a domain constructor --R Abbreviation for ODEIntensityFunctionsTable is ODEIFTBL --R This constructor is exposed in this frame. @@ -85334,10 +85536,10 @@ Octonion(R:CommutativeRing): export == impl where --R --R------------------------------- Operations -------------------------------- --R clearTheIFTable : () -> Void showTheIFTable : () -> % ---R iFTable : List Record(key: Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),entry: Record(stiffness: Float,stability: Float,expense: Float,accuracy: Float,intermediateResults: Float)) -> % ---R insert! : Record(key: Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),entry: Record(stiffness: Float,stability: Float,expense: Float,accuracy: Float,intermediateResults: Float)) -> % ---R keys : % -> List Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat) ---R showIntensityFunctions : Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat) -> Union(Record(stiffness: Float,stability: Float,expense: Float,accuracy: Float,intermediateResults: Float),"failed") +--R iFTable : List(Record(key: Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector(Expression(DoubleFloat)),yinit: List(DoubleFloat),intvals: List(DoubleFloat),g: Expression(DoubleFloat),abserr: DoubleFloat,relerr: DoubleFloat),entry: Record(stiffness: Float,stability: Float,expense: Float,accuracy: Float,intermediateResults: Float))) -> % +--R insert! : Record(key: Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector(Expression(DoubleFloat)),yinit: List(DoubleFloat),intvals: List(DoubleFloat),g: Expression(DoubleFloat),abserr: DoubleFloat,relerr: DoubleFloat),entry: Record(stiffness: Float,stability: Float,expense: Float,accuracy: Float,intermediateResults: Float)) -> % +--R keys : % -> List(Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector(Expression(DoubleFloat)),yinit: List(DoubleFloat),intvals: List(DoubleFloat),g: Expression(DoubleFloat),abserr: DoubleFloat,relerr: DoubleFloat)) +--R showIntensityFunctions : Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector(Expression(DoubleFloat)),yinit: List(DoubleFloat),intvals: List(DoubleFloat),g: Expression(DoubleFloat),abserr: DoubleFloat,relerr: DoubleFloat) -> Union(Record(stiffness: Float,stability: Float,expense: Float,accuracy: Float,intermediateResults: Float),"failed") --R --E 1 @@ -85466,7 +85668,7 @@ oneDimensionalArray [i**2 for i in 1..10] --R --R --R (1) [1,4,9,16,25,36,49,64,81,100] ---R Type: OneDimensionalArray PositiveInteger +--R Type: OneDimensionalArray(PositiveInteger) --E 1 --S 2 of 9 @@ -85474,7 +85676,7 @@ a : ARRAY1 INT := new(10,0) --R --R --R (2) [0,0,0,0,0,0,0,0,0,0] ---R Type: OneDimensionalArray Integer +--R Type: OneDimensionalArray(Integer) --E 2 --S 3 of 9 @@ -85482,7 +85684,7 @@ for i in 1..10 repeat a.i := i; a --R --R --R (3) [1,2,3,4,5,6,7,8,9,10] ---R Type: OneDimensionalArray Integer +--R Type: OneDimensionalArray(Integer) --E 3 --S 4 of 9 @@ -85490,7 +85692,7 @@ map!(i +-> i ** 2,a); a --R --R --R (4) [1,4,9,16,25,36,49,64,81,100] ---R Type: OneDimensionalArray Integer +--R Type: OneDimensionalArray(Integer) --E 4 --S 5 of 9 @@ -85498,7 +85700,7 @@ reverse! a --R --R --R (5) [100,81,64,49,36,25,16,9,4,1] ---R Type: OneDimensionalArray Integer +--R Type: OneDimensionalArray(Integer) --E 5 --S 6 of 9 @@ -85506,7 +85708,7 @@ swap!(a,4,5); a --R --R --R (6) [100,81,64,36,49,25,16,9,4,1] ---R Type: OneDimensionalArray Integer +--R Type: OneDimensionalArray(Integer) --E 6 --S 7 of 9 @@ -85514,7 +85716,7 @@ sort! a --R --R --R (7) [1,4,9,16,25,36,49,64,81,100] ---R Type: OneDimensionalArray Integer +--R Type: OneDimensionalArray(Integer) --E 7 --S 8 of 9 @@ -85522,7 +85724,7 @@ b := a(6..10) --R --R --R (8) [36,49,64,81,100] ---R Type: OneDimensionalArray Integer +--R Type: OneDimensionalArray(Integer) --E 8 --S 9 of 9 @@ -85530,7 +85732,7 @@ copyInto!(a,b,1) --R --R --R (9) [36,49,64,81,100,36,49,64,81,100] ---R Type: OneDimensionalArray Integer +--R Type: OneDimensionalArray(Integer) --E 9 )spool )lisp (bye) @@ -85734,7 +85936,8 @@ OneDimensionalArray(S:Type): Exports == Implementation where --S 1 of 1 )show OnePointCompletion ---R OnePointCompletion R: SetCategory is a domain constructor +--R +--R OnePointCompletion(R: SetCategory) is a domain constructor --R Abbreviation for OnePointCompletion is ONECOMP --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ONECOMP @@ -85763,22 +85966,22 @@ OneDimensionalArray(S:Type): Exports == Implementation where --R ?^? : (%,PositiveInteger) -> % if R has ORDRING --R abs : % -> % if R has ORDRING --R characteristic : () -> NonNegativeInteger if R has ORDRING ---R coerce : Integer -> % if R has ORDRING or R has RETRACT INT ---R coerce : Fraction Integer -> % if R has RETRACT FRAC INT +--R coerce : Integer -> % if R has ORDRING or R has RETRACT(INT) +--R coerce : Fraction(Integer) -> % if R has RETRACT(FRAC(INT)) --R max : (%,%) -> % if R has ORDRING --R min : (%,%) -> % if R has ORDRING --R negative? : % -> Boolean if R has ORDRING --R one? : % -> Boolean if R has ORDRING --R positive? : % -> Boolean if R has ORDRING ---R rational : % -> Fraction Integer if R has INS +--R rational : % -> Fraction(Integer) if R has INS --R rational? : % -> Boolean if R has INS ---R rationalIfCan : % -> Union(Fraction Integer,"failed") if R has INS +--R rationalIfCan : % -> Union(Fraction(Integer),"failed") if R has INS --R recip : % -> Union(%,"failed") if R has ORDRING ---R retract : % -> Fraction Integer if R has RETRACT FRAC INT ---R retract : % -> Integer if R has RETRACT INT +--R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT)) +--R retract : % -> Integer if R has RETRACT(INT) --R retractIfCan : % -> Union(R,"failed") ---R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT ---R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT)) +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT) --R sample : () -> % if R has ABELGRP --R sign : % -> Integer if R has ORDRING --R subtractIfCan : (%,%) -> Union(%,"failed") if R has ABELGRP @@ -86467,6 +86670,7 @@ OpenMathEncoding(): SetCategory with --S 1 of 1 )show OpenMathError +--R --R OpenMathError is a domain constructor --R Abbreviation for OpenMathError is OMERR --R This constructor is exposed in this frame. @@ -86474,10 +86678,10 @@ OpenMathEncoding(): SetCategory with --R --R------------------------------- Operations -------------------------------- --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm ---R errorInfo : % -> List Symbol hash : % -> SingleInteger +--R errorInfo : % -> List(Symbol) hash : % -> SingleInteger --R latex : % -> String ?~=? : (%,%) -> Boolean --R errorKind : % -> OpenMathErrorKind ---R omError : (OpenMathErrorKind,List Symbol) -> % +--R omError : (OpenMathErrorKind,List(Symbol)) -> % --R --E 1 @@ -86702,7 +86906,7 @@ t := operator("tilde") :: OP(R) --R --R --R (2) tilde ---R Type: Operator SquareMatrix(2,Integer) +--R Type: Operator(SquareMatrix(2,Integer)) --E 2 --S 3 of 21 @@ -86716,7 +86920,7 @@ evaluate(t, m +-> transpose m) --R --R --R (3) tilde ---R Type: Operator SquareMatrix(2,Integer) +--R Type: Operator(SquareMatrix(2,Integer)) --E 4 --S 5 of 21 @@ -86736,7 +86940,7 @@ rho := t * s --R +0 1+ --R (5) tilde| | --R +1 0+ ---R Type: Operator SquareMatrix(2,Integer) +--R Type: Operator(SquareMatrix(2,Integer)) --E 6 --S 7 of 21 @@ -86746,7 +86950,7 @@ z := rho**4 - 1 --R +0 1+ +0 1+ +0 1+ +0 1+ --R (6) - 1 + tilde| |tilde| |tilde| |tilde| | --R +1 0+ +1 0+ +1 0+ +1 0+ ---R Type: Operator SquareMatrix(2,Integer) +--R Type: Operator(SquareMatrix(2,Integer)) --E 7 --S 8 of 21 @@ -86806,7 +87010,7 @@ b := t * s - s * t --R +0 1+ +0 1+ --R (12) - | |tilde + tilde| | --R +1 0+ +1 0+ ---R Type: Operator SquareMatrix(2,Integer) +--R Type: Operator(SquareMatrix(2,Integer)) --E 13 --S 14 of 21 @@ -86833,7 +87037,7 @@ dx := operator("D") :: OP(POLY FRAC INT) --R --R --R (15) D ---R Type: Operator Polynomial Fraction Integer +--R Type: Operator(Polynomial(Fraction(Integer))) --E 16 --S 17 of 21 @@ -86841,7 +87045,7 @@ evaluate(dx, p +-> D(p, 'x)) --R --R --R (16) D ---R Type: Operator Polynomial Fraction Integer +--R Type: Operator(Polynomial(Fraction(Integer))) --E 17 --S 18 of 21 @@ -86853,8 +87057,8 @@ E n == (1 - x**2) * dx**2 - 2 * x * dx + n*(n+1) --S 19 of 21 L 15 --R ---R Compiling function L with type Integer -> Polynomial Fraction ---R Integer +--R Compiling function L with type Integer -> Polynomial(Fraction( +--R Integer)) --R Compiling function L as a recurrence relation. --R --R (18) @@ -86865,18 +87069,18 @@ L 15 --R 2909907 5 255255 3 6435 --R - ------- x + ------ x - ---- x --R 2048 2048 2048 ---R Type: Polynomial Fraction Integer +--R Type: Polynomial(Fraction(Integer)) --E 19 --S 20 of 21 E 15 --R ---R Compiling function E with type PositiveInteger -> Operator ---R Polynomial Fraction Integer +--R Compiling function E with type PositiveInteger -> Operator( +--R Polynomial(Fraction(Integer))) --R --R 2 2 --R (19) 240 - 2x D - (x - 1)D ---R Type: Operator Polynomial Fraction Integer +--R Type: Operator(Polynomial(Fraction(Integer))) --E 20 --S 21 of 21 @@ -86884,7 +87088,7 @@ E 15 --R --R --R (20) 0 ---R Type: Polynomial Fraction Integer +--R Type: Polynomial(Fraction(Integer)) --E 21 )spool )lisp (bye) @@ -87136,7 +87340,8 @@ Operator(R: Ring) == ModuleOperator(R,R) --S 1 of 1 )show OppositeMonogenicLinearOperator ---R OppositeMonogenicLinearOperator(P: MonogenicLinearOperator R,R: Ring) is a domain constructor +--R +--R OppositeMonogenicLinearOperator(P: MonogenicLinearOperator(R),R: Ring) is a domain constructor --R Abbreviation for OppositeMonogenicLinearOperator is OMLO --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for OMLO @@ -87280,7 +87485,8 @@ OppositeMonogenicLinearOperator(P, R): OPRcat == OPRdef where --S 1 of 1 )show OrderedCompletion ---R OrderedCompletion R: SetCategory is a domain constructor +--R +--R OrderedCompletion(R: SetCategory) is a domain constructor --R Abbreviation for OrderedCompletion is ORDCOMP --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ORDCOMP @@ -87310,22 +87516,22 @@ OppositeMonogenicLinearOperator(P, R): OPRcat == OPRdef where --R ?^? : (%,PositiveInteger) -> % if R has ORDRING --R abs : % -> % if R has ORDRING --R characteristic : () -> NonNegativeInteger if R has ORDRING ---R coerce : Integer -> % if R has ORDRING or R has RETRACT INT ---R coerce : Fraction Integer -> % if R has RETRACT FRAC INT +--R coerce : Integer -> % if R has ORDRING or R has RETRACT(INT) +--R coerce : Fraction(Integer) -> % if R has RETRACT(FRAC(INT)) --R max : (%,%) -> % if R has ORDRING --R min : (%,%) -> % if R has ORDRING --R negative? : % -> Boolean if R has ORDRING --R one? : % -> Boolean if R has ORDRING --R positive? : % -> Boolean if R has ORDRING ---R rational : % -> Fraction Integer if R has INS +--R rational : % -> Fraction(Integer) if R has INS --R rational? : % -> Boolean if R has INS ---R rationalIfCan : % -> Union(Fraction Integer,"failed") if R has INS +--R rationalIfCan : % -> Union(Fraction(Integer),"failed") if R has INS --R recip : % -> Union(%,"failed") if R has ORDRING ---R retract : % -> Fraction Integer if R has RETRACT FRAC INT ---R retract : % -> Integer if R has RETRACT INT +--R retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT)) +--R retract : % -> Integer if R has RETRACT(INT) --R retractIfCan : % -> Union(R,"failed") ---R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT ---R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT)) +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT) --R sample : () -> % if R has ABELGRP --R sign : % -> Integer if R has ORDRING --R subtractIfCan : (%,%) -> Union(%,"failed") if R has ABELGRP @@ -87544,19 +87750,20 @@ OrderedCompletion(R:SetCategory): Exports == Implementation where --S 1 of 1 )show OrderedDirectProduct ---R OrderedDirectProduct(dim: NonNegativeInteger,S: OrderedAbelianMonoidSup,f: ((Vector S,Vector S) -> Boolean)) is a domain constructor +--R +--R OrderedDirectProduct(dim: NonNegativeInteger,S: OrderedAbelianMonoidSup,f: ((Vector(S),Vector(S)) -> Boolean)) is a domain constructor --R Abbreviation for OrderedDirectProduct is ODP --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ODP --R --R------------------------------- Operations -------------------------------- --R -? : % -> % if S has RING 1 : () -> % if S has MONOID ---R 0 : () -> % if S has CABMON coerce : % -> Vector S ---R copy : % -> % directProduct : Vector S -> % +--R 0 : () -> % if S has CABMON coerce : % -> Vector(S) +--R copy : % -> % directProduct : Vector(S) -> % --R ?.? : (%,Integer) -> S elt : (%,Integer,S) -> S --R empty : () -> % empty? : % -> Boolean ---R entries : % -> List S eq? : (%,%) -> Boolean ---R index? : (Integer,%) -> Boolean indices : % -> List Integer +--R entries : % -> List(S) eq? : (%,%) -> Boolean +--R index? : (Integer,%) -> Boolean indices : % -> List(Integer) --R map : ((S -> S),%) -> % qelt : (%,Integer) -> S --R sample : () -> % --R #? : % -> NonNegativeInteger if $ has finiteAggregate @@ -87578,10 +87785,10 @@ OrderedCompletion(R:SetCategory): Exports == Implementation where --R ?>=? : (%,%) -> Boolean if S has OAMONS or S has ORDRING --R D : (%,(S -> S)) -> % if S has RING --R D : (%,(S -> S),NonNegativeInteger) -> % if S has RING ---R D : (%,List Symbol,List NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING ---R D : (%,Symbol,NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING ---R D : (%,List Symbol) -> % if S has PDRING SYMBOL and S has RING ---R D : (%,Symbol) -> % if S has PDRING SYMBOL and S has RING +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if S has PDRING(SYMBOL) and S has RING +--R D : (%,Symbol,NonNegativeInteger) -> % if S has PDRING(SYMBOL) and S has RING +--R D : (%,List(Symbol)) -> % if S has PDRING(SYMBOL) and S has RING +--R D : (%,Symbol) -> % if S has PDRING(SYMBOL) and S has RING --R D : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING --R D : % -> % if S has DIFRING and S has RING --R ?^? : (%,PositiveInteger) -> % if S has MONOID @@ -87590,26 +87797,26 @@ OrderedCompletion(R:SetCategory): Exports == Implementation where --R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R characteristic : () -> NonNegativeInteger if S has RING --R coerce : S -> % if S has SETCAT ---R coerce : Fraction Integer -> % if S has RETRACT FRAC INT and S has SETCAT ---R coerce : Integer -> % if S has RETRACT INT and S has SETCAT or S has RING +--R coerce : Fraction(Integer) -> % if S has RETRACT(FRAC(INT)) and S has SETCAT +--R coerce : Integer -> % if S has RETRACT(INT) and S has SETCAT or S has RING --R coerce : % -> OutputForm if S has SETCAT --R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT --R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate --R differentiate : (%,(S -> S)) -> % if S has RING --R differentiate : (%,(S -> S),NonNegativeInteger) -> % if S has RING ---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING ---R differentiate : (%,Symbol,NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING ---R differentiate : (%,List Symbol) -> % if S has PDRING SYMBOL and S has RING ---R differentiate : (%,Symbol) -> % if S has PDRING SYMBOL and S has RING +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if S has PDRING(SYMBOL) and S has RING +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if S has PDRING(SYMBOL) and S has RING +--R differentiate : (%,List(Symbol)) -> % if S has PDRING(SYMBOL) and S has RING +--R differentiate : (%,Symbol) -> % if S has PDRING(SYMBOL) and S has RING --R differentiate : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING --R differentiate : % -> % if S has DIFRING and S has RING --R dimension : () -> CardinalNumber if S has FIELD --R dot : (%,%) -> S if S has RING --R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT ---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R fill! : (%,S) -> % if $ has shallowlyMutable --R first : % -> S if Integer has ORDSET @@ -87622,27 +87829,27 @@ OrderedCompletion(R:SetCategory): Exports == Implementation where --R max : (%,%) -> % if S has OAMONS or S has ORDRING --R maxIndex : % -> Integer if Integer has ORDSET --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT ---R members : % -> List S if $ has finiteAggregate +--R members : % -> List(S) if $ has finiteAggregate --R min : (%,%) -> % if S has OAMONS or S has ORDRING --R minIndex : % -> Integer if Integer has ORDSET --R more? : (%,NonNegativeInteger) -> Boolean --R negative? : % -> Boolean if S has ORDRING --R one? : % -> Boolean if S has MONOID ---R parts : % -> List S if $ has finiteAggregate +--R parts : % -> List(S) if $ has finiteAggregate --R positive? : % -> Boolean if S has ORDRING --R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable --R random : () -> % if S has FINITE --R recip : % -> Union(%,"failed") if S has MONOID ---R reducedSystem : Matrix % -> Matrix S if S has RING ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix S,vec: Vector S) if S has RING ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if S has LINEXP INT and S has RING ---R reducedSystem : Matrix % -> Matrix Integer if S has LINEXP INT and S has RING +--R reducedSystem : Matrix(%) -> Matrix(S) if S has RING +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(S),vec: Vector(S)) if S has RING +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if S has LINEXP(INT) and S has RING +--R reducedSystem : Matrix(%) -> Matrix(Integer) if S has LINEXP(INT) and S has RING --R retract : % -> S if S has SETCAT ---R retract : % -> Fraction Integer if S has RETRACT FRAC INT and S has SETCAT ---R retract : % -> Integer if S has RETRACT INT and S has SETCAT +--R retract : % -> Fraction(Integer) if S has RETRACT(FRAC(INT)) and S has SETCAT +--R retract : % -> Integer if S has RETRACT(INT) and S has SETCAT --R retractIfCan : % -> Union(S,"failed") if S has SETCAT ---R retractIfCan : % -> Union(Fraction Integer,"failed") if S has RETRACT FRAC INT and S has SETCAT ---R retractIfCan : % -> Union(Integer,"failed") if S has RETRACT INT and S has SETCAT +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if S has RETRACT(FRAC(INT)) and S has SETCAT +--R retractIfCan : % -> Union(Integer,"failed") if S has RETRACT(INT) and S has SETCAT --R setelt : (%,Integer,S) -> S if $ has shallowlyMutable --R sign : % -> Integer if S has ORDRING --R size : () -> NonNegativeInteger if S has FINITE @@ -87809,7 +88016,7 @@ m1:=(x*y*y*z)$OFMONOID(Symbol) --R --R 2 --R (1) x y z ---R Type: OrderedFreeMonoid Symbol +--R Type: OrderedFreeMonoid(Symbol) --E 1 --S 2 of 24 @@ -87817,7 +88024,7 @@ m2:=(x*y)$OFMONOID(Symbol) --R --R --R (2) x y ---R Type: OrderedFreeMonoid Symbol +--R Type: OrderedFreeMonoid(Symbol) --E 2 --S 3 of 24 @@ -87825,7 +88032,7 @@ lquo(m1,m2) --R --R --R (3) y z ---R Type: Union(OrderedFreeMonoid Symbol,...) +--R Type: Union(OrderedFreeMonoid(Symbol),...) --E 3 --S 4 of 24 @@ -87834,7 +88041,7 @@ m3:=(y*y)$OFMONOID(Symbol) --R --R 2 --R (4) y ---R Type: OrderedFreeMonoid Symbol +--R Type: OrderedFreeMonoid(Symbol) --E 4 --S 5 of 24 @@ -87842,7 +88049,7 @@ divide(m1,m2) --R --R --R (5) [lm= y z,rm= "failed"] ---RType: Union(Record(lm: Union(OrderedFreeMonoid Symbol,"failed"),rm: Union(OrderedFreeMonoid Symbol,"failed")),...) +--IType: Union(Record(lm: Union(OrderedFreeMonoid(Symbol),"failed"),... --E 5 --S 6 of 24 @@ -87850,7 +88057,7 @@ divide(m1,m3) --R --R --R (6) [lm= "failed",rm= "failed"] ---RType: Union(Record(lm: Union(OrderedFreeMonoid Symbol,"failed"),rm: Union(OrderedFreeMonoid Symbol,"failed")),...) +--IType: Union(Record(lm: Union(OrderedFreeMonoid(Symbol),"failed"),... --E 6 --S 7 of 24 @@ -87859,7 +88066,7 @@ m4:=(y^3)$OFMONOID(Symbol) --R --R 3 --R (7) y ---R Type: OrderedFreeMonoid Symbol +--R Type: OrderedFreeMonoid(Symbol) --E 7 --S 8 of 24 @@ -87867,7 +88074,7 @@ divide(m1,m4) --R --R --R (8) [lm= "failed",rm= "failed"] ---RType: Union(Record(lm: Union(OrderedFreeMonoid Symbol,"failed"),rm: Union(OrderedFreeMonoid Symbol,"failed")),...) +--IType: Union(Record(lm: Union(OrderedFreeMonoid(Symbol),"failed"),... --E 8 )set function compile on @@ -87946,10 +88153,10 @@ subs(w:M):H == monom(n2,1)$H * (a::K*x::V+b::K)$H * monom(n2,1)$H monom(n1,1)$H * (y::V*x::V*y::V)$H * monom(n1,1)$H --R ---R Function declaration subs : OrderedFreeMonoid OrderedVariableList [x ---R ,y] -> XDistributedPolynomial(OrderedVariableList [x,y], ---R SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList ---R [a,b])) has been added to workspace. +--R Function declaration subs : OrderedFreeMonoid(OrderedVariableList([x +--R ,y])) -> XDistributedPolynomial(OrderedVariableList([x,y]), +--R SparseMultivariatePolynomial(Fraction(Integer), +--R OrderedVariableList([a,b]))) has been added to workspace. --R Type: Void --E 14 @@ -87957,12 +88164,12 @@ subs(w:M):H == --S 15 of 24 newterm(x:Record(k:M,c:K)):H == x.c*subs(x,k) --R ---R Function declaration newterm : Record(k: OrderedFreeMonoid ---R OrderedVariableList [x,y],c: SparseMultivariatePolynomial( ---R Fraction Integer,OrderedVariableList [a,b])) -> ---R XDistributedPolynomial(OrderedVariableList [x,y], ---R SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList ---R [a,b])) has been added to workspace. +--R Function declaration newterm : Record(k: OrderedFreeMonoid( +--R OrderedVariableList([x,y])),c: SparseMultivariatePolynomial( +--R Fraction(Integer),OrderedVariableList([a,b]))) -> +--R XDistributedPolynomial(OrderedVariableList([x,y]), +--R SparseMultivariatePolynomial(Fraction(Integer), +--R OrderedVariableList([a,b]))) has been added to workspace. --R Type: Void --E 15 @@ -87972,10 +88179,11 @@ newterm(x:Record(k:M,c:K)):H == x.c*subs(x,k) newpoly(t:H):H == reduce(+,map(newterm,listOfTerms(t))) --R --R Function declaration newpoly : XDistributedPolynomial( ---R OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction ---R Integer,OrderedVariableList [a,b])) -> XDistributedPolynomial( ---R OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction ---R Integer,OrderedVariableList [a,b])) has been added to workspace. +--R OrderedVariableList([x,y]),SparseMultivariatePolynomial(Fraction( +--R Integer),OrderedVariableList([a,b]))) -> XDistributedPolynomial( +--R OrderedVariableList([x,y]),SparseMultivariatePolynomial(Fraction( +--R Integer),OrderedVariableList([a,b]))) has been added to +--R workspace. --R Type: Void --E 16 @@ -87993,10 +88201,10 @@ p1:(x::V+y::V)$H^2 newpoly(p1) --R --R Compiling function newpoly with type XDistributedPolynomial( ---R OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction ---R Integer,OrderedVariableList [a,b])) -> XDistributedPolynomial( ---R OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction ---R Integer,OrderedVariableList [a,b])) +--R OrderedVariableList([x,y]),SparseMultivariatePolynomial(Fraction( +--R Integer),OrderedVariableList([a,b]))) -> XDistributedPolynomial( +--R OrderedVariableList([x,y]),SparseMultivariatePolynomial(Fraction( +--R Integer),OrderedVariableList([a,b]))) --R There are no library operations named subs --R Use HyperDoc Browse or issue --R )what op subs @@ -88004,18 +88212,18 @@ newpoly(p1) --R name. --R Cannot find a definition or applicable library operation named subs --R with argument type(s) ---RRecord(k: OrderedFreeMonoid OrderedVariableList [x,y],c: SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList [a,b])) ---R Variable k +--RRecord(k: OrderedFreeMonoid(OrderedVariableList([x,y])),c: SparseMultivariatePolynomial(Fraction(Integer),OrderedVariableList([a,b]))) +--R Variable(k) --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. --R AXIOM will attempt to step through and interpret the code. ---R Compiling function newterm with type Record(k: OrderedFreeMonoid ---R OrderedVariableList [x,y],c: SparseMultivariatePolynomial( ---R Fraction Integer,OrderedVariableList [a,b])) -> ---R XDistributedPolynomial(OrderedVariableList [x,y], ---R SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList ---R [a,b])) +--R Compiling function newterm with type Record(k: OrderedFreeMonoid( +--R OrderedVariableList([x,y])),c: SparseMultivariatePolynomial( +--R Fraction(Integer),OrderedVariableList([a,b]))) -> +--R XDistributedPolynomial(OrderedVariableList([x,y]), +--R SparseMultivariatePolynomial(Fraction(Integer), +--R OrderedVariableList([a,b]))) --R There are no library operations named subs --R Use HyperDoc Browse or issue --R )what op subs @@ -88025,8 +88233,8 @@ newpoly(p1) --RDaly Bug --R Cannot find a definition or applicable library operation named subs --R with argument type(s) ---RRecord(k: OrderedFreeMonoid OrderedVariableList [x,y],c: SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList [a,b])) ---R Variable k +--RRecord(k: OrderedFreeMonoid(OrderedVariableList([x,y])),c: SparseMultivariatePolynomial(Fraction(Integer),OrderedVariableList([a,b]))) +--R Variable(k) --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. @@ -88038,7 +88246,7 @@ p2:=(x::V+y::V)$H^3 --R --R 3 2 2 2 2 3 --R (17) y + y x + y x y + y x + x y + x y x + x y + x ---RType: XDistributedPolynomial(OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList [a,b])) +--IType: XDistributedPolynomial(OrderedVariableList([x,y]),... --E 19 --S 20 of 24 @@ -88051,8 +88259,8 @@ pNew:=newpoly(p2) --R name. --R Cannot find a definition or applicable library operation named subs --R with argument type(s) ---RRecord(k: OrderedFreeMonoid OrderedVariableList [x,y],c: SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList [a,b])) ---R Variable k +--RRecord(k: OrderedFreeMonoid(OrderedVariableList([x,y])),c: SparseMultivariatePolynomial(Fraction(Integer),OrderedVariableList([a,b]))) +--R Variable(k) --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. @@ -88072,8 +88280,8 @@ pNew:=newpoly(p2) --RDaly Bug --R Cannot find a definition or applicable library operation named subs --R with argument type(s) ---RRecord(k: OrderedFreeMonoid OrderedVariableList [x,y],c: SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList [a,b])) ---R Variable k +--RRecord(k: OrderedFreeMonoid(OrderedVariableList([x,y])),c: SparseMultivariatePolynomial(Fraction(Integer),OrderedVariableList([a,b]))) +--R Variable(k) --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. @@ -88092,18 +88300,18 @@ while pNew ~= p2 repeat --R name. --R Cannot find a definition or applicable library operation named subs --R with argument type(s) ---RRecord(k: OrderedFreeMonoid OrderedVariableList [x,y],c: SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList [a,b])) ---R Variable k +--RRecord(k: OrderedFreeMonoid(OrderedVariableList([x,y])),c: SparseMultivariatePolynomial(Fraction(Integer),OrderedVariableList([a,b]))) +--R Variable(k) --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. --R AXIOM will attempt to step through and interpret the code. ---R Compiling function newterm with type Record(k: OrderedFreeMonoid ---R OrderedVariableList [x,y],c: SparseMultivariatePolynomial( ---R Fraction Integer,OrderedVariableList [a,b])) -> ---R XDistributedPolynomial(OrderedVariableList [x,y], ---R SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList ---R [a,b])) +--R Compiling function newterm with type Record(k: OrderedFreeMonoid( +--R OrderedVariableList([x,y])),c: SparseMultivariatePolynomial( +--R Fraction(Integer),OrderedVariableList([a,b]))) -> +--R XDistributedPolynomial(OrderedVariableList([x,y]), +--R SparseMultivariatePolynomial(Fraction(Integer), +--R OrderedVariableList([a,b]))) --R There are no library operations named subs --R Use HyperDoc Browse or issue --R )what op subs @@ -88113,8 +88321,8 @@ while pNew ~= p2 repeat --RDaly Bug --R Cannot find a definition or applicable library operation named subs --R with argument type(s) ---RRecord(k: OrderedFreeMonoid OrderedVariableList [x,y],c: SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList [a,b])) ---R Variable k +--RRecord(k: OrderedFreeMonoid(OrderedVariableList([x,y])),c: SparseMultivariatePolynomial(Fraction(Integer),OrderedVariableList([a,b]))) +--R Variable(k) --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. @@ -88138,10 +88346,11 @@ reduce(p:H):H == p3 --R --R Function declaration reduce : XDistributedPolynomial( ---R OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction ---R Integer,OrderedVariableList [a,b])) -> XDistributedPolynomial( ---R OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction ---R Integer,OrderedVariableList [a,b])) has been added to workspace. +--R OrderedVariableList([x,y]),SparseMultivariatePolynomial(Fraction( +--R Integer),OrderedVariableList([a,b]))) -> XDistributedPolynomial( +--R OrderedVariableList([x,y]),SparseMultivariatePolynomial(Fraction( +--R Integer),OrderedVariableList([a,b]))) has been added to +--R workspace. --R Compiled code for newpoly has been cleared. --R Type: Void --E 23 @@ -88150,15 +88359,15 @@ reduce(p:H):H == reduce(p2) --R --R Compiling function newpoly with type XDistributedPolynomial( ---R OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction ---R Integer,OrderedVariableList [a,b])) -> XDistributedPolynomial( ---R OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction ---R Integer,OrderedVariableList [a,b])) +--R OrderedVariableList([x,y]),SparseMultivariatePolynomial(Fraction( +--R Integer),OrderedVariableList([a,b]))) -> XDistributedPolynomial( +--R OrderedVariableList([x,y]),SparseMultivariatePolynomial(Fraction( +--R Integer),OrderedVariableList([a,b]))) --R Compiling function reduce with type XDistributedPolynomial( ---R OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction ---R Integer,OrderedVariableList [a,b])) -> XDistributedPolynomial( ---R OrderedVariableList [x,y],SparseMultivariatePolynomial(Fraction ---R Integer,OrderedVariableList [a,b])) +--R OrderedVariableList([x,y]),SparseMultivariatePolynomial(Fraction( +--R Integer),OrderedVariableList([a,b]))) -> XDistributedPolynomial( +--R OrderedVariableList([x,y]),SparseMultivariatePolynomial(Fraction( +--R Integer),OrderedVariableList([a,b]))) --R There are no library operations named subs --R Use HyperDoc Browse or issue --R )what op subs @@ -88166,18 +88375,18 @@ reduce(p2) --R name. --R Cannot find a definition or applicable library operation named subs --R with argument type(s) ---RRecord(k: OrderedFreeMonoid OrderedVariableList [x,y],c: SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList [a,b])) ---R Variable k +--RRecord(k: OrderedFreeMonoid(OrderedVariableList([x,y])),c: SparseMultivariatePolynomial(Fraction(Integer),OrderedVariableList([a,b]))) +--R Variable(k) --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. --R AXIOM will attempt to step through and interpret the code. ---R Compiling function newterm with type Record(k: OrderedFreeMonoid ---R OrderedVariableList [x,y],c: SparseMultivariatePolynomial( ---R Fraction Integer,OrderedVariableList [a,b])) -> ---R XDistributedPolynomial(OrderedVariableList [x,y], ---R SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList ---R [a,b])) +--R Compiling function newterm with type Record(k: OrderedFreeMonoid( +--R OrderedVariableList([x,y])),c: SparseMultivariatePolynomial( +--R Fraction(Integer),OrderedVariableList([a,b]))) -> +--R XDistributedPolynomial(OrderedVariableList([x,y]), +--R SparseMultivariatePolynomial(Fraction(Integer), +--R OrderedVariableList([a,b]))) --R There are no library operations named subs --R Use HyperDoc Browse or issue --R )what op subs @@ -88187,8 +88396,8 @@ reduce(p2) --RDaly Bug --R Cannot find a definition or applicable library operation named subs --R with argument type(s) ---RRecord(k: OrderedFreeMonoid OrderedVariableList [x,y],c: SparseMultivariatePolynomial(Fraction Integer,OrderedVariableList [a,b])) ---R Variable k +--RRecord(k: OrderedFreeMonoid(OrderedVariableList([x,y])),c: SparseMultivariatePolynomial(Fraction(Integer),OrderedVariableList([a,b]))) +--R Variable(k) --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. @@ -88617,14 +88826,14 @@ ls:List Symbol:=['x,'a,'z] --R --R --R (1) [x,a,z] ---R Type: List Symbol +--R Type: List(Symbol) --E 1 --S 2 of 5 Z:=OVAR ls --R --R ---R (2) OrderedVariableList [x,a,z] +--R (2) OrderedVariableList([x,a,z]) --R Type: Domain --E 2 @@ -88643,7 +88852,7 @@ lv:=[index(i::PI)$Z for i in 1..size()$Z] --I Compiling function G1572 with type NonNegativeInteger -> Boolean --R --R (4) [x,a,z] ---R Type: List OrderedVariableList [x,a,z] +--R Type: List(OrderedVariableList([x,a,z])) --E 4 --S 5 of 5 @@ -88776,7 +88985,7 @@ OrderedVariableList(VariableList:List Symbol): dpol:= ODPOL(FRAC INT) --R --R ---R (1) OrderlyDifferentialPolynomial Fraction Integer +--R (1) OrderlyDifferentialPolynomial(Fraction(Integer)) --R Type: Domain --E 1 @@ -88785,7 +88994,7 @@ w := makeVariable('w)$dpol --R --R --R (2) theMap(DPOLCAT-;makeVariable;AM;17!0,0) ---R Type: (NonNegativeInteger -> OrderlyDifferentialPolynomial Fraction Integer) +--RType: (NonNegativeInteger -> OrderlyDifferentialPolynomial(Fraction(Integer))) --E 2 --S 3 of 36 @@ -88793,7 +89002,7 @@ z := makeVariable('z)$dpol --R --R --R (3) theMap(DPOLCAT-;makeVariable;AM;17!0,0) ---R Type: (NonNegativeInteger -> OrderlyDifferentialPolynomial Fraction Integer) +--RType: (NonNegativeInteger -> OrderlyDifferentialPolynomial(Fraction(Integer))) --E 3 --S 4 of 36 @@ -88802,7 +89011,7 @@ w.5 --R --R (4) w --R 5 ---R Type: OrderlyDifferentialPolynomial Fraction Integer +--R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 4 --S 5 of 36 @@ -88810,7 +89019,7 @@ w 0 --R --R --R (5) w ---R Type: OrderlyDifferentialPolynomial Fraction Integer +--R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 5 --S 6 of 36 @@ -88819,7 +89028,7 @@ w 0 --R --R (6) [z ,z ,z ,z ,z ] --R 1 2 3 4 5 ---R Type: List OrderlyDifferentialPolynomial Fraction Integer +--R Type: List(OrderlyDifferentialPolynomial(Fraction(Integer))) --E 6 --S 7 of 36 @@ -88829,7 +89038,7 @@ f:= w.4 - w.1 * w.1 * z.3 --R 2 --R (7) w - w z --R 4 1 3 ---R Type: OrderlyDifferentialPolynomial Fraction Integer +--R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 7 --S 8 of 36 @@ -88839,7 +89048,7 @@ g:=(z.1)**3 * (z.2)**2 - w.2 --R 3 2 --R (8) z z - w --R 1 2 2 ---R Type: OrderlyDifferentialPolynomial Fraction Integer +--R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 8 --S 9 of 36 @@ -88849,7 +89058,7 @@ D(f) --R 2 --R (9) w - w z - 2w w z --R 5 1 4 1 2 3 ---R Type: OrderlyDifferentialPolynomial Fraction Integer +--R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 9 --S 10 of 36 @@ -88864,7 +89073,7 @@ D(f,4) --R 2 --R (- 8w w - 24w w )z - 8w z w - 6w z --R 1 4 2 3 4 2 3 4 3 3 ---R Type: OrderlyDifferentialPolynomial Fraction Integer +--R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 10 --S 11 of 36 @@ -88872,7 +89081,7 @@ df:=makeVariable(f)$dpol --R --R --R (11) theMap(DPOLCAT-;makeVariable;AM;17!0,0) ---R Type: (NonNegativeInteger -> OrderlyDifferentialPolynomial Fraction Integer) +--RType: (NonNegativeInteger -> OrderlyDifferentialPolynomial(Fraction(Integer))) --E 11 --S 12 of 36 @@ -88887,7 +89096,7 @@ df.4 --R 2 --R (- 8w w - 24w w )z - 8w z w - 6w z --R 1 4 2 3 4 2 3 4 3 3 ---R Type: OrderlyDifferentialPolynomial Fraction Integer +--R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 12 --S 13 of 36 @@ -88911,7 +89120,7 @@ differentialVariables(g) --R --R --R (15) [z,w] ---R Type: List Symbol +--R Type: List(Symbol) --E 15 --S 16 of 36 @@ -88921,7 +89130,7 @@ degree(g) --R 2 3 --R (16) z z --R 2 1 ---R Type: IndexedExponents OrderlyDifferentialVariable Symbol +--R Type: IndexedExponents(OrderlyDifferentialVariable(Symbol)) --E 16 --S 17 of 36 @@ -88937,7 +89146,7 @@ weights(g) --R --R --R (18) [7,2] ---R Type: List NonNegativeInteger +--R Type: List(NonNegativeInteger) --E 18 --S 19 of 36 @@ -88945,7 +89154,7 @@ weights(g,'w) --R --R --R (19) [2] ---R Type: List NonNegativeInteger +--R Type: List(NonNegativeInteger) --E 19 --S 20 of 36 @@ -88971,7 +89180,7 @@ eval(g,['w::Symbol],[f]) --R 2 2 3 2 --R (22) - w + w z + 4w w z + (2w w + 2w )z + z z --R 6 1 5 1 2 4 1 3 2 3 1 2 ---R Type: OrderlyDifferentialPolynomial Fraction Integer +--R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 22 --S 23 of 36 @@ -88981,7 +89190,7 @@ eval(g,variables(w.0),[f]) --R 3 2 --R (23) z z - w --R 1 2 2 ---R Type: OrderlyDifferentialPolynomial Fraction Integer +--R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 23 --S 24 of 36 @@ -88991,7 +89200,7 @@ monomials(g) --R 3 2 --R (24) [z z ,- w ] --R 1 2 2 ---R Type: List OrderlyDifferentialPolynomial Fraction Integer +--R Type: List(OrderlyDifferentialPolynomial(Fraction(Integer))) --E 24 --S 25 of 36 @@ -89000,7 +89209,7 @@ variables(g) --R --R (25) [z ,w ,z ] --R 2 2 1 ---R Type: List OrderlyDifferentialVariable Symbol +--R Type: List(OrderlyDifferentialVariable(Symbol)) --E 25 --S 26 of 36 @@ -89008,7 +89217,7 @@ gcd(f,g) --R --R --R (26) 1 ---R Type: OrderlyDifferentialPolynomial Fraction Integer +--R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 26 --S 27 of 36 @@ -89018,7 +89227,7 @@ groebner([f,g]) --R 2 3 2 --R (27) [w - w z ,z z - w ] --R 4 1 3 1 2 2 ---R Type: List OrderlyDifferentialPolynomial Fraction Integer +--R Type: List(OrderlyDifferentialPolynomial(Fraction(Integer))) --E 27 --S 28 of 36 @@ -89027,7 +89236,7 @@ lg:=leader(g) --R --R (28) z --R 2 ---R Type: OrderlyDifferentialVariable Symbol +--R Type: OrderlyDifferentialVariable(Symbol) --E 28 --S 29 of 36 @@ -89037,7 +89246,7 @@ sg:=separant(g) --R 3 --R (29) 2z z --R 1 2 ---R Type: OrderlyDifferentialPolynomial Fraction Integer +--R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 29 --S 30 of 36 @@ -89047,7 +89256,7 @@ ig:=initial(g) --R 3 --R (30) z --R 1 ---R Type: OrderlyDifferentialPolynomial Fraction Integer +--R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 30 --S 31 of 36 @@ -89057,7 +89266,7 @@ g1 := D g --R 3 2 3 --R (31) 2z z z - w + 3z z --R 1 2 3 3 1 2 ---R Type: OrderlyDifferentialPolynomial Fraction Integer +--R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 31 --S 32 of 36 @@ -89066,7 +89275,7 @@ lg1:= leader g1 --R --R (32) z --R 3 ---R Type: OrderlyDifferentialVariable Symbol +--R Type: OrderlyDifferentialVariable(Symbol) --E 32 --S 33 of 36 @@ -89076,7 +89285,7 @@ pdf:=D(f, lg1) --R 2 --R (33) - w --R 1 ---R Type: OrderlyDifferentialPolynomial Fraction Integer +--R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 33 --S 34 of 36 @@ -89086,7 +89295,7 @@ prf:=sg * f- pdf * g1 --R 3 2 2 2 3 --R (34) 2z z w - w w + 3w z z --R 1 2 4 1 3 1 1 2 ---R Type: OrderlyDifferentialPolynomial Fraction Integer +--R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 34 --S 35 of 36 @@ -89096,7 +89305,7 @@ lcf:=leadingCoefficient univariate(prf, lg) --R 2 2 --R (35) 3w z --R 1 1 ---R Type: OrderlyDifferentialPolynomial Fraction Integer +--R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 35 --S 36 of 36 @@ -89106,7 +89315,7 @@ ig * prf - lcf * g * lg --R 6 2 3 2 2 --R (36) 2z z w - w z w + 3w z w z --R 1 2 4 1 1 3 1 1 2 2 ---R Type: OrderlyDifferentialPolynomial Fraction Integer +--R Type: OrderlyDifferentialPolynomial(Fraction(Integer)) --E 36 )spool )lisp (bye) @@ -89575,7 +89784,8 @@ OrderlyDifferentialPolynomial(R): --S 1 of 1 )show OrderlyDifferentialVariable ---R OrderlyDifferentialVariable S: OrderedSet is a domain constructor +--R +--R OrderlyDifferentialVariable(S: OrderedSet) is a domain constructor --R Abbreviation for OrderlyDifferentialVariable is ODVAR --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ODVAR @@ -89693,7 +89903,8 @@ OrderlyDifferentialVariable(S:OrderedSet):DifferentialVariableCategory(S) --S 1 of 1 )show OrdinaryDifferentialRing ---R OrdinaryDifferentialRing(Kernels: SetCategory,R: PartialDifferentialRing Kernels,var: Kernels) is a domain constructor +--R +--R OrdinaryDifferentialRing(Kernels: SetCategory,R: PartialDifferentialRing(Kernels),var: Kernels) is a domain constructor --R Abbreviation for OrdinaryDifferentialRing is ODR --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for ODR @@ -89713,8 +89924,8 @@ OrderlyDifferentialVariable(S:OrderedSet):DifferentialVariableCategory(S) --R one? : % -> Boolean recip : % -> Union(%,"failed") --R sample : () -> % zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean ---R ?*? : (%,Fraction Integer) -> % if R has FIELD ---R ?*? : (Fraction Integer,%) -> % if R has FIELD +--R ?*? : (%,Fraction(Integer)) -> % if R has FIELD +--R ?*? : (Fraction(Integer),%) -> % if R has FIELD --R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,Integer) -> % if R has FIELD --R ?**? : (%,NonNegativeInteger) -> % @@ -89724,27 +89935,27 @@ OrderlyDifferentialVariable(S:OrderedSet):DifferentialVariableCategory(S) --R associates? : (%,%) -> Boolean if R has FIELD --R characteristic : () -> NonNegativeInteger --R coerce : % -> % if R has FIELD ---R coerce : Fraction Integer -> % if R has FIELD +--R coerce : Fraction(Integer) -> % if R has FIELD --R differentiate : (%,NonNegativeInteger) -> % --R divide : (%,%) -> Record(quotient: %,remainder: %) if R has FIELD --R euclideanSize : % -> NonNegativeInteger if R has FIELD ---R expressIdealMember : (List %,%) -> Union(List %,"failed") if R has FIELD +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") if R has FIELD --R exquo : (%,%) -> Union(%,"failed") if R has FIELD --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has FIELD --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if R has FIELD ---R factor : % -> Factored % if R has FIELD +--R factor : % -> Factored(%) if R has FIELD --R gcd : (%,%) -> % if R has FIELD ---R gcd : List % -> % if R has FIELD ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has FIELD +--R gcd : List(%) -> % if R has FIELD +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has FIELD --R lcm : (%,%) -> % if R has FIELD ---R lcm : List % -> % if R has FIELD ---R multiEuclidean : (List %,%) -> Union(List %,"failed") if R has FIELD +--R lcm : List(%) -> % if R has FIELD +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") if R has FIELD --R prime? : % -> Boolean if R has FIELD ---R principalIdeal : List % -> Record(coef: List %,generator: %) if R has FIELD +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) if R has FIELD --R ?quo? : (%,%) -> % if R has FIELD --R ?rem? : (%,%) -> % if R has FIELD --R sizeLess? : (%,%) -> Boolean if R has FIELD ---R squareFree : % -> Factored % if R has FIELD +--R squareFree : % -> Factored(%) if R has FIELD --R squareFreePart : % -> % if R has FIELD --R subtractIfCan : (%,%) -> Union(%,"failed") --R unit? : % -> Boolean if R has FIELD @@ -89879,7 +90090,8 @@ OrdinaryDifferentialRing(Kernels,R,var): DRcategory == DRcapsule where --S 1 of 1 )show OrdinaryWeightedPolynomials ---R OrdinaryWeightedPolynomials(R: Ring,vl: List Symbol,wl: List NonNegativeInteger,wtlevel: NonNegativeInteger) is a domain constructor +--R +--R OrdinaryWeightedPolynomials(R: Ring,vl: List(Symbol),wl: List(NonNegativeInteger),wtlevel: NonNegativeInteger) is a domain constructor --R Abbreviation for OrdinaryWeightedPolynomials is OWP --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for OWP @@ -89890,8 +90102,8 @@ OrdinaryDifferentialRing(Kernels,R,var): DRcategory == DRcapsule where --R ?+? : (%,%) -> % ?-? : (%,%) -> % --R -? : % -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % ---R ?^? : (%,PositiveInteger) -> % coerce : Polynomial R -> % ---R coerce : % -> Polynomial R coerce : Integer -> % +--R ?^? : (%,PositiveInteger) -> % coerce : Polynomial(R) -> % +--R coerce : % -> Polynomial(R) coerce : Integer -> % --R coerce : % -> OutputForm hash : % -> SingleInteger --R latex : % -> String one? : % -> Boolean --R recip : % -> Union(%,"failed") sample : () -> % @@ -90115,6 +90327,7 @@ OrdSetInts: Export == Implement where --S 1 of 1 )show OutputForm +--R --R OutputForm is a domain constructor --R Abbreviation for OutputForm is OUTFORM --R This constructor is not exposed in this frame. @@ -90130,30 +90343,30 @@ OrdSetInts: Export == Implement where --R ?SEGMENT : % -> % ?..? : (%,%) -> % --R ?^=? : (%,%) -> % ?and? : (%,%) -> % --R assign : (%,%) -> % binomial : (%,%) -> % ---R blankSeparate : List % -> % box : % -> % ---R brace : List % -> % brace : % -> % ---R bracket : List % -> % bracket : % -> % +--R blankSeparate : List(%) -> % box : % -> % +--R brace : List(%) -> % brace : % -> % +--R bracket : List(%) -> % bracket : % -> % --R center : % -> % center : (%,Integer) -> % ---R coerce : % -> OutputForm commaSeparate : List % -> % +--R coerce : % -> OutputForm commaSeparate : List(%) -> % --R ?div? : (%,%) -> % dot : % -> % ---R ?.? : (%,List %) -> % empty : () -> % +--R ?.? : (%,List(%)) -> % empty : () -> % --R exquo : (%,%) -> % hash : % -> SingleInteger ---R hconcat : List % -> % hconcat : (%,%) -> % +--R hconcat : List(%) -> % hconcat : (%,%) -> % --R height : () -> Integer height : % -> Integer --R hspace : Integer -> % infix : (%,%,%) -> % ---R infix : (%,List %) -> % infix? : % -> Boolean +--R infix : (%,List(%)) -> % infix? : % -> Boolean --R int : (%,%,%) -> % int : (%,%) -> % --R int : % -> % label : (%,%) -> % --R latex : % -> String left : % -> % ---R left : (%,Integer) -> % matrix : List List % -> % +--R left : (%,Integer) -> % matrix : List(List(%)) -> % --R message : String -> % messagePrint : String -> Void --R not? : % -> % ?or? : (%,%) -> % --R outputForm : DoubleFloat -> % outputForm : String -> % --R outputForm : Symbol -> % outputForm : Integer -> % --R over : (%,%) -> % overbar : % -> % ---R overlabel : (%,%) -> % paren : List % -> % ---R paren : % -> % pile : List % -> % ---R postfix : (%,%) -> % prefix : (%,List %) -> % +--R overlabel : (%,%) -> % paren : List(%) -> % +--R paren : % -> % pile : List(%) -> % +--R postfix : (%,%) -> % prefix : (%,List(%)) -> % --R presub : (%,%) -> % presuper : (%,%) -> % --R prime : % -> % print : % -> Void --R prod : (%,%,%) -> % prod : (%,%) -> % @@ -90162,13 +90375,13 @@ OrdSetInts: Export == Implement where --R ?rem? : (%,%) -> % right : % -> % --R right : (%,Integer) -> % root : (%,%) -> % --R root : % -> % rspace : (Integer,Integer) -> % ---R scripts : (%,List %) -> % semicolonSeparate : List % -> % +--R scripts : (%,List(%)) -> % semicolonSeparate : List(%) -> % --R slash : (%,%) -> % string : % -> % --R sub : (%,%) -> % subHeight : % -> Integer --R sum : (%,%,%) -> % sum : (%,%) -> % --R sum : % -> % super : (%,%) -> % ---R superHeight : % -> Integer supersub : (%,List %) -> % ---R vconcat : List % -> % vconcat : (%,%) -> % +--R superHeight : % -> Integer supersub : (%,List(%)) -> % +--R vconcat : List(%) -> % vconcat : (%,%) -> % --R vspace : Integer -> % width : () -> Integer --R width : % -> Integer zag : (%,%) -> % --R ?~=? : (%,%) -> Boolean @@ -90754,7 +90967,8 @@ OutputForm(): SetCategory with --S 1 of 1 )show PAdicInteger ---R PAdicInteger p: Integer is a domain constructor +--R +--R PAdicInteger(p: Integer) is a domain constructor --R Abbreviation for PAdicInteger is PADIC --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for PADIC @@ -90768,10 +90982,10 @@ OutputForm(): SetCategory with --R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean --R coerce : % -> % coerce : Integer -> % --R coerce : % -> OutputForm complete : % -> % ---R digits : % -> Stream Integer extend : (%,Integer) -> % ---R gcd : List % -> % gcd : (%,%) -> % +--R digits : % -> Stream(Integer) extend : (%,Integer) -> % +--R gcd : List(%) -> % gcd : (%,%) -> % --R hash : % -> SingleInteger latex : % -> String ---R lcm : List % -> % lcm : (%,%) -> % +--R lcm : List(%) -> % lcm : (%,%) -> % --R moduloP : % -> Integer modulus : () -> Integer --R one? : % -> Boolean order : % -> NonNegativeInteger --R ?quo? : (%,%) -> % quotientByP : % -> % @@ -90787,14 +91001,14 @@ OutputForm(): SetCategory with --R characteristic : () -> NonNegativeInteger --R divide : (%,%) -> Record(quotient: %,remainder: %) --R euclideanSize : % -> NonNegativeInteger ---R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") --R exquo : (%,%) -> Union(%,"failed") --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % ---R multiEuclidean : (List %,%) -> Union(List %,"failed") ---R principalIdeal : List % -> Record(coef: List %,generator: %) ---R root : (SparseUnivariatePolynomial Integer,Integer) -> % +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) +--R root : (SparseUnivariatePolynomial(Integer),Integer) -> % --R subtractIfCan : (%,%) -> Union(%,"failed") --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) --R @@ -90912,14 +91126,15 @@ PAdicInteger(p:Integer) == InnerPAdicInteger(p,true$Boolean) --S 1 of 1 )show PAdicRational ---R PAdicRational p: Integer is a domain constructor +--R +--R PAdicRational(p: Integer) is a domain constructor --R Abbreviation for PAdicRational is PADICRAT --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for PADICRAT --R --R------------------------------- Operations -------------------------------- ---R ?*? : (%,PAdicInteger p) -> % ?*? : (PAdicInteger p,%) -> % ---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (%,PAdicInteger(p)) -> % ?*? : (PAdicInteger(p),%) -> % +--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % --R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % @@ -90927,107 +91142,107 @@ PAdicInteger(p:Integer) == InnerPAdicInteger(p,true$Boolean) --R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean --R 1 : () -> % 0 : () -> % --R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % ---R associates? : (%,%) -> Boolean coerce : PAdicInteger p -> % ---R coerce : Fraction Integer -> % coerce : % -> % +--R associates? : (%,%) -> Boolean coerce : PAdicInteger(p) -> % +--R coerce : Fraction(Integer) -> % coerce : % -> % --R coerce : Integer -> % coerce : % -> OutputForm ---R denom : % -> PAdicInteger p denominator : % -> % ---R factor : % -> Factored % gcd : List % -> % +--R denom : % -> PAdicInteger(p) denominator : % -> % +--R factor : % -> Factored(%) gcd : List(%) -> % --R gcd : (%,%) -> % hash : % -> SingleInteger --R inv : % -> % latex : % -> String ---R lcm : List % -> % lcm : (%,%) -> % ---R numer : % -> PAdicInteger p numerator : % -> % +--R lcm : List(%) -> % lcm : (%,%) -> % +--R numer : % -> PAdicInteger(p) numerator : % -> % --R one? : % -> Boolean prime? : % -> Boolean --R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") --R ?rem? : (%,%) -> % removeZeroes : (Integer,%) -> % ---R removeZeroes : % -> % retract : % -> PAdicInteger p +--R removeZeroes : % -> % retract : % -> PAdicInteger(p) --R sample : () -> % sizeLess? : (%,%) -> Boolean ---R squareFree : % -> Factored % squareFreePart : % -> % +--R squareFree : % -> Factored(%) squareFreePart : % -> % --R unit? : % -> Boolean unitCanonical : % -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,NonNegativeInteger) -> % ---R ?/? : (PAdicInteger p,PAdicInteger p) -> % ---R ? Boolean if PAdicInteger p has ORDSET ---R ?<=? : (%,%) -> Boolean if PAdicInteger p has ORDSET ---R ?>? : (%,%) -> Boolean if PAdicInteger p has ORDSET ---R ?>=? : (%,%) -> Boolean if PAdicInteger p has ORDSET ---R D : (%,(PAdicInteger p -> PAdicInteger p)) -> % ---R D : (%,(PAdicInteger p -> PAdicInteger p),NonNegativeInteger) -> % ---R D : (%,List Symbol,List NonNegativeInteger) -> % if PAdicInteger p has PDRING SYMBOL ---R D : (%,Symbol,NonNegativeInteger) -> % if PAdicInteger p has PDRING SYMBOL ---R D : (%,List Symbol) -> % if PAdicInteger p has PDRING SYMBOL ---R D : (%,Symbol) -> % if PAdicInteger p has PDRING SYMBOL ---R D : (%,NonNegativeInteger) -> % if PAdicInteger p has DIFRING ---R D : % -> % if PAdicInteger p has DIFRING +--R ?/? : (PAdicInteger(p),PAdicInteger(p)) -> % +--R ? Boolean if PAdicInteger(p) has ORDSET +--R ?<=? : (%,%) -> Boolean if PAdicInteger(p) has ORDSET +--R ?>? : (%,%) -> Boolean if PAdicInteger(p) has ORDSET +--R ?>=? : (%,%) -> Boolean if PAdicInteger(p) has ORDSET +--R D : (%,(PAdicInteger(p) -> PAdicInteger(p))) -> % +--R D : (%,(PAdicInteger(p) -> PAdicInteger(p)),NonNegativeInteger) -> % +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if PAdicInteger(p) has PDRING(SYMBOL) +--R D : (%,Symbol,NonNegativeInteger) -> % if PAdicInteger(p) has PDRING(SYMBOL) +--R D : (%,List(Symbol)) -> % if PAdicInteger(p) has PDRING(SYMBOL) +--R D : (%,Symbol) -> % if PAdicInteger(p) has PDRING(SYMBOL) +--R D : (%,NonNegativeInteger) -> % if PAdicInteger(p) has DIFRING +--R D : % -> % if PAdicInteger(p) has DIFRING --R ?^? : (%,NonNegativeInteger) -> % ---R abs : % -> % if PAdicInteger p has OINTDOM ---R approximate : (%,Integer) -> Fraction Integer ---R ceiling : % -> PAdicInteger p if PAdicInteger p has INS +--R abs : % -> % if PAdicInteger(p) has OINTDOM +--R approximate : (%,Integer) -> Fraction(Integer) +--R ceiling : % -> PAdicInteger(p) if PAdicInteger(p) has INS --R characteristic : () -> NonNegativeInteger ---R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and PAdicInteger p has PFECAT or PAdicInteger p has CHARNZ ---R coerce : Symbol -> % if PAdicInteger p has RETRACT SYMBOL ---R conditionP : Matrix % -> Union(Vector %,"failed") if $ has CHARNZ and PAdicInteger p has PFECAT ---R continuedFraction : % -> ContinuedFraction Fraction Integer ---R convert : % -> DoubleFloat if PAdicInteger p has REAL ---R convert : % -> Float if PAdicInteger p has REAL ---R convert : % -> InputForm if PAdicInteger p has KONVERT INFORM ---R convert : % -> Pattern Float if PAdicInteger p has KONVERT PATTERN FLOAT ---R convert : % -> Pattern Integer if PAdicInteger p has KONVERT PATTERN INT ---R differentiate : (%,(PAdicInteger p -> PAdicInteger p)) -> % ---R differentiate : (%,(PAdicInteger p -> PAdicInteger p),NonNegativeInteger) -> % ---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if PAdicInteger p has PDRING SYMBOL ---R differentiate : (%,Symbol,NonNegativeInteger) -> % if PAdicInteger p has PDRING SYMBOL ---R differentiate : (%,List Symbol) -> % if PAdicInteger p has PDRING SYMBOL ---R differentiate : (%,Symbol) -> % if PAdicInteger p has PDRING SYMBOL ---R differentiate : (%,NonNegativeInteger) -> % if PAdicInteger p has DIFRING ---R differentiate : % -> % if PAdicInteger p has DIFRING +--R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and PAdicInteger(p) has PFECAT or PAdicInteger(p) has CHARNZ +--R coerce : Symbol -> % if PAdicInteger(p) has RETRACT(SYMBOL) +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and PAdicInteger(p) has PFECAT +--R continuedFraction : % -> ContinuedFraction(Fraction(Integer)) +--R convert : % -> DoubleFloat if PAdicInteger(p) has REAL +--R convert : % -> Float if PAdicInteger(p) has REAL +--R convert : % -> InputForm if PAdicInteger(p) has KONVERT(INFORM) +--R convert : % -> Pattern(Float) if PAdicInteger(p) has KONVERT(PATTERN(FLOAT)) +--R convert : % -> Pattern(Integer) if PAdicInteger(p) has KONVERT(PATTERN(INT)) +--R differentiate : (%,(PAdicInteger(p) -> PAdicInteger(p))) -> % +--R differentiate : (%,(PAdicInteger(p) -> PAdicInteger(p)),NonNegativeInteger) -> % +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if PAdicInteger(p) has PDRING(SYMBOL) +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if PAdicInteger(p) has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol)) -> % if PAdicInteger(p) has PDRING(SYMBOL) +--R differentiate : (%,Symbol) -> % if PAdicInteger(p) has PDRING(SYMBOL) +--R differentiate : (%,NonNegativeInteger) -> % if PAdicInteger(p) has DIFRING +--R differentiate : % -> % if PAdicInteger(p) has DIFRING --R divide : (%,%) -> Record(quotient: %,remainder: %) ---R ?.? : (%,PAdicInteger p) -> % if PAdicInteger p has ELTAB(PADIC p,PADIC p) +--R ?.? : (%,PAdicInteger(p)) -> % if PAdicInteger(p) has ELTAB(PADIC(p),PADIC(p)) --R euclideanSize : % -> NonNegativeInteger ---R eval : (%,Symbol,PAdicInteger p) -> % if PAdicInteger p has IEVALAB(SYMBOL,PADIC p) ---R eval : (%,List Symbol,List PAdicInteger p) -> % if PAdicInteger p has IEVALAB(SYMBOL,PADIC p) ---R eval : (%,List Equation PAdicInteger p) -> % if PAdicInteger p has EVALAB PADIC p ---R eval : (%,Equation PAdicInteger p) -> % if PAdicInteger p has EVALAB PADIC p ---R eval : (%,PAdicInteger p,PAdicInteger p) -> % if PAdicInteger p has EVALAB PADIC p ---R eval : (%,List PAdicInteger p,List PAdicInteger p) -> % if PAdicInteger p has EVALAB PADIC p ---R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R eval : (%,Symbol,PAdicInteger(p)) -> % if PAdicInteger(p) has IEVALAB(SYMBOL,PADIC(p)) +--R eval : (%,List(Symbol),List(PAdicInteger(p))) -> % if PAdicInteger(p) has IEVALAB(SYMBOL,PADIC(p)) +--R eval : (%,List(Equation(PAdicInteger(p)))) -> % if PAdicInteger(p) has EVALAB(PADIC(p)) +--R eval : (%,Equation(PAdicInteger(p))) -> % if PAdicInteger(p) has EVALAB(PADIC(p)) +--R eval : (%,PAdicInteger(p),PAdicInteger(p)) -> % if PAdicInteger(p) has EVALAB(PADIC(p)) +--R eval : (%,List(PAdicInteger(p)),List(PAdicInteger(p))) -> % if PAdicInteger(p) has EVALAB(PADIC(p)) +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") --R exquo : (%,%) -> Union(%,"failed") --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) ---R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if PAdicInteger p has PFECAT ---R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if PAdicInteger p has PFECAT ---R floor : % -> PAdicInteger p if PAdicInteger p has INS ---R fractionPart : % -> % if PAdicInteger p has EUCDOM ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % ---R init : () -> % if PAdicInteger p has STEP ---R map : ((PAdicInteger p -> PAdicInteger p),%) -> % ---R max : (%,%) -> % if PAdicInteger p has ORDSET ---R min : (%,%) -> % if PAdicInteger p has ORDSET ---R multiEuclidean : (List %,%) -> Union(List %,"failed") ---R negative? : % -> Boolean if PAdicInteger p has OINTDOM ---R nextItem : % -> Union(%,"failed") if PAdicInteger p has STEP ---R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if PAdicInteger p has PATMAB FLOAT ---R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if PAdicInteger p has PATMAB INT ---R positive? : % -> Boolean if PAdicInteger p has OINTDOM ---R principalIdeal : List % -> Record(coef: List %,generator: %) ---R random : () -> % if PAdicInteger p has INS ---R reducedSystem : Matrix % -> Matrix PAdicInteger p ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix PAdicInteger p,vec: Vector PAdicInteger p) ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if PAdicInteger p has LINEXP INT ---R reducedSystem : Matrix % -> Matrix Integer if PAdicInteger p has LINEXP INT ---R retract : % -> Integer if PAdicInteger p has RETRACT INT ---R retract : % -> Fraction Integer if PAdicInteger p has RETRACT INT ---R retract : % -> Symbol if PAdicInteger p has RETRACT SYMBOL ---R retractIfCan : % -> Union(Integer,"failed") if PAdicInteger p has RETRACT INT ---R retractIfCan : % -> Union(Fraction Integer,"failed") if PAdicInteger p has RETRACT INT ---R retractIfCan : % -> Union(Symbol,"failed") if PAdicInteger p has RETRACT SYMBOL ---R retractIfCan : % -> Union(PAdicInteger p,"failed") ---R sign : % -> Integer if PAdicInteger p has OINTDOM ---R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if PAdicInteger p has PFECAT ---R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if PAdicInteger p has PFECAT +--R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if PAdicInteger(p) has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if PAdicInteger(p) has PFECAT +--R floor : % -> PAdicInteger(p) if PAdicInteger(p) has INS +--R fractionPart : % -> % if PAdicInteger(p) has EUCDOM +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) +--R init : () -> % if PAdicInteger(p) has STEP +--R map : ((PAdicInteger(p) -> PAdicInteger(p)),%) -> % +--R max : (%,%) -> % if PAdicInteger(p) has ORDSET +--R min : (%,%) -> % if PAdicInteger(p) has ORDSET +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") +--R negative? : % -> Boolean if PAdicInteger(p) has OINTDOM +--R nextItem : % -> Union(%,"failed") if PAdicInteger(p) has STEP +--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if PAdicInteger(p) has PATMAB(FLOAT) +--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if PAdicInteger(p) has PATMAB(INT) +--R positive? : % -> Boolean if PAdicInteger(p) has OINTDOM +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) +--R random : () -> % if PAdicInteger(p) has INS +--R reducedSystem : Matrix(%) -> Matrix(PAdicInteger(p)) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(PAdicInteger(p)),vec: Vector(PAdicInteger(p))) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if PAdicInteger(p) has LINEXP(INT) +--R reducedSystem : Matrix(%) -> Matrix(Integer) if PAdicInteger(p) has LINEXP(INT) +--R retract : % -> Integer if PAdicInteger(p) has RETRACT(INT) +--R retract : % -> Fraction(Integer) if PAdicInteger(p) has RETRACT(INT) +--R retract : % -> Symbol if PAdicInteger(p) has RETRACT(SYMBOL) +--R retractIfCan : % -> Union(Integer,"failed") if PAdicInteger(p) has RETRACT(INT) +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if PAdicInteger(p) has RETRACT(INT) +--R retractIfCan : % -> Union(Symbol,"failed") if PAdicInteger(p) has RETRACT(SYMBOL) +--R retractIfCan : % -> Union(PAdicInteger(p),"failed") +--R sign : % -> Integer if PAdicInteger(p) has OINTDOM +--R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if PAdicInteger(p) has PFECAT +--R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if PAdicInteger(p) has PFECAT --R subtractIfCan : (%,%) -> Union(%,"failed") --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) ---R wholePart : % -> PAdicInteger p if PAdicInteger p has EUCDOM +--R wholePart : % -> PAdicInteger(p) if PAdicInteger(p) has EUCDOM --R --E 1 @@ -91178,14 +91393,15 @@ PAdicRational(p:Integer) == PAdicRationalConstructor(p,PAdicInteger p) --S 1 of 1 )show PAdicRationalConstructor ---R PAdicRationalConstructor(p: Integer,PADIC: PAdicIntegerCategory p) is a domain constructor +--R +--R PAdicRationalConstructor(p: Integer,PADIC: PAdicIntegerCategory(p)) is a domain constructor --R Abbreviation for PAdicRationalConstructor is PADICRC --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for PADICRC --R --R------------------------------- Operations -------------------------------- --R ?*? : (%,PADIC) -> % ?*? : (PADIC,%) -> % ---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % --R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % @@ -91195,20 +91411,20 @@ PAdicRational(p:Integer) == PAdicRationalConstructor(p,PAdicInteger p) --R 1 : () -> % 0 : () -> % --R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % --R associates? : (%,%) -> Boolean coerce : PADIC -> % ---R coerce : Fraction Integer -> % coerce : % -> % +--R coerce : Fraction(Integer) -> % coerce : % -> % --R coerce : Integer -> % coerce : % -> OutputForm --R denom : % -> PADIC denominator : % -> % ---R factor : % -> Factored % gcd : List % -> % +--R factor : % -> Factored(%) gcd : List(%) -> % --R gcd : (%,%) -> % hash : % -> SingleInteger --R inv : % -> % latex : % -> String ---R lcm : List % -> % lcm : (%,%) -> % +--R lcm : List(%) -> % lcm : (%,%) -> % --R map : ((PADIC -> PADIC),%) -> % numer : % -> PADIC --R numerator : % -> % one? : % -> Boolean --R prime? : % -> Boolean ?quo? : (%,%) -> % --R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % --R removeZeroes : (Integer,%) -> % removeZeroes : % -> % --R retract : % -> PADIC sample : () -> % ---R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored % +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored(%) --R squareFreePart : % -> % unit? : % -> Boolean --R unitCanonical : % -> % zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean @@ -91219,77 +91435,77 @@ PAdicRational(p:Integer) == PAdicRationalConstructor(p,PAdicInteger p) --R ?>? : (%,%) -> Boolean if PADIC has ORDSET --R ?>=? : (%,%) -> Boolean if PADIC has ORDSET --R D : (%,(PADIC -> PADIC),NonNegativeInteger) -> % ---R D : (%,List Symbol,List NonNegativeInteger) -> % if PADIC has PDRING SYMBOL ---R D : (%,Symbol,NonNegativeInteger) -> % if PADIC has PDRING SYMBOL ---R D : (%,List Symbol) -> % if PADIC has PDRING SYMBOL ---R D : (%,Symbol) -> % if PADIC has PDRING SYMBOL +--R D : (%,List(Symbol),List(NonNegativeInteger)) -> % if PADIC has PDRING(SYMBOL) +--R D : (%,Symbol,NonNegativeInteger) -> % if PADIC has PDRING(SYMBOL) +--R D : (%,List(Symbol)) -> % if PADIC has PDRING(SYMBOL) +--R D : (%,Symbol) -> % if PADIC has PDRING(SYMBOL) --R D : (%,NonNegativeInteger) -> % if PADIC has DIFRING --R D : % -> % if PADIC has DIFRING --R ?^? : (%,NonNegativeInteger) -> % --R abs : % -> % if PADIC has OINTDOM ---R approximate : (%,Integer) -> Fraction Integer +--R approximate : (%,Integer) -> Fraction(Integer) --R ceiling : % -> PADIC if PADIC has INS --R characteristic : () -> NonNegativeInteger --R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and PADIC has PFECAT or PADIC has CHARNZ ---R coerce : Symbol -> % if PADIC has RETRACT SYMBOL ---R conditionP : Matrix % -> Union(Vector %,"failed") if $ has CHARNZ and PADIC has PFECAT ---R continuedFraction : % -> ContinuedFraction Fraction Integer +--R coerce : Symbol -> % if PADIC has RETRACT(SYMBOL) +--R conditionP : Matrix(%) -> Union(Vector(%),"failed") if $ has CHARNZ and PADIC has PFECAT +--R continuedFraction : % -> ContinuedFraction(Fraction(Integer)) --R convert : % -> DoubleFloat if PADIC has REAL --R convert : % -> Float if PADIC has REAL ---R convert : % -> InputForm if PADIC has KONVERT INFORM ---R convert : % -> Pattern Float if PADIC has KONVERT PATTERN FLOAT ---R convert : % -> Pattern Integer if PADIC has KONVERT PATTERN INT +--R convert : % -> InputForm if PADIC has KONVERT(INFORM) +--R convert : % -> Pattern(Float) if PADIC has KONVERT(PATTERN(FLOAT)) +--R convert : % -> Pattern(Integer) if PADIC has KONVERT(PATTERN(INT)) --R differentiate : (%,(PADIC -> PADIC)) -> % --R differentiate : (%,(PADIC -> PADIC),NonNegativeInteger) -> % ---R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if PADIC has PDRING SYMBOL ---R differentiate : (%,Symbol,NonNegativeInteger) -> % if PADIC has PDRING SYMBOL ---R differentiate : (%,List Symbol) -> % if PADIC has PDRING SYMBOL ---R differentiate : (%,Symbol) -> % if PADIC has PDRING SYMBOL +--R differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if PADIC has PDRING(SYMBOL) +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if PADIC has PDRING(SYMBOL) +--R differentiate : (%,List(Symbol)) -> % if PADIC has PDRING(SYMBOL) +--R differentiate : (%,Symbol) -> % if PADIC has PDRING(SYMBOL) --R differentiate : (%,NonNegativeInteger) -> % if PADIC has DIFRING --R differentiate : % -> % if PADIC has DIFRING --R divide : (%,%) -> Record(quotient: %,remainder: %) --R ?.? : (%,PADIC) -> % if PADIC has ELTAB(PADIC,PADIC) --R euclideanSize : % -> NonNegativeInteger --R eval : (%,Symbol,PADIC) -> % if PADIC has IEVALAB(SYMBOL,PADIC) ---R eval : (%,List Symbol,List PADIC) -> % if PADIC has IEVALAB(SYMBOL,PADIC) ---R eval : (%,List Equation PADIC) -> % if PADIC has EVALAB PADIC ---R eval : (%,Equation PADIC) -> % if PADIC has EVALAB PADIC ---R eval : (%,PADIC,PADIC) -> % if PADIC has EVALAB PADIC ---R eval : (%,List PADIC,List PADIC) -> % if PADIC has EVALAB PADIC ---R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R eval : (%,List(Symbol),List(PADIC)) -> % if PADIC has IEVALAB(SYMBOL,PADIC) +--R eval : (%,List(Equation(PADIC))) -> % if PADIC has EVALAB(PADIC) +--R eval : (%,Equation(PADIC)) -> % if PADIC has EVALAB(PADIC) +--R eval : (%,PADIC,PADIC) -> % if PADIC has EVALAB(PADIC) +--R eval : (%,List(PADIC),List(PADIC)) -> % if PADIC has EVALAB(PADIC) +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") --R exquo : (%,%) -> Union(%,"failed") --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) ---R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if PADIC has PFECAT ---R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if PADIC has PFECAT +--R factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if PADIC has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if PADIC has PFECAT --R floor : % -> PADIC if PADIC has INS --R fractionPart : % -> % if PADIC has EUCDOM ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) --R init : () -> % if PADIC has STEP --R max : (%,%) -> % if PADIC has ORDSET --R min : (%,%) -> % if PADIC has ORDSET ---R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") --R negative? : % -> Boolean if PADIC has OINTDOM --R nextItem : % -> Union(%,"failed") if PADIC has STEP ---R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if PADIC has PATMAB FLOAT ---R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if PADIC has PATMAB INT +--R patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if PADIC has PATMAB(FLOAT) +--R patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if PADIC has PATMAB(INT) --R positive? : % -> Boolean if PADIC has OINTDOM ---R principalIdeal : List % -> Record(coef: List %,generator: %) +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) --R random : () -> % if PADIC has INS ---R reducedSystem : Matrix % -> Matrix PADIC ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix PADIC,vec: Vector PADIC) ---R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if PADIC has LINEXP INT ---R reducedSystem : Matrix % -> Matrix Integer if PADIC has LINEXP INT ---R retract : % -> Integer if PADIC has RETRACT INT ---R retract : % -> Fraction Integer if PADIC has RETRACT INT ---R retract : % -> Symbol if PADIC has RETRACT SYMBOL ---R retractIfCan : % -> Union(Integer,"failed") if PADIC has RETRACT INT ---R retractIfCan : % -> Union(Fraction Integer,"failed") if PADIC has RETRACT INT ---R retractIfCan : % -> Union(Symbol,"failed") if PADIC has RETRACT SYMBOL +--R reducedSystem : Matrix(%) -> Matrix(PADIC) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(PADIC),vec: Vector(PADIC)) +--R reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if PADIC has LINEXP(INT) +--R reducedSystem : Matrix(%) -> Matrix(Integer) if PADIC has LINEXP(INT) +--R retract : % -> Integer if PADIC has RETRACT(INT) +--R retract : % -> Fraction(Integer) if PADIC has RETRACT(INT) +--R retract : % -> Symbol if PADIC has RETRACT(SYMBOL) +--R retractIfCan : % -> Union(Integer,"failed") if PADIC has RETRACT(INT) +--R retractIfCan : % -> Union(Fraction(Integer),"failed") if PADIC has RETRACT(INT) +--R retractIfCan : % -> Union(Symbol,"failed") if PADIC has RETRACT(SYMBOL) --R retractIfCan : % -> Union(PADIC,"failed") --R sign : % -> Integer if PADIC has OINTDOM ---R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if PADIC has PFECAT ---R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if PADIC has PFECAT +--R solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if PADIC has PFECAT +--R squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if PADIC has PFECAT --R subtractIfCan : (%,%) -> Union(%,"failed") --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) --R wholePart : % -> PADIC if PADIC has EUCDOM @@ -91734,7 +91950,8 @@ Palette(): Exports == Implementation where --S 1 of 1 )show ParametricPlaneCurve ---R ParametricPlaneCurve ComponentFunction: Type is a domain constructor +--R +--R ParametricPlaneCurve(ComponentFunction: Type) is a domain constructor --R Abbreviation for ParametricPlaneCurve is PARPCURV --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for PARPCURV @@ -91828,7 +92045,8 @@ ParametricPlaneCurve(ComponentFunction): Exports == Implementation where --S 1 of 1 )show ParametricSpaceCurve ---R ParametricSpaceCurve ComponentFunction: Type is a domain constructor +--R +--R ParametricSpaceCurve(ComponentFunction: Type) is a domain constructor --R Abbreviation for ParametricSpaceCurve is PARSCURV --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for PARSCURV @@ -91925,7 +92143,8 @@ ParametricSpaceCurve(ComponentFunction): Exports == Implementation where --S 1 of 1 )show ParametricSurface ---R ParametricSurface ComponentFunction: Type is a domain constructor +--R +--R ParametricSurface(ComponentFunction: Type) is a domain constructor --R Abbreviation for ParametricSurface is PARSURF --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for PARSURF @@ -92028,7 +92247,7 @@ partialFraction(1,factorial 10) --R (1) --- - -- - -- + - --R 8 4 2 7 --R 2 3 5 ---R Type: PartialFraction Integer +--R Type: PartialFraction(Integer) --E 1 --S 2 of 22 @@ -92039,7 +92258,7 @@ f := padicFraction(%) --R (2) - + -- + -- + -- + -- + -- - -- - -- - -- - - - -- + - --R 2 4 5 6 7 8 2 3 4 5 2 7 --R 2 2 2 2 2 3 3 3 5 ---R Type: PartialFraction Integer +--R Type: PartialFraction(Integer) --E 2 --S 3 of 22 @@ -92050,7 +92269,7 @@ compactFraction(f) --R (3) --- - -- - -- + - --R 8 4 2 7 --R 2 3 5 ---R Type: PartialFraction Integer +--R Type: PartialFraction(Integer) --E 3 --S 4 of 22 @@ -92069,7 +92288,7 @@ nthFractionalTerm(f,3) --R (5) -- --R 5 --R 2 ---R Type: PartialFraction Integer +--R Type: PartialFraction(Integer) --E 5 --S 6 of 22 @@ -92079,7 +92298,7 @@ partialFraction(1,- 13 + 14 * %i) --R 1 4 --R (6) - ------- + ------- --R 1 + 2%i 3 + 8%i ---R Type: PartialFraction Complex Integer +--R Type: PartialFraction(Complex(Integer)) --E 6 --S 7 of 22 @@ -92089,7 +92308,7 @@ partialFraction(1,- 13 + 14 * %i) --R %i --R (7) - --------- --R 14 + 13%i ---R Type: Fraction Complex Integer +--R Type: Fraction(Complex(Integer)) --E 7 --S 8 of 22 @@ -92098,7 +92317,7 @@ u : FR UP(x, FRAC INT) := reduce(*,[primeFactor(x+i,i) for i in 1..4]) --R --R 2 3 4 --R (8) (x + 1)(x + 2) (x + 3) (x + 4) ---R Type: Factored UnivariatePolynomial(x,Fraction Integer) +--R Type: Factored(UnivariatePolynomial(x,Fraction(Integer))) --E 8 --S 9 of 22 @@ -92112,7 +92331,7 @@ partialFraction(1,u) --R ----- + -------- + ------------------- + --------------------------------- --R x + 1 2 3 4 --R (x + 2) (x + 3) (x + 4) ---R Type: PartialFraction UnivariatePolynomial(x,Fraction Integer) +--R Type: PartialFraction(UnivariatePolynomial(x,Fraction(Integer))) --E 9 --S 10 of 22 @@ -92133,14 +92352,14 @@ padicFraction % --R -------- + -------- --R 3 4 --R (x + 4) (x + 4) ---R Type: PartialFraction UnivariatePolynomial(x,Fraction Integer) +--R Type: PartialFraction(UnivariatePolynomial(x,Fraction(Integer))) --E 10 --S 11 of 22 fraction:=Fraction(Polynomial(Integer)) --R --R ---R (11) Fraction Polynomial Integer +--R (11) Fraction(Polynomial(Integer)) --R Type: Domain --E 11 @@ -92148,7 +92367,7 @@ fraction:=Fraction(Polynomial(Integer)) up:=UnivariatePolynomial(y,fraction) --R --R ---R (12) UnivariatePolynomial(y,Fraction Polynomial Integer) +--R (12) UnivariatePolynomial(y,Fraction(Polynomial(Integer))) --R Type: Domain --E 12 @@ -92156,7 +92375,8 @@ up:=UnivariatePolynomial(y,fraction) pfup:=PartialFraction(up) --R --R ---R (13) PartialFraction UnivariatePolynomial(y,Fraction Polynomial Integer) +--R (13) +--R PartialFraction(UnivariatePolynomial(y,Fraction(Polynomial(Integer)))) --R Type: Domain --E 13 @@ -92167,7 +92387,7 @@ a:=x+1/(y+1) --R x y + x + 1 --R (14) ----------- --R y + 1 ---R Type: Fraction Polynomial Integer +--R Type: Fraction(Polynomial(Integer)) --E 14 --S 15 of 22 @@ -92177,7 +92397,7 @@ b:=partialFraction(a,y)$PartialFractionPackage(Integer) --R 1 --R (15) x + ----- --R y + 1 ---R Type: PartialFraction UnivariatePolynomial(y,Fraction Polynomial Integer) +--R Type: PartialFraction(UnivariatePolynomial(y,Fraction(Polynomial(Integer)))) --E 15 --S 16 of 22 @@ -92187,7 +92407,7 @@ c:=b::pfup --R 1 --R (16) x + ----- --R y + 1 ---R Type: PartialFraction UnivariatePolynomial(y,Fraction Polynomial Integer) +--R Type: PartialFraction(UnivariatePolynomial(y,Fraction(Polynomial(Integer)))) --E 16 --S 17 of 22 @@ -92195,7 +92415,7 @@ cw:=(wholePart c)::Expression(Integer) --R --R --R (17) x ---R Type: Expression Integer +--R Type: Expression(Integer) --E 17 --S 18 of 22 @@ -92213,7 +92433,7 @@ crList:=[nthFractionalTerm(c,i) for i in 1..m] --R 1 --R (19) [-----] --R y + 1 ---RType: List PartialFraction UnivariatePolynomial(y,Fraction Polynomial Integer) +--RType: List(PartialFraction(UnivariatePolynomial(y,Fraction(Polynomial(Integer))))) --E 19 --S 20 of 22 @@ -92223,7 +92443,7 @@ cc:=reduce(+,crList) --R 1 --R (20) ----- --R y + 1 ---R Type: PartialFraction UnivariatePolynomial(y,Fraction Polynomial Integer) +--R Type: PartialFraction(UnivariatePolynomial(y,Fraction(Polynomial(Integer)))) --E 20 --S 21 of 22 @@ -92233,7 +92453,7 @@ ccx:=cc::(Fraction(up))::(Expression(Integer)) --R 1 --R (21) ----- --R y + 1 ---R Type: Expression Integer +--R Type: Expression(Integer) --E 21 --S 22 of 22 @@ -92243,7 +92463,7 @@ sin(cw)*cos(ccx)+sin(ccx)*cos(cw) --R 1 1 --R (22) cos(-----)sin(x) + cos(x)sin(-----) --R y + 1 y + 1 ---R Type: Expression Integer +--R Type: Expression(Integer) --E 22 )spool @@ -92839,6 +93059,7 @@ PartialFraction(R: EuclideanDomain): Cat == Capsule where --S 1 of 1 )show Partition +--R --R Partition is a domain constructor --R Abbreviation for Partition is PRTITION --R This constructor is not exposed in this frame. @@ -92849,15 +93070,15 @@ PartialFraction(R: EuclideanDomain): Cat == Capsule where --R ? Boolean ?<=? : (%,%) -> Boolean --R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean --R ?>=? : (%,%) -> Boolean 0 : () -> % ---R coerce : % -> List Integer coerce : % -> OutputForm ---R conjugate : % -> % convert : % -> List Integer +--R coerce : % -> List(Integer) coerce : % -> OutputForm +--R conjugate : % -> % convert : % -> List(Integer) --R hash : % -> SingleInteger latex : % -> String --R max : (%,%) -> % min : (%,%) -> % ---R partition : List Integer -> % pdct : % -> Integer +--R partition : List(Integer) -> % pdct : % -> Integer --R sample : () -> % zero? : % -> Boolean --R ?~=? : (%,%) -> Boolean --R ?*? : (NonNegativeInteger,%) -> % ---R powers : List Integer -> List List Integer +--R powers : List(Integer) -> List(List(Integer)) --R subtractIfCan : (%,%) -> Union(%,"failed") --R --E 1 @@ -93056,7 +93277,8 @@ Partition: Exports == Implementation where --S 1 of 1 )show Pattern ---R Pattern R: SetCategory is a domain constructor +--R +--R Pattern(R: SetCategory) is a domain constructor --R Abbreviation for Pattern is PATTERN --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for PATTERN @@ -93068,34 +93290,34 @@ Partition: Exports == Implementation where --R 0 : () -> % addBadValue : (%,Any) -> % --R coerce : Symbol -> % coerce : R -> % --R coerce : % -> OutputForm constant? : % -> Boolean ---R convert : List % -> % copy : % -> % +--R convert : List(%) -> % copy : % -> % --R depth : % -> NonNegativeInteger generic? : % -> Boolean ---R getBadValues : % -> List Any hasPredicate? : % -> Boolean +--R getBadValues : % -> List(Any) hasPredicate? : % -> Boolean --R hasTopPredicate? : % -> Boolean hash : % -> SingleInteger --R inR? : % -> Boolean latex : % -> String --R multiple? : % -> Boolean optional? : % -> Boolean ---R predicates : % -> List Any quoted? : % -> Boolean +--R predicates : % -> List(Any) quoted? : % -> Boolean --R resetBadValues : % -> % retract : % -> Symbol --R retract : % -> R symbol? : % -> Boolean ---R variables : % -> List % ?~=? : (%,%) -> Boolean +--R variables : % -> List(%) ?~=? : (%,%) -> Boolean --R ?**? : (%,NonNegativeInteger) -> % ---R elt : (BasicOperator,List %) -> % +--R elt : (BasicOperator,List(%)) -> % --R isExpt : % -> Union(Record(val: %,exponent: NonNegativeInteger),"failed") ---R isList : % -> Union(List %,"failed") ---R isOp : % -> Union(Record(op: BasicOperator,arg: List %),"failed") ---R isOp : (%,BasicOperator) -> Union(List %,"failed") ---R isPlus : % -> Union(List %,"failed") +--R isList : % -> Union(List(%),"failed") +--R isOp : % -> Union(Record(op: BasicOperator,arg: List(%)),"failed") +--R isOp : (%,BasicOperator) -> Union(List(%),"failed") +--R isPlus : % -> Union(List(%),"failed") --R isPower : % -> Union(Record(val: %,exponent: %),"failed") --R isQuotient : % -> Union(Record(num: %,den: %),"failed") ---R isTimes : % -> Union(List %,"failed") ---R optpair : List % -> Union(List %,"failed") +--R isTimes : % -> Union(List(%),"failed") +--R optpair : List(%) -> Union(List(%),"failed") --R patternVariable : (Symbol,Boolean,Boolean,Boolean) -> % --R retractIfCan : % -> Union(Symbol,"failed") --R retractIfCan : % -> Union(R,"failed") ---R setPredicates : (%,List Any) -> % ---R setTopPredicate : (%,List Symbol,Any) -> % ---R topPredicate : % -> Record(var: List Symbol,pred: Any) ---R withPredicates : (%,List Any) -> % +--R setPredicates : (%,List(Any)) -> % +--R setTopPredicate : (%,List(Symbol),Any) -> % +--R topPredicate : % -> Record(var: List(Symbol),pred: Any) +--R withPredicates : (%,List(Any)) -> % --R --E 1 @@ -93559,7 +93781,8 @@ Pattern(R:SetCategory): Exports == Implementation where --S 1 of 1 )show PatternMatchListResult ---R PatternMatchListResult(R: SetCategory,S: SetCategory,L: ListAggregate S) is a domain constructor +--R +--R PatternMatchListResult(R: SetCategory,S: SetCategory,L: ListAggregate(S)) is a domain constructor --R Abbreviation for PatternMatchListResult is PATLRES --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for PATLRES @@ -93674,23 +93897,24 @@ PatternMatchListResult(R:SetCategory, S:SetCategory, L:ListAggregate S): --S 1 of 1 )show PatternMatchResult +--R --R PatternMatchResult(R: SetCategory,S: SetCategory) is a domain constructor --R Abbreviation for PatternMatchResult is PATRES --R This constructor is not exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for PATRES --R --R------------------------------- Operations -------------------------------- ---R ?=? : (%,%) -> Boolean addMatch : (Pattern R,S,%) -> % +--R ?=? : (%,%) -> Boolean addMatch : (Pattern(R),S,%) -> % --R coerce : % -> OutputForm failed : () -> % --R failed? : % -> Boolean hash : % -> SingleInteger --R latex : % -> String new : () -> % --R union : (%,%) -> % ?~=? : (%,%) -> Boolean ---R addMatchRestricted : (Pattern R,S,%,S) -> % ---R construct : List Record(key: Symbol,entry: S) -> % ---R destruct : % -> List Record(key: Symbol,entry: S) ---R getMatch : (Pattern R,%) -> Union(S,"failed") ---R insertMatch : (Pattern R,S,%) -> % ---R satisfy? : (%,Pattern R) -> Union(Boolean,"failed") +--R addMatchRestricted : (Pattern(R),S,%,S) -> % +--R construct : List(Record(key: Symbol,entry: S)) -> % +--R destruct : % -> List(Record(key: Symbol,entry: S)) +--R getMatch : (Pattern(R),%) -> Union(S,"failed") +--R insertMatch : (Pattern(R),S,%) -> % +--R satisfy? : (%,Pattern(R)) -> Union(Boolean,"failed") --R --E 1 @@ -93853,20 +94077,21 @@ PatternMatchResult(R:SetCategory, S:SetCategory): SetCategory with --S 1 of 1 )show PendantTree ---R PendantTree S: SetCategory is a domain constructor +--R +--R PendantTree(S: SetCategory) is a domain constructor --R Abbreviation for PendantTree is PENDTREE --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for PENDTREE --R --R------------------------------- Operations -------------------------------- ---R children : % -> List % coerce : % -> Tree S +--R children : % -> List(%) coerce : % -> Tree(S) --R copy : % -> % cyclic? : % -> Boolean --R distance : (%,%) -> Integer ?.right : (%,right) -> % --R ?.left : (%,left) -> % ?.value : (%,value) -> S --R empty : () -> % empty? : % -> Boolean --R eq? : (%,%) -> Boolean leaf? : % -> Boolean ---R leaves : % -> List S left : % -> % ---R map : ((S -> S),%) -> % nodes : % -> List % +--R leaves : % -> List(S) left : % -> % +--R map : ((S -> S),%) -> % nodes : % -> List(%) --R ptree : (%,%) -> % ptree : S -> % --R right : % -> % sample : () -> % --R value : % -> S @@ -93877,21 +94102,21 @@ PatternMatchResult(R:SetCategory, S:SetCategory): SetCategory with --R coerce : % -> OutputForm if S has SETCAT --R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT --R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate ---R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT ---R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT +--R eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT --R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate --R hash : % -> SingleInteger if S has SETCAT --R latex : % -> String if S has SETCAT --R less? : (%,NonNegativeInteger) -> Boolean --R map! : ((S -> S),%) -> % if $ has shallowlyMutable --R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT ---R members : % -> List S if $ has finiteAggregate +--R members : % -> List(S) if $ has finiteAggregate --R more? : (%,NonNegativeInteger) -> Boolean --R node? : (%,%) -> Boolean if S has SETCAT ---R parts : % -> List S if $ has finiteAggregate ---R setchildren! : (%,List %) -> % if $ has shallowlyMutable +--R parts : % -> List(S) if $ has finiteAggregate +--R setchildren! : (%,List(%)) -> % if $ has shallowlyMutable --R setelt : (%,right,%) -> % if $ has shallowlyMutable --R setelt : (%,left,%) -> % if $ has shallowlyMutable --R setelt : (%,value,S) -> S if $ has shallowlyMutable @@ -94043,7 +94268,7 @@ p := coercePreimagesImages([[1,2,3],[1,2,3]]) --R --R --R (1) 1 ---R Type: Permutation PositiveInteger +--R Type: Permutation(PositiveInteger) --E 1 --S 2 of 8 @@ -94051,7 +94276,7 @@ movedPoints p -- should return {} --R --R --R (2) {} ---R Type: Set PositiveInteger +--R Type: Set(PositiveInteger) --E 2 --S 3 of 8 @@ -94067,7 +94292,7 @@ p := coercePreimagesImages([[0,1,2,3],[3,0,2,1]])$PERM ZMOD 4 --R --R --R (4) (1 0 3) ---R Type: Permutation IntegerMod 4 +--R Type: Permutation(IntegerMod(4)) --E 4 --S 5 of 8 @@ -94075,7 +94300,7 @@ fixedPoints p -- should return {2} --R --R --R (5) {2} ---R Type: Set IntegerMod 4 +--R Type: Set(IntegerMod(4)) --E 5 --S 6 of 8 @@ -94083,7 +94308,7 @@ q := coercePreimagesImages([[0,1,2,3],[1,0]])$PERM ZMOD 4 --R --R --R (6) (1 0) ---R Type: Permutation IntegerMod 4 +--R Type: Permutation(IntegerMod(4)) --E 6 --S 7 of 8 @@ -94091,7 +94316,7 @@ fixedPoints(p*q) -- should return {2,0} --R --R --R (7) {2,0} ---R Type: Set IntegerMod 4 +--R Type: Set(IntegerMod(4)) --E 7 --S 8 of 8 @@ -94612,32 +94837,35 @@ Permutation(S:SetCategory): public == private where --S 1 of 1 )show PermutationGroup ---R PermutationGroup S: SetCategory is a domain constructor +--R +--R PermutationGroup(S: SetCategory) is a domain constructor --R Abbreviation for PermutationGroup is PERMGRP --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for PERMGRP --R --R------------------------------- Operations -------------------------------- --R ? Boolean ?<=? : (%,%) -> Boolean ---R ?=? : (%,%) -> Boolean base : % -> List S ---R coerce : List Permutation S -> % coerce : % -> List Permutation S +--R ?=? : (%,%) -> Boolean base : % -> List(S) --R coerce : % -> OutputForm degree : % -> NonNegativeInteger --R hash : % -> SingleInteger latex : % -> String ---R movedPoints : % -> Set S orbit : (%,List S) -> Set List S ---R orbit : (%,Set S) -> Set Set S orbit : (%,S) -> Set S ---R orbits : % -> Set Set S order : % -> NonNegativeInteger ---R random : % -> Permutation S ?~=? : (%,%) -> Boolean ---R ?.? : (%,NonNegativeInteger) -> Permutation S ---R generators : % -> List Permutation S +--R movedPoints : % -> Set(S) orbit : (%,Set(S)) -> Set(Set(S)) +--R orbit : (%,S) -> Set(S) orbits : % -> Set(Set(S)) +--R order : % -> NonNegativeInteger random : % -> Permutation(S) +--R ?~=? : (%,%) -> Boolean +--R coerce : List(Permutation(S)) -> % +--R coerce : % -> List(Permutation(S)) +--R ?.? : (%,NonNegativeInteger) -> Permutation(S) +--R generators : % -> List(Permutation(S)) --R initializeGroupForWordProblem : (%,Integer,Integer) -> Void --R initializeGroupForWordProblem : % -> Void ---R member? : (Permutation S,%) -> Boolean ---R permutationGroup : List Permutation S -> % ---R random : (%,Integer) -> Permutation S ---R strongGenerators : % -> List Permutation S ---R wordInGenerators : (Permutation S,%) -> List NonNegativeInteger ---R wordInStrongGenerators : (Permutation S,%) -> List NonNegativeInteger ---R wordsForStrongGenerators : % -> List List NonNegativeInteger +--R member? : (Permutation(S),%) -> Boolean +--R orbit : (%,List(S)) -> Set(List(S)) +--R permutationGroup : List(Permutation(S)) -> % +--R random : (%,Integer) -> Permutation(S) +--R strongGenerators : % -> List(Permutation(S)) +--R wordInGenerators : (Permutation(S),%) -> List(NonNegativeInteger) +--R wordInStrongGenerators : (Permutation(S),%) -> List(NonNegativeInteger) +--R wordsForStrongGenerators : % -> List(List(NonNegativeInteger)) --R --E 1 @@ -95462,13 +95690,14 @@ PermutationGroup(S:SetCategory): public == private where --S 1 of 1 )show Pi +--R --R Pi is a domain constructor --R Abbreviation for Pi is HACKPI --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for HACKPI --R --R------------------------------- Operations -------------------------------- ---R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (Fraction(Integer),%) -> % ?*? : (%,Fraction(Integer)) -> % --R ?*? : (%,%) -> % ?*? : (Integer,%) -> % --R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % --R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % @@ -95477,37 +95706,37 @@ PermutationGroup(S:SetCategory): public == private where --R 1 : () -> % 0 : () -> % --R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % --R associates? : (%,%) -> Boolean coerce : % -> Float ---R coerce : % -> DoubleFloat coerce : Fraction Integer -> % +--R coerce : % -> DoubleFloat coerce : Fraction(Integer) -> % --R coerce : % -> % coerce : Integer -> % --R coerce : % -> OutputForm convert : % -> InputForm --R convert : % -> DoubleFloat convert : % -> Float ---R factor : % -> Factored % gcd : List % -> % +--R factor : % -> Factored(%) gcd : List(%) -> % --R gcd : (%,%) -> % hash : % -> SingleInteger --R inv : % -> % latex : % -> String ---R lcm : List % -> % lcm : (%,%) -> % +--R lcm : List(%) -> % lcm : (%,%) -> % --R one? : % -> Boolean pi : () -> % --R prime? : % -> Boolean ?quo? : (%,%) -> % --R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % ---R retract : % -> Fraction Integer retract : % -> Integer +--R retract : % -> Fraction(Integer) retract : % -> Integer --R sample : () -> % sizeLess? : (%,%) -> Boolean ---R squareFree : % -> Factored % squareFreePart : % -> % +--R squareFree : % -> Factored(%) squareFreePart : % -> % --R unit? : % -> Boolean unitCanonical : % -> % --R zero? : % -> Boolean ?~=? : (%,%) -> Boolean --R ?*? : (NonNegativeInteger,%) -> % --R ?**? : (%,NonNegativeInteger) -> % --R ?^? : (%,NonNegativeInteger) -> % --R characteristic : () -> NonNegativeInteger ---R convert : % -> Fraction SparseUnivariatePolynomial Integer +--R convert : % -> Fraction(SparseUnivariatePolynomial(Integer)) --R divide : (%,%) -> Record(quotient: %,remainder: %) --R euclideanSize : % -> NonNegativeInteger ---R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R expressIdealMember : (List(%),%) -> Union(List(%),"failed") --R exquo : (%,%) -> Union(%,"failed") --R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") --R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) ---R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % ---R multiEuclidean : (List %,%) -> Union(List %,"failed") ---R principalIdeal : List % -> Record(coef: List %,generator: %) ---R retractIfCan : % -> Union(Fraction Integer,"failed") +--R gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) +--R multiEuclidean : (List(%),%) -> Union(List(%),"failed") +--R principalIdeal : List(%) -> Record(coef: List(%),generator: %) +--R retractIfCan : % -> Union(Fraction(Integer),"failed") --R retractIfCan : % -> Union(Integer,"failed") --R subtractIfCan : (%,%) -> Union(%,"failed") --R unitNormal : % -> Record(unit: %,canonical: %,associate: %) @@ -95944,7 +96173,7 @@ refined:=refine(sketch,0.1) listBranches(sketch) --R --R (3) [[[0.5,- 0.5],[- 0.5,0.5]]] ---R Type: List List Point DoubleFloat +--R Type: List(List(Point(DoubleFloat))) --E 3 --S 4 of 5 @@ -96202,11 +96431,12 @@ listBranches(refined) --R [- 0.49199999999999999,0.49199999999999999], [- 0.496,0.496], --R [- 0.5,0.5]] --R ] ---R Type: List List Point DoubleFloat +--R Type: List(List(Point(DoubleFloat))) --E 4 --S 5 of 5 )show ACPLOT +--R --R PlaneAlgebraicCurvePlot is a domain constructor --R Abbreviation for PlaneAlgebraicCurvePlot is ACPLOT --R This constructor is not exposed in this frame. @@ -96214,9 +96444,10 @@ listBranches(refined) --R --R------------------------------- Operations -------------------------------- --R coerce : % -> OutputForm refine : (%,DoubleFloat) -> % ---R xRange : % -> Segment DoubleFloat yRange : % -> Segment DoubleFloat ---R listBranches : % -> List List Point DoubleFloat ---R makeSketch : (Polynomial Integer,Symbol,Symbol,Segment Fraction Integer,Segment Fraction Integer) -> % +--R listBranches : % -> List(List(Point(DoubleFloat))) +--R makeSketch : (Polynomial(Integer),Symbol,Symbol,Segment(Fraction(Integer)),Segment(Fraction(Integer))) -> % +--R xRange : % -> Segment(DoubleFloat) +--R yRange : % -> Segment(DoubleFloat) --R --E 5 @@ -97525,29 +97756,30 @@ PlaneAlgebraicCurvePlot(): PlottablePlaneCurveCategory _ --S 1 of 1 )show Places ---R Places K: Field is a domain constructor +--R +--R Places(K: Field) is a domain constructor --R Abbreviation for Places is PLACES --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for PLACES --R --R------------------------------- Operations -------------------------------- ---R ?*? : (Integer,%) -> Divisor % ?+? : (%,%) -> Divisor % ---R -? : % -> Divisor % ?-? : (%,%) -> Divisor % +--R ?*? : (Integer,%) -> Divisor(%) ?+? : (%,%) -> Divisor(%) +--R -? : % -> Divisor(%) ?-? : (%,%) -> Divisor(%) --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm ---R create : Symbol -> % create : List K -> % +--R create : Symbol -> % create : List(K) -> % --R degree : % -> PositiveInteger ?.? : (%,Integer) -> K ---R foundPlaces : () -> List % hash : % -> SingleInteger +--R foundPlaces : () -> List(%) hash : % -> SingleInteger --R itsALeaf! : % -> Void latex : % -> String ---R leaf? : % -> Boolean reduce : List % -> Divisor % +--R leaf? : % -> Boolean reduce : List(%) -> Divisor(%) --R ?~=? : (%,%) -> Boolean ---R ?+? : (%,Divisor %) -> Divisor % ---R ?+? : (Divisor %,%) -> Divisor % ---R ?-? : (%,Divisor %) -> Divisor % ---R ?-? : (Divisor %,%) -> Divisor % ---R localParam : % -> List NeitherSparseOrDensePowerSeries K +--R ?+? : (%,Divisor(%)) -> Divisor(%) +--R ?+? : (Divisor(%),%) -> Divisor(%) +--R ?-? : (%,Divisor(%)) -> Divisor(%) +--R ?-? : (Divisor(%),%) -> Divisor(%) +--R localParam : % -> List(NeitherSparseOrDensePowerSeries(K)) --R setDegree! : (%,PositiveInteger) -> Void ---R setFoundPlacesToEmpty : () -> List % ---R setParam! : (%,List NeitherSparseOrDensePowerSeries K) -> Void +--R setFoundPlacesToEmpty : () -> List(%) +--R setParam! : (%,List(NeitherSparseOrDensePowerSeries(K))) -> Void --R --E 1 @@ -97627,30 +97859,31 @@ Places(K):Exports == Implementation where --S 1 of 1 )show PlacesOverPseudoAlgebraicClosureOfFiniteField ---R PlacesOverPseudoAlgebraicClosureOfFiniteField K: FiniteFieldCategory is a domain constructor +--R +--R PlacesOverPseudoAlgebraicClosureOfFiniteField(K: FiniteFieldCategory) is a domain constructor --R Abbreviation for PlacesOverPseudoAlgebraicClosureOfFiniteField is PLACESPS --R This constructor is exposed in this frame. --R Issue )edit bookvol10.3.pamphlet to see algebra source code for PLACESPS --R --R------------------------------- Operations -------------------------------- ---R ?*? : (Integer,%) -> Divisor % ?+? : (%,%) -> Divisor % ---R -? : % -> Divisor % ?-? : (%,%) -> Divisor % +--R ?*? : (Integer,%) -> Divisor(%) ?+? : (%,%) -> Divisor(%) +--R -? : % -> Divisor(%) ?-? : (%,%) -> Divisor(%) --R ?=? : (%,%) -> Boolean coerce : % -> OutputForm --R create : Symbol -> % degree : % -> PositiveInteger ---R foundPlaces : () -> List % hash : % -> SingleInteger +--R foundPlaces : () -> Lis