diff --git a/books/axbook.tgz b/books/axbook.tgz index 19e4933..9f7b342 100644 Binary files a/books/axbook.tgz and b/books/axbook.tgz differ diff --git a/books/bookvol0.pamphlet b/books/bookvol0.pamphlet index 1bfc227..2137839 100644 --- a/books/bookvol0.pamphlet +++ b/books/bookvol0.pamphlet @@ -252,6 +252,9 @@ November 10, 2003 ((iHy)) \vfill \eject %\noindent + +%Original Page vii + {\Large{\bf Foreword}} \vskip .25in @@ -282,6 +285,8 @@ symbolic notations, operations and conventions. In the third decade of symbolic computations, a couple of these early systems---REDUCE and MACSYMA---still hold their own among faithful users. +%Original Page viii + Axiom was born in the mid-70's as a system called Scratchpad developed by IBM researchers. Scratchpad/Axiom was born big---its original platform was an IBM mainframe 3081, and later a 3090. The @@ -330,6 +335,8 @@ very powerful system, the prospect of scientists using the system to develop their own fields of Science is truly exciting---the day is still young for Axiom. +%Original Page ix + Over the last several years Scratchpad/Axiom has scored many successes in theoretical mathematics, mathematical physics, combinatorics, digital signal processing, cryptography and parallel @@ -480,10 +487,209 @@ David V. Chudnovsky \hfill Gregory V. Chudnovsky +----------------------------------------------------------------------------+ \end{verbatim} \eject + +%Original Page xxi + +\pseudoChapter{\Huge Contributors} +\addcontentsline{toc}{chapter}{Contributors} +The design and development of AXIOM was led by the Symbolic Computation +Group of the Mathematical Sciences Department, IBM Thomas J. Watson +Research Center, Yorktown Heights, New York. The current implemention +of AXIOM is the product of many people. The primary contributors are: + +{\bf Richard D. Jenks} (IBM, Yorktown) received a Ph.D. from the University +of Illinois and was a principal architect of the {\bf Scratchpad} computer +algebra system (1971). In 1977, Jenks initiated the AXIOM effort with +the design of MODLISP, inspired by earlier work with R\"udiger Loos +(T\"ubingen), James Griesmer (IBM, Yorktown), and David Y. Y. Yun (Hawaii). +Joint work with David R. Barton (Berkeley, California) and James Davenport +led to the design and implementation of prototypes and the concept of +categories (1980). Mor recently, Jenks led the effort on user interface +software for AXIOM. + +{\bf Barry M. Trager} (IBM, Yorktown) received a Ph.D. from MIT while +working in the {\bf MACSYMA} computer algebra group. Trager's thesis +laid the groundwork for a complete theory for closed-form integration +of elementary functions and its implementation in AXIOM. Trager and +Richrd Jenks are responsible for the original abstract datatype design +and implementation of the programming language with its current +MODLISP-based compiler and run-time system. Trager is also responsible +for the overall design of the current AXIOM library and for the +implementation of many of its components. + +{\bf Stephen M. Watt} (IBM, Yorktown) received a Ph.D. from the +University of Waterloo and is one of the original authors of the {\bf +Maple} computer algebra system. Since joining IBM in 1984, he has made +central contributions to the AXIOM language and system design, as well +as numerous contributions to the library. He is the principal +architect of the new AXIOM compiler, planned for Release 2. + +%Original Page xxii + + +{\bf Robert S. Sutor} (IBM, Yorktown) received a Ph.D. in mathematics +from Princeton University and has been involved with the design and +implementation of the system interpreter, system commands, and +documentation since 1984. Sutor's contributions to the AXIOM library +include factored objects, partial fractions, and the original +implementation of finite field extensions. Recently, he has devised +technology for producing automatic hard-copy and on-line documentation +from single source files. + +{\bf Scott C. Morrison} (IBM, Yorktown) received an M.S. from the +University of California, Berkeley, and is a principal person +responsible for the design and implementation of the AXIOM interface, +including the interpreter, HyperDoc, and applications of the computer +graphics system. + +{\bf Manuel Bronstein} (ETH, Zurich) received a Ph.D. in mathematics +from the University of California, Berkeley, completing the +theoretical work on closed-form integration by Barry Trager. Bronstein +designed and implemented the algebraic structures and algorithms in +the AXIOM library for integration, closed form solution of +differential equations, operator algebras, and manipulation of +top-level mathematical expressions. He also designed (with Richard +Jenks) and implemented the current pattern match facility for AXIOM. + +{\bf William H. Burge} (IBM, Yorktown) received a Ph.D. from Cambridge +University, implemented the AXIOM parser, designed (with Stephen Watt) +and implemented the stream and power series structures, and numerous +algebraic facilities including those for data structures, power +series, and combinatorics. + +{\bf Timothy P. Daly} (IBM, Yorktown) is pursuing a Ph.D. in computer +science at Brooklyn Polytechnic Institute and is responsible for +porting, testing, performance, and system support work for AXIOM. + +{\bf James Davenport} (Bath) received a Ph.D. from Cambridge +University, is the author of several computer algebra textbooks, and +has long recognized the need for AXIOM's generality for computer +algebra. He was involved with the early prototype design of system +internals and the original category hierarchy for AXIOM (with David +R. Barton). More recently, Davenport and Barry Trager designed the +algebraic category hierarchy currently used in AXIOM. Davenport is +Hebron and Medlock Professor of Information Technology at Bath +University. + +{\bf Michael Dewar} (Bath) received a Ph.D. from the University of +Bath for his work on the IRENA system (an interface between the {\bf +REDUCE} computer algebra system and the NAG Library of numerical +subprograms), and work on interfacing algebraic and numerical systems +in general. He has contributed code to produce FORTRAN output from +AXIOM, and is currently developing a comprehensive foreign language +interface and a link to the NAG Library for release 2 of AXIOM. + +%Original Page xxiii + + +{\bf Albrecht Fortenbacher} (IBM Scientific Center, Heidelberg) +received a doctorate from the University of Karlsruhe and is a +designer and implementer of the type-inferencing code in the AXIOM +interpreter. The result of research by Fortenbacher on type coercion +by rewrite rules will soon be incorporated into AXIOM. + +{\bf Patrizia Gianni} (Pisa) received a Laurea in mathematics from the +University of Pisa and is the prime author of the polynomial and +rational funtion component of the AXIOM library. Her contributions +include algorithms for greatest common divisors, factorization, +ideals, Gr\"obner bases, solutions of polynomial systems, and linear +algebra. she is currently Associate Professor of Mathematics at the +University of Pisa. + +{\bf Johannes Grabmeier} (IBM Scientific Center, Heidelberg) received a +Ph.D from University Bayreuth (Bavaria) and is responsible for many +AXIOM packages, including those for representation theory (with Holger +Gollan (Essen)), permutation groups (with Gerhard Schneider (Essen)), +finite fields (with Alfred Scheerhorn), and non-associative algebra +(with Robert Wisbauer (D\"usseldorf)). + +{\bf Larry Lambe} received a Ph.D. from the University of Illinois +(Chicago) and has been using AXIOM for research in homological +algebra. Lambe contributed facilities for Lie ring and exterior +algebra calculations and has worked with Scott Morrison on various +graphics applications. + +{\bf Michael Monagan} (ETH, Z\"urich) received a Ph.D. from the +University of Waterloo and is a principal contributor to the {\bf +Maple} computer algebra system. He designed and implemented the +category hierarchy and domains for data structures (with Stephen Watt), +multi-precision floating point arithmetic, code for polynomials modulo +a prime, and also worked on the new compiler. + +{\bf William Sit} (CCNY) received a Ph.D. from Columbia University. He +has been using AXIOM for research in differential algebra, and +contributed operations for differential polynomials (with Manuel +Bronstein). + +{\bf Jonathan M. Steinbach} (IBM, Yorktown) received a B.A. degree +from Ohio State University and has responsibility for the AXIOM +computer graphics facility. He has modified and extended this facility +from the original design by Jim Wen. Steinbach is currently involved +in the new compiler effort. + +{\bf Jim Wen}, a graduate student in computer graphics at Brown +University designed and implemented the original computer graphics +system for AXIOM with pop-up control panels for interactive +manipulation of graphic objects. + + +%Original Page xxiv + + +{\bf Clifton J. Williamson} (Cal Poly) received a Ph.D. in Mathematics +from the University of California, Berkeley. He implemented the power +series (with William Burge and Stephen Watt), matrix, and limit +facilities in the library and made numerous contributions to the +HyperDoc documentation and algebraic side of the computer graphics +facility. Williamson is currently an Assistant Professor of Mathematics +at California Polytechnic State University, San Luis Obispo. + +Contributions to the current AXIOM system were also made by: Yurig +Baransky (IBM Research, Yorktown), David R. Barton, Bruce Char +(Drexel), Korrinn Fu, R\"udiger Gebauer, Holger Gollan (Essen), Steven +J. Gortler, Michael Lucks, Victor Miller (IBM Research, Yorktown), +C. Andrew Neff (IBM Research, Yorktown), H. Michael M\"oller (Hagen), +Simon Robinson, Gerhard Schneider (Essen), Thorsten Werther (Bonn), +John M. Wiley, Waldermar Wiwianka (Paderborn), David Y. Y. Yun (Hawaii). + +Other group members, visitors and contributors to AXIOM include +Richard Anderson, George Andrews, Alexandre Bouyer, Martin Brock, +Florian Bundschuh, Cheekai Chin, David V. Chudnovsky, Gregory +V. Chudnovsky, Josh Cohen, Gary Cornell, Jean Della Dora, Clair Di +Cresendo, Domonique Duval, Lars Erickson, Timothy Freeman, Marc +Gaetano, Vladimir A. Grinberg, Oswald Gschnitzer, Klaus Kusche, +Bernhard Kutzler, Mohammed, Mobarak, Julian A. Padget, Michael +Rothstein, Alfred Scheerhorn, William F. Schelter, Marten Sch\"onert, +Fritz Schwarz, Christine J. Sundaresan, Moss E. Sweedler, Themos +T. Tsikas, Berhard Wall, Robert Wisbauer, and Knut Wolf. + +This book has contributions from several people in addition to its +principal authors. Scott Morrison is responsible for the computer +graphics gallery and the programs in Appendix F. Jonathon Steinbach +wrote the original version of Chapter 7. Michael Dewar contributed +material on the FORTRAN interface in Chapter 4. Manuel Bronstein, +Clifton Williamson, Patricia Gianni, Johannes Grabmeier, Barry Trager, +and Stephen Watt contributed to Chapters 8 and 9 and Appendix +E. William Burge, Timothy Daly, Larry Lambe, and William Sit +contributed material to Chapter 9. The original version of the +documentation was created and maintained by Christine Sundaresan. + +The authors would like to thank the production staff at +Springer-Verlag for their guidance in the preparation of this book, +and Jean K. Rivlin of IBM Yorktown Heights for her assistance in +producing the camera-ready copy. Also, thanks to Robert F. Caviness, +James H. Davenport, Sam Dooley, Richard J. Fateman, Stuart I. Feldman, +Stephen J. Hague, John A. Nelder, Eugene J. Surowitz, Themos +T. Tsikas, James W. Thatcher, and Richard E. Zippel for their +constructive suggestions on drafts of this book. +\newpage \pagenumbering{arabic} -\pseudoChapter{Introduction to Axiom} + +%Original Page 1 + +\pseudoChapter{\Huge Introduction to Axiom} +\addcontentsline{toc}{chapter}{0 Introduction to Axiom} \label{ugNewIntro} -\section{Introduction to Axiom} Welcome to the world of Axiom. We call Axiom a scientific computation system: a self-contained toolbox designed to meet @@ -529,6 +735,9 @@ $$ \right)}{{18}\ {a^2}\ {x^2}\ {\sqrt{3}}\ {\root{3}\of{a}}} $$ \returnType{Type: Union(Expression Integer,...)} + +%Original Page 2 + Axiom provides state-of-the-art algebraic machinery to handle your most advanced symbolic problems. For example, Axiom's integrator gives you the answer when an answer exists. If one does not, it @@ -600,6 +809,8 @@ a graph from a set of numerical values. To do this, you can call upon the Axiom graphics capability. +%Original Page 3 + Draw $J_0(\sqrt{x^2+y^2})$ for $-20 \leq x,y \leq 20$. \spadcommand{draw(5*besselJ(0,sqrt(x**2+y**2)), x=-20..20, y=-20..20)} @@ -649,6 +860,8 @@ you define these polynomials in a piece-wise way. The first Legendre polynomial. +%Original Page 4 + \spadcommand{p(0) == 1} \returnType{Type: Void} The second Legendre polynomial. @@ -660,6 +873,8 @@ The $n$-th Legendre polynomial for $(n > 1)$. \spadcommand{p(n) == ((2*n-1)*x*p(n-1) - (n-1) * p(n-2))/n} \returnType{Type: Void} +%Original Page 5 + In addition to letting you define simple functions like this, the interactive language can be used to create entire application packages. All the graphs in the Axiom images section were created by @@ -761,6 +976,8 @@ $$ Streams display only a few of their initial elements. Otherwise, they are ``lazy'': they only compute elements when you ask for them. +%Original Page 6 + Data structures are an important component for building application software. Advanced users can represent data for applications in optimal fashion. In all, Axiom offers over forty kinds of @@ -846,6 +1063,8 @@ $$ \subsection{Pattern Matching} +%Original Page 7 + A convenient facility for symbolic computation is ``pattern matching.'' Suppose you have a trigonometric expression and you want to transform it to some equivalent form. Use a $rule$ command to @@ -919,6 +1138,8 @@ $$ $$ \returnType{Type: List Equation Polynomial Integer} +%Original Page 8 + Solve the system $S$ using rational number arithmetic and 30 digits of accuracy. @@ -978,7 +1199,10 @@ terms of a database of algebraic properties. By following the language protocols, there is an automatic, guaranteed interaction between your code and that of colleagues and system implementers. \vfill\eject -\pseudoChapter{A Technical Introduction} + +%Original Page 9 + +\pseudoChapter{\Huge A Technical Introduction} \label{ugTechIntro} Axiom has both an {\it interactive language} for user interactions and a {\it programming language} for building library @@ -1002,6 +1226,8 @@ are OK, but matrices of input files are not. Through categories, programs can discover that polynomials of continued fractions have a commutative multiplication whereas polynomials of matrices do not. +%Original Page 10 + Categories allow algorithms to be defined in their most natural setting. For example, an algorithm can be defined to solve polynomial equations over {\it any} field. Likewise a greatest common divisor @@ -1070,6 +1296,8 @@ operation from {\tt Float}. \subsection{The Type of Basic Objects is a Domain or Subdomain} +%Original Page 11 + Every Axiom object belongs to a {\it unique} domain. The domain of an object is also called its {\it type.} Thus the integer $7$ has type {\tt Integer} and the string {\tt "daniel"} has type @@ -1135,6 +1363,8 @@ power: (R, NonNegativeInteger): R -> R power(x, n) == x ** n \end{verbatim} +%Original Page 12 + Line 1 declares the symbol $R$ to be a ring. Line 2 declares the type of $power$ in terms of $R$. From the definition on line 3, $power(3,2)$ produces 9 for $x = 3$ and $R =$ @@ -1168,6 +1398,8 @@ SetCategory +---- Ring ---- IntegralDomain ---- Field Figure 1. A simplified category hierarchy. \end{center} +%Original Page 13 + \subsection{Domains Belong to Categories by Assertion} A category designates a class of domains. Which domains? You might @@ -1230,6 +1462,9 @@ you can do so with a package of the form: \begin{verbatim} MySolve(F: Field): Exports == Implementation \end{verbatim} + +%Original Page 14 + where {\tt Exports} specifies the {\bf solve} operations you wish to export from the domain and the {\tt Implementation} defines functions for implementing your algorithms. Once Axiom has @@ -1306,6 +1541,8 @@ add facilities to the Axiom library. The entire Axiom library is in fact written in the Axiom source code and available for user modification and/or extension. +%Original Page 15 + Axiom's use of abstract datatypes clearly separates the exports of a domain (what operations are defined) from its implementation (how the objects are represented and operations are defined). Users of a @@ -3762,7 +3999,7 @@ General-Distributed-Mul-ti-var-iate-Poly-nomial When we start cataloging the gains in tools sitting on a computer, the benefits of software are amazing. But, if the benefits of software are so great, why do we worry about making it easier -- don't the ends pay -for the means? We worry becuase making such software is extraordinarily +for the means? We worry because making such software is extraordinarily hard and almost no one can do it -- the detail is exhausting, the creativity required is extreme, the hours of failure upon failure requiring patience and persistence would tax anyone claiming to be @@ -3776,6 +4013,8 @@ employed and employed cheaply. \end{quote} \label{ugIntro} +%Original Page 19 + Welcome to the Axiom environment for interactive computation and problem solving. Consider this chapter a brief, whirlwind tour of the Axiom world. We introduce you to Axiom's graphics and the @@ -3807,6 +4046,8 @@ is a prompt that \index{prompt} looks like (1) -> \end{verbatim} +%Original Page 20 + When you want to enter input to Axiom, you do so on the same line after the prompt. The ``1'' in ``(1)'', also called the equation number, is the computation step number and is incremented @@ -3854,6 +4095,8 @@ a closing parenthesis and are used to change your environment. For example, you can set a system variable so that you are not prompted for confirmation when you want to leave Axiom. +%Original Page 21 + \subsection{Clef} \label{ugAvailCLEF} If you are using Axiom under the X Window System, the @@ -3912,6 +4155,8 @@ form by the Axiom {\tt TexFormat} package. We have deleted system messages from the example output if those messages are not important for the discussions in which the examples appear. +%Original Page 22 + \section{The Axiom Language} \label{ugIntroExpressions} The Axiom language is a rich language for performing interactive @@ -3974,6 +4219,8 @@ $$ $$ \returnType{Type: PositiveInteger} +%Original Page 23 + This is the last result minus one. \spadcommand{\% - 1} $$ @@ -4038,6 +4285,8 @@ $$ A {\it symbol} is a literal used for the input of things like the ``variables'' in polynomials and power series. +%Original Page 24 + We use the three symbols $x$, $y$, and $z$ in entering this polynomial. \spadcommand{(x - y*z)**2} @@ -4109,6 +4358,8 @@ Axiom refuses to assign a value to $y$. to an object of the type Integer of the left-hand side. \end{verbatim} +%Original Page 25 + A type declaration can also be given together with an assignment. The declaration can assist Axiom in choosing the correct operations to apply. @@ -4182,6 +4433,8 @@ infix operator.\footnote{Conversion is discussed in detail in to display an object, it is necessary to convert the object to type {\tt OutputForm}. +%Original Page 26 + This produces a polynomial with rational number coefficients. \spadcommand{p := r**2 + 2/3} @@ -4263,6 +4516,8 @@ object returned by the operation and not rely on a physical change having occurred within the object. Usually, destructive operations are provided for efficiency reasons. +%Original Page 27 + \subsection{Some Predefined Macros} \label{ugIntroMacros} Axiom provides several macros for your convenience.\footnote{See @@ -4334,6 +4589,8 @@ $$ There is no way to write long multi-line comments other than starting each line with ``{\tt --}'' or ``{\tt ++}''. +%Original Page 29 + \section{Numbers} \label{ugIntroNumbers} Axiom distinguishes very carefully between different kinds of @@ -4417,6 +4674,8 @@ $$ $$ \returnType{Type: DoubleFloat} +%Original Page 30 + The normal floating-point type in Axiom, {\tt Float}, is a software implementation of floating-point numbers in which the exponent and the mantissa may have any number of digits. @@ -4512,6 +4771,8 @@ $$ $$ \returnType{Type: Complex Polynomial Integer} +%Original Page 31 + Every rational number has an exact representation as a repeating decimal expansion \spadcommand{decimal(1/352)} @@ -4595,6 +4856,8 @@ $$ $$ \returnType{Type: PrimeField 7} +%Original Page 32 + You can also compute modulo an integer that is not a prime. \spadcommand{y : IntegerMod 6 := 5} $$ @@ -4680,6 +4943,8 @@ $$ \returnType{Type: Expression Integer} +%Original Page 33 + If we do this, we should get $b$. \spadcommand{2/\%+1} $$ @@ -4759,6 +5024,8 @@ $$ $$ \returnType{Type: PositiveInteger} +%Original Page 34 + Many operations are defined on lists, such as: {\bf empty?}, to test that a list has no elements; {\bf cons}$(x,l)$, to create a new list with {\bf first} element $x$ and {\bf rest} $l$; {\bf reverse}, to @@ -4844,6 +5111,8 @@ arrays are inflexible---they are \index{array!one-dimensional} implemented using a fixed block of storage. Their advantage is that they give quick and equal access time to any element. +%Original Page 35 + A simple way to create a one-dimensional array is to apply the operation {\bf oneDimensionalArray} to a list of elements. \spadcommand{a := oneDimensionalArray [1, -7, 3, 3/2]} @@ -4924,6 +5193,8 @@ $$ $$ \returnType{Type: FlexibleArray Integer} +%Original Page 36 + Flexible arrays are used to implement ``heaps.'' A {\it heap} \footnote{\domainref{Heap}} is an example of a data structure called a {\it priority queue}, where @@ -4997,7 +5268,7 @@ irrelevant. \footnote{\domainref{Set}} Sets are always finite and have no corresponding structure like streams for infinite collections. -Create sets using braces ``\{`` and ``\}'' rather than brackets. +Create sets using braces ``\{'' and ``\}'' rather than brackets. \spadcommand{fs := set [1/3,4/5,-1/3,4/5]} $$ @@ -5010,6 +5281,8 @@ $$ A {\it multiset} is a set that keeps track of the number of duplicate values. \footnote{\domainref{Multiset}} +%Original Page 37 + For all the primes $p$ between 2 and 1000, find the distribution of $p \bmod 5$. \spadcommand{multiset [x rem 5 for x in primes(2,1000)]} @@ -5040,7 +5313,7 @@ $$ We define a function {\bf howMany} to return the number of values of a given modulus $k$ seen so far. It calls {\bf search}$(k,t)$ which returns the number of values -stored under the key $k$ in table $t$, or {\tt ``failed''} +stored under the key $k$ in table $t$, or {\tt "failed"} if no such value is yet stored in $t$ under $k$. In English, this says ``Define $howMany(k)$ as follows. @@ -5076,6 +5349,8 @@ assigned a record with two prescribed fields. \spadcommand{daniel : Record(age : Integer, salary : Float)} \returnType{Type: Void} +%Original Page 38 + Give $daniel$ a value, using square brackets to enclose the values of the fields. \spadcommand{daniel := [28, 32005.12]} @@ -5154,6 +5429,8 @@ $$ $$ \returnType{Type: Matrix Integer} +%Original Page 39 + The ``collections'' construct (see \sectionref{ugLangIts}) is useful for creating matrices whose entries are given by formulas. \index{matrix!Hilbert} @@ -5240,6 +5517,8 @@ fractions of polynomials with complex floating point numbers as coefficients. Moreover, the library provides a wealth of operations that allow you to create and manipulate these objects. +%Original Page 40 + For many applications, you need to interact with the interpreter and write some Axiom programs to tackle your application. Axiom allows you to write functions interactively, @@ -5304,6 +5583,8 @@ $$ $$ \returnType{Type: PositiveInteger} +%Original Page 41 + A final version appears to construct a large list and then reduces over it with multiplication. \spadcommand{f(n) == reduce(*,[i for i in 2..n])} @@ -5390,6 +5671,8 @@ $$ $$ \returnType{Type: Matrix Integer} +%Original Page 42 + Interchange the second and third rows of m. \spadcommand{permMat(4,2,3) * m} $$ @@ -5453,6 +5736,8 @@ $$\sqrt{a}\sqrt{b} \mapsto \sqrt{ab}, \quad Note that such a transformation is not generally correct. Axiom never uses it automatically. +%Original Page 43 + Give this rule the name {\bf groupSqrt}. \spadcommand{groupSqrt := rule(sqrt(a) * sqrt(b) == sqrt(a*b))} $$ @@ -5546,6 +5831,8 @@ $$ $$ \returnType{Type: MultivariatePolynomial([x,y],Integer)} +%Original Page 44 + You can change the way the polynomial appears by modifying the variable ordering in the explicit list. \spadcommand{m :: MPOLY([y,x],INT)} @@ -5619,6 +5906,8 @@ $$ $$ \returnType{Type: Expression Integer} +%Original Page 45 + Use {\tt \%plusInfinity} and {\tt \%minusInfinity} to denote $\infty$ and $-\infty$. \spadcommand{limit(h,x=\%plusInfinity)} @@ -5682,6 +5971,8 @@ $$ $$ \returnType{Type: UnivariatePuiseuxSeries(Expression Integer,x,0)} +%Original Page 46 + This expression expands {\tt sin(a*x)} in powers of {\tt (x - \%pi/4)}. \spadcommand{series(sin(a*x),x = \%pi/4)} $$ @@ -5792,6 +6083,8 @@ x+ $$ \returnType{Type: UnivariatePuiseuxSeries(Expression Integer,x,0)} +%Original Page 47 + \spadcommand{exp(g)} $$ 1+x+{x \sp 2}+{x \sp 3}+{x \sp 4}+{x \sp 5}+{x \sp 6}+{x \sp 7}+{x \sp 8}+{x @@ -5893,6 +6186,8 @@ $$ $$ \returnType{Type: Expression Integer} +%Original Page 48 + \spadcommand{D(g, y)} $$ \cos @@ -6012,6 +6307,8 @@ z}, {\log \left({z + 1}\right)}, {z^2}}\right)}+ $$ \returnType{Type: Expression Integer} +%Original Page 49 + You obtain the same result by first evaluating $a$ and then differentiating. @@ -6107,6 +6404,8 @@ $$ $$ \returnType{Type: Expression Integer} +%Original Page 50 + The following two examples illustrate the limitations of table-based approaches. The two integrands are very similar, but the answer to one of them requires the addition of two new algebraic numbers. @@ -6201,6 +6500,8 @@ $$ $$ \returnType{Type: Union(Expression Integer,...)} +%Original Page 51 + A strong structure-checking algorithm in Axiom finds hidden algebraic relationships between functions. @@ -6266,6 +6567,8 @@ $$ More examples of Axiom's integration capabilities are discussed in \sectionref{ugProblemIntegration}. +%Original Page 52 + \section{Differential Equations} \label{ugIntroDiffEqns} The general approach used in integration also carries over to the @@ -6370,6 +6673,8 @@ $$ $$ \returnType{Type: List Expression Integer} +%Original Page 53 + Here's another differential equation to solve. \spadcommand{deq := D(y x, x) = y(x) / (x + y(x) * log y x)} $$ @@ -6475,6 +6780,8 @@ want your result to be. All operations in the {\it solve} family return answers in the form of a list of solution sets, where each solution set is a list of equations. +%Original Page 54 + A system of two equations involving a symbolic parameter $t$. \spadcommand{S(t) == [x**2-2*y**2 - t,x*y-y-5*x + 5]} \returnType{Type: Void} @@ -6553,6 +6860,8 @@ z} -{b \ x} -a} $$ \returnType{Type: List Polynomial Integer} +%Original Page 55 + Solve the system for unknowns $[x,y,z]$, reducing the solution to triangular form. \spadcommand{solve(eqns,[x,y,z])} @@ -6625,6 +6934,8 @@ Other system commands include: {\tt )history}, to display previous input and/or output lines; {\tt )display}, to display properties and values of workspace variables; and {\tt )what}. +%Original Page 56 + Issue {\tt )what} to get a list of Axiom objects that contain a given substring in their name. \spadcommand{)what operations integrate} @@ -6680,7 +6991,9 @@ two mutually dependent functions $f$ and $g$ piece-wise.'' \spadcommand{g(n) == -x*f(n-1) + d/3*g(n-1)} \returnType{Type: Void} -``What is value of $f(3)$?'' +%Original Page 57 + +``What is the value of $f(3)$?'' \spadcommand{f(3)} $$ -{x \sp 3}+{{\left( e+{{\frac{1}{3}} \ d} \right)} @@ -6790,6 +7103,8 @@ disregarding those undone. The system command {\tt )history )write mynew.input} writes a clean straight-line program onto the file {\bf mynew.input} on your disk. +%Original Page 28 + \section{Graphics} \label{ugIntroGraphics} Axiom has a two- and three-dimensional drawing and rendering @@ -6871,6 +7186,8 @@ act -- every single little thing you do -- \ldots \end{quote} \label{ugTypes} +%Original Page 59 + In this chapter we look at the key notion of {\it type} and its generalization {\it mode}. We show that every Axiom object has a type that determines what you can do with the object. In particular, we @@ -6904,6 +7221,8 @@ to the domain {\tt Polynomial(Integer)}. The domain of an object is also called its {\it type}. Thus we speak of ``the type {\tt Integer}'' and ``the type {\tt Polynomial(Integer)}.'' +%Original Page 60 + After an Axiom computation, the type is displayed toward the right-hand side of the page (or screen). \spadcommand{-3} @@ -6966,6 +7285,8 @@ used as the {\it type} of that object. The type of $3$ is indeed both of integer whose predicate is satisfied, such as ``the prime integers,'' ``the odd positive integers between 3 and 17,'' and so on. +%Original Page 61 + \subsection{Domain Constructors} \label{ugTypesBasicDomainCons} @@ -7031,6 +7352,8 @@ $$ $$ \returnType{Type: Domain} +%Original Page 62 + Try to create a meaningless domain. \spadcommand{Polynomial(String)} \begin{verbatim} @@ -7092,6 +7415,8 @@ Thus you can never build polynomials over matrices. Polynomial Matrix Integer is not a valid type. \end{verbatim} +%Original Page 63 + Use {\tt SquareMatrix(n,R)} instead. For any positive integer $n$, it builds ``the ring of $n$ by $n$ matrices over $R$.'' \spadcommand{Polynomial(SquareMatrix(7,Complex(Integer)))} @@ -7149,7 +7474,7 @@ category {\tt Type}. Now, you may ask, what exactly is a category? \index{category} Like domains, categories can be defined in the Axiom language. A category is defined by three components: -% + \begin{enumerate} \item a name (for example, {\tt Ring}), used to refer to the class of domains that the category represents; @@ -7158,7 +7483,9 @@ the domains of this class support (for example, ``{\tt +}'', ``{\tt -}'', and ``{\tt *}'' for rings); and \item an optional list of other categories that this category extends. \end{enumerate} -% + +%Original Page 64 + This last component is a new idea. And it is key to the design of Axiom! Because categories can extend one another, they form hierarchies. Detailed charts showing the category hierarchies @@ -7212,6 +7539,8 @@ presume that the ring axioms hold. Enough on categories. To learn more about them, see \sectionref{ugCategories}. We now return to our discussion of domains. +%Original Page 65 + Domains {\it export} a set of operations to make them available for system-wide use. {\tt Integer}, for example, exports the operations \spadopFrom{+}{Integer} and \spadopFrom{=}{Integer} given by the @@ -7260,6 +7589,8 @@ compiled into machine code. This is what comprises the Axiom {\it library}. We will show you how to use these domains and their functions and how to write your own functions. +%Original Page 66 + \section{Writing Types and Modes} \label{ugTypesWriting} @@ -7334,6 +7665,8 @@ You need to use parentheses to force the application of a constructor to the correct argument, but you need not use any more than is necessary to remove ambiguities. +%Original Page 67 + Here are some guidelines for using parentheses (they are possibly slightly more restrictive than they need to be). @@ -7393,6 +7726,8 @@ parentheses. Some examples are \\ {\tt SquareMatrix(3, Integer)} \\ {\tt FactoredFunctions2(Integer,Fraction Integer)} +%Original Page 68 + \subsection{Modes} \label{ugTypesWritingModes} @@ -7468,6 +7803,8 @@ type expression. Here are some types using abbreviations. \end{tabular} \end{center} +%Original Page 69 + There are several ways of finding the names of constructors and their abbreviations. For a specific constructor, use {\tt )abbreviation query}. \index{abbreviation} You can also use the {\tt )what} system @@ -7523,6 +7860,8 @@ A {\it declaration} is an expression used to restrict the type of values that can be assigned to variables. A colon ``{\tt :}'' is always used after a variable or list of variables to be declared. +%Original Page 70 + \boxed{4.6in}{ For a single variable, the syntax for declaration is \begin{center} @@ -7579,6 +7918,8 @@ This declares several variables with a mode. \spadcommand{(p,q,r) : Matrix Polynomial ?} \returnType{Type: Void} +%Original Page 71 + This complex object has integer real and imaginary parts. \spadcommand{n := -36 + 9 * \%i} $$ @@ -7669,6 +8010,8 @@ workspace. If this occurs, precede the selector name by a single \index{quote} quote.\\ } +%Original Page 72 + Record components are implicitly ordered. All the components of a record can be set at once by assigning the record a bracketed {\it tuple} of values of the proper length. For example: @@ -7757,6 +8100,8 @@ $$ $$ \returnType{Type: Record(name: String,birthdayMonth: Integer)} +%Original Page 73 + Once set, you can change any of the individual components. \spadcommand{bd.name := "Katie"} $$ @@ -7837,6 +8182,8 @@ finite set of types. \index{Union} Two versions of unions are available, one with selectors (like records) and one without. \index{union} +%Original Page 74 + \subsection{Unions Without Selectors} \label{ugTypesUnionsWOSel} @@ -7900,6 +8247,8 @@ This tries {\bf sayBranch} with a floating-point number. \end{verbatim} \returnType{Type: Void} +%Original Page 75 + There are two things of interest about this particular example to which we would like to draw your attention. \begin{enumerate} @@ -7979,6 +8328,8 @@ $$ $$ \returnType{Type: Union(Integer,...)} +%Original Page 76 + Assign it a rational number. \spadcommand{r := 3/2} $$ @@ -8041,6 +8392,8 @@ Note that {\tt case} uses the selector name as its right-hand argument. \index{case} If you accidentally use the branch type on the right-hand side of {\tt case}, {\tt false} will be returned. +%Original Page 77 + Declare variable $u$ to have a union type with selectors. \spadcommand{u : Union(i : Integer, s : String)} \returnType{Type: Void} @@ -8110,6 +8463,8 @@ $$ $$ \returnType{Type: Fraction Integer} +%Original Page 78 + Since type {\tt Any} can be anything, it can only belong to type {\tt Type}. Therefore it cannot be used in algebraic domains. \spadcommand{v : Matrix(Any)} @@ -8172,6 +8527,8 @@ number coefficients. \index{SquareMatrix} \spadcommand{m : SquareMatrix(2,POLY COMPLEX FRAC INT)} \returnType{Type: Void} +%Original Page 79 + \spadcommand{m := matrix [ [x-3/4*\%i,z*y**2+1/2],[3/7*\%i*y**4 - x,12-\%i*9/5] ]} $$ \left[ @@ -8253,6 +8610,8 @@ brief discussion of categories. The {\tt Integer} level did not move anywhere because it does not allow any arguments. We also did not move the {\tt SquareMatrix} part anywhere, but we could have. +%Original Page 80 + Recall that $m$ looks like this. \spadcommand{m} @@ -8378,6 +8737,8 @@ A {\it subdomain} {\rm S} of a domain {\rm D} is a domain consisting of Every domain is a subdomain of itself, trivially satisfying the membership test: {\tt true}. +%Original Page 81 + Currently, there are only two system-defined subdomains in Axiom that receive substantial use. {\tt PositiveInteger} and {\tt NonNegativeInteger} are subdomains of {\tt Integer}. An element $x$ @@ -8450,6 +8811,8 @@ $$ $$ \returnType{Type: PositiveInteger} +%Original Page 82 + This is an element of {\tt Fraction Integer}. \spadcommand{2 ** (-2)} $$ @@ -8527,6 +8890,8 @@ $$ $$ \returnType{Type: Complex Integer} +%Original Page 83 + \section{Package Calling and Target Types} \label{ugTypesPkgCall} @@ -8585,6 +8950,8 @@ call causes AXIOM to convert $(2+3)$ and $4$ to type of {\rm Float} by AXIOM and then evaluated. The target type causes the ``+'' from {\tt Float} to be used. +%Original Page 84 + \boxed{4.6in}{ For an operator written before its arguments, you must use parentheses around the arguments (even if there is only one), and follow the closing @@ -8593,7 +8960,7 @@ $$ fun\ (\ arg_1, arg_2, \ldots, arg_N\ )\$type$$ } For example, to call the ``minimum'' function from {\rm DoubleFloat} on two -integers, you could write {\bf min}(4,89){\tt DoubleFloat}. Another use of +integers, you could write {\bf min}(4,89){\tt \$DoubleFloat}. Another use of package calling is to tell AXIOM to use a library function rather than a function you defined. We discuss this in \sectionref{ugUserUse}. @@ -8635,8 +9002,12 @@ exported by {\tt String}. The function + is not implemented in String . \end{verbatim} -(By the way, the operation \spadfunFrom{concat}{String} or juxtaposition -is used to concatenate two strings.) +The operation \spadfunFrom{concat}{String} +is used to concatenate two strings. One can also concatenate strings +by juxtaposition. For instance, by writing +\begin{verbatim} + "asdf" "jkl" +\end{verbatim} \index{String} When we have more than one operation in an expression, the difference @@ -8645,6 +9016,8 @@ uses the target type to create different objects. The ``{\tt +}'', ``{\tt *}'' and ``{\tt **}'' operations are all chosen so that an object of the correct final type is created. +%Original Page 85 + This says that the operations should be chosen so that the result is a {\tt Complex} object. \spadcommand{((x + y * \%i)**2)@(Complex Polynomial Integer)} @@ -8733,6 +9106,8 @@ $$ $$ \returnType{Type: Matrix Fraction Integer} +%Original Page 86 + \section{Resolving Types} \label{ugTypesResolve} @@ -8819,6 +9194,8 @@ to ``do what I mean.'' If Axiom is still being obtuse, give it some hints. As you work with Axiom, you will learn where it needs a little help to analyze quickly and perform your computations. +%Original Page 87 + \section{Exposing Domains and Packages} \label{ugTypesExpose} @@ -8878,6 +9255,8 @@ categories ... \end{verbatim} +%Original Page 88 + For each constructor in a group, the full name and the abbreviation is given. There are other groups in {\bf exposed.lsp} but initially only the constructors in exposure groups ``basic'' ``categories'' @@ -8931,6 +9310,8 @@ $$ $$ \returnType{Type: Polynomial Integer} +%Original Page 89 + Expose {\tt OutputForm}. \spadcommand{)set expose add constructor OutputForm } \begin{verbatim} @@ -8999,6 +9380,8 @@ To get more information about an operation such as complexZeros, issue the command )display op complexZeros \end{verbatim} +%Original Page 90 + If you want to see all domains with ``{\tt matrix}'' in their names, issue this. \index{what domain} \spadcommand{)what domain matrix} @@ -9068,6 +9451,8 @@ There is one exposed function called complex : Let's analyze this output. +%Original Page 91 + First we find out what some of the abbreviations mean. \spadcommand{)abbreviation query COMPCAT} \begin{verbatim} @@ -9089,6 +9474,8 @@ domains belonging to {\tt ComplexCategory} is {\tt Complex}. See \setcounter{chapter}{2} +%Original Page 93 + \chapter{Using HyperDoc} \label{ugHyper} @@ -9105,6 +9492,8 @@ to use Axiom simply by using the mouse and filling in templates. HyperDoc is available to you if you are running Axiom under the X Window System. +%Original Page 94 + Pages usually have active areas, marked in {\bf this font} (bold face). As you move the mouse pointer to an active area, the pointer changes from a filled dot to an open circle. The active areas are @@ -9177,6 +9566,8 @@ scroll bar lets you move up and down in the text to see different parts. It also shows where the aperture is relative to the whole text. The aperture is indicated by a strip on the scroll bar. +%Original Page 95 + Move the cursor with the mouse to the ``down-arrow'' at the bottom of the scroll bar and click. See that the aperture moves down one line. Do it several times. Each time you click, the aperture moves down one @@ -9236,6 +9627,8 @@ You can also move from one input area to another using your mouse. Notice that each input area is active. Click on one of the areas. As you can see, the underscore cursor moves to that window. +%Original Page 96 + \section{Radio Buttons and Toggles} \label{ugHyperButtons} @@ -9293,6 +9686,8 @@ not adjacent. Try search strings such as ``{\tt *dom*}''. As you see, this search string matches ``{\tt domain}'', ``{\tt domain constructor}'', ``{\tt subdomain}'', and so on. +%Original Page 97 + \subsection{Logical Searches} \label{ugLogicalSearches} @@ -9360,6 +9755,9 @@ The default value is {\tt black} \item[{\tt Axiom.hyperdoc.ActiveFont:} {\it font}] \ \newline This is the font used for HyperDoc link buttons. The default value is {\tt Bld14} + +%Original Page 98 + \item[{\tt Axiom.hyperdoc.ActiveColor:} {\it color}] \ \newline This is the color used for HyperDoc link buttons. The default value is {\tt black} @@ -9406,6 +9804,8 @@ The default value is {\tt white} \setcounter{chapter}{3} +%Original Page 99 + \chapter{Input Files and Output Styles} \label{ugInOut} @@ -9438,6 +9838,8 @@ Anything that you can enter directly to Axiom can be put into an input file. This is how you save input functions and expressions that you wish to read into Axiom more than one time. +%Original Page 100 + To read an input file into Axiom, use the {\tt )read} system command. \index{read} For example, you can read a file in a particular directory by issuing @@ -9505,6 +9907,9 @@ computations, place the system command {\tt )set output fortran on} in for confirmation when you issue the {\tt )quit} system command, place {\tt )set quit unprotected} in {\bf .axiom.input}. \index{set quit unprotected} + +%Original Page 101 + If you then decide that you do want to be prompted, issue {\tt )set quit protected}. \index{set quit protected} This is the default setting so that new users do not leave Axiom @@ -9565,6 +9970,8 @@ You can always direct output back to the screen by issuing this. \index{output formats!sending to screen} \spadcommand{)set output fortran console} +%Original Page 102 + Let's make sure FORTRAN formatting is off so that nothing we do from now on produces FORTRAN output. \spadcommand{)set output fortran off} @@ -9625,6 +10032,8 @@ does not support the IBM extended ASCII character set. If you are running on an IBM workstation, for example, issue {\tt )set output characters default} to get better looking output. +%Original Page 103 + \section{TeX Format} \label{ugInOutTeX} @@ -9681,6 +10090,8 @@ are all standard except for the following definitions: } \end{verbatim} +%Original Page 104 + \section{IBM Script Formula Format} \label{ugInOutScript} @@ -9745,6 +10156,8 @@ are used in the following examples so that the output fits nicely on the page. \spadcommand{)set fortran fortlength 60} +%Original Page 105 + By default, the output goes to the screen and is displayed before the standard Axiom two-dimensional output. In this example, an assignment to the variable $R1$ was generated because this is the result of step 1. @@ -9817,6 +10230,8 @@ At optimization level 1, Axiom removes common subexpressions. \index{set fortran optlevel} \spadcommand{)set fortran optlevel 1} +%Original Page 106 + \spadcommand{(x+y+z)**3} \begin{verbatim} T2=y*y @@ -9888,6 +10303,9 @@ $$ \right) $$ \returnType{Type: Expression Integer} + +%Original Page 107 + Expressions that look like lists, streams, sets or matrices cause array code to be generated. \spadcommand{[x+1,y+1,z+1]} @@ -9947,6 +10365,8 @@ To change the starting index for generated FORTRAN arrays to be $1$, or $1$. \spadcommand{)set fortran startindex 1} +%Original Page 108 + Look at the code generated for the matrix again. \spadcommand{matrix [ [2.3,9.7],[0.0,18.778] ]} \begin{verbatim} @@ -9969,6 +10389,8 @@ $$ \setcounter{chapter}{4} +%Original Page + \chapter{Overview of Interactive Language} \label{ugLang} @@ -9995,6 +10417,8 @@ A %j numberOfPoints beta6 %J numberofpoints \end{verbatim} +%Original Page 110 + The ``{\tt :=}'' operator is the immediate {\it assignment} operator. \index{assignment!immediate} Use it to associate a value with a variable. \index{immediate assignment} @@ -10058,6 +10482,8 @@ The syntax for delayed assignment is The value returned by a delayed assignment is the unique value of {\tt Void}.\\ } +%Original Page 111 + Using $a$ and $b$ as above, these are the corresponding delayed assignments. \spadcommand{a == 1} \returnType{Type: Void} @@ -10126,6 +10552,8 @@ immediate assignment} a {\it tuple} of variables and a tuple of expressions. Note that a {\it tuple} is a collection of things separated by commas, often surrounded by parentheses. +%Original Page 112 + \boxed{4.6in}{ The syntax for multiple immediate assignments is \begin{center} @@ -10199,6 +10627,9 @@ indented the same number of spaces (which must be greater than zero). A block entered in this form is called a {\it pile}. \end{enumerate} + +%Original Page 113 + Only the first form is available if you are entering expressions directly to Axiom. Both forms are available in {\bf .input} files. @@ -10259,6 +10690,8 @@ further indent its lines to the right of the outer pile. Axiom knows where a pile ends. It ends when a subsequent line is indented to the left of the pile or the end of the file. +%Original Page 114 + Blocks can be used to perform several steps before an assignment (immediate or delayed) is made. \begin{verbatim} @@ -10340,6 +10773,8 @@ $$ $$ \returnType{Type: PositiveInteger} +%Original Page 115 + Since $c + d$ does equal $3628855$, $a$ has the value of $c$ and the last line is never evaluated. \begin{verbatim} @@ -10407,6 +10842,8 @@ may need to tell Axiom that you want to test for equality rather than create an equation. In those cases, use ``{\tt @}'' and a target type of {\tt Boolean}. See \sectionref{ugTypesPkgCall} for more information. +%Original Page 116 + The compound symbol meaning ``not equal'' in Axiom is \index{inequality testing} ``{$\sim =$}''. \index{\_notequal@$\sim =$} This can be used directly without a package call or a target @@ -10471,6 +10908,8 @@ a := else (j := cos(i * 0.5 * pi()); log(abs(j)**5 + 1)) \end{verbatim} +%Original Page 117 + \section{Loops} \label{ugLangLoops} @@ -10537,6 +10976,8 @@ think). \spadcommand{f()} \returnType{Type: Void} +%Original Page 118 + What went wrong? Isn't it obvious that this function should return an integer? Well, Axiom makes no attempt to analyze the structure of a loop to determine if it always returns a value because, in general, @@ -10619,6 +11060,8 @@ $$ $$ \returnType{Type: PositiveInteger} +%Original Page 119 + You can only use {\tt break} to terminate the evaluation of one loop. Let's consider a loop within a loop, that is, a loop with a nested loop. First, we initialize two counter variables. @@ -10689,6 +11132,8 @@ repeat \end{verbatim} \returnType{Type: Void} +%Original Page 120 + Upon completion, $i$ should have the value $11$. \spadcommand{i} $$ @@ -10766,6 +11211,8 @@ $$ $$ \returnType{Type: PositiveInteger} +%Original Page 121 + Also, let {\tt lastrow} and {\tt lastcol} be the final row and column index. \spadcommand{(lastrow, lastcol) := (nrows(m), ncols(m))} @@ -10832,6 +11279,8 @@ immediately following the {\tt while} keyword. The predicate is tested {\it before} the evaluation of the body of the loop. The loop body is evaluated whenever the predicates in a {\tt while} clause are all {\tt true}. +%Original Page 122 + \boxed{4.6in}{ The syntax for a simple loop using {\tt while} is \begin{center} @@ -10906,6 +11355,8 @@ while x < 4 while y < 10 repeat \end{verbatim} \returnType{Type: Void} +%Original Page 123 + Here's a different version of the nested loops that looked for the first negative element in a matrix. \spadcommand{m := matrix [ [21,37,53,14], [8,-24,22,-16], [2,10,15,14], [26,33,55,-13] ]} @@ -10964,6 +11415,8 @@ present in addition to {\tt while} clauses. As with all other types of {\tt repeat} loops, {\tt break} can \index{break} be used to prematurely terminate the evaluation of the loop. +%Original Page 124 + \boxed{4.6in}{ The syntax for a simple loop using {\tt for} is \begin{center} @@ -11026,6 +11479,8 @@ a list and the ``{\bf \#}'' operation to count its elements. This type of iteration is applicable to anything that uses ``{\tt .}''. You can also use it with functions that use indices to extract elements. +%Original Page 125 + Define $m$ to be a matrix. \spadcommand{m := matrix [ [1,2],[4,3],[9,0] ]} $$ @@ -11096,6 +11551,8 @@ Use this to display the numbers in reverse order. \subsection{for i in n.. repeat} \label{ugLangLoopsForInN} +%Original Page 126 + If the value after the ``{\tt ..}'' is omitted, the loop has no end test. A potentially infinite loop is thus created. The variable is given the successive values ${n}, {n+1}, {n+2}, ...$ and the loop is terminated @@ -11162,6 +11619,8 @@ the index variable $i$ is simply incremented once per loop and the list is not actually created. Using the first form is much more efficient. +%Original Page 127 + Of course, sometimes you really want to iterate across a specific list. This displays each of the factors of $2400000$. \spadcommand{for f in factors(factor(2400000)) repeat output(f)} @@ -11232,6 +11691,8 @@ gives an example of {\it nested iteration}: a loop is contained Sometimes you want to iterate across two lists in parallel, or perhaps you want to traverse a list while incrementing a variable. +%Original Page 128 + \boxed{4.6in}{ The general syntax of a repeat loop is $$ @@ -11309,6 +11770,8 @@ the {\tt for i in 0..} specifies no terminating condition. \spadcommand{for i in 0.. for x in l repeat sum := i * x} \returnType{Type: Void} +%Original Page 129 + Display this weighted sum. \spadcommand{sum} $$ @@ -11368,6 +11831,8 @@ or any {\tt for} clause to the left. \section{Creating Lists and Streams with Iterators} \label{ugLangIts} +%Original Page 130 + All of what we did for loops in \sectionref{ugLangLoops} \index{iteration} can be transformed into expressions that create lists @@ -11451,6 +11916,8 @@ collection is either a list or a stream of elements, one for each iteration of the {\it collectExpression}.\\ } +%Original Page 131 + Be careful when you use {\tt while} \index{stream!using while @{using {\tt while}}} to create a stream. By default, Axiom tries to compute and @@ -11611,6 +12078,8 @@ $$ $$ \returnType{Type: List List List PositiveInteger} +%Original Page 132 + See \domainref{List} and \domainref{Stream} for more information on creating and manipulating lists and streams, respectively. @@ -11701,6 +12170,8 @@ $$ $$ \returnType{Type: Stream Integer} +%Original Page 133 + Twin primes are consecutive odd number pairs which are prime. Here is the stream of twin primes. \spadcommand{twinPrimes := [ [p,p+2] for p in primes | prime?(p + 2)]} @@ -11780,6 +12251,9 @@ second, the third, and so on. But since there isn't even a second triplet prime, Axiom will compute forever. Nonetheless, this effort can produce a useful result. After waiting a bit, hit \fbox{\bf Ctrl-c}. The system responds as follows. + +%Original Page 134 + \begin{verbatim} >> System error: Console interrupt. @@ -11812,6 +12286,8 @@ it left off. \setcounter{chapter}{5} +%Original Page 135 + \chapter{User-Defined Functions, Macros and Rules} \label{ugUser} @@ -11846,6 +12322,8 @@ $$ $$ \returnType{Type: PositiveInteger} +%Original Page 136 + Functions can be used alone or serve as the building blocks for larger programs. Usually they return a value that you might want to use in the next stage of a computation, but not always (for example, see @@ -11902,6 +12380,8 @@ $$ $$ \returnType{Type: Polynomial Integer} +%Original Page 137 + Macros can be parameterized and so can be used for many different kinds of objects. \spadcommand{macro ff(x) == x**2 + 1} @@ -11961,6 +12441,8 @@ $$ $$ \returnType{Type: Integer} +%Original Page 138 + Here is the infinite stream of the rest of the Fibonacci numbers. \spadcommand{[next for i in 1..]} $$ @@ -12031,6 +12513,8 @@ $$ $$ \returnType{Type: Factored Integer} +%Original Page 139 + Some functions like ``{\tt +}'' have {\it infix} {\it operators} as names. \spadcommand{3 + 4} $$ @@ -12080,6 +12564,8 @@ Overloading is the rule rather than the exception. You can add two integers, two polynomials, two matrices or two power series. These are all done with the same function name but with different functions. +%Original Page 140 + \section{Declaring the Type of Functions} \label{ugUserDeclare} @@ -12141,6 +12627,8 @@ g(arg1: INT, arg2: FLOAT, arg3: INT): STRING == ... h(): POLY INT == ... \end{verbatim} +%Original Page 141 + A current restriction on function declarations is that they must involve fully specified types (that is, cannot include modes involving explicit or implicit ``{\tt ?}''). For more information on declaring @@ -12196,6 +12684,8 @@ $$ $$ \returnType{Type: Stream Integer} +%Original Page 142 + Create a stream of those values of $i$ such that {\tt mersenne(i)} is prime. \spadcommand{mersenneIndex := [n for n in 1.. | prime?(mersenne(n))]} \begin{verbatim} @@ -12262,6 +12752,9 @@ but not to values that cannot be converted to integers. \end{verbatim} To make the function over a wide range of types, do not declare its type. + +%Original Page 143 + Give the same definition with no declaration. \spadcommand{g x == x + 1} \returnType{Type: Void} @@ -12287,7 +12780,7 @@ $$ $$ \returnType{Type: Fraction Integer} -Here $x+1$ for $x = "axiom"$ makes no sense. +Here $x+1$ for $x = ``axiom''$ makes no sense. \spadcommand{g("axiom")} \begin{verbatim} There are 11 exposed and 5 unexposed library operations named + @@ -12341,6 +12834,8 @@ assign $n$ an integer value. You then speak of the integer $n$. However, note that the integer is not the name $n$ itself, but the value that you assign to $n$. +%Original Page 144 + Similarly, you can declare a variable $f$ in your workspace to have type {\sf Integer $\rightarrow$ Integer}, then assign $f$, through a definition or an assignment of an anonymous function. You then speak @@ -12404,6 +12899,8 @@ You do not use the parentheses ``{\tt ()}'' in a delayed assignment\ldots \spadcommand{cos24 == cos(24.0)} \returnType{Type: Void} +%Original Page 145 + nor in the evaluation. \spadcommand{cos24} @@ -12474,6 +12971,8 @@ AXIOM cannot determine the type of sin because it cannot analyze by declaring the function. \end{verbatim} +%Original Page 146 + Again, we could package-call the inside function. \spadcommand{sin x == sin(x)\$Float} \begin{verbatim} @@ -12540,6 +13039,8 @@ you call the function and results in a computational delay. Subsequent function calls with the same argument types use the compiled version of the code without delay. +%Original Page 147 + If Axiom cannot determine the type of everything, the function may still be executed \index{function!interpretation} but \index{interpret-code mode} in interpret-code mode: each statement in @@ -12600,6 +13101,8 @@ Cannot compile conversion for types involving local variables. \end{verbatim} \returnType{Type: Void} +%Original Page 148 + Sometimes you can help a function to compile by using an extra conversion or by using $pretend$. \index{pretend} See \sectionref{ugTypesSubdomains} for details. @@ -12665,6 +13168,8 @@ What is the value for $n = -3$? You did not define fact for argument -3 . \end{verbatim} +%Original Page 149 + Now for a second definition. Here is the value for $n = 0$. \spadcommand{facto(0) == 1} \returnType{Type: Void} @@ -12722,6 +13227,8 @@ Here is the first of two pieces. \spadcommand{eleven(n | n < 1) == n + 11} \returnType{Type: Void} +%Original Page 150 + And the general case. \spadcommand{eleven(m) == eleven(eleven(m - 12))} \returnType{Type: Void} @@ -12786,6 +13293,8 @@ the previous section. \spadcommand{eleven(n | n < 1) == n + 11} \returnType{Type: Void} +%Original Page 151 + \spadcommand{eleven(m) == eleven(eleven(m - 12))} \returnType{Type: Void} @@ -12855,6 +13364,8 @@ an integer. \spadcommand{t(n | even?(n)) == s(n quo 2)} \returnType{Type: Void} +%Original Page 152 + Finally, the odd numbered terms are the $s(i)$ for negative $i$. In piece-wise definitions, you can use different variables to define different pieces. Axiom will not get confused. @@ -12924,6 +13435,8 @@ Compiling function opposite with type The function opposite is not defined for the given argument(s). \end{verbatim} +%Original Page 153 + Explicit predicates tell Axiom that the given function definition piece is to be applied if the predicate evaluates to {\tt true} for the arguments to the function. You can use such ``constant'' @@ -13000,6 +13513,8 @@ functions will have the caching behavior. If you explicitly turn on caching for one or more names, you must explicitly turn off caching for those names when you want to stop saving their values. +%Original Page 154 + This causes the functions {\bf f} and {\bf g} to have the last three computed values saved. \spadcommand{)set functions cache 3 f g} @@ -13056,6 +13571,8 @@ highly unlikely that a function with no arguments should be cached.\\ You should also be careful about caching functions that depend on free variables. See \sectionref{ugUserFreeLocal} for an example. +%Original Page 155 + \section{Recurrence Relations} \label{ugUserRecur} @@ -13107,6 +13624,8 @@ than $10^{104}$ function calls. And, given all this, our definition of {\bf fib} obviously could not be used to calculate the five-hundredth Fibonacci number. +%Original Page 156 + Let's try it anyway. \spadcommand{fib(500)} \begin{verbatim} @@ -13162,6 +13681,8 @@ The Legendre polynomial of degree $n$. \spadcommand{p(n) == ((2*n-1)*x*p(n-1) - (n-1)*p(n-2))/n} \returnType{Type: Void} +%Original Page 157 + Compute the Legendre polynomial of degree $6.$ \spadcommand{p(6)} \begin{verbatim} @@ -13238,6 +13759,8 @@ f1 \ x \ == \ {-{z \sp 3}+{y \sp 2} -x} $$ \returnType{Type: FunctionCalled f1} +%Original Page 158 + This is the value of {\bf f1} at $x = 3$. Notice that the return type of the function is {\tt Polynomial (Integer)}, the same as $p$. \spadcommand{f1(3)} @@ -13318,6 +13841,8 @@ $$ $$ \returnType{Type: Expression Integer} +%Original Page 159 + \spadcommand{function(\%,'g,'x,'y)} $$ g @@ -13392,6 +13917,8 @@ $$ $$ \returnType{Type: PositiveInteger} +%Original Page 160 + You see that the second and fourth elements are interchanged. \spadcommand{k} $$ @@ -13485,6 +14012,8 @@ $$ $$ \returnType{Type: List Integer} +%Original Page 161 + \spadcommand{m} $$ \left[ @@ -13545,6 +14074,8 @@ ensures that it comes first. If it is in the second, then a swap occurs. In any case, the {\bf rest} of the original list must be updated to hold the result of the recursive call. +%Original Page 162 + \section{Free and Local Variables} \label{ugUserFreeLocal} @@ -13621,6 +14152,8 @@ $$ Parameters to a function are local variables in the function. Even if you issue a {\tt free} declaration for a parameter, it is still local. +%Original Page 163 + What happens if you do not declare that a variable $x$ in the body of your function is {\tt local} or {\tt free}? Well, Axiom decides on this basis: \begin{enumerate} @@ -13747,6 +14280,8 @@ Values are passed to functions by {\it reference}: a pointer to the value is passed rather than a copy of the value or a pointer to a copy. +%Original Page 164 + This is a global variable that is bound to a record object. \spadcommand{r : Record(i : Integer) := [1]} $$ @@ -13822,6 +14357,8 @@ fib(n) == \end{verbatim} \returnType{Type: Void} +%Original Page 165 + Compute the infinite stream of Fibonacci numbers. \spadcommand{fibs := [fib(n) for n in 1..]} $$ @@ -13889,6 +14426,8 @@ Anonymous functions are particularly useful for defining functions used only in one place. In the following examples, we show how to write some simple anonymous functions. +%Original Page 166 + This is a simple absolute value function. \spadcommand{x +-> if x < 0 then -x else x} $$ @@ -13989,6 +14528,8 @@ The one you use is a matter of taste. \subsection{Declaring Anonymous Functions} \label{ugUserAnonDeclare} +%Original Page 167 + If you declare any of the arguments you must declare all of them. Thus, \begin{verbatim} (x: INT,y): FRAC INT +-> (x + 2*y)/(y - 1) @@ -14107,6 +14648,8 @@ This family tree thus spans four generations. \spadcommand{children("douglas") == ["dougie","valerie"]} \returnType{Type: Void} +%Original Page 169 + Say ``no one else has children.'' \spadcommand{children(x) == []} \returnType{Type: Void} @@ -14165,6 +14708,8 @@ information. Then, once and for all, the functions are analyzed and compiled to machine code for run-time efficiency. Notice that no types are given anywhere in this example. They are not needed. +%Original Page 170 + Who are the grandchildren of ``richard''? \spadcommand{grandchildren "richard"} \begin{verbatim} @@ -14240,6 +14785,8 @@ separating entries by blanks and centering. \spadcommand{displayRow(n) == output center blankSeparate pascalRow(n)} \returnType{Type: Void} +%Original Page 171 + Here we have used three output operations. Operation \spadfunFrom{output}{OutputForm} displays the printable form of objects on the screen, \spadfunFrom{center}{OutputForm} centers a @@ -14320,6 +14867,8 @@ and so is the number $123454321$. The definition works for any datatype that has $n$ components that are accessed by the indices $1\ldots n$. +%Original Page 172 + Here is the definition for {\bf pal?}. It is simply a call to an auxiliary function called {\bf palAux?}. We are following the convention of ending a function's name with {\tt ?} if the function @@ -14433,6 +14982,8 @@ $$ \spadcommand{)set streams calculate 7} +%Original Page 173 + \section{Rules and Pattern Matching} \label{ugUserRules} @@ -14523,6 +15074,8 @@ subexpression is found that ``matches'' the pattern, the subexpression is replaced by the right-hand side of the rule. The details of what happens will be covered later. +%Original Page 174 + The customary Axiom notation for patterns is actually a shorthand for a longer, more general notation. Pattern variables can be made explicit by using a percent ``{\tt \%}'' as the first character of the @@ -14587,6 +15140,8 @@ $$ $$ \returnType{Type: Ruleset(Integer,Integer,Expression Integer)} +%Original Page 175 + Again, create an expression $f$ containing logarithms. \spadcommand{f := a * log(sin x) - 2 * log x} $$ @@ -14696,6 +15251,8 @@ $$ $$ \returnType{Type: Expression Integer} +%Original Page 176 + \spadcommand{sinCosProducts g} \begin{verbatim} Compiling body of rule sinCosProducts to compute value of type @@ -14766,6 +15323,8 @@ $$ $$ \returnType{Type: Expression Integer} +%Original Page 177 + Here is one final adornment you will find useful. When matching a pattern of the form $x + y$ to an expression containing a long sum of the form $a +\ldots+ b$, there is no way to predict in advance which @@ -14842,6 +15401,8 @@ Summary of pattern variable adornments: \end{tabular}\\ } +%Original Page 178 + Here are some final remarks on pattern matching. Pattern matching provides a very useful paradigm for solving certain classes of problems, namely, those that involve transformations of one form to @@ -14875,6 +15436,8 @@ application. \setcounter{chapter}{6} +%Original Page 179 + \chapter{Graphics} \label{ugGraph} @@ -14899,6 +15462,8 @@ A graph is displayed in a viewport window and it has a PostScript and other output forms are available so that Axiom \index{PostScript} images can be printed or used by other programs. +%Original Page 180 + \section{Two-Dimensional Graphics} \label{ugGraphTwoD} @@ -14940,32 +15505,32 @@ argument is the formula. For the second argument, write the name of the independent variable (here, $x$), followed by an ``{\tt =}'', and the range of values. +%Original Page 181 + Display this formula over the range $0 \leq x \leq 6$. Axiom converts your formula to a compiled function so that the results can be computed quickly and efficiently. \spadgraph{draw(sin(tan(x)) - tan(sin(x)),x = 0..6)} -%\begin{figure}[htbp] -%{\rm draw(sin(tan(x)) - tan(sin(x)),x = 0..6)\\} -%\vskip 0.2cm -%\includegraphics{ps/2d1vara.ps} -%\caption{$sin(tan(x)) - tan(sin(x))\ \ \ x = 0 \ldots6$} -%\end{figure} -%{\rm -%\par -%Notice that Axiom compiled the function before the graph was put -%on the screen. -% -%Here is the same graph on a different interval.\\ -% -%draw(sin(tan(x)) - tan(sin(x)),x = 10..16)\\ -%} -%\vskip 0.2cm -%\spadgraph{draw(sin(tan(x)) - tan(sin(x)),x = 10..16)} -%\begin{figure}[htbp] -%\includegraphics{ps/2d1varb.ps} -%\caption{$sin(tan(x)) - tan(sin(x))\ \ \ x = 10 \ldots16$} -%\end{figure} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/2d1vara.eps}} +\begin{center} +$sin(tan(x)) - tan(sin(x))\ \ \ x = 0 \ldots6$ +\end{center} +\end{minipage} + +Notice that Axiom compiled the function before the graph was put +on the screen. + +Here is the same graph on a different interval. + +\spadgraph{draw(sin(tan(x)) - tan(sin(x)),x = 10..16)} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/2d1varb.eps}} +\begin{center} +$sin(tan(x)) - tan(sin(x))\ \ \ x = 10 \ldots16$ +\end{center} +\end{minipage} Once again the formula is converted to a compiled function before any points were computed. If you want to graph the same function on @@ -14974,18 +15539,18 @@ that the function has to be compiled only once. This time we first define the function. \spadcommand{f(x) == (x-1)*(x-2)*(x-3) } -%\begin{figure} -%\tpd{0 0 300 300 ps/2d1vard.ps} -%\end{figure} -\returnType{Type: Void} -%\epsffile[14 14 188 199]{ps/2d1vard.ps} -%\hspace*{\baseLeftSkip}\special{psfile=ps/2dctrl.ps} + +%Original Page 182 To draw the function, the first argument is its name and the second is just the range with no independent variable. \spadgraph{draw(f, 0..4) } -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/2d1vard.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/2d1vard.eps}} +\begin{center} +$f(x) == (x-1)(x-2)(x-3)$ +\end{center} +\end{minipage} \subsection{Plotting Two-Dimensional Parametric Plane Curves} \label{ugGraphTwoDPar} @@ -15011,18 +15576,28 @@ example of an option is $curveColor == bright\ red().$\\ } Here's an example: +%Original Page 183 + Define a parametric curve using a range involving $\%pi$, Axiom's way of saying $\pi$. For parametric curves, Axiom compiles two functions, one for each of the functions $f$ and $g$. \spadgraph{draw(curve(sin(t)*sin(2*t)*sin(3*t), sin(4*t)*sin(5*t)*sin(6*t)), t = 0..2*\%pi)} -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/2dppca.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/2dppca.eps}} +\begin{center} +$curve(sin(t)*sin(2t)*sin(3t), sin(4t)*sin(5t)*sin(6t))$ +\end{center} +\end{minipage} The title may be an arbitrary string and is an optional argument to the {\bf draw} command. \spadgraph{draw(curve(cos(t), sin(t)), t = 0..2*\%pi)} -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/2dppcb.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/2dppcb.eps}} +\begin{center} +$curve(cos(t), sin(t)), \quad t = 0..2\pi$ +\end{center} +\end{minipage} If you plan on plotting $x = f(t)$, $y = g(t)$ as $t$ ranges over several intervals, you may want to define functions $f$ and $g$ first, @@ -15046,20 +15621,29 @@ values. \end{verbatim} \returnType{Type: Void} +%Original Page 184 + Give to {\tt curve} the names of the functions, then write the range without the name of the independent variable. \spadgraph{draw(curve(f,g),0..\%pi) } -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/2dppcc.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/2dppcc.eps}} +\begin{center} +$curve(f,g) \quad 0..\pi$ +\end{center} +\end{minipage} Here is another look at the same curve but over a different range. Notice that $f$ and $g$ are not recompiled. Also note that Axiom provides a default title based on the first function specified in {\bf curve}. \spadgraph{draw(curve(f,g),-4*\%pi..4*\%pi) } - -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/2dppce.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/2dppce.eps}} +\begin{center} +$curve(f,g)\quad -4\pi..4\pi$ +\end{center} +\end{minipage} \subsection{Plotting Plane Algebraic Curves} \label{ugGraphTwoDPlane} @@ -15077,6 +15661,8 @@ ${\frac{\partial p}{\partial y}}(x,y)$ are not both zero. \index{curve!smooth} \index{curve!non-singular} \index{smooth curve} \index{non-singular curve} +%Original Page 185 + \boxed{4.6in}{ The general format for drawing a non-singular solution curve given by a polynomial of the form $p(x,y) = 0$ is: @@ -15107,9 +15693,12 @@ $$ The first argument is always expressed as an equation of the form $p = 0$ where $p$ is a polynomial. \spadgraph{draw(p = 0, x, y, range == [-1..11, -7..7]) } - -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/2dpaca.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/2dpaca.eps}} +\begin{center} +$p = 0, x, y,\quad range == [-1..11, -7..7]$ +\end{center} +\end{minipage} \subsection{Two-Dimensional Options} \label{ugGraphTwoDOptions} @@ -15126,6 +15715,10 @@ clip&curveColor&range\\ toScale&pointColor&coordinates\\ \end{tabular} + +%Original Page 186 + + The $adaptive$ option turns adaptive plotting on or off. \index{adaptive plotting} Adaptive plotting uses an algorithm that traverses a graph and computes more points for those parts of the @@ -15136,8 +15729,12 @@ the more points the algorithm computes. The {\tt adaptive} option is normally on. Here we turn it off. \spadgraph{draw(sin(1/x),x=-2*\%pi..2*\%pi, adaptive == false)} -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/2doptad.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/2doptad.eps}} +\begin{center} +$sin(1/x),x=-2\pi..2\pi,\quad adaptive == false$ +\end{center} +\end{minipage} The {\tt clip} option turns clipping on or off. \index{graphics!2D options!clipping} @@ -15146,8 +15743,12 @@ If on, large values are cut off according to \spadgraph{draw(tan(x),x=-2*\%pi..2*\%pi, clip == true)} -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/2doptcp.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/2doptcp.eps}} +\begin{center} +$tan(x),x=-2\pi..2\pi,\quad clip == true$ +\end{center} +\end{minipage} Option {\tt toScale} does plotting to scale if {\tt true} or uses the entire viewport if {\tt false}. The default can be determined using @@ -15156,8 +15757,14 @@ entire viewport if {\tt false}. The default can be determined using \spadgraph{draw(sin(x),x=-\%pi..\%pi, toScale == true, unit == [1.0,1.0])} -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/2doptsc.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/2doptsc.eps}} +\begin{center} +$sin(x),x=-\pi..\pi,\quad toScale == true,\quad unit == [1.0,1.0]$ +\end{center} +\end{minipage} + +%Original Page 187 Option {\tt clip} with a range sets point clipping of a graph within the \index{graphics!2D options!clip in a range} ranges specified in @@ -15165,8 +15772,13 @@ the list $[x range,y range]$. \index{clipping} If only one range is specified, clipping applies to the y-axis. \spadgraph{draw(sec(x),x=-2*\%pi..2*\%pi, clip == [-2*\%pi..2*\%pi,-\%pi..\%pi], unit == [1.0,1.0])} -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/2doptcpr.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/2doptcpr.eps}} +\begin{center} +$sec(x),x=-2\pi..2\pi, \quad clip == [-2\pi..2\pi,-\pi..\pi], + unit == [1.0,1.0]$ +\end{center} +\end{minipage} Option {\tt curveColor} sets the color of the graph curves or lines to be the \index{graphics!2D options!curve color} indicated palette color @@ -15176,8 +15788,12 @@ be the \index{graphics!2D options!curve color} indicated palette color \spadgraph{draw(sin(x),x=-\%pi..\%pi, curveColor == bright red())} -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/2doptcvc.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/2doptcvc.eps}} +\begin{center} +$sin(x),x=-\pi..\pi, \quad curveColor == bright red()$ +\end{center} +\end{minipage} Option {\tt pointColor} sets the color of the graph points to the indicated \index{graphics!2D options!point color} palette color (see @@ -15185,30 +15801,50 @@ indicated \index{graphics!2D options!point color} palette color (see \index{color!point} \spadgraph{draw(sin(x),x=-\%pi..\%pi, pointColor == pastel yellow())} -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/2doptptc.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/2doptptc.eps}} +\begin{center} +$sin(x),x=-\pi..\pi, \quad pointColor == pastel yellow()$ +\end{center} +\end{minipage} + +%Original Page 188 Option {\tt unit} sets the intervals at which the axis units are plotted \index{graphics!2D options!set units} according to the indicated steps [$x$ interval, $y$ interval]. \spadgraph{draw(curve(9*sin(3*t/4),8*sin(t)), t = -4*\%pi..4*\%pi, unit == [2.0,1.0])} -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/2doptut.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/2doptut.eps}} +\begin{center} +$9sin(3t/4),8sin(t)), t = -4\pi..4\pi, \quad unit == [2.0,1.0]$ +\end{center} +\end{minipage} Option {\tt range} sets the range of variables in a graph to be within the ranges \index{graphics!2D options!range} for solving plane algebraic curve plots. \spadgraph{draw(y**2 + y - (x**3 - x) = 0, x, y, range == [-2..2,-2..1], unit==[1.0,1.0])} -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/2doptrga.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/2doptrga.eps}} +\begin{center} +$y^2 + y - (x^3 - x) = 0, x, y, range == [-2..2,-2..1], unit==[1.0,1.0]$ +\end{center} +\end{minipage} A second example of a solution plot. \spadgraph{draw(x**2 + y**2 = 1, x, y, range == [-3/2..3/2,-3/2..3/2], unit==[0.5,0.5])} -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/2doptrgb.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/2doptrgb.eps}} +\begin{center} +$x^2 + y^2 = 1, x, y, range == [-3/2..3/2,-3/2..3/2], unit==[0.5,0.5]$ +\end{center} +\end{minipage} + +%Original Page 189 Option $coordinates$ indicates the coordinate system in which the graph \index{graphics!2D options!coordinates} is plotted. The default @@ -15220,8 +15856,12 @@ is to use the Cartesian coordinate system. \spadgraph{draw(curve(sin(5*t),t),t=0..2*\%pi, coordinates == polar)} -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/2doptplr.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/2doptplr.eps}} +\begin{center} +$sin(5t),t),t=0..2\pi,\quad coordinates == polar$ +\end{center} +\end{minipage} \subsection{Color} \label{ugGraphColor} @@ -15267,22 +15907,31 @@ Color multiplication is not associative: changing the order of grouping produces different results. \end{description} +%Original Page 190 + These functions can be used to change the point and curve colors for two- and three-di\-men\-sion\-al graphs. Use the {\tt pointColor} option for points. \spadgraph{draw(x**2,x=-1..1,pointColor == green())} -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/23dcola.ps} - +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/23dcola.eps}} +\begin{center} +$x^2, x=-1..1, \quad pointColor == green()$ +\end{center} +\end{minipage} Use the {\tt curveColor} option for curves. \spadgraph{draw(x**2,x=-1..1,curveColor == color(13) + 2*blue())} -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/23dcolb.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/23dcolb.eps}} +\begin{center} +$x^2, x=-1..1, \quad curveColor == color(13) + 2*blue()$ +\end{center} +\end{minipage} \subsection{Palette} \label{ugGraphColorPalette} @@ -15307,8 +15956,8 @@ To change the shade of a color, apply the name of a shade to it. \spadcommand{myFavoriteColor := dark blue() } $$ -[{ \mbox{\rm Hue: } {22} \mbox{\rm Weight: } {1.0}} \mbox{\rm ] from the } -Dark \mbox{\rm palette} +[{ \mbox{\rm Hue: }{22}\quad \mbox{\rm Weight: }{1.0}} \mbox{\rm ] from the } +Dark\ \mbox{\rm palette} $$ \returnType{Type: Palette} @@ -15321,11 +15970,13 @@ $$ $$ \returnType{Type: PositiveInteger} +%Original Page 191 + The expression $hue(color)$ returns its hue. \spadcommand{hue myFavoriteColor } $$ -\mbox{\rm Hue: } {22} \mbox{\rm Weight: } {1.0} +\mbox{\rm Hue: } {22}\quad \mbox{\rm Weight: } {1.0} $$ \returnType{Type: Color} @@ -15333,9 +15984,12 @@ Palettes can be used in specifying colors in two-di\-men\-sion\-al graphs. \spadgraph{draw(x**2,x=-1..1,curveColor == dark blue())} -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/23dpal.ps} - +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/23dpal.eps}} +\begin{center} +$x^2,x=-1..1, \quad curveColor == dark blue()$ +\end{center} +\end{minipage} \subsection{Two-Dimensional Control-Panel} \label{ugGraphTwoDControl} @@ -15347,18 +16001,12 @@ The panel is displayed on the side of the viewport closest to where you clicked. Each of the buttons which toggle on and off show the current state of the graph. -%\begin{texonly} -%\typeout{2D control-panel.} -\begin{figure}[htbp] -%{\epsfverbosetrue\epsfxsize=2in% -%\def\epsfsize#1#2{\epsfxsize}\hspace*{\baseLeftSkip}% -%%\epsffile[0 0 144 289]{ps/2dctrl.ps}} -%\begin{picture}(147,252)%(-143,0) -%\hspace*{\baseLeftSkip}\special{psfile=ps/2dctrl.ps} -%\end{picture} -\caption{Two-dimensional control-panel.} -\end{figure} -%\end{texonly} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=1.0]{ps/2dctrl.eps}} +\begin{center} +Two-dimensional control-panel. +\end{center} +\end{minipage} \subsubsection{Transformations} \index{graphics!2D control-panel!transformations} @@ -15396,6 +16044,9 @@ The window directly below the transformation potentiometer windows is used to display system messages relating to the viewport and the control-panel. The following format is displayed: \newline % + +%Original Page 192 + \begin{center} [scaleX, scaleY] $>$graph$<$ [translateX, translateY] \newline \end{center} @@ -15424,7 +16075,9 @@ will be manipulated. Initially, the graph for which the viewport is created occupies the first slot, is displayed, and is selected. % -% + +%%Original Page 193 + \begin{description} % \item[Clear:] The {\bf Clear} button deselects every viewport graph slot. @@ -15513,7 +16166,9 @@ to the type of the argument (for example, {\it integer}). If appropriate, a default value for an argument is given in parentheses immediately following the name. -% + +%%Original Page 194 + \begin{description} % \item[{\bf adaptive}]\funArgs{\optArg{boolean\argDef{true}}} @@ -15590,7 +16245,9 @@ upper left-hand corner of a two-di\-men\-sion\-al viewport, relative to the display root window. The upper left-hand corner of the display is considered to be at the (0, 0) position. -% + +%%Original Page 195 + \item[{\bf viewSizeDefault}]\funArgs{\optArg{list\argDef{[200,200]}}} sets or indicates the default size in which two @@ -15670,7 +16327,9 @@ to be displayed or not. \item[{\bf region}]\funArgs{viewport, integer\argDef{1}, string\argDef{"off"}} declares whether graph {\it integer} is or is not to be displayed with a bounding rectangle. -% + +%%Original Page 196 + \item[{\bf reset}]\funArgs{viewport} resets all the properties of {\it viewport}. % @@ -15696,7 +16355,8 @@ designates the title for {\it viewport}. $integer_{n}$\argDef{1}, $float_{x}$\argDef{0.0}, $float_{y}$\argDef{0.0}} \index{graphics!2D commands!translate} -causes graph {\it n} to be moved {\it x} and {\it y} units in the respective directions. +causes graph {\it n} to be moved {\it x} and {\it y} units in the respective +directions. % \item[{\bf write}]\funArgs{viewport, $string_{directory}$, \optArg{strings}} @@ -15827,68 +16487,56 @@ Finally, here is the list. \spadcommand{llp := [ [p1,p2], [p2,p3], [p3,p4], [p4,p1], [p5,p6], [p6,p7], [p7,p8], [p8,p5], [p9,p10], [p10,p11], [p11,p12], [p12,p9] ] } $$ +\begin{array}{@{}l} +\displaystyle \left[ -{\left[ {\left[ {1.0}, {1.0} -\right]}, - {\left[ {0.0}, {1.0} -\right]} -\right]}, - {\left[ {\left[ {0.0}, {1.0} -\right]}, - {\left[ {0.0}, {0.0} -\right]} -\right]}, - {\left[ {\left[ {0.0}, {0.0} -\right]}, - {\left[ {1.0}, {0.0} -\right]} -\right]}, - {\left[ {\left[ {1.0}, {0.0} -\right]}, - {\left[ {1.0}, {1.0} -\right]} -\right]}, - {\left[ {\left[ {1.0}, {0.5} -\right]}, - {\left[ {0.5}, {0.0} -\right]} -\right]}, - {\left[ {\left[ {0.5}, {0.0} -\right]}, - {\left[ {0.0}, {0.5} -\right]} -\right]}, - {\left[ {\left[ {0.0}, {0.5} -\right]}, - {\left[ {0.5}, {1.0} -\right]} -\right]}, - {\left[ {\left[ {0.5}, {1.0} -\right]}, - {\left[ {1.0}, {0.5} -\right]} -\right]}, - {\left[ {\left[ {0.25}, {0.25} -\right]}, - {\left[ {0.25}, {0.75} -\right]} -\right]}, - {\left[ {\left[ {0.25}, {0.75} -\right]}, - {\left[ {0.75}, {0.75} -\right]} -\right]}, - {\left[ {\left[ {0.75}, {0.75} -\right]}, - {\left[ {0.75}, {0.25} -\right]} -\right]}, - {\left[ {\left[ {0.75}, {0.25} -\right]}, - {\left[ {0.25}, {0.25} -\right]} -\right]} + {\left[ {\left[ {1.0}, {1.0} \right]}, + {\left[ {0.0}, {1.0} \right]} + \right]}, + {\left[ {\left[ {0.0}, {1.0} \right]}, + {\left[ {0.0}, {0.0} \right]} + \right]}, + {\left[ {\left[ {0.0}, {0.0} \right]}, + {\left[ {1.0}, {0.0} \right]} + \right]}, + {\left[ {\left[ {1.0}, {0.0} \right]}, + {\left[ {1.0}, {1.0} \right]} + \right]}, +\right.\\ +\left. +\displaystyle + {\left[ {\left[ {1.0}, {0.5} \right]}, + {\left[ {0.5}, {0.0} \right]}, + \right]}, + {\left[ {\left[ {0.5}, {0.0} \right]}, + {\left[ {0.0}, {0.5} \right]} + \right]}, + {\left[ {\left[ {0.0}, {0.5} \right]}, + {\left[ {0.5}, {1.0} \right]} + \right]}, +\right.\\ +\left. +\displaystyle + {\left[ {\left[ {0.5}, {1.0} \right]}, + {\left[ {1.0}, {0.5} \right]} + \right]}, + {\left[ {\left[ {0.25}, {0.25} \right]}, + {\left[ {0.25}, {0.75} \right]}, + \right]}, + {\left[ {\left[ {0.25}, {0.75} \right]}, + {\left[ {0.75}, {0.75} \right]} + \right]}, +\right.\\ +\left. +\displaystyle + {\left[ {\left[ {0.75}, {0.75} \right]}, + {\left[ {0.75}, {0.25} \right]} + \right]}, + {\left[ {\left[ {0.75}, {0.25} \right]}, + {\left[ {0.25}, {0.25} \right]} + \right]} \right] +\end{array} $$ \returnType{Type: List List Point DoubleFloat} @@ -15911,8 +16559,7 @@ $$ \spadcommand{lsize := [size1, size1, size1, size1, size2, size2, size2, size2, size3, size3, size3, size3] } $$ \left[ -6, 6, 6, 6, 8, 8, 8, 8, size3, size3, size3, -size3 +6, 6, 6, 6, 8, 8, 8, 8, 10, 10, 10, 10 \right] $$ \returnType{Type: List Polynomial Integer} @@ -15942,25 +16589,43 @@ $$ \spadcommand{lpc := [pc1, pc1, pc1, pc1, pc2, pc2, pc2, pc2, pc3, pc3, pc3, pc3] } $$ +\begin{array}{@{}l} \left[ {[{ \mbox{\rm Hue: } 1 \mbox{\rm Weight: } {1.0}} \mbox{\rm ] from the } Pastel \mbox{\rm palette} }, {[{ \mbox{\rm Hue: } 1 \mbox{\rm Weight: } -{1.0}} \mbox{\rm ] from the } Pastel \mbox{\rm palette} }, {[{ \mbox{\rm -Hue: } 1 \mbox{\rm Weight: } {1.0}} \mbox{\rm ] from the } Pastel \mbox{\rm -palette} }, {[{ \mbox{\rm Hue: } 1 \mbox{\rm Weight: } {1.0}} \mbox{\rm ] -from the } Pastel \mbox{\rm palette} }, {[{ \mbox{\rm Hue: } {14} -\mbox{\rm Weight: } {1.0}} \mbox{\rm ] from the } Dim \mbox{\rm palette} }, - {[{ \mbox{\rm Hue: } {14} \mbox{\rm Weight: } {1.0}} \mbox{\rm ] from the -} Dim \mbox{\rm palette} }, {[{ \mbox{\rm Hue: } {14} \mbox{\rm Weight: } -{1.0}} \mbox{\rm ] from the } Dim \mbox{\rm palette} }, {[{ \mbox{\rm Hue: -} {14} \mbox{\rm Weight: } {1.0}} \mbox{\rm ] from the } Dim \mbox{\rm -palette} }, {[{ \mbox{\rm Hue: } {11} \mbox{\rm Weight: } {1.0}} \mbox{\rm -] from the } Pastel \mbox{\rm palette} }, {[{ \mbox{\rm Hue: } {11} -\mbox{\rm Weight: } {1.0}} \mbox{\rm ] from the } Pastel \mbox{\rm palette} -}, {[{ \mbox{\rm Hue: } {11} \mbox{\rm Weight: } {1.0}} \mbox{\rm ] from -the } Pastel \mbox{\rm palette} }, {[{ \mbox{\rm Hue: } {11} \mbox{\rm -Weight: } {1.0}} \mbox{\rm ] from the } Pastel \mbox{\rm palette} } -\right] +{1.0}} \mbox{\rm ] from the } Pastel \mbox{\rm palette} }, +\right. \\ +\\ +\left. +{[{ \mbox{\rm Hue: } 1 \mbox{\rm Weight: } {1.0}} \mbox{\rm ] from the } +Pastel \mbox{\rm palette} }, {[{ \mbox{\rm Hue: } 1 \mbox{\rm Weight: } +{1.0}} \mbox{\rm ] from the } Pastel \mbox{\rm palette} }, +\right. \\ +\\ +\left. +{[{ \mbox{\rm Hue: } {14} \mbox{\rm Weight: } {1.0}} \mbox{\rm ] from the } +Dim \mbox{\rm palette} }, {[{ \mbox{\rm Hue: } {14} \mbox{\rm Weight: } +{1.0}} \mbox{\rm ] from the } Dim \mbox{\rm palette} }, +\right. \\ +\\ +\left. +{[{ \mbox{\rm Hue: } {14} \mbox{\rm Weight: } {1.0}} \mbox{\rm ] from the } +Dim \mbox{\rm palette} }, {[{ \mbox{\rm Hue: } {14} \mbox{\rm Weight: } +{1.0}} \mbox{\rm ] from the } Dim \mbox{\rm palette} }, +\right. \\ +\\ +\left. +{[{ \mbox{\rm Hue: } {11} \mbox{\rm Weight: } {1.0}} \mbox{\rm ] from the } +Pastel \mbox{\rm palette} }, {[{ \mbox{\rm Hue: } {11} \mbox{\rm Weight: } +{1.0}} \mbox{\rm ] from the } Pastel \mbox{\rm palette} }, +\right. \\ +\\ +\left. +{[{ \mbox{\rm Hue: } {11} \mbox{\rm Weight: } {1.0}} \mbox{\rm ] from the } +Pastel \mbox{\rm palette} }, {[{ \mbox{\rm Hue: } {11} \mbox{\rm Weight: } +{1.0}} \mbox{\rm ] from the } Pastel \mbox{\rm palette} } + \right] +\end{array} $$ \returnType{Type: List Palette} @@ -15968,25 +16633,43 @@ Here are the colors for the lines. \spadcommand{lc := [pastel blue(), light yellow(), dim green(), bright red(), light green(), dim yellow(), bright blue(), dark red(), pastel red(), light blue(), dim green(), light yellow()] } $$ -\left[ -{[{ \mbox{\rm Hue: } {22} \mbox{\rm Weight: } {1.0}} \mbox{\rm ] from the } -Pastel \mbox{\rm palette} }, {[{ \mbox{\rm Hue: } {11} \mbox{\rm Weight: } -{1.0}} \mbox{\rm ] from the } Light \mbox{\rm palette} }, {[{ \mbox{\rm -Hue: } {14} \mbox{\rm Weight: } {1.0}} \mbox{\rm ] from the } Dim \mbox{\rm -palette} }, {[{ \mbox{\rm Hue: } 1 \mbox{\rm Weight: } {1.0}} \mbox{\rm ] -from the } Bright \mbox{\rm palette} }, {[{ \mbox{\rm Hue: } {14} -\mbox{\rm Weight: } {1.0}} \mbox{\rm ] from the } Light \mbox{\rm palette} }, - {[{ \mbox{\rm Hue: } {11} \mbox{\rm Weight: } {1.0}} \mbox{\rm ] from the -} Dim \mbox{\rm palette} }, {[{ \mbox{\rm Hue: } {22} \mbox{\rm Weight: } -{1.0}} \mbox{\rm ] from the } Bright \mbox{\rm palette} }, {[{ \mbox{\rm -Hue: } 1 \mbox{\rm Weight: } {1.0}} \mbox{\rm ] from the } Dark \mbox{\rm -palette} }, {[{ \mbox{\rm Hue: } 1 \mbox{\rm Weight: } {1.0}} \mbox{\rm ] -from the } Pastel \mbox{\rm palette} }, {[{ \mbox{\rm Hue: } {22} -\mbox{\rm Weight: } {1.0}} \mbox{\rm ] from the } Light \mbox{\rm palette} }, - {[{ \mbox{\rm Hue: } {14} \mbox{\rm Weight: } {1.0}} \mbox{\rm ] from the -} Dim \mbox{\rm palette} }, {[{ \mbox{\rm Hue: } {11} \mbox{\rm Weight: } -{1.0}} \mbox{\rm ] from the } Light \mbox{\rm palette} } -\right] ++\begin{array}{@{}l} + \left[ + {[{ \mbox{\rm Hue: } {22} \mbox{\rm Weight: } {1.0}} \mbox{\rm ] from the } + Pastel \mbox{\rm palette} }, {[{ \mbox{\rm Hue: } {11} \mbox{\rm Weight: } +{1.0}} \mbox{\rm ] from the } Light \mbox{\rm palette} }, +\right. \\ +\\ +\left. +{[{ \mbox{\rm Hue: } {14} \mbox{\rm Weight: } {1.0}} \mbox{\rm ] from the } +Dim \mbox{\rm palette} }, {[{ \mbox{\rm Hue: } 1 \mbox{\rm Weight: } +{1.0}} \mbox{\rm ] from the } Bright \mbox{\rm palette} }, +\right. \\ +\\ +\left. +{[{ \mbox{\rm Hue: } {14} \mbox{\rm Weight: } {1.0}} \mbox{\rm ] from the } +Light \mbox{\rm palette} }, {[{ \mbox{\rm Hue: } {11} \mbox{\rm Weight: } +{1.0}} \mbox{\rm ] from the } Dim \mbox{\rm palette} }, +\right. \\ +\\ +\left. +{[{ \mbox{\rm Hue: } {22} \mbox{\rm Weight: } {1.0}} \mbox{\rm ] from the } +Bright \mbox{\rm palette} }, {[{ \mbox{\rm Hue: } 1 \mbox{\rm Weight: } +{1.0}} \mbox{\rm ] from the } Dark \mbox{\rm palette} }, +\right. \\ +\\ +\left. +{[{ \mbox{\rm Hue: } 1 \mbox{\rm Weight: } {1.0}} \mbox{\rm ] from the } +Pastel \mbox{\rm palette} }, {[{ \mbox{\rm Hue: } {22} \mbox{\rm Weight: } +{1.0}} \mbox{\rm ] from the } Light \mbox{\rm palette} }, +\right. \\ +\\ +\left. +{[{ \mbox{\rm Hue: } {14} \mbox{\rm Weight: } {1.0}} \mbox{\rm ] from the } +Dim \mbox{\rm palette} }, {[{ \mbox{\rm Hue: } {11} \mbox{\rm Weight: } + {1.0}} \mbox{\rm ] from the } Light \mbox{\rm palette} } + \right] +\end{array} $$ \returnType{Type: List Palette} @@ -16143,7 +16826,7 @@ plotData2D(name, title) == \end{verbatim} % This command will actually create the viewport and the graph if -the point data is in the file $"file.data"$. +the point data is in the file $``file.data''$. \begin{verbatim} plotData2D("file.data", "2D Data Plot") \end{verbatim} @@ -16209,6 +16892,8 @@ of a surface. The simplest three-di\-men\-sion\-al graph is that of a surface defined by a function of two variables, $z = f(x,y)$. +%Original Page 197 + \boxed{4.6in}{ The general format for drawing a surface defined by a formula $f(x,y)$ of two variables $x$ and $y$ is: @@ -16219,7 +16904,7 @@ of two variables $x$ and $y$ is: where $a..b$ and $c..d$ define the range of $x$ and $y$, and where {\it options} prescribes zero or more options as described in \sectionref{ugGraphThreeDOptions}. -An example of an option is $title == "Title\ of\ Graph".$ +An example of an option is $title == ``Title\ of\ Graph''.$ An alternative format involving a function $f$ is also available.\\ } @@ -16230,8 +16915,12 @@ the variable name and an {\tt =} sign. \spadgraph{draw(cos(x*y),x=-3..3,y=-3..3)} -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/3d2vara.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/3d2vara.eps}} +\begin{center} +$cos(xy), x=-3..3, y=-3..3$ +\end{center} +\end{minipage} If you intend to use a function more than once, or it is long and complex, then first @@ -16249,13 +16938,18 @@ default title. \spadgraph{draw(f,-\%pi..\%pi,-\%pi..\%pi) } -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/3d2varb.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/3d2varb.eps}} +\begin{center} +$f, -\pi..\pi, -\pi..\pi$ +\end{center} +\end{minipage} + +%Original Page 198 \subsection{Plotting Three-Dimensional Parametric Space Curves} \label{ugGraphThreeDParm} - A second kind of three-di\-men\-sion\-al graph is a three-di\-men\-sion\-al space curve \index{curve!parametric space} defined by the parametric equations for $x(t)$, $y(t)$, @@ -16273,7 +16967,7 @@ $z = h(t)$ is: where $a..b$ defines the range of the independent variable $t$, and where {\it options} prescribes zero or more options as described in \sectionref{ugGraphThreeDOptions}. -An example of an option is $title == "Title\ of\ Graph".$ +An example of an option is $title == ``Title\ of\ Graph''.$ An alternative format involving functions $f$, $g$ and $h$ is also available.\\ } @@ -16284,8 +16978,12 @@ the range specification with the variable name and an \spadgraph{draw(curve(5*cos(t), 5*sin(t),t), t=-12..12)} -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/3dpsca.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/3dpsca.eps}} +\begin{center} +$curve(5cos(t), 5sin(t),t),\quad t=-12..12$ +\end{center} +\end{minipage} Alternatively, you can draw space curves by referring to functions. @@ -16314,14 +17012,20 @@ or if the functions are long and complex. \end{verbatim} \returnType{Type: Void} +%Original Page 199 + Give the names of the functions and drop the variable name specification in the second argument. Again, Axiom supplies a default title. \spadgraph{draw(curve(i1,i2,i3),0..15*\%pi) } -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/3dpscb.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/3dpscb.eps}} +\begin{center} +$curve(i1,i2,i3),\quad 0..15\pi$ +\end{center} +\end{minipage} \subsection{Plotting Three-Dimensional Parametric Surfaces} \label{ugGraphThreeDPar} @@ -16332,7 +17036,6 @@ A third kind of three-di\-men\-sion\-al graph is a surface defined by parametric equations for $x(u,v)$, $y(u,v)$, and $z(u,v)$ of two independent variables $u$ and $v$. - \boxed{4.6in}{ The general format for drawing a three-di\-men\-sion\-al graph defined by parametric formulas $x = f(u,v)$, $y = g(u,v)$, @@ -16345,7 +17048,7 @@ where $a..b$ and $c..d$ define the range of the independent variables $u$ and $v$, and where {\it options} prescribes zero or more options as described in \sectionref{ugGraphThreeDOptions}. -An example of an option is $title == "Title\ of\ Graph".$ +An example of an option is $title == ``Title\ of\ Graph''.$ An alternative format involving functions $f$, $g$ and $h$ is also available.\\ } @@ -16361,8 +17064,15 @@ here as parabolic cylindrical coordinates (see \spadgraph{draw(surface(u*cos(v), u*sin(v), v*cos(u)), u=-4..4, v=0..\%pi, coordinates== parabolicCylindrical)} -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/3dpsa.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/3dpsa.eps}} +\begin{center} +$surface(u cos(v), u sin(v), v cos(u)), u=-4..4, v=0..\pi, +coordinates==parabolicCylindrical$ +\end{center} +\end{minipage} + +%Original Page 200 Again, you can graph these parametric surfaces using functions, if the functions are long and complex. @@ -16414,8 +17124,12 @@ choosing the toroidal coordinate system. \spadgraph{draw(surface(n1,n2,n3), 1..4, 1..2*\%pi, coordinates == toroidal(1\$DFLOAT)) } -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/3dpsb.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/3dpsb.eps}} +\begin{center} +$surface(n1,n2,n3), 1..4, 1..2\pi, coordinates == toroidal(1\$DFLOAT)$ +\end{center} +\end{minipage} \subsection{Axiom Images} \newpage @@ -16459,13 +17173,19 @@ style&tubeRadius&var2Steps\\ colorFunction&tubePoints&space\\ \end{tabular} +%Original Page 201 + The option $title$ gives your graph a title. \index{graphics!3D options!title} \spadgraph{draw(cos(x*y),x=0..2*\%pi,y=0..\%pi,title == "Title of Graph") } -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/3doptttl.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/3doptttl.eps}} +\begin{center} +$cos(xy),x=0..2\pi,y=0..\pi,\quad title == "{\rm Title\ of\ Graph}"$ +\end{center} +\end{minipage} The $style$ determines which of four rendering algorithms is used for \index{rendering} @@ -16475,8 +17195,12 @@ The choices are \spadgraph{draw(cos(x*y),x=-3..3,y=-3..3, style=="smooth", title=="Smooth Option")} -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/3doptsty.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/3doptsty.eps}} +\begin{center} +$cos(xy),x=-3..3,y=-3..3, style=="smooth", title=="{\rm Smooth\ Option}"$ +\end{center} +\end{minipage} In all but the wire-mesh style, polygons in a surface or tube plot are normally colored in a graph according to their @@ -16494,10 +17218,16 @@ value of the parametric variable specified for a tube plot. \spadcommand{color1(t) == t } \returnType{Type: Void} +%Original Page 202 + \spadgraph{draw(curve(sin(t), cos(t),0), t=0..2*\%pi, tubeRadius == .3, colorFunction == color1) } -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/3doptcf1.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/3doptcf1.eps}} +\begin{center} +$curve(sin(t), cos(t),0), t=0..2\pi, tubeRadius== .3, colorFunction== color1$ +\end{center} +\end{minipage} A function of two variables makes the color depend on the values of the independent variables. @@ -16509,8 +17239,12 @@ Use the option {\tt colorFunction} for special coloring. \spadgraph{draw(cos(u*v), u=-3..3, v=-3..3, colorFunction == color2) } -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/3doptcf2.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/3doptcf2.eps}} +\begin{center} +$cos(uv), u=-3..3, v=-3..3, colorFunction == color2$ +\end{center} +\end{minipage} With a three variable function, the color also depends on the value of the function. @@ -16518,10 +17252,16 @@ color also depends on the value of the function. \spadcommand{color3(x,y,fxy) == sin(x*fxy) + cos(y*fxy) } \returnType{Type: Void} +%Original Page 203 + \spadgraph{draw(cos(x*y), x=-3..3, y=-3..3, colorFunction == color3) } -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/3doptcf3.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/3doptcf3.eps}} +\begin{center} +$cos(xy), x=-3..3, y=-3..3, colorFunction == color3$ +\end{center} +\end{minipage} Normally the Cartesian coordinate system is used. \index{Cartesian!coordinate system} @@ -16543,8 +17283,12 @@ coordinate system. \spadgraph{draw(m, 0..2*\%pi,0..\%pi, coordinates == spherical, style=="shade") } -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/3doptcrd.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/3doptcrd.eps}} +\begin{center} +$m, 0..2\pi,0..\pi, coordinates == spherical, style=="shade"$ +\end{center} +\end{minipage} Space curves may be displayed as tubes with polygonal cross sections. \index{tube} @@ -16552,14 +17296,20 @@ Two options, {\tt tubeRadius} and {\tt tubePoints}, control the size and shape of this cross section. % +%Original Page 204 + The {\tt tubeRadius} option specifies the radius of the tube that \index{tube!radius} encircles the specified space curve. \spadgraph{draw(curve(sin(t),cos(t),0),t=0..2*\%pi, style=="shade", tubeRadius == .3)} -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/3doptrad.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/3doptrad.eps}} +\begin{center} +$curve(sin(t),cos(t),0),t=0..2\pi, style=="shade", tubeRadius == .3$ +\end{center} +\end{minipage} The {\tt tubePoints} option specifies the number of vertices \index{tube!points in polygon} @@ -16569,11 +17319,15 @@ The larger this number is, the more cylindrical the tube becomes. \spadgraph{draw(curve(sin(t), cos(t), 0), t=0..2*\%pi, style=="shade", tubeRadius == .25, tubePoints == 3)} -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/3doptpts.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/3doptpts.eps}} +\begin{center} +$curve(sin(t),cos(t),0), t=0..2\pi, style=="shade", tubeRadius == .25, +tubePoints == 3$ +\end{center} +\end{minipage} \index{graphics!3D options!variable steps} -% Options \spadfunFrom{var1Steps}{DrawOption} and \spadfunFrom{var2Steps}{DrawOption} specify the number of intervals into @@ -16582,8 +17336,12 @@ first and second parameters of the surface function(s). \spadgraph{draw(cos(x*y),x=-3..3,y=-3..3, style=="shade", var1Steps == 30, var2Steps == 30)} -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/3doptvb.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/3doptvb.eps}} +\begin{center} +$cos(xy),x=-3..3,y=-3..3, style=="shade", var1Steps == 30, var2Steps == 30$ +\end{center} +\end{minipage} The {\tt space} option of a {\bf draw} command lets you build multiple graphs in three space. @@ -16592,6 +17350,8 @@ then use the {\tt space} option thereafter. There is no restriction as to the number or kinds of graphs that can be combined this way. +%Original Page 205 + Create an empty three-space object. \spadcommand{s := create3Space()\$(ThreeSpace DFLOAT) } @@ -16613,15 +17373,23 @@ into $s$. \spadgraph{draw(m,0..\%pi,0..2*\%pi, coordinates == spherical, space == s) } -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/3dmult1a.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/3dmult1a.eps}} +\begin{center} +$m,0..\pi,0..2\pi, coordinates == spherical, space == s$ +\end{center} +\end{minipage} Add a second graph to $s$. \spadgraph{v := draw(curve(1.5*sin(t), 1.5*cos(t),0), t=0..2*\%pi, tubeRadius == .25, space == s) } -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/3dmult1b.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/3dmult1b.eps}} +\begin{center} +$curve(1.5 sin(t), 1.5 cos(t),0), t=0..2\pi, tubeRadius == .25, space == s$ +\end{center} +\end{minipage} A three-space object can also be obtained from an existing three-di\-men\-sion\-al viewport using the \spadfunFrom{subspace}{ThreeSpace} command. @@ -16631,6 +17399,8 @@ Assign to $subsp$ the three-space object in viewport $v$. \spadcommand{subsp := subspace v } +%Original Page 206 + Reset the space component of $v$ to the value of $subsp$. \spadcommand{subspace(v, subsp) } @@ -16723,6 +17493,8 @@ exported by the {\tt ThreeSpace} domain. \index{ThreeSpace} The following examples place curves into $space$. +%Original Page 207 + Add these eight curves to the space. \spadcommand{closedCurve(space,[ [0,30,20], [0,30,30], [0,40,30], [0,40,100], [0,30,100],[0,30,110], [0,60,110], [0,60,100], [0,50,100], [0,50,30], [0,60,30], [0,60,20] ]) } @@ -16767,6 +17539,8 @@ $$ $$ \returnType{Type: ThreeSpace DoubleFloat} +%Original Page 208 + \spadcommand{closedCurve(space,[ [200,0,20], [200,0,110], [189,0,110], [160,0,45], [160,0,110], [150,0,110], [150,0,20], [161,0,20], [190,0,85], [190,0,20] ]) } $$ {3-Space with }8 \mbox{\rm components} @@ -16779,8 +17553,12 @@ enclosed in parentheses. \spadgraph{makeViewport3D(space, title == "Letters") } -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/3dbuilda.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/3dbuilda.eps}} +\begin{center} +$makeViewport3D(space, title == "Letters")$ +\end{center} +\end{minipage} \subsubsection{Cube Example} @@ -16830,6 +17608,8 @@ $$ $$ \returnType{Type: Point DoubleFloat} +%Original Page 209 + \spadcommand{c := point [y,x,x,8::DFLOAT]\$(Point DFLOAT) } $$ \left[ @@ -16905,6 +17685,8 @@ $$ $$ \returnType{Type: ThreeSpace DoubleFloat} +%Original Page 210 + \spadcommand{polygon(spaceC,[h,g,f,e]) } $$ {3-Space with }5 \mbox{\rm components} @@ -16921,8 +17703,12 @@ Create and display the viewport. \spadgraph{makeViewport3D(spaceC, title == "Cube") } -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/3dbuildb.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/3dbuildb.eps}} +\begin{center} +$makeViewport3D(spaceC, title == "Cube")$ +\end{center} +\end{minipage} \subsection{Coordinate System Transformations} \label{ugGraphCoord} @@ -16947,8 +17733,14 @@ Graph plotted in default coordinate system. \spadgraph{draw(m,0..3,0..5) } -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/defcoord.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/defcoord.eps}} +\begin{center} +$m,0..3,0..5$ +\end{center} +\end{minipage} + +%Original Page 211 The $z$ coordinate comes first since the first argument of the {\bf draw} command gives its values. @@ -16973,8 +17765,12 @@ parameter to the {\bf draw} command. \spadgraph{draw(m,0..3,0..5,coordinates==cartesian) } -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/cartcoord.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/cartcoord.eps}} +\begin{center} +$m, 0..3,0..5, coordinates==cartesian$ +\end{center} +\end{minipage} What happened? The option {\tt coordinates == cartesian} directs Axiom to treat the dependent variable $m$ defined by $m=u^2$ as the @@ -17004,12 +17800,18 @@ coordinates for the constant $r = 3$. \end{verbatim} \returnType{Type: Void} +%Original Page 212 + Graph plotted in cylindrical coordinates. \spadgraph{draw(f,0..\%pi,0..6,coordinates==cylindrical) } -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/cylcoord.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/cylcoord.eps}} +\begin{center} +$f, 0..\pi,0..6, coordinates==cylindrical$ +\end{center} +\end{minipage} Suppose you would like to specify $z$ as a function of $r$ and $\theta$ instead of just $r$? @@ -17079,14 +17881,20 @@ $$ $$ \returnType{Type: Point DoubleFloat} +%Original Page 213 + Graph the same function $f$ using the coordinate mapping of the function $newmap$, so it is now interpreted as $z=3$: \spadgraph{draw(f,0..3,0..2*\%pi,coordinates==newmap) } -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/newmap.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/newmap.eps}} +\begin{center} +$f,0..3,0..2\pi,coordinates==newmap$ +\end{center} +\end{minipage} % I think this is good to say here: it shows a lot of depth. RSS %{\sloppy @@ -17134,27 +17942,30 @@ the gamma function in order to eliminate the extreme divergence it creates. \spadgraph{draw(gamma,-\%pi..\%pi,-\%pi..\%pi,var1Steps==50,var2Steps==50) } -% window was 300 x 300 -%\epsffile[0 0 295 295]{ps/clipgamma.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/clipgamma.eps}} +\begin{center} +$gamma, -\pi..\pi, -\pi..\pi, var1Steps==50, var2Steps==50$ +\end{center} +\end{minipage} \subsection{Three-Dimensional Control-Panel} \label{ugGraphThreeDControl} +%Original Page 214 + \index{graphics!3D control-panel} Once you have created a viewport, move your mouse to the viewport and click with your left mouse button. This displays a control-panel on the side of the viewport that is closest to where you clicked. -\begin{figure}[htbp] -%{\epsfverbosetrue\epsfxsize=2in% -%\def\epsfsize#1#2{\epsfxsize}\hspace*{\baseLeftSkip}% -%%\epsffile[0 0 144 289]{ps/3dctrl.ps}} -\begin{picture}(183,252)%(-125,0) -\hspace*{\baseLeftSkip}\special{psfile=ps/3dctrl.ps} -\end{picture} -\caption{Three-dimensional control-panel.} -\end{figure} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=1.0]{ps/3dctrl.eps}} +\begin{center} +Three-dimensional control-panel. +\end{center} +\end{minipage} \subsubsection{Transformations} @@ -17186,7 +17997,9 @@ pattern for black and white. \item[origin:] The {\bf origin} button indicates that the rotation is to occur with respect to the origin of the viewing space, that is indicated by the axes. -% + +%%Original Page 215 + \item[object:] The {\bf object} button indicates that the rotation is to occur with respect to the center of volume of the object, independent of the axes' origin position. @@ -17258,6 +18071,8 @@ marker. \subsubsection{Buttons} \index{graphics!3D control-panel!buttons} +%Original Page 216 + Below the Colormap window and to the left are located various buttons that determine the characteristics of a graph. The buttons along the bottom and right hand side all have special @@ -17323,7 +18138,9 @@ smooth shaded graphs at the same time on some systems. viewgraph within a bounding box, or removes the box if previously selected. \index{graphics!3D control-panel!bounds} The region that encloses the entire volume of the viewport graph is displayed. -% + +%%Original Page 217 + \item[Axes] displays Cartesian \index{graphics!3D control-panel!axes} coordinate axes of the space, or turns them off if previously selected. @@ -17418,6 +18235,9 @@ Below the {\bf Lighting Control-Panel} title and to the right is the light intensity meter. Moving the intensity indicator down decreases the amount of light emitted from the light source. + +%Original Page 218 + When the indicator is at the top of the meter the light source is emitting at 100\% intensity. At the bottom of the meter the light source is emitting at a level @@ -17511,6 +18331,8 @@ adaptive refinement algorithm. turns the axes on and off. \index{graphics!3D commands!axes} +%Original Page 219 + % \item[{\bf close}]\funArgs{viewport} closes the viewport. @@ -17619,6 +18441,8 @@ Angles designate radians if given as floats, or degrees if given \index{graphics!3D commands!rotate} as integers. +%Original Page 220 + % \item[{\bf setAdaptive3D}]\funArgs{boolean\argDef{true}} sets whether space curves are to be plotted @@ -17708,7 +18532,9 @@ sets or indicates the default number of increments into which the grid defining a surface plot is subdivided with respect to the second parameter declared in the surface function. -% + +%%Original Page 221 + \item[{\bf viewDefaults}]\funArgs{{\tt [}$integer_{point}$, $integer_{line}$, $integer_{axes}$, $integer_{units}$, $float_{point}$, @@ -17803,7 +18629,9 @@ sets the default scaling factor, or returns \index{graphics!3D commands!scale default} the current factor if no argument is given. -% + +%%Original Page 222 + \item[{\bf write}]\funArgs{viewport, directory, \optArg{option}} writes the file {\bf data} for {\it viewport} in the directory {\it directory}. @@ -17884,7 +18712,9 @@ These indicate the font type \index{graphics!.Xdefaults!message font} to be used for the text in the control-panel message window. {\bf Rom14} -% + +%%Original Page 223 + \item[{\tt Axiom*monochrome:\ \it switch}] \ \newline This indicates whether the \index{graphics!.Xdefaults!monochrome} @@ -17942,6 +18772,8 @@ three-di\-men\-sion\-al control-panel. \setcounter{chapter}{7} % Chapter 8 % viewSizeDefault [300,300] +%Original Page 227 + \chapter{Advanced Problem Solving} \label{ugProblem} @@ -17985,10 +18817,11 @@ These include (where {\tt \$} means {\tt Complex DoubleFloat}, or {\tt Complex Float}): +%Original Page 228 + \noindent {\bf exp}, {\bf log}: $\$ -> \$$ \newline {\bf sin}, {\bf cos}, {\bf tan}, {\bf cot}, {\bf sec}, {\bf csc}: $\$ -> \$$ \newline -{\bf sin}, {\bf cos}, {\bf tan}, {\bf cot}, {\bf sec}, {\bf csc}: $\$ -> \$$ \newline {\bf asin}, {\bf acos}, {\bf atan}, {\bf acot}, {\bf asec}, {\bf acsc}: $\$ -> \$$ \newline {\bf sinh}, {\bf cosh}, {\bf tanh}, {\bf coth}, {\bf sech}, {\bf csch}: $\$ -> \$$ \newline {\bf asinh}, {\bf acosh}, {\bf atanh}, {\bf acoth}, {\bf asech}, {\bf acsch}: $\$ -> \$$ \newline @@ -18063,6 +18896,8 @@ $Gamma(z)$ is the Euler gamma function, $$\Gamma(z) = \int_{0}^{\infty} t^{z-1} e^{-t} dt.$$ +%Original Page 229 + \noindent {\bf Beta}: $F -> F$\hfill\newline $Beta(u, v)$ is the Euler Beta function, @@ -18111,7 +18946,7 @@ is the function $\psi(z)$, \noindent {\bf Ei}: $(OnePointCompletion DFLOAT) -> OnePointCompletion DFLOAT$ \hfill\newline - Ei is the Exponential Integral function + Ei is the Exponential Integral function. This is computed using a 6 part piecewise approximation. DoubleFloat can only preserve about 16 digits but the Chebyshev approximation used can give 30 digits. @@ -18120,13 +18955,13 @@ is the function $\psi(z)$, \noindent {\bf Ei1}: $(DoubleFloat) -> DoubleFloat$\hfill\newline Ei1 is the first approximation of Ei where the result is - $x*e^-x*Ei(x)$ from -infinity to -10 (preserves digits) + $x*e^{-x}*Ei(x)$ from -infinity to -10 (preserves digits) \index{function!Ei1} \noindent {\bf Ei2}: $(DoubleFloat) -> DoubleFloat$\hfill\newline Ei2 is the first approximation of Ei where the result is - $x*e^-x*Ei(x)$ from -10 to -4 (preserves digits) + $x*e^{-x}*Ei(x)$ from -10 to -4 (preserves digits) \index{function!Ei2} \noindent @@ -18138,19 +18973,19 @@ is the function $\psi(z)$, \noindent {\bf Ei4}: $(DoubleFloat) -> DoubleFloat$\hfill\newline Ei4 is the first approximation of Ei where the result is - $x*e^-x*Ei(x)$ from 4 to 12 (preserves digits) + $x*e^{-x}*Ei(x)$ from 4 to 12 (preserves digits) \index{function!Ei4} \noindent {\bf Ei5}: $(DoubleFloat) -> DoubleFloat$\hfill\newline Ei5 is the first approximation of Ei where the result is - $x*e^-x*Ei(x)$ from 12 to 32 (preserves digits) + $x*e^{-x}*Ei(x)$ from 12 to 32 (preserves digits) \index{function!Ei5} \noindent {\bf Ei6}: $(DoubleFloat) -> DoubleFloat$\hfill\newline Ei6 is the first approximation of Ei where the result is - $x*e^-x*Ei(x)$ from 32 to infinity (preserves digits) + $x*e^{-x}*Ei(x)$ from 32 to infinity (preserves digits) \index{function!Ei6} \noindent @@ -18190,6 +19025,8 @@ is the function $\psi(z)$, $$K_\nu (z) = \pi \frac{I_{-\nu} (z) - I_{\nu} (z)}{2 \sin(\nu \pi)}.$$ +%Original Page 230 + \noindent {\bf airyAi}: $F -> F$\hfill\newline $airyAi(z)$ is the Airy function $Ai(z)$. @@ -18250,6 +19087,8 @@ The following operations are provided by the package kind, $U_n (z)$. These are defined by $$\frac{1}{1-2 t z+t^2} = \sum_{n=0}^{\infty} U_n (z) t^n.$$ +%Original Page 231 + \noindent {\bf hermiteH}: $(NonNegativeInteger, R) -> R$\hbox{}\hfill\newline $hermiteH(n,z)$ is the $n$-th Hermite polynomial, @@ -18319,6 +19158,8 @@ $$ $$ \returnType{Type: List Polynomial Integer} +%Original Page 232 + \spadcommand{chebyshevU(3, 0.2)} $$ -{0.736} @@ -18396,6 +19237,8 @@ $$ $$ \returnType{Type: List Polynomial Fraction Integer} +%Original Page 233 + \spadcommand{legendreP(3, 3.0*\%i)} $$ -{{72.0} \ i} @@ -18406,7 +19249,7 @@ Finally, three number-theoretic polynomial operations may be evaluated. \index{number theory} The following operations are provided by the package {\tt NumberTheoreticPolynomialFunctions}. -\index{NumberTheoreticPolynomialFunctions}. +\index{NumberTheoreticPolynomialFunctions} \noindent {\bf bernoulliB}: $(NonNegativeInteger, R) -> R$ \hbox{}\hfill\newline @@ -18465,6 +19308,8 @@ $$ $$ \returnType{Type: Complex Float} +%Original Page 234 + The expression \index{polynomial!cyclotomic} $cyclotomic(n,z)$ evaluates to the $n$-th cyclotomic polynomial. @@ -18496,7 +19341,14 @@ values near zero and blue/violet indicates large positive imaginary values. \spadgraph{draw((x,y)+-> real exp complex(x,y), -2..2, -2*\%pi..2*\%pi, colorFunction == (x, y) +-> imag exp complex(x,y), title=="exp(x+\%i*y)", style=="smooth")} -%\epsffile[0 0 295 295]{ps/compexp.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/compexp.eps}} +\begin{center} +$(x,y)+-> real exp complex(x,y), -2..2, -2\pi..2\pi, $\\ +$colorFunction == (x, y) +-> imag exp complex(x,y), $\\ +$title=="exp(x+\%i*y)", style=="smooth"$ +\end{center} +\end{minipage} This is the complex arctangent function. \index{function!complex arctangent} @@ -18507,19 +19359,41 @@ see that the function is real only for a real argument. \spadgraph{vp := draw((x,y) +-> real atan complex(x,y), -\%pi..\%pi, -\%pi..\%pi, colorFunction==(x,y) +->argument atan complex(x,y), title=="atan(x+\%i*y)", style=="shade"); rotate(vp,-160,-45); vp} -%\epsffile[0 0 295 295]{ps/compatan.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/compatan.eps}} +\begin{center} +$(x,y) +-> real atan complex(x,y), -\pi..\pi, -\pi..\pi,$\\ +$colorFunction==(x,y) +->argument atan complex(x,y), $\\ +$title=="atan(x+\%i*y)", style=="shade"$ +\end{center} +\end{minipage} + +%Original Page 235 This is the complex Gamma function. \spadgraph{draw((x,y) +-> max(min(real Gamma complex(x,y),4),-4), -\%pi..\%pi, -\%pi..\%pi, style=="shade", colorFunction == (x,y) +-> argument Gamma complex(x,y), title == "Gamma(x+\%i*y)", var1Steps == 50, var2Steps== 50)} -%\epsffile[0 0 295 295]{ps/compgamm.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/compgamma.eps}} +\begin{center} +$(x,y) +-> max(min(real Gamma complex(x,y),4),-4), -\pi..\pi, -\pi..\pi, $\\ +$style=="shade", colorFunction == (x,y) +-> argument Gamma complex(x,y), $\\ +$title == "Gamma(x+\%i*y)", var1Steps == 50, var2Steps== 50$ +\end{center} +\end{minipage} This shows the real Beta function near the origin. \spadgraph{draw(Beta(x,y)/100, x=-1.6..1.7, y = -1.6..1.7, style=="shade", title=="Beta(x,y)", var1Steps==40, var2Steps==40)} -%\epsffile[0 0 295 295]{ps/realbeta.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/realbeta.eps}} +\begin{center} +$Beta(x,y)/100, x=-1.6..1.7, y = -1.6..1.7, $\\ +$style=="shade", title=="Beta(x,y)", var1Steps==40, var2Steps==40$ +\end{center} +\end{minipage} This is the Bessel function $J_\alpha (x)$ for index $\alpha$ in the range $-6..4$ and @@ -18527,7 +19401,15 @@ argument $x$ in the range $2..14$. \spadgraph{draw((alpha,x) +-> min(max(besselJ(alpha, x+8), -6), 6), -6..4, -6..6, title=="besselJ(alpha,x)", style=="shade", var1Steps==40, var2Steps==40)} -%\epsffile[0 0 295 295]{ps/bessel.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/bessel.eps}} +\begin{center} +$(alpha,x) +-> min(max(besselJ(alpha, x+8), -6), 6), -6..4, -6..6, $\\ +$title=="besselJ(alpha,x)", style=="shade", var1Steps==40, var2Steps==40$ +\end{center} +\end{minipage} + +%Original Page 236 This is the modified Bessel function $I_\alpha (x)$ @@ -18536,15 +19418,27 @@ and fixed argument $x = 5$. \spadgraph{draw(besselI(alpha, 5), alpha = -12..12, unit==[5,20])} -%\epsffile[0 0 295 295]{ps/modbess.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/modbess.eps}} +\begin{center} +$besselI(alpha, 5), alpha = -12..12, unit==[5,20]$ +\end{center} +\end{minipage} This is similar to the last example except the index $\alpha$ -takes on complex values in a $6 x 6$ rectangle centered on the origin. +takes on complex values in a $6 \times 6$ rectangle centered on the origin. \spadgraph{draw((x,y) +-> real besselI(complex(x/20, y/20),5), -60..60, -60..60, colorFunction == (x,y)+-> argument besselI(complex(x/20,y/20),5), title=="besselI(x+i*y,5)", style=="shade")} -%\epsffile[0 0 295 295]{ps/modbessc.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/modbessc.eps}} +\begin{center} +$(x,y) +-> real besselI(complex(x/20, y/20),5), -60..60, -60..60, $\\ +$colorFunction == (x,y)+-> argument besselI(complex(x/20,y/20),5), $\\ +$title=="besselI(x+i*y,5)", style=="shade"$ +\end{center} +\end{minipage} \section{Polynomial Factorization} \label{ugProblemFactor} @@ -18574,6 +19468,8 @@ $$ $$ \returnType{Type: Polynomial Integer} +%Original Page 237 + \spadcommand{factor v } $$ -{{\left( {{x \sp 3} \ y} -{{12} \ {x \sp 5}} -{12} @@ -18720,6 +19616,8 @@ $$ $$ \returnType{Type: Factored Polynomial AlgebraicNumber} +%Original Page 238 + This factors $x**2+3$ over the integers. \spadcommand{factor(x**2+3)} @@ -18818,6 +19716,8 @@ $$ $$ \returnType{Type: Fraction Factored Polynomial Integer} +%Original Page 239 + \section{Manipulating Symbolic Roots of a Polynomial} \label{ugProblemSymRoot} @@ -18904,6 +19804,8 @@ e $$ \returnType{Type: Expression Integer} +%Original Page 240 + \spadcommand{zeroOf(f**5-2,f)} $$ \root {5} \of {2} @@ -18980,6 +19882,8 @@ $$ $$ \returnType{Type: Expression Integer} +%Original Page 241 + Corresponding to the pair of operations {\bf rootOf}/{\bf zeroOf} in \sectionref{ugxProblemOnePol}, there is @@ -19073,6 +19977,9 @@ the value explicitly; otherwise, its minimal polynomial is given, (the polynomial of lowest degree with the eigenvalues as roots), together with a parametric representation of the eigenvector using the eigenvalue. + +%Original Page 242 + This means that if you ask Axiom to {\bf solve} the minimal polynomial, then you can substitute these roots \index{polynomial!minimal} @@ -19187,6 +20094,8 @@ In the complex case, this means that each approximation will be within $\pm\epsilon$ of the actual result in each of the real and imaginary parts. +%Original Page 243 + The precision can be specified as a {\tt Float} if the results are desired in floating-point notation, or as {\tt Fraction Integer} if the results are to be expressed using rational (or complex rational) numbers. @@ -19307,6 +20216,8 @@ $$ $$ \returnType{Type: List Matrix Expression Integer} +%Original Page 244 + \section{Solution of Linear and Polynomial Equations} \label{ugProblemLinPolEqn} % @@ -19408,6 +20319,8 @@ If the system of linear equations does not have a unique solution, then the {\it basis} component contains non-trivial vectors. +%Original Page 245 + This happens when you solve the linear system $$ \begin{array}{rcrcrcr} @@ -19491,6 +20404,8 @@ $$ $$ \returnType{Type: List Equation Fraction Polynomial Integer} +%Original Page 246 + If you want solutions expressed in terms of radicals you would use this instead. \index{radical} @@ -19594,6 +20509,8 @@ $$ $$ \returnType{Type: List Equation Expression Integer} +%Original Page 247 + \subsection{Solution of Systems of Polynomial Equations} \label{ugxProblemPolSys} @@ -19654,6 +20571,8 @@ $$ $$ \returnType{Type: List List Equation Fraction Polynomial Integer} +%Original Page 248 + Use {\bf radicalSolve} if you want your solutions expressed in terms of radicals. @@ -19743,6 +20662,8 @@ $$ \returnType{Type: List List Equation Polynomial Float} +%Original Page 249 + When solving equations with denominators, all solutions where the denominator vanishes are discarded. @@ -19829,6 +20750,8 @@ function $\sqrt{y^2} / y$ is simply the sign ($+1$ or $-1$) of the nonzero real number $y$. Therefore, $\sqrt{y^2} / y = -1$ for $y < 0$ and $\sqrt{y^2} / y = +1$ for $y > 0$. +%Original Page 250 + This is what happens when we take the limit at $y = 0$. The answer returned by Axiom gives both a ``left-hand'' and a ``right-hand'' limit. @@ -19904,6 +20827,8 @@ behaved near $0$ (one says that $sin(1/z)$ has an {\it essential singularity} at $z = 0$). \index{singularity!essential} +%Original Page 251 + When viewed as a function of a complex variable, $z * sin(1/z)$ does not approach any limit as $z$ tends to $0$ in the complex plane. Axiom indicates this when we call {\bf complexLimit}. @@ -19995,6 +20920,8 @@ $$ $$ \returnType{Type: Expression Integer} +%Original Page 252 + \spadcommand{laplace(exp(-a*t) * sin(b*t) / b**2, t, s)} $$ \frac{1}{{b \ {s \sp 2}}+{2 \ a \ b \ s}+{b \sp 3}+{{a \sp 2} \ b}} @@ -20072,6 +20999,8 @@ elementary and not when it cannot determine the integral. In this rare case it prints a message that it cannot determine if an elementary integral exists. +%Original Page 253 + Similar functions may have antiderivatives \index{antiderivative} that look quite different because the form of the antiderivative depends on the sign of a constant that appears in the function. @@ -20102,6 +21031,7 @@ functions} the answer involving the square root of $-a$ when $a < 0$. \spadcommand{integrate(x**2 / (x**4 - a**2), x)} $$ \begin{array}{@{}l} +\displaystyle \left[ {\frac{{\log \left( @@ -20141,6 +21071,7 @@ functions. $$ \frac{\left( \begin{array}{@{}l} +\displaystyle {{\sqrt {{4 \ a}}} \ {\log \left( {{\frac{{x \ {\sqrt {-{4 \ a}}}}+{2 \ a}}{\sqrt {-{4 \ a}}}}} @@ -20166,6 +21097,8 @@ $$ $$ \returnType{Type: Expression Integer} +%Original Page 254 + As with the real case, antiderivatives for most complex-valued functions cannot be expressed in terms of elementary functions. @@ -20230,9 +21163,11 @@ $$ If you know that you are using values of the parameter for which the function has no pole in the interval of integration, use the -string {\tt ``noPole''} as a third argument to +string {\tt "noPole"} as a third argument to \spadfunFrom{integrate}{RationalFunctionDefiniteIntegration}: +%Original Page 255 + The value here is, of course, incorrect if $sqrt(a)$ is between $1$ and $2.$ @@ -20294,6 +21229,8 @@ situations where you know what kind of exponents are involved. For information about solving differential equations in terms of power series, see \sectionref{ugxProblemDEQSeries}. +%Original Page 256 + \subsection{Creation of Power Series} \label{ugxProblemSeriesCreate} @@ -20351,6 +21288,7 @@ $sin(1)$ and $cos(1).$ \spadcommand{sin(1 + x) } $$ \begin{array}{@{}l} +\displaystyle {\sin \left({1} \right)}+ {{\cos\left({1} \right)}\ x} - {{\frac{\sin \left({1} \right)}{2}} \ {x \sp 2}} - @@ -20392,6 +21330,7 @@ For details and more examples, see \sectionref{ugxProblemSeriesConversions}. \spadcommand{series(1/log(y),y = 1)} $$ \begin{array}{@{}l} +\displaystyle {{\left( y -1 \right)}\sp {\left( -1 \right)}}+ {\frac{1}{2}} -{{\frac{1}{12}} \ {\left( y -1 \right)}}+ {{\frac{1}{24}} \ {{\left( y -1 \right)}\sp 2}} - @@ -20419,6 +21358,8 @@ normally accomplish this via a type declaration (see See \sectionref{ugxProblemSeriesFunctions} for some warnings about working with declared series. +%Original Page 257 + We declare that $y$ is a one-variable Taylor series \index{series!Taylor} ({\tt UTS} is the abbreviation for {\tt UnivariateTaylorSeries}) in the variable $z$ with {\tt FLOAT} @@ -20467,6 +21408,7 @@ expansion of $exp(w)$ at $w = 0$. \spadcommand{series(1/factorial(n),n,w = 0)} $$ \begin{array}{@{}l} +\displaystyle 1+w+ {{\frac{1}{2}} \ {w \sp 2}}+ {{\frac{1}{6}} \ {w \sp 3}}+ @@ -20510,6 +21452,7 @@ $$ \spadcommand{y := exp(x) * sin(x) } $$ \begin{array}{@{}l} +\displaystyle x+ {x \sp 2}+ {{\frac{1}{3}} \ {x \sp 3}} - @@ -20527,6 +21470,8 @@ x+ $$ \returnType{Type: UnivariatePuiseuxSeries(Expression Integer,x,0)} +%Original Page 258 + This coefficient is readily available. \spadcommand{coefficient(y,6) } @@ -20549,6 +21494,7 @@ have all been computed. \spadcommand{y } $$ \begin{array}{@{}l} +\displaystyle x+ {x \sp 2}+ {{\frac{1}{3}} \ {x \sp 3}} - @@ -20642,9 +21588,12 @@ x+ $$ \returnType{Type: UnivariatePuiseuxSeries(Expression Integer,x,0)} +%Original Page 259 + \spadcommand{base ** expon } $$ \begin{array}{@{}l} +\displaystyle 1+ {x \sp 2}+ {{\frac{3}{2}} \ {x \sp 3}}+ @@ -20715,6 +21664,7 @@ you simply compute the sine of $rat$. \spadcommand{sin(rat) } $$ \begin{array}{@{}l} +\displaystyle {x \sp 2}+ {6 \ {x \sp 3}}+ {{35} \ {x \sp 4}}+ @@ -20753,12 +21703,15 @@ y $$ \returnType{Type: UnivariateTaylorSeries(Fraction Integer,y,0)} +%Original Page 260 + You can now compute certain power series in $y$, {\it provided} that these series have rational coefficients. \spadcommand{exp(y) } $$ \begin{array}{@{}l} +\displaystyle 1+y+ {{\frac{1}{2}} \ {y \sp 2}}+ {{\frac{1}{6}} \ {y \sp 3}}+ @@ -20807,6 +21760,7 @@ coefficients if the constant coefficient is $1.$ \spadcommand{log(1 + sin(y)) } $$ \begin{array}{@{}l} +\displaystyle y - {{\frac{1}{2}} \ {y \sp 2}}+ {{\frac{1}{6}} \ {y \sp 3}} - @@ -20849,6 +21803,7 @@ this presents no problems. \spadcommand{exp(2 + tan(z)) } $$ \begin{array}{@{}l} +\displaystyle {e \sp 2}+ {{e \sp 2} \ z}+ {{\frac{e \sp 2}{2}} \ {z \sp 2}}+ @@ -20872,6 +21827,8 @@ Another way to create Taylor series whose coefficients are expressions over the integers is to use {\bf taylor} which works similarly to \index{series!Taylor} {\bf series}. +%Original Page 261 + This is equivalent to the previous computation, except that now we are using the variable $w$ instead of $z$. @@ -20884,6 +21841,7 @@ $$ \spadcommand{exp(2 + tan(w)) } $$ \begin{array}{@{}l} +\displaystyle {e \sp 2}+ {{e \sp 2} \ w}+ {{\frac{e \sp 2}{2}} \ {w \sp 2}}+ @@ -20910,7 +21868,7 @@ The {\tt ExpressionToUnivariatePowerSeries} package provides operations for computing series expansions of functions. \index{ExpressionToUnivariatePowerSeries} -Evaluate this to compute the Taylor expansion of $sin x$ about +Evaluate this to compute the Taylor expansion of $sin(x)$ about \index{series!Taylor} $x = 0$. The first argument, $sin(x)$, specifies the function whose series expansion is to be computed and the second argument, $x = 0$, specifies that the series is to be @@ -20932,6 +21890,7 @@ Here is the Taylor expansion of $sin x$ about $x = \frac{\pi}{6}$: \spadcommand{taylor(sin(x),x = \%pi/6)} $$ \begin{array}{@{}l} +\displaystyle {\frac{1}{2}}+ {{\frac{\sqrt {3}}{2}} \ {\left( x -{\frac{\pi}{6}} \right)}} -{{\frac{1}{4}} \ {{\left( x -{\frac{\pi}{6}} \right)}\sp 2}} - @@ -20958,6 +21917,8 @@ $$ The function to be expanded into a series may have variables other than \index{series!multiple variables} the series variable. +%Original Page 262 + For example, we may expand $tan(x*y)$ as a Taylor series in $x$ \spadcommand{taylor(tan(x*y),x = 0)} @@ -20994,6 +21955,7 @@ divided by $n!$. \spadcommand{bern := taylor(t*exp(x*t)/(exp(t) - 1),t = 0) } $$ \begin{array}{@{}l} +\displaystyle 1+ {{\frac{{2 \ x} -1}{2}} \ t}+ {{\frac{{6 \ {x \sp 2}} -{6 \ x}+1}{12}} \ {t \sp 2}}+ @@ -21066,11 +22028,14 @@ expansion about this point has terms of negative degree. A series with finitely many terms of negative degree is called a Laurent series. +%Original Page 263 + You get the desired series expansion by issuing this. \spadcommand{laurent(x/log(x),x = 1)} $$ \begin{array}{@{}l} +\displaystyle {{\left( x -1 \right)}\sp {\left( -1\right)}}+ {\frac{3}{2}}+ {{\frac{5}{12}} \ {\left( x -1 \right)}} @@ -21125,6 +22090,7 @@ because of the $log(x)$ in the expansion. \spadcommand{series(x**x,x=0)} $$ \begin{array}{@{}l} +\displaystyle 1+ {{\log \left({x} \right)}\ x}+ {{\frac{{\log \left({x} \right)}\sp 2}{2}} \ {x \sp 2}}+ @@ -21165,6 +22131,8 @@ function and the point about which the series is to be expanded. \index{GenerateUnivariatePowerSeries} See \sectionref{ugxProblemSeriesConversions} for more information. +%Original Page 264 + Consider the Taylor expansion of $e^x$ \index{series!Taylor} about $x = 0$: @@ -21182,6 +22150,7 @@ This is how you create this series in Axiom. \spadcommand{series(n +-> 1/factorial(n),x = 0)} $$ \begin{array}{@{}l} +\displaystyle 1+x+ {{\frac{1}{2}} \ {x \sp 2}}+ {{\frac{1}{6}} \ {x \sp 3}}+ @@ -21228,6 +22197,7 @@ $n = 1, ...$ are to be computed. \spadcommand{series(n +-> (-1)**(n-1)/n,x = 1,1..)} $$ \begin{array}{@{}l} +\displaystyle {\left( x -1 \right)} -{{\frac{1}{2}} \ {{\left( x -1 \right)}\sp 2}}+ {{\frac{1}{3}} \ {{\left( x -1 \right)}\sp 3}} - @@ -21250,6 +22220,8 @@ $$ $$ \returnType{Type: UnivariatePuiseuxSeries(Expression Integer,x,1)} +%Original Page 265 + Next consider the Taylor expansion of an odd function, say, $sin(x)$: $$\sin(x) = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \cdots$$ @@ -21377,6 +22349,8 @@ the operations {\bf taylor}, {\bf laurent} and {\bf puiseux} instead of {\bf series} if you know ahead of time what kind of exponents a series has. You can't go wrong using {\bf series}, though. +%Original Page 266 + \subsection{Substituting Numerical Values in Power Series} \label{ugxProblemSeriesSubstitute} @@ -21391,6 +22365,7 @@ First you create the desired Taylor expansion. \spadcommand{f := taylor(exp(x)) } $$ \begin{array}{@{}l} +\displaystyle 1+x+ {{\frac{1}{2}} \ {x \sp 2}}+ {{\frac{1}{6}} \ {x \sp 3}}+ @@ -21484,6 +22459,8 @@ formulas using Bernoulli polynomials; \index{Bernoulli!polynomial} we \index{polynomial!Bernoulli} use the rest of this section to describe this method. +%Original Page 267 + First consider this function of $t$ and $x$. \spadcommand{f := t*exp(x*t) / (exp(t) - 1) } @@ -21506,6 +22483,7 @@ in $x$. \spadcommand{ff := taylor(f,t = 0) } $$ \begin{array}{@{}l} +\displaystyle 1+ {{\frac{{2 \ x} -1}{2}} \ t}+ {{\frac{{6 \ {x \sp 2}} -{6 \ x}+1}{12}} \ {t \sp 2}}+ @@ -21561,6 +22539,8 @@ $$ From this it follows that the $n$-th coefficient in the Taylor expansion of $g(x,t)$ at $t = 0$ is $${\frac{1}{(n-1)!}}x^{n-1}$$. +%Original Page 268 + If you want to check this, evaluate the next expression. \spadcommand{taylor(g,t = 0) } @@ -21639,6 +22619,8 @@ $$ $$ \returnType{Type: Fraction Polynomial Integer} +%Original Page 269 + At this point you may want to do the same computation, but with an exponent other than $4.$ For example, you might try to find a formula for the sum of the first $k$ 20th powers. @@ -21709,6 +22691,8 @@ arguments. \item the dependent variable. \end{itemize} +%Original Page 270 + So, to solve the above equation, we enter this. \spadcommand{solve(deq, y, x) } @@ -21778,9 +22762,12 @@ $$ $$ \returnType{Type: Equation Expression Integer} +%Original Page 271 + \spadcommand{solve(deq, y, x) } $$ \begin{array}{@{}l} +\displaystyle \left[ {particular={\frac{{x \sp 5} -{{10} \ {x \sp 3}}+{{20} \ {x \sp 2}}+4} {{15} \ x}}}, @@ -21836,7 +22823,7 @@ following statements are correct and form good guidelines for linear ordinary differential equations: \begin{itemize} \item If the coefficients are constants, Axiom finds a complete basis -of solutions (i,e, all solutions). +of solutions (i,e. all solutions). \item If the coefficients are rational functions in the dependent variable, Axiom at least finds all solutions that do not involve algebraic functions. @@ -21856,6 +22843,8 @@ $$ $$ \returnType{Type: Equation Expression Integer} +%Original Page 272 + \spadcommand{solve(deq, y, x) } $$ \left[ @@ -21922,6 +22911,8 @@ $$ $$ \returnType{Type: Expression Integer} +%Original Page 273 + If the above is zero for a function $mu$ that does {\it not} depend on $y$, then $mu(x)$ is an integrating factor. @@ -21995,6 +22986,8 @@ $$ We must solve the exact equation, that is, find a function $s(x,y)$ such that $ds/dx = m$ and $ds/dy = n$. +%Original Page 274 + We start by writing $s(x, y) = h(y) + integrate(m, x)$ where $h(y)$ is an unknown function of $y$. This guarantees that $ds/dx = m$. @@ -22072,6 +23065,8 @@ $$ $$ \returnType{Type: Union(Expression Integer,...)} +%Original Page 275 + \subsection{Power Series Solutions of Differential Equations} \label{ugxProblemDEQSeries} @@ -22154,6 +23149,8 @@ $$ $$ \returnType{Type: Equation Expression Integer} +%Original Page 276 + Solve the system around $t = 0$ with the initial conditions $x(0) = 0$ and $y(0) = 1$. Notice that since we give the unknowns in the order $[x, y]$, the answer is a list of two series in the order @@ -22196,7 +23193,7 @@ same laws (for example, commutativity, associativity or distributivity) as apply to the rational, real or complex numbers. Unlike those three fields, for any finite field there exists a positive prime integer $p$, called the {\bf characteristic}, such that -$p x = 0$ for any element $x$ in the finite field. In fact, the +$p\ x = 0$ for any element $x$ in the finite field. In fact, the number of elements in a finite field is a power of the characteristic and for each prime $p$ and positive integer $n$ there exists exactly one finite field with $p^n$ elements, up to isomorphism.\footnote{For @@ -22236,6 +23233,8 @@ first done such remaindering on the operands, performed the arithmetic and then (if necessary) done remaindering again. This allows us to speak of arithmetic {\it modulo} $n$ or, more simply {\it mod} $n$. +%Original Page 277 + In Axiom, you use {\tt IntegerMod} to do such arithmetic. \spadcommand{(a,b) : IntegerMod 12 } @@ -22317,6 +23316,8 @@ $$ $$ \returnType{Type: PrimeField 11} +%Original Page 278 + {\tt PrimeField} (abbreviation {\tt PF}) checks if its argument is prime when you try to use an operation from it. If you know the argument is prime (particularly if it is large), {\tt InnerPrimeField} @@ -22406,6 +23407,8 @@ $$ $$ \returnType{Type: List PrimeField 101} +%Original Page 279 + If every nonzero element is a power of a primitive element, how do you determine what the exponent is? Use \index{discrete logarithm} {\bf discreteLog}. \index{logarithm!discrete} @@ -22473,6 +23476,8 @@ application best. We first tell you what domain constructors to use for each case above, and then give some examples. +%Original Page 280 + \hangafter=1\hangindent=2pc Constructors that automatically generate extensions of the prime field: \newline @@ -22535,6 +23540,8 @@ implementation aspects of finite fields, see J. Grabmeier, A. Scheerhorn, {\it Finite Fields in AXIOM,} Technical Report, IBM Heidelberg Scientific Center, 1992.} +%Original Page 281 + If you don't really care about all this detail, just use {\tt FiniteField}. As your knowledge of your application and its Axiom implementation grows, you can come back and choose an alternative @@ -22603,6 +23610,8 @@ $$ $$ \returnType{Type: FiniteField(2,12)} +%Original Page 282 + \spadcommand{c := a/b } $$ { \%A \sp {11}}+ @@ -22683,6 +23692,8 @@ $$ is similar to {\tt FiniteField} and {\tt FiniteFieldExtension} but is more general. +%Original Page 283 + \spadcommand{GF4 := FF(2,2); } \returnType{Type: Domain} @@ -22751,6 +23762,8 @@ $$ $$ \returnType{Type: FiniteFieldCyclicGroup(3,4)} +%Original Page 284 + In this representation of finite fields the discrete logarithm of an element can be seen directly in its output form. @@ -22802,6 +23815,8 @@ polynomial. \spadcommand{GF3 := PrimeField 3; } \returnType{Type: Domain} +%Original Page 285 + We use a utility operation to generate an irreducible primitive polynomial (see \sectionref{ugxProblemFiniteUtility}). The polynomial has one variable that is ``anonymous'': @@ -22876,6 +23891,8 @@ $$ $$ \returnType{Type: FiniteFieldNormalBasis(3,8)} +%Original Page 286 + You can calculate in $K$ using $a$. \spadcommand{b := a**12 - a**5 + a } @@ -22923,6 +23940,8 @@ The degree of the extension is the degree of the polynomial. \spadcommand{GF3 := PrimeField 3; } \returnType{Type: Domain} +%Original Page 287 + We use a utility operation to generate an irreducible normal polynomial (see \sectionref{ugxProblemFiniteUtility}). p The polynomial has @@ -22992,6 +24011,8 @@ K different extensions of one fixed finite ground field and between different representations of these finite fields. +%Original Page 288 + Let's choose $m$ and $n$, \spadcommand{(m,n) := (4,8) } @@ -23066,6 +24087,8 @@ $K_n$ are represented in different ways (see $K_m$ where the representation is 0 plus the cyclic multiplicative group and $K_n$ with a normal basis representation. +%Original Page 289 + \spadcommand{Km := FFCGX(K,m) } $$ \mbox{\rm FiniteFieldCyclicGroupExtension(PrimeField 3,4)} @@ -23142,7 +24165,9 @@ to the degree of the polynomial. In what follows, many of the generated polynomials have one ``anonymous'' variable. This indeterminate is displayed as a question -mark ({\tt ``?''}). +mark ({\tt "?"}). + +%Original Page 290 To fix ideas, let's use the field with five elements for the first few examples. @@ -23227,6 +24252,8 @@ degree of the polynomial.\footnote{Cf. Lidl, R. \& Niederreiter, H., {\it Finite Fields,} Encycl. of Math. 20, (Addison-Wesley, 1983), p.90, Th. 3.18.} +%Original Page 291 + What about polynomials that are both primitive and normal? The existence of such a polynomial is by no means obvious. \footnote{The existence of such polynomials is proved in @@ -23301,6 +24328,8 @@ $$ $$ \returnType{Type: PositiveInteger} +%Original Page 292 + We hope that ``natural order'' on polynomials is now clear: first we compare the number of monomials of two polynomials (``more'' is ``greater''); then, if necessary, the degrees of these monomials @@ -23371,6 +24400,8 @@ $$ $$ \returnType{Type: Union(SparseUnivariatePolynomial PrimeField 5,...)} +%Original Page 293 + \spadcommand{nextNormalPoly(f1)\$FFPOLY(GF5) } $$ {? \sp 3}+{2 \ {? \sp 2}}+1 @@ -23452,6 +24483,8 @@ $$ $$ \returnType{Type: SparseUnivariatePolynomial PrimeField 2} +%Original Page 293 + We compute a root of $f$. \spadcommand{root := rootOfIrreduciblePoly(f)\$FFPOLY2(F,GF2) } @@ -23533,6 +24566,8 @@ $$ DirectProduct(2,NonNegativeInteger),OrderedVariableList [x,y], DistributedMultivariatePolynomial([x,y],Fraction Integer))} +%Original Page 295 + We can check if the locus contains only a finite number of points, that is, if the ideal is zero-dimensional. @@ -23595,6 +24630,8 @@ $$ \returnType{Type: List DistributedMultivariatePolynomial([x,y,z],Fraction Integer)} +%Original Page 296 + \spadcommand{ld:=primaryDecomp ideal l } $$ \left[ @@ -23679,6 +24716,8 @@ with roots $b_i \ldots b_n$, then the polynomial $h(x) = resultant(f(y), g(x-y), y)$ is a polynomial of degree $m*n$ with roots $a_i + b_j, i = 1 \ldots m, j = 1 \ldots n$. +%Original Page 297 + For $f(x)$ we use the polynomial $p(x)$. For $g(x)$ we use the polynomial $-p(-x)$. Thus, the polynomial we first construct is $resultant(p(y), -p(y-x), y)$. @@ -23782,6 +24821,8 @@ $p(x)$ contains a subfield of degree $10$. We show that this subfield is, in fact, the splitting field of $p(x)$ by showing that $p(x)$ factors completely over this field. +%Original Page 298 + First we create a symbolic root of the polynomial $r(x)$. (We replaced $x$ by $b$ in the polynomial $r$ so that our symbolic root would be printed as $b$.) @@ -23898,6 +24939,9 @@ field over which the polynomial is to be factored, as polynomials have different factorizations over different fields. When you use the operation {\bf factor}, the field over which the polynomial is factored is the field generated by + +%Original Page 299 + \begin{enumerate} \item the algebraic numbers that appear in the coefficients of the polynomial, and @@ -23979,11 +25023,14 @@ $$ $$ \returnType{Type: AlgebraicNumber} +%Original Page 300 + We can obtain a list of all the roots in this way. \spadcommand{roots := [-coefficient(nthFactor(algFactors,i),0) for i in 1..5] } $$ \begin{array}{@{}l} +\displaystyle \left[ \frac{\left( \begin{array}{@{}l} @@ -24056,7 +25103,7 @@ $$ The expression \begin{verbatim} -- coefficient(nthFactor(algFactors, i), 0)} +- coefficient(nthFactor(algFactors, i), 0) \end{verbatim} is the $i $-th root of $p(x)$ and the elements of $roots$ are the $i$-th roots of $p(x)$ as $i$ ranges from $1$ to $5$. @@ -24085,6 +25132,8 @@ $$ $$ \returnType{Type: AlgebraicNumber} +%Original Page 301 + Next we express the roots of $r(x)$ as polynomials in $beta$. We could obtain these roots by calling the operation {\bf factor}: $factor(r, [beta])$ factors $r(x)$ over ${\bf Q}(\beta)$. However, @@ -24175,6 +25224,8 @@ $$ Of course, if the difference is, in fact, equal to the root $beta$, you should choose another root of $r(x)$. +%Original Page 302 + Automorphisms of the splitting field are given by mapping a generator of the field, namely $beta$, to other roots of its minimal polynomial. Let's see what happens when $beta$ is mapped to $bb$. @@ -24275,6 +25326,8 @@ $$ $$ \returnType{Type: Boolean} +%Original Page 303 + \spadcommand{(aa1 = a3) :: Boolean } $$ {\tt true} @@ -24342,6 +25395,8 @@ these aspects of the Axiom library from the paper ``Computations in Algebras of Finite Rank,'' by Johannes Grabmeier and Robert Wisbauer, Technical Report, IBM Heidelberg Scientific Center, 1992.} +%Original Page 304 + Mendel's genetic laws are often written in a form like $$Aa \times Aa = {\frac{1}{4}}AA + {\frac{1}{2}}Aa + {\frac{1}{4}}aa$$ @@ -24379,6 +25434,8 @@ Mendelian segregation. Zygote $a_1a_4$ undergoes transition to $a_2a_3$ and vice versa with probability $0 \le \theta \le {\frac{1}{2}}$. +%Original Page 305 + Define a list $[(\gamma_{i,j}^k) 1 \le k \le 4]$ of four four-by-four matrices giving the segregation rates. We use the value $1/10$ for $\theta$. @@ -24493,6 +25550,8 @@ $$ $$ \returnType{Type: Boolean} +%Original Page 306 + In general, it is not associative. \spadcommand{associative?()\$A } @@ -24598,6 +25657,8 @@ Y - $$ \returnType{Type: Factored Polynomial Fraction Integer} +%Original Page 307 + The second question is answered by searching for idempotents in the algebra. \spadcommand{cI := conditionsForIdempotents()\$GCNAALG(FRAC INT, 4, gametes, segregationRates) } @@ -24731,6 +25792,8 @@ AlgebraGivenByStructuralConstants(Fraction Integer,4,[AB,Ab,aB,ab], [MATRIX,MATRIX,MATRIX,MATRIX])} +%Original Page 309 + %\setcounter{chapter}{9} % Chapter 10 \chapter{Some Examples of Domains and Packages} In this chapter we show examples of many of the most commonly used @@ -25015,6 +26078,8 @@ $$ $$ \returnType{Type: Domain} +%Original Page 310 + In this expression, {\tt al} is declared to be an association list whose keys are strings and whose entries are the above records. @@ -25144,6 +26209,8 @@ AssociationList(String,Record(monthsOld: Integer,gender: String))} For more information about tables, see \domainref{Table}. For more information about lists, see \domainref{List}. +%Original Page 311 + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \domainhead{BalancedBinaryTree} @@ -25218,6 +26285,8 @@ $$ $$ \returnType{Type: BalancedBinaryTree NonNegativeInteger} +%Original Page 312 + Use {\tt mapUp!} to do a bottom-up traversal of {\tt t}, setting each interior node to the product of the values at the nodes of its children. @@ -25495,6 +26564,8 @@ $$ $$ \returnType{Type: BinaryExpansion} +%Original Page 313 + The period of the expansion can be short or long \ldots \spadcommand{[binary(1/i) for i in 102..106] } @@ -25596,6 +26667,8 @@ $$ $$ \returnType{Type: List PositiveInteger} +%Original Page 311314 + A convenient way to create a binary search tree is to apply the operation {\tt binarySearchTree} to a list of elements. @@ -25703,6 +26776,8 @@ $$ $$ \returnType{Type: BinarySearchTree Integer} +%Original Page 315 + Have Axiom check that these are equal. \spadcommand{(t = rt)@Boolean} @@ -25782,6 +26857,8 @@ $$ $$ \returnType{Type: Boolean} +%Original Page 316 + \spadcommand{finite? A0} $$ {\tt false} @@ -25869,6 +26946,9 @@ The generalized continuum hypothesis asserts that \begin{verbatim} 2**Aleph i = Aleph(i+1) \end{verbatim} + +%Original Page 317 + and is independent of the axioms of set theory.\footnote{Goedel, {\it The consistency of the continuum hypothesis,} Ann. Math. Studies, Princeton Univ. Press, 1940.} @@ -25941,6 +27021,8 @@ The {\tt CartesianTensor} constructor allows you to specify the minimum index for subscripting. In what follows we discuss in detail how to manipulate tensors. +%Original Page 318 + Here we construct the domain of Cartesian tensors of dimension 2 over the integers, with indices starting at 1. @@ -26031,6 +27113,8 @@ $$ $$ \returnType{Type: CartesianTensor(1,2,Integer)} +%Original Page 319 + In general, a tensor of rank {\tt k} can be formed by making a list of rank {\tt k-1} tensors or, alternatively, a {\tt k}-deep nested list of lists. @@ -26197,6 +27281,8 @@ tensor of rank {\tt k1+k2-2}. This product generalizes the vector dot product and matrix-vector product by summing component products along two indices. +%Original Page 320 + Here we sum along the second index of $T_m$ and the first index of $T_v$. Here @@ -26278,6 +27364,8 @@ $$ $$ \returnType{Type: PositiveInteger} +%Original Page 321 + \spadcommand{t1[2]} $$ 3 @@ -26376,6 +27464,8 @@ $$ $$ \returnType{Type: Equation CartesianTensor(1,2,Integer)} +%Original Page 322 + \spadcommand{contract(Tmn,1,4) = transpose(m) * transpose(n)} $$ {\left[ @@ -26540,6 +27630,8 @@ If a more complicated reordering of the indices is required, then the \spadfunFrom{reindex}{CartesianTensor} operation can be used. This operation allows the indices to be arbitrarily permuted. +%Original Page 323 + This defines $rT_{mn}(i,j,k,l) = \allowbreak T_{mn}(i,l,j,k).$ \spadcommand{rTmn := reindex(Tmn, [1,4,2,3])} @@ -26723,6 +27815,8 @@ $$ $$ \returnType{Type: Equation CartesianTensor(1,2,Integer)} +%Original Page 324 + The Levi Civita symbol determines the sign of a permutation of indices. \spadcommand{epsilon:CT := leviCivitaSymbol()} @@ -26794,6 +27888,8 @@ where {\tt *} denotes the {\tt R}-module tensor is the graded algebra in which the degree {\tt k} module is {\tt T[k](V)}. +%Original Page 325 + \subsubsection{Tensor Calculus} It should be noted here that often tensors are used in the context of @@ -26877,6 +27973,8 @@ A, A, X, 8, + $$ \returnType{Type: List Character} +%Original Page 326 + Likewise, the \spadfunFrom{upperCase}{Character} operation converts lower case letters to upper case. @@ -26960,6 +28058,8 @@ $$ $$ \returnType{Type: CharacterClass} +%Original Page 327 + A number of character classes are predefined for convenience. \spadcommand{digit()} @@ -27027,6 +28127,8 @@ $$ $$ \returnType{Type: CharacterClass} +%Original Page 328 + \spadcommand{difference(cl1,cl2) } $$ \mbox{\tt "aeiou"} @@ -27080,6 +28182,8 @@ Examples of Clifford Algebras are gaussians (complex numbers), quaternions, exterior algebras and spin algebras. +%Original Page 329 + \subsection{The Complex Numbers as a Clifford Algebra} This is the field over which we will work, rational functions with @@ -27155,6 +28259,8 @@ $$ $$ \returnType{Type: Domain} +%Original Page 330 + We use this matrix for the quadratic form. \spadcommand{m := matrix [ [-1,0],[0,-1] ] } @@ -27238,6 +28344,8 @@ $$ $$ \returnType{Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX)} +%Original Page 331 + See \domainref{Quaternion} for examples of Axiom's constructor implementing quaternions. @@ -27323,6 +28431,8 @@ $$ $$ \returnType{Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX)} +%Original Page 332 + \spadcommand{x * y + y * x } $$ 0 @@ -27407,6 +28517,8 @@ g(l,t)*gam(l)*gam(m)*gam(n)*gam(r)*gam(s)*gam(t) = \end{verbatim} where a sum over {\tt l} and {\tt t} is implied. +%Original Page 333 + Verify this identity for particular values of {\tt m,n,r,s}. \spadcommand{m := 1; n:= 2; r := 3; s := 4; } @@ -27468,6 +28580,8 @@ $$ $$ \returnType{Type: Complex Fraction Integer} +%Original Page 334 + If {\tt R} is a field, you can also divide the complex objects. \spadcommand{a / b } @@ -27541,6 +28655,8 @@ $$ $$ \returnType{Type: Complex Integer} +%Original Page 335 + You can \spadfunFrom{factor}{Complex} Gaussian integers. \spadcommand{factor(13 - 13*\%i)} @@ -27627,6 +28743,8 @@ continued fraction of the form a(n) \end{verbatim} +%Original Page 336 + The $a_i$ are called partial quotients and the operation \spadfunFrom{partialQuotients}{ContinuedFraction} creates a stream of them. @@ -27722,6 +28840,8 @@ approximations of {\tt e}.\footnote{For this and other interesting expansions, see C. D. Olds, {\it Continued Fractions,} New Mathematical Library, (New York: Random House, 1963), pp. 134--139.} +%Original Page 337 + By looking at the above expansion, we see that the whole part is {\tt 0} and the numerators are all equal to {\tt 1}. This constructs the stream of denominators. @@ -27814,6 +28934,8 @@ for $4 / \pi$, 2 + ... \end{verbatim} +%Original Page 338 + Let's use this expansion to compute rational and floating point approximations for $\pi$. @@ -27911,6 +29033,8 @@ To conclude this section, we give you evidence that 3 + ... \end{verbatim} +%Original Page 339 + is the expansion of $\sqrt{11}$. \spadcommand{[i*i for i in convergents(z) :: Stream Float] } @@ -27975,6 +29099,8 @@ $$ $$ \returnType{Type: SymmetricPolynomial Fraction Integer} +%Original Page 340 + \spadcommand{complete 3} $$ {{\frac{1}{3}} \ {\left( 3 \right)}} @@ -28011,6 +29137,8 @@ $$ $$ \returnType{Type: SymmetricPolynomial Fraction Integer} +%Original Page + The operation {\tt elementary} computes the $n$-th elementary symmetric function for argument {\tt n.} @@ -28072,6 +29200,8 @@ $$ $$ \returnType{Type: SymmetricPolynomial Fraction Integer} +%Original Page 341 + The operation {\tt dihedral} is the cycle index of the dihedral group. @@ -28150,6 +29280,8 @@ In this case the configurations enumerated are easily constructed, however the theory merely enumerates them providing little help in actually constructing them. +%Original Page 342 + Here are the number of 6-pairs, first from {\tt a a a b b c,} second from {\tt d d e e f g.} @@ -28235,6 +29367,8 @@ $$ $$ \returnType{Type: SymmetricPolynomial Fraction Integer} +%Original Page 343 + The number of cubes with 4 red vertices and 4 blue vertices. \spadcommand{cap(complete 4**2,cube)} @@ -28294,6 +29428,8 @@ $$ \spadcommand{Integers: INT -> ULS(FRAC INT, 'x, 0) } \returnType{Type: Void} +%Original Page 344 + For the integers 0 and 1, or two colors. \spadcommand{ZeroOrOne n == 1+x**n } @@ -28438,6 +29574,8 @@ $$ $$ \returnType{Type: UnivariateLaurentSeries(Fraction Integer,x,0)} +%Original Page 345 + The coefficient of $x^n$ is the number of graphs with 5 nodes and with integers on the edges whose sum is {\tt n.} In other words, the enumeration is of multigraphs with 5 nodes and {\tt n} edges. @@ -28542,6 +29680,8 @@ $$ $$ \returnType{Type: Fraction Integer} +%Original Page 346 + The coefficient of $x^n$ is the number of column strict reverse plane partitions of {\tt n} of shape {\tt 3 2 2 1.} @@ -28622,6 +29762,8 @@ $$ $$ \returnType{Type: Expression Integer} +%Original Page 347 + \spadcommand{g : R := z**2*y*cos(z)-7*sin(x**3*y**2)*z**2 } $$ -{7 \ {z \sp 2} \ {\sin \left({{{x \sp 3} \ {y \sp 2}}} \right)}}+ @@ -28729,6 +29871,8 @@ $$ $$ \returnType{Type: DeRhamComplex(Integer,[x,y,z])} +%Original Page 348 + We see a lengthy output of the last expression, but nevertheless, the composition is zero. @@ -28830,6 +29974,8 @@ $$ $$ \returnType{Type: DeRhamComplex(Integer,[x,y,z])} +%Original Page 349 + This allows us to get formal definitions for the ``gradient'' \ldots \spadcommand{totalDifferential(a(x,y,z))\$der } @@ -28932,6 +30078,8 @@ $$ $$ \returnType{Type: DeRhamComplex(Integer,[x,y,z])} +%Original Page 350 + \spadcommand{exteriorDifferential h1 } $$ \begin{array}{@{}l} @@ -29037,6 +30185,8 @@ $$ $$ \returnType{Type: DecimalExpansion} +%Original Page 351 + Arithmetic is exact. \spadcommand{r + decimal(6/7) } @@ -29431,6 +30581,8 @@ and using member? we can test if the dequeue holds a given element: See \domainref{Stack}, \domainref{ArrayStack}, \domainref{Queue}, \domainref{Dequeue}, \domainref{Heap} +%Original Page 352 + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \domainhead{DistributedMultivariatePolynomial} @@ -29529,6 +30681,8 @@ $$ $$ \returnType{Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)} +%Original Page 353 + Note that we get a different Gr\"{o}bner basis when we use the {\tt HDMP} polynomials, as expected. @@ -29724,6 +30878,8 @@ table() $$ \returnType{Type: EqTable(List Integer,Integer)} +%Original Page 354 + These two lists are equal according to \spadopFrom{=}{List}, but not according to \spadfunFrom{eq?}{List}. @@ -29800,6 +30956,8 @@ $$ $$ \returnType{Type: Polynomial Integer} +%Original Page 355 + Arithmetic operations are supported and operate on both sides of the equation. @@ -29935,6 +31093,8 @@ $$ $$ \returnType{Type: NonNegativeInteger} +%Original Page 356 + The function {\tt gasp} is given return type {\tt Exit} since it is guaranteed never to return a value to its caller. @@ -30293,6 +31453,8 @@ respectively. The current restriction to factored objects of integral domains allows simplification to be performed without worrying about multiplication order. +%Original Page 357 + \subsection{Decomposing Factored Objects} In this section we will work with a factored integer. @@ -30375,6 +31537,8 @@ $$ List Record(flg: Union("nil","sqfr","irred","prime"), fctr: Integer,xpnt: Integer)} +%Original Page 358 + If you don't care about the flags, use \spadfunFrom{factors}{Factored}. \spadcommand{factors(g) } @@ -30451,6 +31615,8 @@ $$ $$ \returnType{Type: Factored Integer} +%Original Page 359 + Operations involving multiplication and division are particularly easy with factored objects. @@ -30530,6 +31696,8 @@ $$ $$ \returnType{Type: Factored Integer} +%Original Page 360 + \spadcommand{1\$Factored(Integer)} $$ 1 @@ -30601,6 +31769,8 @@ $$ $$ \returnType{Type: Factored Integer} +%Original Page 361 + \subsection{Factored Objects with Variables} Some of the operations available for polynomials are also available @@ -30678,6 +31848,8 @@ $$ $$ \returnType{Type: Factored Integer} +%Original Page 362 + If we want to use an operation that returns an object that has a type different from the operation's argument, the \spadfunFrom{map}{FactoredFunctions2} in {\tt Factored} @@ -30755,6 +31927,8 @@ $$ $$ \returnType{Type: List Integer} +%Original Page 363 + \spadcommand{write!(ifile, [7])} $$ \left[ @@ -30838,6 +32012,8 @@ For more information on related topics, see \domainref{TextFile}, \domainref{KeyedAccessFile}, \domainref{Library}, and \domainref{FileName}. +%Original Page 364 + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \domainhead{FileName} @@ -30899,6 +32075,8 @@ $$ $$ \returnType{Type: FileName} +%Original Page 365 + When writing programs, it is helpful to refer to directories via variables. @@ -30978,6 +32156,8 @@ $$ $$ \returnType{Type: Boolean} +%Original Page 366 + \spadcommand{writable? "/tmp/DoesNotExist"} $$ {\tt true} @@ -31012,7 +32192,7 @@ the new block. Flexible arrays have available most of the operations provided by {\tt OneDimensionalArray} (see -\domainref{OneDimensionalArray} and \domainref{Vector}. +\domainref{OneDimensionalArray} and \domainref{Vector}). Since flexible arrays are also of category {\tt ExtensibleLinearAggregate}, they have operations {\tt concat!}, {\tt delete!}, {\tt insert!}, {\tt merge!}, {\tt remove!}, @@ -31051,6 +32231,8 @@ $$ $$ \returnType{Type: FlexibleArray Integer} +%Original Page 367 + Initially, the physical length is the same as the number of elements. \spadcommand{physicalLength f} @@ -31154,6 +32336,8 @@ $$ $$ \returnType{Type: FlexibleArray Integer} +%Original Page 368 + Remove all odd integers. \spadcommand{select!(i +-> even? i,f)} @@ -31219,6 +32403,8 @@ $$ $$ \returnType{Type: Float} +%Original Page 369 + A decimal base for the exponent is assumed, so the number {\tt 1.234E2} denotes $1.234 \cdot 10^2$. @@ -31238,7 +32424,7 @@ $$ \subsection{Conversion Functions} -You can use conversion (\sectionref{ugTypesConvert} to +You can use conversion (\sectionref{ugTypesConvert}) to go back and forth between {\tt Integer}, {\tt Fraction Integer} and {\tt Float}, as appropriate. @@ -31293,6 +32479,8 @@ $$ $$ \returnType{Type: Float} +%Original Page 370 + and round to the nearest integral {\tt Float} respectively. \spadcommand{round 3.6} @@ -31384,6 +32572,8 @@ $$ $$ \returnType{Type: Float} +%Original Page 371 + Reset \spadfunFrom{digits}{Float} to its default value. \spadcommand{digits 20} @@ -31457,6 +32647,8 @@ $$ $$ \returnType{Type: Float} +%Original Page 372 + \spadcommand{outputFixed 2; x } $$ 0.45 @@ -31544,6 +32736,8 @@ the display of the matrix. \spadcommand{b: Matrix DoubleFloat := matrix [ [1/(i+j+1\$DoubleFloat) for j in 0..9] for i in 0..9]; } \returnType{Type: Matrix DoubleFloat} +%Original Page 373 + The result given by hardware floats is correct only to four significant digits of precision. In the jargon of numerical analysis, the Hilbert matrix is said to be ``ill-conditioned.'' @@ -31611,6 +32805,8 @@ $$ $$ \returnType{Type: Fraction Integer} +%Original Page 374 + Extract the numerator and denominator by using \spadfunFrom{numer}{Fraction} and \spadfunFrom{denom}{Fraction}, respectively. @@ -31690,6 +32886,8 @@ $$ $$ \returnType{Type: Complex Fraction Integer} +%Original Page 375 + Conversion is discussed in detail in \sectionref{ugTypesConvert}. \spadcommand{g :: FRAC COMPLEX INT } @@ -32173,6 +33371,8 @@ $$ $$ \returnType{Type: PositiveInteger} +%Original Page 376 + So the project is cancelled and we can delete the data base: \spadcommand{)system rm -r kaf*.sdata } @@ -32229,6 +33429,8 @@ $$ $$ \returnType{Type: SquareMatrix(6,DistributedMultivariatePolynomial([x,y,z],Fraction Integer))} +%Original Page 377 + For the cyclohexan, the distances have to satisfy this equation. \spadcommand{eq := determinant mfzn } @@ -32422,6 +33624,8 @@ See \domainref{HomogeneousDistributedMultivariatePolynomial}\\ \domainref{EuclideanGroebnerBasisPackage} +%Original Page 378 + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \domainhead{Heap} @@ -32497,6 +33701,8 @@ $$ $$ \returnType{Type: Heap Integer} +%Original Page 379 + Apply {\tt heapsort} to present elements in order. \spadcommand{heapsort h1} @@ -32697,6 +33903,8 @@ See \domainref{DistributedMultivariatePolynomial}, and\\ \domainref{GeneralDistributedMultivariatePolynomial} +%Original Page 380 + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \domainhead{Integer} @@ -32758,6 +33966,8 @@ $$ $$ \returnType{Type: Integer} +%Original Page 381 + You can determine if an integer is negative in several other ways. \spadcommand{x < 0 } @@ -32825,6 +34035,8 @@ $$ $$ \returnType{Type: Boolean} +%Original Page 382 + This syntax is used to test equality using \spadopFrom{=}{Integer}. It says that you want a {\tt Boolean} ({\tt true} or {\tt false}) answer rather than an equation. @@ -32907,6 +34119,8 @@ $$ $$ \returnType{Type: PositiveInteger} +%Original Page 383 + \spadcommand{reduce(lcm,[2,45,-89,78,100,-45])} $$ 1041300 @@ -32989,6 +34203,8 @@ $$ $$ \returnType{Type: Factored Integer} +%Original Page 384 + The operation \spadfunFrom{prime?}{Integer} returns {\tt true} or {\tt false} depending on whether its argument is a prime. @@ -33078,6 +34294,8 @@ $$ $$ \returnType{Type: List Integer} +%Original Page 385 + The operation \spadfunFrom{jacobi}{IntegerNumberTheoryFunctions} computes the Jacobi symbol for its two integer arguments. By convention, {\tt 0} is returned if the greatest common divisor of the @@ -33161,6 +34379,8 @@ for testing whether some elements of a module over the integers are linearly dependent over the integers, and to find the linear dependence relations, if any. +%Original Page 386 + Consider the domain of two by two square matrices with integer entries. \spadcommand{M := SQMATRIX(2,INT) } @@ -33252,6 +34472,8 @@ $$ $$ \returnType{Type: Union(Vector Fraction Integer,...)} +%Original Page 387 + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \domainhead{IntegerNumberTheoryFunctions} @@ -33329,17 +34551,21 @@ function, defined as follows: {\tt $\mu$(1) = 1}, {\tt $\mu$(n) = 0}, when {\tt n} is divisible by a square, and {\tt $\mu = {(-1)}^k$, when {\tt n} is the product of {\tt k} distinct primes. The corresponding Axiom operation is \spadfunFrom{moebiusMu}{IntegerNumberTheoryFunctions}. + This function occurs in the following theorem: +%Original Page 388 + \noindent {\bf Theorem} (M\"{o}bius Inversion Formula): \newline Let {\tt f(n)} be a function on the positive integers and let {\tt F(n)} be defined -by $${F(n) = \sum_{d \mid n} f(n)}$$ sum of {\tt f(n)} over +by +\[F(n) = \sum_{d \mid n} f(n)\] sum of {\tt f(n)} over {\tt d | n}} where the sum is taken over the positive divisors of {\tt n}. Then the values of {\tt f(n)} can be recovered from the values of {\tt F(n)}: -$${f(n) = \sum_{d \mid n} \mu(n) F({\frac{n}{d}})}$$ +\[f(n) = \sum_{d \mid n} \mu(n) F({\frac{n}{d}})\] where again the sum is taken over the positive divisors of {\tt n}. When {\tt f(n) = 1}, then {\tt F(n) = d(n)}. Thus, if you sum $\mu(d) @@ -33380,6 +34606,43 @@ $$ $$ \returnType{Type: PositiveInteger} +The M\"obius inversion formula is derived from the multiplication of +formal Dirichlet series. A Dirichlet series is an infinite series of +the form: +\[\sum_{n=1}^\infty a(n)n^{-s}\] + +%Original Page 389 + +When +\[\sum_{n=1}^\infty a(n)n^{-s} \cdot \sum_{n=1}^\infty b(n)n^{-s} = + \sum_{n=1}^\infty c(n)n^{-s} \] +then +\[c(n) = \sum_{d \mid n} a(d)b(n/d)\] +Recall that the Riemann $\zeta$ function is defined by +\[ +\zeta(s) = \prod_p (1-p^{-s})^{-1} = \sigma_{n=1}^\infty n^{-s} +\] +where the product is taken over the set of (positive) primes. Thus, +\[ +\zeta(s)^{-1} = \prod_p(1-p^{-s}) = \sigma_{n=1}^\infty\mu(n)n^{-s} +\] +Now if +\[ +F(n) = \sum_{(d \mid n)}f(d) +\] +then +\[ +\sum{f(n)n^{-s}} \cdot \zeta(s) = \sum{F(n)n^{-s}} +\] +thus +\[ +\zeta(s)^{-1} \cdot \sum{F(n)n^{-s}} = \sum{f(n)n^{-s}} +\] +and +\[ +f(n) = \sum_{(d \mid n)} \mu(d)F(n/d) +\] + The Fibonacci numbers are defined by $F(1) = F(2) = 1$ and $F(n) = F(n-1) + F(n-2)$ for $n = 3,4,\ldots$. @@ -33421,6 +34684,8 @@ $$ $$ \returnType{Type: List Integer} +%Original Page 390 + Quadratic symbols can be computed with the operations \spadfunFrom{legendre}{IntegerNumberTheoryFunctions} and \spadfunFrom{jacobi}{IntegerNumberTheoryFunctions}. The Legendre @@ -33711,6 +34976,8 @@ difference is that keyed access files reside in secondary storage while string tables are kept in memory. For more information on table-oriented operations, see the description of {\tt Table}. +%Original Page 391 + Before a keyed access file can be used, it must first be opened. A new file can be created by opening it for output. @@ -33777,6 +35044,8 @@ $$ $$ \returnType{Type: Union("failed",...)} +%Original Page 392 + When an entry is no longer needed, it can be removed from the file. \spadcommand{remove!("Char", ey) } @@ -33858,6 +35127,8 @@ $$ $$ \returnType{Type: KeyedAccessFile Integer} +%Original Page 393 + The \spadfunFrom{read}{KeyedAccessFile} operation is also available from the file view, but it returns elements in a random order. It is generally clearer and more efficient to use the @@ -39037,6 +40308,8 @@ $$ $$ \returnType{Type: List String} +%Original Page 394 + You extract values by giving the desired key in this way. \spadcommand{stuff.poly} @@ -39797,6 +41070,8 @@ $$ ordinary differential operators with coefficients in the differential ring {\tt A}. +%Original Page 396 + \subsection{Differential Operators with Rational Function Coefficients} This example shows differential operators with rational function @@ -39861,6 +41136,8 @@ $$ $$ \returnType{Type: Fraction UnivariatePolynomial(x,Integer)} +%Original Page 397 + When the coefficients of operator polynomials come from a field, as in this case, it is possible to define operator division. Division on the left and division on the right yield different results when the @@ -39934,6 +41211,8 @@ remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer))} +%Original Page 398 + \spadcommand{a = rd.quotient * b + rd.remainder } $$ \begin{array}{@{}l} @@ -40033,6 +41312,8 @@ LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)} Similarly, a least common multiple is not necessarily divisible from both sides. +%Original Page 399 + % NOTE: the book has a different answer \spadcommand{f := rightLcm(a,b) } $$ @@ -40113,6 +41394,8 @@ LinearOrdinaryDifferentialOperator2( Fraction Integer, UnivariatePolynomial(x,Fraction Integer))} +%Original Page 399 + New operators are created as polynomials in {\tt D()}. \spadcommand{a := Dx + 1 } @@ -40182,6 +41465,8 @@ $$ $$ \returnType{Type: UnivariatePolynomial(x,Fraction Integer)} +%Original Page 401 + \subsection{ Differential Operators with Matrix Coefficients Operating on Vectors} @@ -40191,6 +41476,8 @@ the differential ring of square matrices (of a given dimension) with univariate polynomial entries does not form a field. Thus the number of operations available is more limited. +%Original Page 402 + In this section, the operators have three by three matrix coefficients with polynomial entries. @@ -40294,6 +41581,8 @@ UnivariatePolynomial(x,Integer), SquareMatrix(3,UnivariatePolynomial(x,Integer)), UnivariatePolynomial(x,Integer))} +%Original Page 403 + Now form a few operators. \spadcommand{Dx : Modo := D()} @@ -40398,6 +41687,8 @@ SquareMatrix(3, UnivariatePolynomial(x,Integer)), UnivariatePolynomial(x,Integer)))} +%Original Page 404 + These operators can be applied to vector values. \spadcommand{a p } @@ -40495,6 +41786,8 @@ Fraction Integer}. Indeed, you can even have {\tt List List List Boolean} (that is, lists of lists of lists of Boolean values). You can have lists of any type of Axiom object. +%Original Page 405 + \subsection{Creating Lists} The easiest way to create a list with, for example, the elements @@ -40585,6 +41878,8 @@ $$ $$ \returnType{Type: List PositiveInteger} +%Original Page 406 + Each of the next four expressions extracts the \spadfunFrom{first}{List} element of {\tt k}. @@ -40657,6 +41952,8 @@ $$ $$ \returnType{Type: PositiveInteger} +%Original Page 407 + \subsection{Changing List Elements} We'll use this in some of the following examples. @@ -40746,6 +42043,8 @@ $$ $$ \returnType{Type: List PositiveInteger} +%Original Page 408 + \subsection{Other Functions} An operation that is used frequently in list processing is that @@ -40831,6 +42130,8 @@ $$ $$ \returnType{Type: List Segment PositiveInteger} +%Original Page 409 + Segments can be expanded into the range of items between the endpoints by using \spadfunFrom{expand}{Segment}. @@ -41415,6 +42716,8 @@ $$ $$ \returnType{Type: List Float} +%Original Page 410 + Use the list {\tt [x1,...,xn]} as the third argument to \spadfunFrom{function}{MakeFunction} to create a multivariate function {\tt f(x1,...,xn)}. @@ -41506,6 +42809,8 @@ $$ For more information, see \sectionref{ugUserMake}. +%Original Page 411 + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \domainhead{MappingPackage1} @@ -41589,6 +42894,8 @@ $$ $$ \returnType{Type: ((Fraction Integer,Fraction Integer) -> Fraction Integer)} +%Original Page 412 + Likewise, {\tt constantLeft(f)} is the function {\tt g} such that {\tt g(a,b)= f(b).} @@ -41674,6 +42981,8 @@ $$ $$ \returnType{Type: List Fraction Integer} +%Original Page 413 + Use the \spadfunFrom{recur}{MappingPackage1} operation for recursion: @@ -41751,6 +43060,8 @@ $$ $$ \returnType{Type: List Integer} +%Original Page 414 + \spadcommand{fibs := curry(shiftfib, fibinit) } $$ \mbox{theMap(...)} @@ -41837,6 +43148,8 @@ $$ $$ \returnType{Type: Matrix Integer} +%Original Page 415 + If you already have the matrix entries as a list of lists, use \spadfunFrom{matrix}{Matrix}. @@ -41948,6 +43261,8 @@ $$ $$ \returnType{Type: List Matrix Polynomial Integer} +%Original Page 416 + Use \spadfunFrom{subMatrix}{Matrix} to extract part of an existing matrix. The syntax is {\tt subMatrix({\it m, firstrow, lastrow, firstcol, lastcol})}. @@ -42036,6 +43351,8 @@ $$ $$ \returnType{Type: Matrix Fraction Integer} +%Original Page 417 + \spadcommand{b := matrix [ [3/5,3/7,3/11],[3/13,3/17,3/19] ] } $$ \left[ @@ -42135,6 +43452,8 @@ $$ $$ \returnType{Type: Matrix Integer} +%Original Page 418 + This following product is defined but {\tt n * m} is not. \spadcommand{m * n } @@ -42236,6 +43555,8 @@ $$ $$ \returnType{Type: Union("failed",...)} +%Original Page 419 + The operation \spadfunFrom{determinant}{Matrix} computes the determinant of a matrix provided that the entries of the matrix belong to a {\tt CommutativeRing}. @@ -42315,6 +43636,8 @@ For more information on related topics, see \domainref{Permanent}, \domainref{Vector}, \domainref{OneDimensionalArray}, and \domainref{TwoDimensionalArray}. +%Original Page 420 + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \domainhead{Multiset} @@ -42433,6 +43756,8 @@ $$ $$ \returnType{Type: Multiset Integer} +%Original Page 421 + Check that the {\tt union} of the {\tt symmetricDifference} and the {\tt intersect} equals the {\tt union} of the elements. @@ -42521,6 +43846,8 @@ $$ $$ \returnType{Type: Polynomial Integer} +%Original Page 422 + Now pull out the variables of interest. \spadcommand{\% :: MPOLY([a,b],POLY INT) } @@ -42612,6 +43939,8 @@ For more information on related topics, see \domainref{Polynomial}, \domainref{UnivariatePolynomial}, and \domainref{DistributedMultivariatePolynomial}. +%Original Page 423 + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \domainhead{None} @@ -42723,6 +44052,8 @@ $$ $$ \returnType{Type: Octonion Integer} +%Original Page 424 + As with the quaternions, we have a real part, the imaginary parts {\tt i}, {\tt j}, {\tt k}, and four additional imaginary parts {\tt E}, {\tt I}, {\tt J} and {\tt K}. These parts correspond to the canonical @@ -42794,6 +44125,8 @@ o1+{oi \ i}+{oj \ j}+{ok \ k}+{oE \ E}+{oI \ I}+{oJ \ J}+{oK \ K} $$ \returnType{Type: Octonion Polynomial Integer} +%Original Page 425 + \spadcommand{norm o } $$ {ok \sp 2}+{oj \sp 2}+{oi \sp 2}+{oK \sp 2}+{oJ \sp 2}+{oI \sp 2}+{oE \sp @@ -42871,6 +44204,8 @@ $$ $$ \returnType{Type: OneDimensionalArray Integer} +%Original Page 426 + Reverse the elements in place. \spadcommand{reverse! a} @@ -42974,6 +44309,8 @@ tilde $$ \returnType{Type: Operator SquareMatrix(2,Integer)} +%Original Page 427 + Operators can be manipulated formally as in any ring: {\tt +} is the pointwise addition and {\tt *} is composition. Any element {\tt x} of {\tt R} can be converted to an operator @@ -43098,6 +44435,8 @@ $$ $$ \returnType{Type: SquareMatrix(2,Integer)} +%Original Page 428 + Do the swapping of rows and transposition commute? We can check by computing their bracket. @@ -43257,6 +44596,8 @@ $$ $$ \returnType{Type: Boolean} +%Original Page 429 + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \domainhead{OrderlyDifferentialPolynomial} @@ -43307,6 +44648,8 @@ $$ \returnType{Type: (NonNegativeInteger -> OrderlyDifferentialPolynomial Fraction Integer)} +%Original Page 430 + \spadcommand{z := makeVariable('z)\$dpol } $$ \mbox{theMap(...)} @@ -43404,6 +44747,8 @@ $$ \returnType{Type: (NonNegativeInteger -> OrderlyDifferentialPolynomial Fraction Integer)} +%Original Page 431 + The fourth derivative of f may be referenced easily. \spadcommand{df.4 } @@ -43505,6 +44850,8 @@ $$ $$ \returnType{Type: PositiveInteger} +%Original Page 432 + A differential polynomial is {\em isobaric} if the weights of all differential monomials appearing in it are equal. @@ -43589,6 +44936,8 @@ z \sb {2} $$ \returnType{Type: OrderlyDifferentialVariable Symbol} +%Original Page 433 + The operation \spadfunFrom{separant}{OrderlyDifferentialPolynomial} returns the separant of a differential polynomial, which is the partial derivative with respect to the leader. @@ -43680,6 +45029,9 @@ primes.\footnote{Most people first encounter partial fractions when they are learning integral calculus. For a technical discussion of partial fractions, see, for example, Lang's {\it Algebra.}} For example, the rational number {\tt 1/6} is decomposed into {\tt 1/2-1/3}. + +%Original Page 434 + You can compute partial fractions of quotients of objects from domains belonging to the category {\tt EuclideanDomain}. For example, {\tt Integer}, {\tt Complex Integer}, and @@ -43754,6 +45106,8 @@ returned is a partial fraction itself. \spadfunFrom{firstDenom}{PartialFraction} extract the numerator and denominator of the first term of the fraction. +%Original Page 435 + \spadcommand{nthFractionalTerm(f,3) } $$ \frac{1}{2 \sp 5} @@ -43823,6 +45177,8 @@ $$ $$ \returnType{Type: PartialFraction UnivariatePolynomial(x,Fraction Integer)} +%Original Page 436 + \spadcommand{padicFraction \% } $$ \displaystyle @@ -43965,6 +45321,8 @@ The domain constructor {\tt Polynomial} (abbreviation: {\tt POLY}) provides polynomials with an arbitrary number of unspecified variables. +%Original Page 437 + It is used to create the default polynomial domains in Axiom. Here the coefficients are integers. @@ -44051,6 +45409,8 @@ $$ $$ \returnType{Type: Polynomial Integer} +%Original Page 438 + The fully factored form can be recovered by using \spadfunFrom{factor}{Polynomial}. @@ -44149,6 +45509,8 @@ Many of the operations on polynomials require you to specify a variable. For example, \spadfunFrom{resultant}{Polynomial} requires you to give the variable in which the polynomials should be expressed. +%Original Page 439 + This computes the resultant of the values of {\tt p} and {\tt q}, considering them as polynomials in the variable {\tt z}. They do not share a root when thought of as polynomials in {\tt z}. @@ -44235,6 +45597,8 @@ $$ $$ \returnType{Type: PositiveInteger} +%Original Page 440 + \spadcommand{degree(p,z) } $$ 1 @@ -44331,6 +45695,8 @@ $$ $$ \returnType{Type: Polynomial Integer} +%Original Page 441 + \spadcommand{eval(p,x,1) } $$ {\left( {y \sp 2} -{2 \ y}+1 @@ -44425,6 +45791,8 @@ $$ $$ \returnType{Type: Polynomial Integer} +%Original Page 442 + Now that we can extract the components, we can demonstrate the relationship among them and the arguments to our original expression {\tt qr := monicDivide(p,x+1,x)}. @@ -44504,6 +45872,8 @@ $$ $$ \returnType{Type: Quaternion Fraction Integer} +%Original Page 443 + The four arguments are the real part, the {\tt i} imaginary part, the {\tt j} imaginary part, and the {\tt k} imaginary part, respectively. @@ -44696,6 +46066,8 @@ $$ For more information on related topics, see Stack \sectionref{Stack}. +%Original Page 444 + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \domainhead{RadixExpansion} @@ -44757,6 +46129,8 @@ $$ $$ \returnType{Type: RadixExpansion 36} +%Original Page 445 + For bases greater than 36, the ragits are separated by blanks. \spadcommand{(5/24)::RadixExpansion(38)} @@ -47020,6 +48394,8 @@ solve your favorite system with {\tt zeroSetSplit}. There exist more options at the development level that are not currently available in this public version. +%Original Page 446 + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \domainhead{RomanNumeral} @@ -47098,6 +48474,8 @@ denominators, as this matrix Hilberticus illustrates. \spadcommand{m : MATRIX FRAC ROMAN } \returnType{Void} +%Original Page 447 + \spadcommand{m := matrix [ [1/(i + j) for i in 1..3] for j in 1..3] } $$ \left[ @@ -47182,6 +48560,8 @@ $$ $$ \returnType{Type: PositiveInteger} +%Original Page 448 + In addition to the end points, each segment has an integer ``increment.'' An increment can be specified using the ``{\tt by}'' construct. @@ -47270,6 +48650,8 @@ x={a..b} $$ \returnType{Type: SegmentBinding Symbol} +%Original Page 449 + This is used to provide a convenient syntax for arguments to certain operations. @@ -47281,6 +48663,13 @@ $$ \spadcommand{draw(x**2, x = -2..2)} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/p449.eps}} +\begin{center} +$x^2, x = -2..2$ +\end{center} +\end{minipage} + The left-hand side must be of type {\tt Symbol} but the right-hand side can be a segment over any type. @@ -47325,6 +48714,8 @@ $$ $$ \returnType{Type: Set Polynomial Integer} +%Original Page 450 + or by using a collect form, just as for lists. In either case, the set is formed from a finite collection of values. @@ -47421,6 +48812,8 @@ $$ $$ \returnType{Type: Set PrimeField 11} +%Original Page 451 + The following values are not generators. \spadcommand{complement gs } @@ -47508,6 +48901,8 @@ $$ For more information about lists, see \domainref{List}. +%Original Page 453 + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \domainhead{SingleInteger} @@ -47532,6 +48927,8 @@ $$ $$ \returnType{Type: SingleInteger} +%Original Page 454 + \spadcommand{max()\$SingleInteger} $$ 134217727 @@ -47628,6 +49025,8 @@ Many other operations are available for small integers, including many of those provided for {\tt Integer}. To see the other operations, use the Browse HyperDoc facility (\sectionref{ugBrowse}) +%Original Page 455 + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \domainhead{SparseTable} @@ -47699,6 +49098,8 @@ If a specific table representation is required, the {\tt GeneralSparseTable(K,E,Table(K,E), dflt)}. For more information, see \domainref{Table} and \domainref{GeneralSparseTable}. +%Original Page 456 + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \domainhead{SquareMatrix} @@ -48319,6 +49720,8 @@ $$ For more information on related topics, see Queue \sectionref{Queue}. +%Original Page 457 + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \domainhead{Stream} @@ -48407,6 +49810,8 @@ $$ $$ \returnType{Type: Stream NonNegativeInteger} +%Original Page 458 + \spadcommand{map(*,ints,odds)} $$ \left[ @@ -48480,6 +49885,8 @@ $$ $$ \returnType{Type: String} +%Original Page 459 + It is also possible to use \spadfunFrom{new}{String} to create a string of any size filled with a given character. Since there are many {\tt new} functions it is necessary to indicate the desired type. @@ -48566,6 +49973,8 @@ $$ $$ \returnType{Type: String} +%Original Page 460 + Substrings are obtained by giving an index range. \spadcommand{hello(1..5) } @@ -48646,6 +50055,8 @@ $$ $$ \returnType{Type: String} +%Original Page 461 + The versions with the exclamation mark change the original string, while the others produce a copy. @@ -48726,6 +50137,8 @@ $$ $$ \returnType{Type: NonNegativeInteger} +%Original Page 462 + To search for a specific character or a member of a character class, a different first argument is used. @@ -48792,6 +50205,8 @@ x $$ \returnType{Type: Symbol} +%Original Page 463 + This gives the symbol even if {\tt x} has been assigned a value. If {\tt x} has not been assigned a value, then it is possible to omit the quote. @@ -48878,6 +50293,8 @@ u \sb {1, 2, 1, 2} $$ \returnType{Type: Symbol} +%Original Page 464 + \spadcommand{V := superscript(v, [n]) } $$ v \sp {n} @@ -48978,6 +50395,8 @@ presup: List OutputForm, presub: List OutputForm, args: List OutputForm)} +%Original Page 465 + The most general form is obtained using the \spadfunFrom{script}{Symbol} operation. This operation takes an argument which is a list containing, in this order, lists of @@ -49082,6 +50501,8 @@ $$ $$ \returnType{Type: String} +%Original Page 466 + \spadcommand{t(x) := "The easiest to factor" } $$ \mbox{\tt "The easiest to factor"} @@ -49166,7 +50587,9 @@ $$ $$ \returnType{Type: Boolean} -The \spadfunFrom{remove}{Table} operation is used to delete values from a +%Original Page 467 + +The \spadfunFrom{remove!}{Table} operation is used to delete values from a table. \spadcommand{remove!(x**2-1, t) } @@ -49241,6 +50664,8 @@ See \domainref{KeyedAccessFile} for more information. \end{list} \noindent +%Original Page 468 + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \domainhead{TextFile} @@ -49322,6 +50747,8 @@ $$ $$ \returnType{Type: String} +%Original Page 469 + \spadcommand{close! f2} $$ \mbox{\tt "/tmp/MOTD"} @@ -49384,6 +50811,8 @@ $$ $$ \returnType{Type: PositiveInteger} +%Original Page 470 + Now the first element of the array is {\tt 17.} \spadcommand{arr } @@ -49469,6 +50898,8 @@ $$ $$ \returnType{Type: PositiveInteger} +%Original Page 471 + \spadcommand{ncols(arr) } $$ 4 @@ -49556,6 +50987,8 @@ $$ $$ \returnType{Type: TwoDimensionalArray Integer} +%Original Page 472 + \spadcommand{arr } $$ \left[ @@ -49880,6 +51313,8 @@ Axiom does not allow you to create types where . } +%Original Page 473 + {\tt UP(x,INT)} is the domain of polynomials in the single variable {\tt x} with integer coefficients. @@ -49967,6 +51402,8 @@ $$ $$ \returnType{Type: NonNegativeInteger} +%Original Page 474 + To compute the derivative of a univariate polynomial with respect to its variable, use \spadfunFrom{D}{UnivariatePolynomial}. @@ -50079,6 +51516,8 @@ coefficients from the list. Sometimes it is useful to convert a univariate polynomial to a vector whose $i$-th position contains the degree {\tt i-1} coefficient of the polynomial. +%Original Page 475 + \spadcommand{ux := (x**4+2*x+3)::UP(x,INT) } $$ {x \sp 4}+{2 \ x}+3 @@ -50144,6 +51583,8 @@ $$ $$ \returnType{Type: UnivariatePolynomial(a1,Fraction Integer)} +%Original Page 476 + \spadcommand{s := a1 + 4} $$ a1+4 @@ -50225,6 +51666,8 @@ $$ $$ \returnType{Type: UnivariatePolynomial(a1,Fraction Polynomial Integer)} +%Original Page 477 + We push all the variables into a single quotient of polynomials. \spadcommand{u : FRAC POLY INT := t } @@ -50772,6 +52215,8 @@ $$ $$ \returnType{Type: Boolean} +%Original Page 478 + \spadcommand{hasHi useg } $$ {\tt true} @@ -50843,6 +52288,8 @@ $$ $$ \returnType{Type: Vector Integer} +%Original Page 479 + This is how you create a vector from a list of its components. \spadcommand{v : VECTOR INT := vector([1,2,3,4,5]) } @@ -50951,6 +52398,8 @@ For more information about other aggregate domains, see the following: Issue the system command {\tt )show Vector} to display the full list of operations defined by {\tt Vector}. +%Original Page 480 + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \domainhead{Void} @@ -55921,6 +57370,8 @@ $$ \returnType{Type: List Float} +%Original Page 483 + \chapter{Interactive Programming} \label{ugIntProg} @@ -55963,15 +57414,21 @@ previous one. A ribbon is simply a function of $x$ and $y$ depending only on $x$. +%Original Page 484 + We illustrate this for $f_i(x)$ defined as simple powers of $x$ for $x$ ranging between $-1$ and $1$. - Draw the ribbon for $z = x^2$. \spadgraph{draw(x**2,x=-1..1,y=0..1)} -%\epsffile[0 0 295 295]{ps/ribbon1.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/ribbon1.eps}} +\begin{center} +$x^2,x=-1..1,y=0..1$ +\end{center} +\end{minipage} Now that was easy! What you get is a ``wire-mesh'' rendition of the ribbon. @@ -55990,7 +57447,12 @@ $y$ direction. \spadgraph{vp := draw(x**2,x=-1..1,y=0..1,var2Steps==1) } -%\epsffile[0 0 295 295]{ps/ribbon2.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/ribbon2.eps}} +\begin{center} +$x^2, x=-1..1,y=0..1, var2Steps==1$ +\end{center} +\end{minipage} The operation has created a viewport, that is, a graphics window on your screen. @@ -56010,13 +57472,19 @@ Issue $rotate(vp, -45, 90)$ to rotate the figure $-45$ longitudinal degrees and $90$ latitudinal degrees. +%Original Page 485 + Here is a different rotation. This turns the graph so you can view it along the $y$-axis. \spadcommand{rotate(vp, 0, -90)} -%\epsffile[0 0 295 295]{ps/ribbon2r.ps} - +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/ribbon2r.eps}} +\begin{center} +$rotate(vp, 0, -90)$ +\end{center} +\end{minipage} There are many other things you can do. In fact, most everything you can do interactively using the @@ -56050,13 +57518,20 @@ Extract the space component of $vp$. \spadcommand{sp := subspace(vp)} +%Original Page 486 + Add the ribbon for $x^3$ alongside that for $x^2$. \spadgraph{vp := draw(x**3,x=-1..1,y=1..2,var2Steps==1, space==sp)} -%\epsffile[0 0 295 295]{ps/ribbons.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/ribbons.eps}} +\begin{center} +$x^3, x=-1..1, y=1..2, var2Steps==1, space==sp$ +\end{center} +\end{minipage} Unless you moved the original viewport, the new viewport covers the old one. @@ -56070,20 +57545,33 @@ Show quadrilateral polygon outlines. \spadcommand{drawStyle(vp,"shade");outlineRender(vp,"on")} -%\epsffile[0 0 295 295]{ps/ribbons2.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/ribbons2.eps}} +\begin{center} +$drawStyle(vp,"shade");outlineRender(vp,"on")$ +\end{center} +\end{minipage} Enclose the ribbons in a box. \spadcommand{rotate(vp,20,-60); showRegion(vp,"on")} -%\epsffile[0 0 295 295]{ps/ribbons2b.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/ribbons2b.eps}} +\begin{center} +$rotate(vp,20,-60); showRegion(vp,"on")$ +\end{center} +\end{minipage} + +%Original Page 487 This process has become tedious! If we had to add two or three more ribbons, we would have to repeat the above steps several more times. It is time to write an interpreter program to help us take care of the details. - +\vfill +\newpage \section{A Ribbon Program} \label{ugIntProgRibbon} @@ -56105,6 +57593,7 @@ Here is the {\bf drawRibbons} program. Invoke your favorite editor and create a file called {\bf ribbon.input} containing the following program. +\line(1,0){380} \begin{figure} \begin{verbatim} drawRibbons(flist, xrange) == @@ -56126,6 +57615,7 @@ drawRibbons(flist, xrange) == \caption{The first {\bf drawRibbons} function.} \label{fig-ribdraw1} \end{figure} +\line(1,0){380} Here are some remarks on the syntax used in the {\bf drawRibbons} function (consult \sectionref{ugUser} for more details). @@ -56137,6 +57627,8 @@ The first line of the function definition always begins in column 1. All other lines of the function are indented with respect to the first line and form a {\it pile} (see \sectionref{ugLangBlocks}). +%Original Page 488 + The definition of {\bf drawRibbons} consists of a pile of expressions to be executed one after another. @@ -56174,7 +57666,12 @@ for $-1 \leq x \leq 1$ \spadgraph{drawRibbons([x**i for i in 1..5],x=-1..1) } -%\epsffile[0 0 295 295]{ps/ribbons5.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/ribbons5.eps}} +\begin{center} +$[x^i {rm\ for\ i\ in\ 1..5}], x=-1..1$ +\end{center} +\end{minipage} \section{Coloring and Positioning Ribbons} \label{ugIntProgColor} @@ -56214,6 +57711,9 @@ The result is assigned to the variable $width$. Note that in the for-loop in line 7, we are iterating in parallel; it is not a nested loop. +%Original Page 489 + +\line(1,0){380} \begin{figure} \hrule \begin{verbatim} @@ -56238,6 +57738,7 @@ drawRibbons(flist, xrange, yrange) == \caption{The final {\bf drawRibbons} function.} \label{fig-ribdraw2} \end{figure} +\line(1,0){380} \section{Points, Lines, and Curves} \label{ugIntProgPLC} @@ -56263,6 +57764,8 @@ The {\tt @} sign means ``of the type.'' Thus $zero$ is $0.0$ of the type {\tt DoubleFloat}. You can also say $0.0::DFLOAT$. +%Original Page 490 + Points can have four small float components: $x, y, z$ coordinates and an optional color. A ``curve'' is simply a list of points connected by straight line @@ -56301,6 +57804,7 @@ $arrowAngle$ and $arrowScale$, then defines the function {\bf makeArrow}$(p_1, p_2)$ to draw an arrow from point $p_1$ to $p_2$. +\line(1,0){380} \begin{verbatim} arrowAngle := \%pi-\%pi/10.0@DFLOAT The angle of the arrowhead. arrowScale := 0.2@DFLOAT The size of the arrowhead @@ -56318,6 +57822,9 @@ makeArrow(p1, p2) == p4 := point [p2.1 + c2, p2.2 + s2, z, p2.4] The right endpoint of head [ [p1, p2, p3], [p2, p4] ] The arrow as a list of curves \end{verbatim} +\line(1,0){380} + +%Original Page 491 Read the file and then create an arrow from the point $origin$ to the point $unit$. @@ -56329,26 +57836,73 @@ Read the input file defining {\bf makeArrow}. Construct the arrow (a list of two curves). \spadcommand{arrow := makeArrow(origin,unit)} +\[ +\left[ + \left[ + \left[0.0, 0.0, 0.0, 0.0\right], + \left[1.0, 1.0, 1.0, 1.0\right], + \right. +\right. +\] +\[ +\left. + \left. + \left[0.69134628604607973, + 0.842733077659504, + 0.80000000000000004, + 0.0 + \right] + \right], +\right. +\] +\[ +\left. + \left[ + \left[1.0, 1.0, 1.0, 1.0 + \right], + \left[0.842733077659504, + 0.69134628604607973, + 0.80000000000000004, + 0.0 + \right] + \right] +\right] +\] +\returnType{Type: List List Point DoubleFloat} Create an empty object $sp$ of type $ThreeSpace$. \spadcommand{sp := createThreeSpace()} +\returnType{Type: ThreeSpace DoubleFloat} Add each curve of the arrow to the space $sp$. \spadcommand{for a in arrow repeat sp := curve(sp,a)} +\returnType{Type: Void} Create a three-di\-men\-sion\-al viewport containing that space. \spadgraph{vp := makeViewport3D(sp,"Arrow")} -%\epsffile[0 0 295 295]{ps/arrow.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/arrow.eps}} +\begin{center} +$makeViewport3D(sp,"Arrow")$ +\end{center} +\end{minipage} Here is a better viewing angle. \spadcommand{rotate(vp,200,-60)} -%\epsffile[0 0 295 295]{ps/arrowr.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/arrowr.eps}} +\begin{center} +$rotate(vp,200,-60)$ +\end{center} +\end{minipage} + +%Original Page 492 \section{A Bouquet of Arrows} \label{ugIntProgColorArr} @@ -56379,6 +57933,7 @@ denoted by $\theta$. In this way, the color of arrows ranges from red to green to violet. Here is a program to draw a bouquet of $n$ arrows. +\line(1,0){380} \begin{verbatim} drawBouquet(n,title) == angle := 0.0@DFLOAT The initial angle @@ -56394,6 +57949,7 @@ drawBouquet(n,title) == angle := angle + 2*\%pi/n The next angle makeViewport3D(sp,title) Create the viewport from $sp$ \end{verbatim} +\line(1,0){380} Read the input file. @@ -56403,7 +57959,12 @@ A bouquet of a dozen arrows. \spadgraph{drawBouquet(12,"A Dozen Arrows")} -%\epsffile[0 0 295 295]{ps/bouquet.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/bouquet.eps}} +\begin{center} +$drawBouquet(12,"A\ Dozen\ Arrows")$ +\end{center} +\end{minipage} \section{Diversion: When Things Go Wrong} \label{ugIntProgDivTwo} @@ -56449,6 +58010,8 @@ A bouquet of a dozen arrows. %to ?? %and run. +%Original Page 493 + \section{Drawing Complex Vector Fields} \label{ugIntProgVecFields} @@ -56483,11 +58046,12 @@ $clipValue$ is used instead of that for $r$. For convenience, we define a function $clipFun(x)$ which uses $clipValue$ to ``clip'' the value of $x$. -% +\line(1,0){380} \begin{verbatim} clipValue : DFLOAT := 6 Maximum value allowed clipFun(x) == min(max(x,-clipValue),clipValue) \end{verbatim} +\line(1,0){380} Notice that we identify $clipValue$ as a small float but do not declare the type of the function {\bf clipFun}. @@ -56499,6 +58063,9 @@ conversion when it is called. The second matter concerns the possible ``poles'' of a function, the actual points where the spikes have infinite values. + +%Original Page 494 + Axiom uses normal {\tt DoubleFloat} arithmetic which does not directly handle infinite values. If your function has poles, you must adjust your step size to @@ -56512,11 +58079,13 @@ Most examples will have ranges centered around the origin. To avoid a pole at the origin, the number of points is taken to be odd. +\line(1,0){380} \begin{verbatim} realSteps: INT := 25 Number of real steps imagSteps: INT := 25 Number of imaginary steps )read arrows \end{verbatim} +\line(1,0){380} Now define the function {\bf drawComplexVectorField} to draw the arrows. It is good practice to declare the type of the main function in @@ -56524,11 +58093,13 @@ the file. This one declaration is usually sufficient to ensure that other lower-level functions are compiled with the correct types. +\line(1,0){380} \begin{verbatim} C := Complex DoubleFloat S := Segment DoubleFloat drawComplexVectorField: (C -> C, S, S) -> VIEW3D \end{verbatim} +\line(1,0){380} The first argument is a function mapping complex small floats into complex small floats. @@ -56537,6 +58108,7 @@ imaginary values as segments like $a..b$. The result is a three-di\-men\-sion\-al viewport. Here is the full function definition: +\line(1,0){380} \begin{verbatim} drawComplexVectorField(f, realRange,imagRange) == delReal := (hi(realRange)-lo(realRange))/realSteps The real step size @@ -56559,6 +58131,9 @@ drawComplexVectorField(f, realRange,imagRange) == real := real + delReal The next real value makeViewport3D(sp, "Complex Vector Field") Draw it \end{verbatim} +\line(1,0){380} + +%Original Page 495 As a first example, let us draw $f(z) == sin(z)$. There is no need to create a user function: just pass the @@ -56572,7 +58147,12 @@ Draw the complex vector field of $sin(x)$. \spadgraph{drawComplexVectorField(sin,-2..2,-2..2) } -%\epsffile[0 0 295 295]{ps/vectorsin.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/vectorsin.eps}} +\begin{center} +$drawBouquet(12,"A\ Dozen\ Arrows")$ +\end{center} +\end{minipage} \section{Drawing Complex Functions} \label{ugIntProgCompFuns} @@ -56593,6 +58173,7 @@ Call this function {\bf drawComplex}. It displays the points using the ``mesh'' of points. The function definition is in three parts. +\line(1,0){380} \begin{verbatim} drawComplex: (C -> C, S, S) -> VIEW3D drawComplex(f, realRange, imagRange) == The first part @@ -56601,6 +58182,7 @@ drawComplex(f, realRange, imagRange) == The first part Initial list of list of points $llp$ llp:List List Point DFLOAT := [] \end{verbatim} +\line(1,0){380} Variables $delReal$ and $delImag$ give the step sizes along the real and imaginary directions as computed by the values @@ -56612,6 +58194,7 @@ to set this initial value you have to tell Axiom what type of empty list it is. Next comes the loop which builds $llp$. +\line(1,0){380} \begin{verbatim} real := lo(realRange) The initial real value for i in 1..realSteps+1 repeat Begin real iteration @@ -56626,15 +58209,20 @@ Next comes the loop which builds $llp$. real := real + delReal The next real value llp := cons(lp, llp) Add $lp$ to $llp$ \end{verbatim} +\line(1,0){380} + +%Original Page 496 The code consists of both an inner and outer loop. Each pass through the inner loop adds one list $lp$ of points to the list of lists of points $llp$. The elements of $lp$ are collected in reverse order. +\line(1,0){380} \begin{verbatim} makeViewport3D(mesh(llp), "Complex Function") Create a mesh and display \end{verbatim} +\line(1,0){380} The operation {\bf mesh} then creates an object of type {\tt ThreeSpace(DoubleFloat)} from the list of lists of points. @@ -56658,7 +58246,14 @@ Draw it with an odd number of steps to avoid the pole. \spadgraph{drawComplex(f,-2..2,-2..2)} -%\epsffile[0 0 295 295]{ps/complexexp.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/complexexp.eps}} +\begin{center} +$drawComplex(f,-2..2,-2..2)$ +\end{center} +\end{minipage} + +%Original Page 497 \section{Functions Producing Functions} \label{ugIntProgFunctions} @@ -56737,12 +58332,15 @@ to produce a Newton iteration function $g$ which, given a complex point $x_n$, delivers the next Newton iteration point $x_{n+1}$. +%Original Page 498 + This time we write an input file called {\bf newton.input}. We need to import {\tt MakeUnaryCompiledFunction} (discussed in the last section), call it with appropriate types, and then define the function $newtonStep$ which references it. Here is the function $newtonStep$: +\line(1,0){380} \begin{verbatim} C := Complex DoubleFloat The complex numbers complexFunPack:=MakeUnaryCompiledFunction(EXPR INT,C,C) @@ -56770,6 +58368,7 @@ theVariableIn f == Returns the variable in $f$ nv = 0 => 'x Return a dummy variable first vl \end{verbatim} +\line(1,0){380} Do you see what is going on here? A formula $f$ is passed into the function {\bf newtonStep}. @@ -56790,6 +58389,8 @@ It returns the dummy variable $x$ if $f$ has no variables. Let's now apply {\bf newtonStep} to the formula for computing cube roots of two. +%Original Page 499 + Read the input file with the definitions. \spadcommand{)read newton} @@ -56817,6 +58418,8 @@ Check the accuracy of the last iterate. \spadcommand{a**3} +%Original Page 500 + In MappingPackage1, we show how functions can be manipulated as objects in Axiom. A useful operation to consider here is $*$, which means @@ -56843,13 +58446,23 @@ The vector field. \spadgraph{drawComplexVectorField(g**3,-3..3,-3..3)} -%\epsffile[0 0 295 295]{ps/vectorroot.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/vectorroot.eps}} +\begin{center} +$drawComplexVectorField(g^3,-3..3,-3..3)$ +\end{center} +\end{minipage} The surface. \spadgraph{drawComplex(g**3,-3..3,-3..3)} -%\epsffile[0 0 295 295]{ps/complexroot.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/complexroot.eps}} +\begin{center} +$drawComplex(g^3,-3..3,-3..3)$ +\end{center} +\end{minipage} \setcounter{chapter}{10} % Chapter 11 @@ -56867,6 +58480,8 @@ Here and throughout the book we should use the terminology "type of a function", rather than talking about source and target. A function is just an object that has a mapping type. +%Original Page 501 + \chapter{Packages} \label{ugPackages} @@ -56907,6 +58522,7 @@ basis. A new, faster compiler will be available in version 2.0 of Axiom. +\line(1,0){380} \begin{figure} \label{pak-cdraw} \begin{verbatim} @@ -56952,6 +58568,9 @@ DrawComplex(): Exports == Implementation where Type definition begins here \caption{The DrawComplex package.} \label{fig-pak-cdraw} \end{figure} +\line(1,0){380} + +%Original Page 502 \section{Names, Abbreviations, and File Structure} \label{ugPackagesNames} @@ -56980,6 +58599,8 @@ can put them all in the same file. Axiom assumes no relationship between the name of a library file, and the name or abbreviation of a package. +%Original Page 503 + Near the top of the ``{\bf .spad}'' file, list all the abbreviations for the packages using {\tt )abbrev}, each command beginning in column one. @@ -57041,6 +58662,9 @@ Each operation is described as a {\it declaration}: a name, followed by a colon ({\tt :}), followed by the type of the operation. All operations have types expressed as mappings with the syntax + +%Original Page 504 + \begin{center} {\it source\quad{\tt ->}\quad target @@ -57100,6 +58724,8 @@ The purpose of a capsule is: \item to define a {\it local environment} for these functions to run. \end{itemize} +%Original Page 505 + What is a local environment? First, what is an environment? \index{environment} @@ -57172,6 +58798,8 @@ Axiom sometimes fails to get it right. Then---and only then---do you need a declaration to tell Axiom what type you want. +%Original Page 506 + Input files are usually written to be read by Axiom---and by you. \index{file!input!vs. package} Without suitable documentation and declarations, your input files @@ -57226,6 +58854,8 @@ a pole at the origin. \spadcommand{setRealSteps 51 } +%Original Page 507 + \spadcommand{setImagSteps 51 } Define {\bf f} to be the Gamma function. @@ -57240,7 +58870,12 @@ Draw the {\bf Gamma} function. \spadgraph{drawComplex(f,-\%pi..\%pi,-\%pi..\%pi, false) } -%\epsffile[0 0 300 300]{ps/3dgamma11.ps} +\begin{minipage}{\linewidth} + \makebox[\linewidth]{\includegraphics[scale=0.5]{ps/3dgamma11.eps}} +\begin{center} +$f, -\pi..\pi, -\pi..\pi, false$ +\end{center} +\end{minipage} \section{Parameters} \label{ugPackagesParameters} @@ -57269,6 +58904,8 @@ bubbleSort(m) == m \end{verbatim} +%Original Page 508 + What properties of ``lists of integers'' are assumed by the sorting algorithm? In the first line, the operation {\bf \#} computes the maximum index of @@ -57339,6 +58976,9 @@ names. This uniform naming convention is used for Axiom operation names that destructively change one or more of their arguments. +%Original Page 509 + +\line(1,0){380} \begin{verbatim} SortPackage(S,A) : Exports == Implementation where S: Object @@ -57364,6 +59004,7 @@ SortPackage(S,A) : Exports == Implementation where j := (j - 1) pretend PositiveInteger m \end{verbatim} +\line(1,0){380} \section{Conditionals} \label{ugPackagesConds} @@ -57378,6 +59019,7 @@ for sorting. The presence of the operation {\tt <} is guaranteed when $S$ is an ordered set. +\line(1,0){380} \begin{verbatim} Exports == with bubbleSort!: (A,(S,S) -> Boolean) -> A @@ -57387,6 +59029,7 @@ Exports == with bubbleSort!: A -> A insertionSort!: A -> A \end{verbatim} +\line(1,0){380} In addition to exporting the one-argument sort operations \index{sort!bubble} @@ -57397,6 +59040,7 @@ This is easy: just have the one-argument functions call the corresponding two-argument functions with the operation {\tt <} from $S$. +\line(1,0){380} \begin{verbatim} Implementation == add ... @@ -57404,6 +59048,9 @@ corresponding two-argument functions with the operation bubbleSort!(m) == bubbleSort!(m,<$S) insertionSort!(m) == insertionSort!(m,<$S) \end{verbatim} +\line(1,0){380} + +%Original Page 510 In \sectionref{ugUserBlocks}, we give an alternative definition of {\bf bubbleSort} using \spadfunFrom{first}{List} and @@ -57421,6 +59068,7 @@ We provide two different implementations for {\bf bubbleSort!} and {\bf insertionSort!}: one for list-like structures, another for array-like structures. +\line(1,0){380} \begin{verbatim} Implementation == add ... @@ -57440,6 +59088,7 @@ Implementation == add insertionSort!(m,fn) == ... \end{verbatim} +\line(1,0){380} The ordering of definitions is important. The standard definitions come first and @@ -57454,12 +59103,16 @@ Another equivalent way to write the capsule is to use an $if-then-else$ expression: \index{if} +\line(1,0){380} \begin{verbatim} if A has UnaryRecursiveAggregate(S) then ... else ... \end{verbatim} +\line(1,0){380} + +%Original Page 511 \section{Testing} \label{ugPackagesCompiling} @@ -57512,6 +59165,8 @@ Set bits 3 through 5 to {\tt false}, then display the result. \spadcommand{u(3..5) := false; u} +%Original Page 512 + Now sort these booleans. \spadcommand{bubbleSort! u} @@ -57574,6 +59229,8 @@ There are 2 exposed functions called bubbleSort! : shallowlyMutable \end{verbatim} +%Original Page 513 + What happens if you ask for $bubbleSort!([1,-5,3])$? There is a unique modemap for an operation named {\bf bubbleSort!} with one argument. @@ -57612,6 +59269,8 @@ environment and produces the result. \setcounter{chapter}{11} % Chapter 12 +%Original Page 515 + \chapter{Categories} \label{ugCategories} @@ -57655,6 +59314,8 @@ Axiom. Once in place, domains can be constructed, either independently or from one another. +%Original Page 516 + Superstructures are built for quality---domains are compiled into machine code for run-time efficiency. You can extend the foundation in directions beyond the space @@ -57688,11 +59349,13 @@ The first example of a category definition is the most basic of the algebraic categories in Axiom. \index{SetCategory} +\line(1,0){380} \begin{verbatim} SetCategory(): Category == Join(Type,CoercibleTo OutputForm) with "=" : ($, $) -> Boolean \end{verbatim} +\line(1,0){380} The definition starts off with the name of the category ({\tt SetCategory}); this is @@ -57725,6 +59388,8 @@ $with$. %\footnote{Debugging hint: it is very easy to forget %the $with$!} +%Original Page 517 + The first part tells what categories the category extends. Here, the category extends two categories: {\tt Type}, the category of all domains, and @@ -57792,6 +59457,8 @@ aTwoArgumentOperation: (Integer,$) -> Void aThreeArgumentOperation: ($,Integer,$) -> Fraction($) \end{verbatim} +%Original Page 518 + \section{Documentation} \label{ugCategoriesDoc} @@ -57800,6 +59467,7 @@ an important component: its library documentation. \index{documentation} Here is its definition, complete with documentation. +\line(1,0){380} \begin{verbatim} ++ Description: ++ \bs{}axiomType\{SetCategory\} is the basic category @@ -57813,6 +59481,7 @@ SetCategory(): Category == ++ \bs{}axiom\{x = y\} tests if \bs{}axiom\{x\} and ++ \bs{}axiom\{y\} are equal. \end{verbatim} +\line(1,0){380} Documentary comments are an important part of constructor definitions. Documentation is given both for the category itself and for @@ -57863,6 +59532,8 @@ $x = y$ tests if $x$ and $y$ are equal. For our purposes in this chapter, we omit the documentation from further category descriptions. +%Original Page 519 + \section{Hierarchies} \label{ugCategoriesHier} @@ -57870,11 +59541,13 @@ A second example of a category is {\tt SemiGroup}, defined by: \index{SemiGroup} +\line(1,0){380} \begin{verbatim} SemiGroup(): Category == SetCategory with "*": ($,$) -> $ "**": ($, PositiveInteger) -> $ \end{verbatim} +\line(1,0){380} This definition is as simple as that for {\tt SetCategory}, except that there are two exported operations. @@ -57949,6 +59622,8 @@ therefore, {\tt SemiGroup}. Thus {\tt Integer} is a semigroup and also exports the operations $*$ and $**$. +%Original Page 520 + \section{Defaults} \label{ugCategoriesDefaults} @@ -57956,6 +59631,7 @@ We actually omitted the last \index{category!defaults} part of the definition of \index{default definitions} {\tt SemiGroup} in \sectionref{ugCategoriesHier}. Here now is its complete Axiom definition. +\line(1,0){380} \begin{verbatim} SemiGroup(): Category == SetCategory with "*": ($, $) -> $ @@ -57964,6 +59640,7 @@ SemiGroup(): Category == SetCategory with import RepeatedSquaring($) x: $ ** n: PositiveInteger == expt(x,n) \end{verbatim} +\line(1,0){380} The $add$ part at the end is used to give ``default definitions'' for \index{add} @@ -58006,6 +59683,8 @@ definition used may come from the package The next line gives the definition in terms of {\bf expt} from that package. +%Original Page 521 + The default definitions are collected to form a ``default package'' for the category. The name of the package is the same as the category but with an @@ -58016,6 +59695,7 @@ Here is the definition of the default package {\tt SemiGroup\&} as automatically generated by Axiom from the above definition of {\tt SemiGroup}. +\line(1,0){380} \begin{verbatim} SemiGroup_&($): Exports == Implementation where $: SemiGroup @@ -58025,6 +59705,7 @@ SemiGroup_&($): Exports == Implementation where import RepeatedSquaring($) x:$ ** n:PositiveInteger == expt(x,n) \end{verbatim} +\line(1,0){380} \section{Axioms} \label{ugCategoriesAxioms} @@ -58075,6 +59756,8 @@ No attempt is made to list them all. Nonetheless, all such mathematical facts are implicit by the use of the name {\tt Ring}. +%Original Page 522 + \section{Correctness} \label{ugCategoriesCorrectness} @@ -58147,6 +59830,8 @@ Just as you can test whether a domain has the category {\tt Ring}, you can test that a domain has a given attribute. +%Original Page 523 + Do polynomials over the integers have commutative multiplication? @@ -58165,6 +59850,7 @@ After mentioning category {\tt Ring} many times in this book, it is high time that we show you its definition: \index{Ring} +\line(1,0){380} \begin{verbatim} Ring(): Category == Join(Rng,Monoid,LeftModule($: Rng)) with @@ -58175,6 +59861,7 @@ Ring(): Category == n:Integer coerce(n) == n * 1$$ \end{verbatim} +\line(1,0){380} There are only two new things here. First, look at the {\tt \$\$} on the last line. @@ -58200,6 +59887,8 @@ Because programs can test for this attribute, Axiom can correctly handle rather more complicated mathematical structures (ones that are similar to rings but do not have this attribute). +%Original Page 524 + \section{Parameters} \label{ugCategoriesParameters} @@ -58211,10 +59900,12 @@ matrix domains can have different representations and indexing schemes. Its definition has the form: +\line(1,0){380} \begin{verbatim} MatrixCategory(R,Row,Col): Category == TwoDimensionalArrayCategory(R,Row,Col) with ... \end{verbatim} +\line(1,0){380} The category extends {\tt TwoDimensionalArrayCategory} with the same arguments. @@ -58242,6 +59933,7 @@ domains are rare. Adding the declarations for parameters to the definition for {\tt MatrixCategory}, we have: +\line(1,0){380} \begin{verbatim} R: Ring (Row, Col): FiniteLinearAggregate(R) @@ -58249,6 +59941,7 @@ R: Ring MatrixCategory(R, Row, Col): Category == TwoDimensionalArrayCategory(R, Row, Col) with ... \end{verbatim} +\line(1,0){380} \section{Conditionals} \label{ugCategoriesConditionals} @@ -58269,6 +59962,9 @@ Conditionals can also define conditional extensions of a category. Here is a portion of the definition of {\tt QuotientFieldCategory}: \index{QuotientFieldCategory} +%Original Page 525 + +\line(1,0){380} \begin{verbatim} QuotientFieldCategory(R) : Category == ... with ... if R has OrderedSet then OrderedSet @@ -58276,6 +59972,7 @@ QuotientFieldCategory(R) : Category == ... with ... ceiling: $ -> R ... \end{verbatim} +\line(1,0){380} Think of category {\tt QuotientFieldCategory(R)} as denoting the domain {\tt Fraction(R)}, the @@ -58321,7 +60018,7 @@ of the package {\tt DrawComplex} (\sectionref{ugPackagesAbstract}) is an anonymous category. This is not necessary. We could, instead, give this category a name: -% +\line(1,0){380} \begin{verbatim} DrawComplexCategory(): Category == with drawComplex: (C -> C,S,S,Boolean) -> VIEW3D @@ -58330,15 +60027,19 @@ DrawComplexCategory(): Category == with setImagSteps: INT -> INT setClipValue: DFLOAT-> DFLOAT \end{verbatim} -% +\line(1,0){380} + and then define {\tt DrawComplex} by: -% + +%%Original Page 526 + +\line(1,0){380} \begin{verbatim} DrawComplex(): DrawComplexCategory == Implementation where ... \end{verbatim} -% +\line(1,0){380} There is no reason, however, to give this list of exports a name since no other domain or package exports it. @@ -58356,6 +60057,8 @@ Quad-rat-ic-Form \spadcommand{)read alql.boot} \spadcommand{)load DLIST ICARD DBASE QEQUAT MTHING OPQUERY )update} +%Original Page 527 + \chapter{Domains} \label{ugDomains} @@ -58400,6 +60103,8 @@ others, like {\tt SortPackage}, describe packages of useful operations. As in the last chapter, we focus here on the first kind. +%Original Page 528 + \section{Definitions} \label{ugDomainsDefs} % @@ -58432,6 +60137,9 @@ shown in \figureref{fig-quadform}. Interestingly, this little domain illustrates all the new concepts you need to learn. +%Original Page 529 + +\line(1,0){380} \begin{figure} \begin{verbatim} )abbrev domain QFORM QuadraticForm @@ -58468,6 +60176,7 @@ QuadraticForm(n, K): Exports == Implementation where \end{verbatim} \caption{The {\tt QuadraticForm} domain.}\label{fig-quadform} \end{figure} +\line(1,0){380} A domain constructor can take any number and type of parameters. {\tt QuadraticForm} takes a positive integer $n$ and a field @@ -58521,6 +60230,8 @@ groups, it is possible to pass quadratic forms to algorithms that only assume arguments to have these abelian group properties. +%Original Page 530 + In \sectionref{ugCategoriesConditionals}, you saw that {\tt Fraction(R)}, a member of {\tt QuotientFieldCategory(R)}, is a member of {\tt OrderedSet} if $R$ is a member of {\tt OrderedSet}. Likewise, @@ -58571,6 +60282,8 @@ are other {\tt QuadraticForm} domains. \spadcommand{q : QF := quadraticForm(A)} +%Original Page 531 + Looks like a matrix. Try computing the number of rows. Axiom won't let you. @@ -58614,7 +60327,7 @@ displayed as well as the fact that {\tt QuadraticForm} returns an {\tt AbelianGroup}. You can go and experiment a bit by selecting {\tt Field} with your mouse. -Eventually, use the ``UP'' button +Eventually, use the \UpBitmap{} button several times to return to the first page on {\tt QuadraticForm}. @@ -58632,6 +60345,8 @@ others. Clicking on {\bf Parents}, you see that {\tt QuadraticForm} has one parent {\tt AbelianMonoid}. +%Original Page 532 + \section{Representation} \label{ugDomainsRep} % @@ -58708,6 +60423,8 @@ For example, the polynomial $3x^2+5$ is %>> clearer. represented by the list $[ [e:2, c:3], [e:0, c:5] ]$. +%Original Page 533 + What is the optimal data structure for a matrix? It depends on the application. For large sparse matrices, a linked-list structure of records @@ -58769,6 +60486,8 @@ So do $*$, $+$ and $-$ (from QuadraticForm) come from {\tt SquareMatrix(n,K)}? %Read on! +%Original Page 534 + \section{Defaults} \label{ugDomainsDefaults} % @@ -58838,6 +60557,8 @@ Now click on {\bf Operations} to get a table of operations and on {\tt *} to get a page describing the {\tt *} operation. Finally, click on {\bf implementation} at the bottom. +%Original Page 535 + \section{Origins} \label{ugDomainsOrigins} % @@ -58888,9 +60609,11 @@ there is no type {\tt RationalNumber} in Axiom. To create such a type, you could compile the following ``short-form'' definition: +\line(1,0){380} \begin{verbatim} RationalNumber() == Fraction(Integer) \end{verbatim} +\line(1,0){380} The {\tt Exports} part of this definition is missing and is taken to be equivalent to that of {\tt Fraction(Integer)}. @@ -58907,11 +60630,15 @@ The short form definition for domains is used to define such domains as {\tt MultivariatePolynomial}: \index{MultivariatePolynomial} +%Original Page 536 + +\line(1,0){380} \begin{verbatim} MultivariatePolynomial(vl: List Symbol, R: Ring) == SparseMultivariatePolynomial(R, OrderedVariableList vl) \end{verbatim} +\line(1,0){380} \section{Example 1: Clifford Algebra} \label{ugDomainsClifford} @@ -58961,6 +60688,26 @@ a ring, an algebra over $K$, and a vector space over $K$. Its explicit exports include $e(n),$ which returns the $n$-th unit element. +The Implementation part begins by defining a local variable {\tt Qeelist} +to hold the list of all {\tt q.v} where {\tt v} runs over the unit vectors +from 1 to the dimension {\tt n}. Another local variable {\tt dim} is set +to $2^n$, computed once and for all. The representation for the domain is +{\tt PrimitiveArray(K)}, which is a basic array of elements from domain +{\tt K}. Line 18 defines {\tt New} as shorthand for a more lengthy +expression {\tt new(dim,0\$K)\$Rep}, which computes a primitive array of +length $2^n$ filled with 0's from domain {\tt K}. + +Lines 19-22 define the sum of two elements {\tt x} and {\tt y} +straightforwardly. First, a new array of all 0's is created, then +filled with the sum of the corresponding elements. Indexing for primitive +arrays start at 0. The definition of the product of {\tt x} and {\tt y} +first requires the definition of a local function {\bf addMonomProd}. +Axiom knows it is local since it is not an exported function. +The types of all local functions must be declared. + +%Original Page 537 + +\line(1,0){380} \begin{figure} \begin{verbatim} NNI ==> NonNegativeInteger @@ -58998,6 +60745,7 @@ CliffordAlgebra(n,K,q): Exports == Implementation where \end{verbatim} \caption{Part of the {\tt CliffordAlgebra} domain.}\label{fig-clifalg} \end{figure} +\line(1,0){380} The {\tt Implementation} part begins by defining a local variable $Qeelist$ to hold the list of all $q.v$ where $v$ @@ -59049,6 +60797,8 @@ The operation {\bf determinant}: \spadsig{\$}{R} with {\it 1} argument, is if {\tt R has commutative("*")}. \end{quotation} +%Original Page 538 + Our task is to create a little query language that allows us to get useful information from this database. @@ -59106,6 +60856,8 @@ What constructors explicitly export a {\bf determinant} operation? \spadcommand{elt(elt(elt(elt(ops,name="determinant"),origin),sort),unique)} +%Original Page 539 + The first {\bf elt} produces the set of all index cards with name {\tt determinant}. The second {\bf elt} extracts the {\tt origin} component from @@ -59134,6 +60886,7 @@ that a database is a box of objects of type $S$. Here is the Axiom program defining the {\tt Database} domain. +\line(1,0){380} \begin{verbatim} PI ==> PositiveInteger Database(S): Exports == Implementation where @@ -59154,6 +60907,7 @@ Database(S): Exports == Implementation where Implementation == add ... \end{verbatim} +\line(1,0){380} The domain constructor takes a parameter $S$, which stands for the class of index cards. @@ -59175,6 +60929,8 @@ operation; The display operations return no useful information and thus have return type {\tt Void}. +%Original Page 540 + Next, we tell Axiom what operations the user can apply to the database. This part defines our little query language. @@ -59199,6 +60955,8 @@ A {\bf coerce} to {\tt OutputForm} creates a display object. The {\tt Implementation} part of {\tt Database} is straightforward. + +\line(1,0){380} \begin{verbatim} Implementation == add s: Symbol @@ -59215,6 +60973,7 @@ The {\tt Implementation} part of {\tt Database} is straightforward. y::Rep)$MergeThing(S) coerce(db): OutputForm == (#db):: OutputForm \end{verbatim} +\line(1,0){380} The database is represented by a list of elements of $S$ (index cards). We leave the definition of the first {\bf elt} operation @@ -59241,6 +61000,8 @@ do care how many ``hits'' we get for a given query. So we define the output representation of a database to be simply the number of index cards our query finds. +%Original Page 541 + \subsection{Query Equations} \label{ugDomainsQueryEquations} @@ -59249,6 +61010,7 @@ The predicate for our search is given by an object of type Axiom does not have such an object yet so we have to invent it. +\line(1,0){380} \begin{verbatim} QueryEquation(): Exports == Implementation where Exports == with @@ -59262,6 +61024,7 @@ QueryEquation(): Exports == Implementation where variable q == q.var value q == q.val \end{verbatim} +\line(1,0){380} Axiom converts an input expression of the form ${\it a} = {\it b}$ to $equation({\it a, b})$. @@ -59277,12 +61040,14 @@ space-efficient representation of an equation. Here is the missing definition for the {\bf elt} function of {\tt Database} in the last section: +\line(1,0){380} \begin{verbatim} elt(db,eq) == field\ := variable eq value := value eq [x for x in db | matches?(value,x.field)] \end{verbatim} +\line(1,0){380} Recall that a database is represented by a list. Line 4 simply runs over that list collecting all elements @@ -59298,6 +61063,9 @@ It is useful to make datalists extensions of lists---lists that have special {\bf elt} operations defined on them for sorting and removing duplicates. +%Original Page 542 + +\line(1,0){380} \begin{verbatim} DataList(S:OrderedSet) : Exports == Implementation where Exports == ListAggregate(S) with @@ -59313,6 +61081,7 @@ DataList(S:OrderedSet) : Exports == Implementation where elt(x,"count") == #x coerce(x:List S) == x :: $ \end{verbatim} +\line(1,0){380} The {\tt Exports} part asserts that datalists belong to the category {\tt ListAggregate}. @@ -59335,6 +61104,7 @@ string. Each field has a name that is passed as a second argument to {\bf elt}. +\line(1,0){380} \begin{verbatim} IndexCard() == Implementation where Exports == with @@ -59344,6 +61114,7 @@ IndexCard() == Implementation where coerce: String -> $ Implementation == String add ... \end{verbatim} +\line(1,0){380} We leave the {\tt Implementation} part to the reader. All operations involve straightforward string manipulations. @@ -59362,7 +61133,10 @@ want from the database: ``{\tt o}'' gives you all operation lines, and ``{\tt k}'', all constructor lines. Similarly, ``{\tt c}'', ``{\tt d}'', and ``{\tt p}'' give you all category, domain and package lines respectively. -% + +%%Original Page 543 + +\line(1,0){380} \begin{verbatim} OperationsQuery(): Exports == Implementation where Exports == with @@ -59371,6 +61145,7 @@ OperationsQuery(): Exports == Implementation where Implementation == add getDatabase(s) == getBrowseDatabase(s)$Lisp \end{verbatim} +\line(1,0){380} We do not bother creating a special name for databases of index cards. @@ -59389,6 +61164,7 @@ the logical thing to do.} At the top of the file put {\tt )abbrev} commands, giving the constructor abbreviations you created. +\line(1,0){380} \begin{verbatim} )abbrev domain ICARD IndexCard )abbrev domain QEQUAT QueryEquation @@ -59397,6 +61173,7 @@ constructor abbreviations you created. )abbrev domain DBASE Database )abbrev package OPQUERY OperationsQuery \end{verbatim} +\line(1,0){380} With all this in {\bf alql.spad}, for example, compile it using \index{compile} @@ -59420,6 +61197,8 @@ How many constructors does Axiom have? \spadcommand{ks := getDatabase "k"} +%Original Page 544 + Break this down into the number of categories, domains, and packages. \spadcommand{[ks.(kind=k) for k in ["c","d","p"] ]} @@ -59451,6 +61230,8 @@ While this information can be obtained with Browse, the use of the query database gives you data that you can manipulate in the workspace. +%Original Page 545 + How many operations have ``eigen'' in the name? \spadcommand{eigens := o.(name="*eigen*")} @@ -59490,6 +61271,8 @@ and come from a constructor having ``Matrix'' in their name. \spadcommand{fullDisplay(fm-\%) } +%Original Page 546 + How many operations involve matrices? \spadcommand{m := tm+fm } @@ -59507,6 +61290,8 @@ How many distinct names of operations involving matrices are there? \setcounter{chapter}{13} % Chapter 14 % +%Original Page 547 + \chapter{Browse} \label{ugBrowse} @@ -59537,6 +61322,8 @@ To use this page, you first enter a {\it search string} into the input area at the top, then click on one of the buttons below. We show the use of each of the buttons by example. +%Original Page 548 + \subsubsection{Constructors} First enter the search string {\tt Matrix} into the input area and @@ -59591,7 +61378,10 @@ pages. Again click on the \UpBitmap{} to return to the table of constructors whose names contain {\tt matrix}. -%Below the table is a {\bf Views} panel. % here & globally MGR 1995oct30 + + +%Original Page 549 + Below the table is a {\it Views} panel. This panel contains buttons that let you view constructors in different ways. @@ -59662,8 +61452,12 @@ matrix} as a part of their name. The summary gives you all the names under a heading when the number of entries is less than 10. +%Original Page 550 + Click on \UpBitmap{} to return to the Browse front page. +%Original Page 551 + \subsubsection{Documentation} Again enter the search key {\tt *matrix*} and this time click on @@ -59707,6 +61501,8 @@ and click on {\bf Constructors}. \caption{Constructor page for {\tt Matrix}.} \end{figure} +%Original Page 552 + The header part tells you that {\tt Matrix} has abbreviation {\tt MATRIX} and one argument called {\tt R} that must be a domain of category {\tt Ring}. @@ -59716,6 +61512,8 @@ heading. What you get is a table of all acceptable domain parameter values of {\tt R}, or a table of {\it rings} in Axiom. +%Original Page 553 + \begin{figure}[htbp] \begin{picture}(324,180)%(-54,0) \special{psfile=ps/h-matargs.ps} @@ -59745,6 +61543,8 @@ We recommend that you leave the editor window up while working through this chapter as you occasionally may want to refer to it. \newpage +%Original Page 554 + \subsection{Constructor Page Buttons} \label{ugBrowseDomainButtons} @@ -59785,6 +61585,8 @@ For a detailed description of these pages, skip to \subsubsection{Attributes} +%Original Page 555 + Click here to get a table of the two attributes exported by {\tt Matrix}: \index{attribute} @@ -59817,6 +61619,8 @@ Notice that if you click on an operation name, such as \spadfunFrom{new}{Matrix}, you bring up a description page for that operation from {\tt Matrix}. +%Original Page 556 + Example pages have several examples of Axiom commands. Each example has an active button to its left. Click on it! @@ -59865,6 +61669,8 @@ Typically they are inherited from several different categories. Let's find out from where the operations of {\tt Matrix} come. +%Original Page 557 + \begin{enumerate} \item Click on {\tt MatrixCategory}, then on {\bf Exports}. Here you see that {\tt MatrixCategory} explicitly exports many matrix @@ -59935,6 +61741,8 @@ Did you perform the exercise in the last section under {\bf Exports}? If so, you see here all the categories you found while ascending the {\bf Exports} chain for {\tt Matrix}. +%Original Page 558 + \subsubsection{Relatives} The relatives of a domain constructor are package @@ -59984,6 +61792,8 @@ signatures of operations exported by these domains. \subsubsection{Lineage} +%Original Page 559 + The term {\it lineage} refers to the {\it search order} for functions. If you are an expert user or curious about how the Axiom system @@ -60053,6 +61863,8 @@ matrices as values.\footnote{A constructor is a client of For example, a constructor having internal (unexported) operations dealing with matrices is also a client.} +%Original Page 560 + \subsubsection{Benefactors} A {\it benefactor} of {\tt Matrix} is any constructor that @@ -60127,6 +61939,8 @@ This view gives you a table of names. Selecting any of these names brings up the constructor page for that constructor. +%Original Page 561 + \subsubsection{abbrs} This view gives you a table of abbreviations, in the same order as the @@ -60209,6 +62023,8 @@ Look at the number of operations you get. This number is greater than what you had before. Find, for example, the operation {\bf inverse}. +%Original Page 562 + \item Click on {\bf inverse} to produce a page describing the operation {\bf inverse}. At the bottom of the description, you notice that the {\bf @@ -60255,6 +62071,8 @@ that is, {\tt Matrix(R)}. This describes the return value for the operation, analogous to the {\bf Arguments} part. +%Original Page 563 + \subsubsection{Origin} This tells you which domain or category explicitly exports the @@ -60314,6 +62132,8 @@ same name. The heading for the page tells you the number of unique names and the number of distinct operations when these numbers are different. +%Original Page 564 + \subsubsection{filter} As for constructors, you can use this button to cut down the list of @@ -60421,6 +62241,11 @@ above, select the {\bf description} button.} \subsubsection{all domains} +%Original Page 565 + + +%Original Page 566 + This button only appears on an operation page resulting from a search from the front page of Browse or from selecting {\bf generalize} from an operation page for a constructor. @@ -60447,6 +62272,8 @@ When there is only one constructor, you get the constructor page for that constructor. \newpage +%Original Page 567 + \subsection{Capitalization Convention} \label{ugBrowseCapitalizationConvention} @@ -60476,6 +62303,9 @@ For example, for the category default package {\tt MATCAT-} since the corresponding category {\tt MatrixCategory} has abbreviation {\tt MATCAT}. +%Original Page 568 + + \setcounter{chapter}{14} % Chapter 15 \chapter{What's New in Axiom Version 2.0} @@ -61475,6 +63305,9 @@ compilers. \newcommand{\ranb}{{\tt ]}} \newcommand{\vertline}{$|$} \appendix + +%Original Page 571 + \chapter{Axiom System Commands} \label{ugSysCmd} @@ -61527,6 +63360,8 @@ System commands may be issued directly to Axiom or be included in {\bf .input} files. \index{file!input} +%Original Page 572 + A system command {\it argument} is a word that directly follows the command name and is not followed or preceded by a right parenthesis. @@ -61609,6 +63444,9 @@ related commands. This command is used to query, set and remove abbreviations for category, domain and package constructors. Every constructor must have a unique abbreviation. + +%Original Page 573 + This abbreviation is part of the name of the subdirectory under which the components of the compiled constructor are stored. @@ -61705,6 +63543,8 @@ Note that it may be necessary to install fonts into the Firefox browser in order to see correct mathML mathematics output. See the faq file for details. +%Original Page 574 + \section{)cd} \label{ugSysCmdcd} \index{ugSysCmdcd} @@ -61832,6 +63672,9 @@ To remove everything in the workspace but not reset the step counter, issue )clear properties all \end{verbatim} To remove everything about the object {\tt x}, issue + +%Original Page 575 + \begin{verbatim} )clear properties x \end{verbatim} @@ -61911,6 +63754,8 @@ system function and constructor caches. \item {\tt )compile {\it fileName} )constructor} {\it nameOrAbbrev} \end{list} +%Original Page 576 + \par\noindent{\bf Command Description:} You use this command to invoke the Axiom library compiler. This @@ -62007,6 +63852,8 @@ variable then controls what happens. {\tt )library} \index{ugSysCmdlibrary}. +%Original Page 577 + \section{)display} \index{ugSysCmddisplay} @@ -62063,6 +63910,9 @@ To just show the value (and the type) of {\tt d}, issue )display value d \end{verbatim} To just show the declared mode of {\tt d}, issue + +%Original Page 578 + \begin{verbatim} )display mode d \end{verbatim} @@ -62162,6 +64012,8 @@ calls {\tt emacs} to edit the file. \end{list} \par\noindent{\bf Command Description:} +%Original Page 579 + This command is used by Axiom developers to leave the Axiom system and return to the underlying Common Lisp system. @@ -62251,6 +64103,8 @@ away a frame (say ``{\bf quark}''), issue If you omit the name, the current frame is dropped. \index{frame drop} +%Original Page 580 + If you do use frames with the history facility on and writing to a file, you may want to delete some of the older history files. \index{file!history} @@ -62332,6 +64186,8 @@ and in HyperDoc. In HyperDoc, choose the {\bf Commands} item from the {\bf Reference} menu. +%Original Page 581 + \section{)history} \index{ugSysCmdhistory} \index{history} @@ -62429,6 +64285,8 @@ If you do so, the workspace will be cleared and history data will begin being saved. You can also turn the facility on by issuing {\tt )set history on}. +%Original Page 582 + \item[{\tt )off}] will stop the recording of information. The {\tt )history )show} command will not work after issuing this @@ -62618,6 +64476,8 @@ evaluated. If this expression is not complete (unbalanced parentheses, say), the reader will wait until a complete expression is entered. +%Original Page 583 + Since this command is only useful for evaluating single expressions, the {\tt )fin} command may be used to drop out of Axiom into Common Lisp. @@ -62835,6 +64695,8 @@ matrix.input. The ``.input.pamphlet'' is optional. \par\noindent{\bf Also See:} {\tt )regress} +%Original Page 584 + \section{)trace} \label{ugSysCmdtrace} \label{ugSysCmdltrace} @@ -62922,6 +64784,8 @@ will be displayed and, indeed, Axiom would still be running. {\tt )system} \index{ugSysCmdsystem}. +%Original Page 585 + \section{)quit} \index{ugSysCmdquit} @@ -63019,6 +64883,8 @@ The {\tt )quiet} option suppresses output while the file is being read. {\tt )history} \index{ugSysCmdhistory}. +%Original Page 586 + \section{)set} \label{ugSysCmdset} \index{ugSysCmdset} @@ -63109,6 +64975,9 @@ For example, to change the {\tt )quit} command to being unprotected This command displays information about Axiom domain, package and category {\it constructors}. If no options are given, the {\tt )operations} option is assumed. + +%Original Page 587 + For example, \begin{verbatim} )show POLY @@ -63206,6 +65075,8 @@ Axiom or is the directory you specified using the \item{\tt )what synonyms} \end{list} +%Original Page 588 + \par\noindent{\bf Command Description:} This command is used to create short synonyms for system command expressions. @@ -63289,6 +65160,8 @@ possible. {\tt )quit} \index{ugSysCmdquit}. +%Original Page 590 + \section{)trace} \index{ugSysCmdtrace} @@ -63361,6 +65234,9 @@ return value will be displayed. Also, optimization of tail recursion may decrease the number of times a function is actually invoked and so may cause less trace information to be displayed. + +%Original Page 590 + Other information can be displayed or collected when a function is traced and this is controlled by the various options. Most options will be of interest only to Axiom system @@ -63476,6 +65352,8 @@ useful if the {\tt )count} or {\tt )timer} options are used and you are interested in the statistics but not the function calling information. +%Original Page 591 + \item[{\tt )off}] causes untracing of all or specific functions. Without an argument, all functions, constructors, domains and packages are @@ -63575,6 +65453,8 @@ to escape them with an underscore. {\tt )lisp} \index{ugSysCmdlisp}, and {\tt )ltrace} \index{ugSysCmdltrace}. +%Original Page 592 + \section{)undo} \index{ugSysCmdundo} @@ -63660,6 +65540,8 @@ lines of your program. \par\noindent{\bf User Level Required:} interpreter +%Original Page 593 + \par\noindent{\bf Command Syntax:} \begin{list}{} \item{\tt )what categories} {\it pattern1} \lanb{}{\it pattern2 ...\ranb{}} @@ -63750,6 +65632,8 @@ The command synonym {\tt )apropos} is equivalent to \setcounter{chapter}{1} % Appendix B +%Original Page 595 + %\twocolumn[% \chapter{Categories} \label{ugAppCategories} @@ -64225,6 +66109,8 @@ $\hbox{{\rm op}}_{j}$ & is an operation exported by the category. %\twocolumn[% +%Original Page 601 + \chapter{Domains} \label{ugAppDomains} @@ -65466,6 +67352,8 @@ $\hbox{{\rm op}}_{j}$ & is an operation exported by the domain. \setcounter{chapter}{3} % Appendix D +%Original Page 619 + %\twocolumn[% \chapter{Packages} \label{ugAppPackages} @@ -66252,7 +68140,9 @@ $\hbox{{\rm op}}_{j}$ & is an operation exported by the package. \setcounter{chapter}{4} % Appendix E -% + +%%Original Page 627 + { %\twocolumn[% \chapter{Operations} @@ -79635,6 +81525,8 @@ of the points on the curve \smath{c}. }\onecolumn \setcounter{chapter}{5} % Appendix F +%Original Page 691 + \chapter{Programs for AXIOM Images} \label{ugAppGraphics} @@ -80378,6 +82270,8 @@ drawOneScherk(s) == Draw the surface by { +%Original Page 703 + \setcounter{chapter}{6} % Appendix G \chapter{Glossary} \label{ugGlossary} diff --git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet index b9dbb6a..50f97c4 100644 --- a/books/bookvolbib.pamphlet +++ b/books/bookvolbib.pamphlet @@ -381,6 +381,12 @@ Hans-J. Boehm. ``Type inference in the presence of type abstraction'' ACM SIGPLAN Notices, 24(7) pp192-206 July 1989 CODEN SINODQ ISSN 0362-1340\\ \verb|www.acm.org/pubs/citations/proceedings/pldi/73141/p192-boehm| +\bibitem[BHGM04]{BHGM04} +Boulton, Richard; Hardy, Ruth; Gottliebsen, Hanne; and Martin, Ursula +``Design verification for control engineering'' +Proc Fourth International Conference on Integrated Formal Methods, +April 2004 + \bibitem[Bou91]{Bou91} Jean-Louis Boulanger ``Etude de la compilation de scratchpad 2'' @@ -475,28 +481,21 @@ W. Burge and S. Watt, ``Infinite structures in SCRATCHPAD II'' Technical Report RC 12794 (\#57573) IBM Thomas J. Watson Research Center, Box 218, Yorktown Heights, NY 10598, USA 1987 +\bibitem[BWM87]{BWM87} +William H. Burge, Stephen M. Watt, Scott C. Morrison +``Streams and Power Series'' +in [Wit87], pp9-12 + \bibitem[BW89]{BW89} W. H. Burge and S. M. Watt ``Infinite structures in Scratchpad II'' in Davenport [Dav89], pp138-148 ISBN 3-540-51517-8 LCCN QA155.7.E4E86 1987 \subsection{C} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - \bibitem[Cal94]{Cal94} J. Calmet, editor Rhine Workshop on Computer Algebra, Proceedings. Universit{\"a}t Karsruhe, Karlsruhe, Germany 1994 -\bibitem[CCxx]{CCxx} -Quentin Carpent, Christophe Conil -``Utilisation de logiciels libres pour la r\'ealisation de TP MT26'' (2004)\\ -\verb|axiom-wiki.newsynthesis.org/public/refs/articles.html| - -\bibitem[CC91]{CC91} -G. Cohen and P. Charpin, editors EUROCODE '90 International Symposium on -Coding Theory and Applications Proceedings. Springer-Verlag, Berlin, Germany -/ Heidelberg, Germany / London, UK / etc., 1991 ISBN 0-387-54303-1 -(New York), 3-540-54303-1 (Berlin), LCCN QA268.E95 1990 - \bibitem[CCM92]{CCM92} Paul Camion, Bernard Courteau, and Andre Montpetit. ``Un probl{\`{e}}me combinatoire dans les graphs de Hamming et sa solution en Scratchpad'' @@ -519,10 +518,20 @@ Capriotti, Olga, Cohen, Arjeh M., Cuypers, Hans, and Sterk, Hans ``OpenMath Technology for Interactive Mathematical Documents''\\ \verb|www.win.tue.nl/~hansc/lisbon.pdf| +\bibitem[CCxx]{CCxx} +Quentin Carpent, Christophe Conil +``Utilisation de logiciels libres pour la r\'ealisation de TP MT26'' (2004)\\ +\verb|axiom-wiki.newsynthesis.org/public/refs/articles.html| + \bibitem[Che86]{Che86} G.W. Cherry "Integration in Finite Terms with Special Functions: The Logarithmic Integral" SIAM J. Comput. Vol 15 No 1 February 1986 +\bibitem[Chu87]{Chu87} +Chudnovsky, D.V. and Chudnovsky, G.V. +``New Analytic Methods of Polynomial Root Finding'' +in [Wit87], p2 + \bibitem[Chu89]{Chu89} Chudnovsky, D.V. and Chudnovsky, G.V. ``The computation of classical constants'' @@ -539,6 +548,12 @@ Cohen, Arjeh M., Cuypers, Hans, Barreiro, Ernesto Reinaldo, Sterk, Hans ``Interactive Mathematical Documents on the Web'' Springer 9783540002576-c1.pdf +\bibitem[CC91]{CC91} +G. Cohen and P. Charpin, editors EUROCODE '90 International Symposium on +Coding Theory and Applications Proceedings. Springer-Verlag, Berlin, Germany +/ Heidelberg, Germany / London, UK / etc., 1991 ISBN 0-387-54303-1 +(New York), 3-540-54303-1 (Berlin), LCCN QA268.E95 1990 + \bibitem[CFMPxxa]{CFMPxxa} Marc Conrad, Tim French, Carsten Maple, Sandra Pott ``Approaching Inheritance from a Natural Mathematical Perspective and from @@ -594,8 +609,9 @@ April 8-9, 2013 Portland Oregon\\ \verb|daly.axiom-developer.org| \bibitem[Dav79a]{Dav79a} -Davenport, J.H. SPAD.SCRIPT -VM/370 SPAD.SCRIPTS August 24, 1979 +Davenport, J.H. +``What can SCRATCHPAD/370 do?'' +VM/370 SPAD.SCRIPTS August 24, 1979 SPAD.SCRIPT \bibitem[Dav79b]{Dav79b} James Harold Davenport @@ -606,7 +622,7 @@ ISBN 0-387-10290-6 \bibitem[Dav80]{Dav80} Davenport, J.H. and Jenks, R.D. ``MODLISP -- an Introduction'' -Proc LISP80, 1980 +Proc LISP80, 1980, and IBM RC8357 Oct 1980 \bibitem[Dav82]{Dav82} Davenport, J.H. ``On the Parallel Risch Algorithm (III): Use of Tangents'' @@ -669,26 +685,6 @@ Davenport, J.H. Davenport, J. H., Siret, and Tournier ``Computer Algebra'' \hfill\\ \verb|staff.bath.ac.uk/masjhd/masternew.pdf| -\bibitem[DD89]{DD89} -C. Dicrescenzo and D. Duval ``Algebraic extensions and algebraic closure in -Scratchpad II'' In Gianni [Gia89], pp440-446 ISBN 3-540-51084-2 -LCCN QA76.95.I57 1998 Conference held jointly with AAECC-6 - -\bibitem[Dev93]{Dev93} -Pinch, R.G.E. ``Some Primality Testing Algorithms'' -Devlin, Keith (ed.) -Computers and Mathematics November 1993, Vol 40, Number 9 pp1203-1210 - -\bibitem[Dew94]{Dew94} -Dewar, M. C. ``Manipulating Fortran Code in AXIOM and the AXIOM-NAG Link'' -Proceedings of the Workshop on Symbolic and Numeric Computing, ed by Apiola, H. -and Laine, M. and Valkeila, E. pp1-12 University of Helsinki, Finland (1994) - -\bibitem[Dew]{Dew} -Dewar, Mike -``OpenMath: An Overview''\\ -\verb|www.sigsam.org/bulletin/articles/132/paper1.pdf| - \bibitem[DGJ84]{DGJ84} J. Davenport, P. Gianni, R. Jenks, V. Miller, S. Morrison, M. Rothstein, C. Sundaresan, R. Sutor and B. Trager ``Scratchpad'' Mathematical Sciences @@ -712,10 +708,20 @@ Dalmas, St\'ephane, Ga\"etano, Marc, and Watt, Stephen ``An OpenMath 1.0 Implementation''\\ \verb|citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.116.4401.pdf| -\bibitem[DJ92]{DJ92} -D. Duval and F. Jung ``Examples of problem solving using computer algebra'' -IFIP Transactions. A. Computer Science and Technology, A-2 pp133-141, 143 1992 -CODEN ITATEC. ISSN 0926-5473 +\bibitem[Dew94]{Dew94} +Dewar, M. C. ``Manipulating Fortran Code in AXIOM and the AXIOM-NAG Link'' +Proceedings of the Workshop on Symbolic and Numeric Computing, ed by Apiola, H. +and Laine, M. and Valkeila, E. pp1-12 University of Helsinki, Finland (1994) + +\bibitem[Dew]{Dew} +Dewar, Mike +``OpenMath: An Overview''\\ +\verb|www.sigsam.org/bulletin/articles/132/paper1.pdf| + +\bibitem[DD89]{DD89} +C. Dicrescenzo and D. Duval ``Algebraic extensions and algebraic closure in +Scratchpad II'' In Gianni [Gia89], pp440-446 ISBN 3-540-51084-2 +LCCN QA76.95.I57 1998 Conference held jointly with AAECC-6 \bibitem[DLMF]{DLMF} \verb|http://dlmf.nist.gov/software/#T1| @@ -804,6 +810,16 @@ Dunstan, Martin, Gottliebsen, Hanne, Kelsey, Tom and Martin, Ursula Calculemus 2001, Siena\\ \verb|www.cs-st-andrews.ac.uk/~tom/pub/dunstanetal.ps| +\bibitem[DJ92]{DJ92} +D. Duval and F. Jung ``Examples of problem solving using computer algebra'' +IFIP Transactions. A. Computer Science and Technology, A-2 pp133-141, 143 1992 +CODEN ITATEC. ISSN 0926-5473 + +\bibitem[Duv94]{Duv94} +Dominique Duval +``Symbolic or algebraic computation?'' +Madrid Spain, NAG conference (private copy of paper) + \bibitem[Du95]{Du95} Duval, D. ``Evaluation dynamique et cl\^oture alg\'ebrique en Axiom''. Journal of Pure and Applied Algebra, no99, 1995, pp. 267--295. @@ -871,12 +887,26 @@ Frisco ``Objectives and Results''\\ \subsection{G} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - \bibitem[GCL92]{GCL92} Geddes, Keith O., Czapor, Stephen R., and Labahn, George ``Algorithms For Computer Algebra'' Kluwer Academic Publishers ISBN 0-7923-9259-0 (Sept 1992) +\bibitem[Gia87]{Gia87} +Patrizia Gianni +``Primary Decomposition of Ideals'' +in [Wit87], pp12-13 + +\bibitem[Gom92]{Gom92} +Teresa G\'omez-D'iaz +``Quelques applications de l`\'evaluation dynamique'' +Ph.D. Thesis L'Universite De Limoges March 1992 + +\bibitem[Gom93]{Gom93} +Teresa G\'omez-D\'iaz +``Examples of using Dynamic Constructible Closure'' +IMACS Symposium SC-1993 + \bibitem[GBL91]{GBL91} B. M. Goodwin, R. A. Buonopane, and A. Lee. ``Using MathCAD in teaching material and energy balance concepts''. In Anonymous [Ano91], pp345-349 @@ -892,12 +922,6 @@ Gottliebsen, Hanne, Kelsey, Tom and Martin, Ursula ``Hidden verification for computational mathematics'' Journal of Symbolic Computation, Vol39, Num 5, 2005 -\bibitem[BHGM04]{BHGM04} -Boulton, Richard, Hardy, Ruth, Gottliebsen, Hanne, and Martin, Ursula -``Design verification for control engineering'' -Proc Fourth International Conference on Integrated Formal Methods, -April 2004 - \bibitem[GHK91]{GHK91} J. Grabmeier, K. Huber, and U. Krieger. ``Das ComputeralgebraSystem AXIOM bei kryptologischen und verkehrstheoretischen Untersuchungen des @@ -944,6 +968,11 @@ Griesmer, J.H., Jenks, R.D., Yun, D.Y.Y ``SCRATCHPAD User's Manual'' IBM Research Publication RA70 June 1975 +\bibitem[GJY76]{GJY76} +Griesmer, J.H., Jenks, R.D., Yun, D.Y.Y +``A Set of SCRATCHPAD Examples'' +April 1976 (private copy) + \bibitem[GKW03]{GKW03} Johannes Grabmeier, Erich Kaltofen, and Volker Weispfenning, editors. Computer algebra handbook: foundations, applications, systems. @@ -984,7 +1013,8 @@ Mathematica, MuPAD, and Reduce''\\ J. Grabmeier and A. Scheerhorn ``Finite fields in Axiom'' AXIOM Technical Report TR7/92 (ATR/5)(NP2522), Numerical Algorithms Group, Inc., Downer's Grove, IL, USA and Oxford, UK, 1992\\ -\verb|http://www.nag.co.uk/doc/TechRep/axiomtr.html| +\verb|http://www.nag.co.uk/doc/TechRep/axiomtr.html|\\ +and Technical Report, IBM Heidelberg Scientific Center, 1992 \bibitem[GM94]{GM94} D. Gruntz and M. Monagan ``Introduction to Gauss'' SIGSAM Bulletin (ACM @@ -1000,6 +1030,11 @@ Diss. ETH No. 11432\\ \subsection{H} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\bibitem[HBW87]{HBW87} +Martin Hassner, William H. Burge, Stephen M. Watt, +``Construction of Algebraic Error Control Codes (ECC) on the Elliptic +Riemann Surface'' +in [Wit87], pp5-8 \bibitem[Hec01]{Hec01} Heck, A. ``Variables in computer algebra, mathematics and science'' @@ -1029,8 +1064,8 @@ Watson Research Center, Yorktown Heights, NY, USA, 1969 RC2968 July 1970 \bibitem[Jen79]{Jen79} Jenks, R. D. -``MODLISP'' -Proc EUROSAM 79, pp466-480, 1979 +``MODLISP: An Introduction'' +Proc EUROSAM 79, pp466-480, 1979 and IBMRC8073 Jan 1980 \bibitem[Jen71]{Jen71} R. D. Jenks ``META/PLUS: The syntax extension facility for SCRATCHPAD'', @@ -1304,6 +1339,16 @@ Proceedings. Springer-Verlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc., 1993 ISBN 3-540-57235-X LCCN QA76.9.S88I576 1993 +\bibitem[Mon87]{Mon87} +Michael B. Monagan +``Support for Data Structures in Scratchpad II'' +in [Wit87], pp17-18 + +\bibitem[Mon87]{Mon87} +Manuel Bronstein +``Integration of Algebraic and Mixed Functions'' +in [Wit87], p18 + \bibitem[Mon93]{Mon93} M. B. Monagan ``Gauss: a parameterized domain of computation system with support for signature functions''. In Miola [Mio93], pp81-94 @@ -1381,6 +1426,11 @@ LIFL, 1990 \bibitem[Pet93]{Pet93} M. Petitot ``Experience with Axiom'' In Jacob et al. [JOS93], page 240 +\bibitem[Pin93]{Pin93} +Pinch, R.G.E. ``Some Primality Testing Algorithms'' +Devlin, Keith (ed.) +Computers and Mathematics November 1993, Vol 40, Number 9 pp1203-1210 + \bibitem[PT99]{PT99} Erik Poll, Simon Thompson ``The Type System of Aldor''\\ @@ -1573,6 +1623,13 @@ Emmanuel Touratier ``Etude du typage dans le syst\`eme de calcul scientifique Aldor'' Universit\'e de Limoges 1998\\ +\subsection{U} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\bibitem[Unk84]{Unk84} +Unknown +``A New Algebra System'' +(private copy of unpublished paper) + \subsection{V} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \verb|axiom-wiki.newsynthesis.org/public/refs/articles.html| @@ -1590,7 +1647,6 @@ ISBN 3-540-21311-2 \subsection{W} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - \bibitem[Wan89]{Wan89} D. Wang ``A program for computing the Liapunov functions and Liapunov constants in Scratchpad II'' SIGSAM Bulletin (ACM Special Interest Group @@ -1608,6 +1664,16 @@ Algebraic Computation 92 ACM Press, New York, NY 10036, USA, 1992 ISBN 0-89791-489-9 (soft cover), 0-89791-490-2 (hard cover), LCCN QA76.95.I59 1992 +\bibitem[Wat87]{Wat87} +Stephen Watt +``Domains and Subdomains in Scratchpad II'' +in [Wit87], pp3-5 + +\bibitem[WB87]{WB87} +Stephen M. Watt and William H. Burge +``Mapping as First Class Objects'' +in [Wit87], pp13-17 + \bibitem[Wat89]{Wat89} S. M. Watt ``A fixed point method for power series computation'' In Gianni [Gia89], pp206-217 ISBN 3-540-51084-2 LCCN QA76.95.I57 1988 Conference held @@ -1679,8 +1745,12 @@ New York, NY, 10036, USA. 1990 ISBN 0-89791-401-5 LCCN QA76.95.I57 1990 Software Preservation Group\\ \verb|www.softwarepresentation.org/projects/LISP/common_lisp_family| -\subsection{Y} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\bibitem[Wit87]{Wit87} +Sandra Wityak +``Scratchpad II Newsletter'' +Volume 2, Number 1, Nov 1987 +\subsection{Y} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \bibitem[Yap00]{Yap00} Yap, Chee Keng ``Fundamental Problems of Algorithmic Algebra'' @@ -1698,7 +1768,6 @@ D. Reidel Publishing Company H. Werner et. al. (eds.) \subsection{Z} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - \bibitem[Zen92]{Zen92} Ch. 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-%%processing (hard) limit: 250 pts or 500 values for the operand stack. -%%EndComments - -%------------------------------- prologue -------------------------------% -%-------------------------- support procedures --------------------------% - -%--------- first create user dictionary with 100 entries max ------------% -% (number can be changed to accomodate definitions) % - -100 dict begin %% using 100 entries in top level dictionary - -/FontHeight 12 def - -/inch - { 72 mul } - def - -% yVal and hVal are necessary because the Xwindow display origin -% is at the upper left corner, while the postscript display -% origin is at the lower left hand corner. - -/yVal %% get Y value -- make upper left corner origin - { maxY sub abs } %% maxY is viewWindow height - def - -/hVal %% get H value -- used for displaying title text - { maxH sub abs } %% maxH is viewWindow height+titleWindow height - def - -% loads in the font - -/loadFont - { /Times-Roman findfont FontHeight scalefont setfont } - def - -% draws a rectangle with input operand: -% height -% width -% notice that this function does not "draw" or ink the rectangle. -/drawRect - { 1 index 1 add 0 rlineto %% draw first side - 0 exch 1 add neg rlineto %% draw second side - 1 add neg 0 rlineto %% draw third side - closepath } %% draw fourth side - def - -% create a rectangle with input operand in the view window: -% y -% x -% height -% width -% notice that this function does not "draw" or ink the rectangle. -/rectangle - { yVal moveto %% set currentpoint for line - drawRect } %% draws the rectangle - def - -% These are global variables that every draw procedure uses -% THe operand should be as follows: -% viewWindow width -% viewWindow height -% title height -/setDim - { /maxX exch def %% width of display - /maxY exch def %% height of display - /titleH exch def %% height of title - /maxH maxY titleH add def %% height of display + title - } def - -%-------------------------- major procedures --------------------------% - -/title %% draws a rectangle around the title of picture - { gsave - newpath - moveto %% lower left of title - titleH 1 add 0 exch rlineto %% draw first side - 1 add 0 rlineto %% draw second side - 1 add neg 0 exch rlineto - begin installGC stroke end %% draw third side - grestore } - def - -/drawFrame %% draw display frame - { gsave - newpath - maxX maxY 0 0 rectangle - begin installGC stroke end - grestore } - def - -% updates the foreground color of existing graphics-context dictionary: -% foreground color -% dictionary name -/setForeground - { /FGcolor exch put } - def - -% updates the background color of existing graphics-context dictionary: -% background color -% dictionary name -/setBackground - { /BGcolor exch put } - def - -% updates the line width, line style, cap style, join style of -% existing graphics-context dictionary: -% dictionary name -% join style -% cap style -% line width -/setLineAttributes - { begin - /JoinStyle exch def - /CapStyle exch def - /LineWidth exch def - end } - def - -% creates a graphics context dictionary with the following information: -% /dictionary name -% foreground color -% background color -% line width -% cap style -% join style -% this creates different graphical contexts for different drawing functions. -/makeDict - { 5 dict 2 copy def begin pop %% with dict name on top of stack - /FGcolor exch def %% define drawing attributes - /BGcolor exch def %% not heavily used - /LineWidth exch def - /CapStyle exch def - /JoinStyle exch def - end } - def - -% makes the current dictionary attributes effective -% this function takes the values in the current dictionary to set the context -% these are the values currently being used: foreground, cap, join, and width -/installGC - { - FGcolor currentgray ne - {FGcolor setgray} if %% foreground color - CapStyle currentlinecap ne - {CapStyle setlinecap} if %% cap style - JoinStyle currentlinejoin ne - {JoinStyle setlinejoin} if %% join style - LineWidth currentlinewidth ne - {LineWidth setlinewidth} if } %% line width - def - -% operand stack configuration in order to use psDrawLine: -% psDrawLine -% y0 -% x0 -% y1 -% x1 -% graphics-context dictionary -% this draws a line from (x0, y0) to (x1, y1). - -/psDrawLine - { gsave - newpath - yVal moveto - yVal lineto - begin installGC stroke end - grestore } - def - -% operand stack configuration in order to use psFillArc: -% psFillArc -% y center of rectangle -% x center of rectangle -% angle2 -% angle1 -% width -% height -% y -% x -% graphics-context dictionary -% this draws and fills an arc whose origin is at x, y, and whose width -% and height specifies the rectangle which encases the arc. -% Origin is at upper left corner of rectangle. -% This function uses "scale" to make cricles and ellipses. -/psFillArc - { gsave - newpath - yVal moveto - /sfactor 4 index 4 index div def - 1 sfactor scale - 6 5 roll %% x on top of stack - 3 index 2 div add %% define x origin - 6 5 roll %% y on top of stack - 6 5 roll %% h on top of stack - 2 div add yVal sfactor div %% define y origin - 5 4 roll %% w on top of stack - 2 div %% define radius - 5 3 roll %% a1 a2 now on top - 1 index add - arcn %% draw clockwise arc - begin installGC fill end %% fills with foreground color - grestore } - def - -%-------------------------- script --------------------------% - -% 1 inch 1 inch translate - - mark %% mark bottom of our stack - - 0 0 1 - 1072693248 0 /globalGC1 makeDict - 0 0 1 - 1072693248 0 /globalGC2 makeDict - 0 0 1 - 1072693248 0 /trashGC makeDict - 0 0 1 - 1072693248 0 /globGC makeDict - 0 0 1 - 1072693248 0 /anotherGC makeDict - 0 0 1 - 1072693248 0 /graphGC makeDict - 0 0 1 - 1072693248 0 /unitGC makeDict - - gsave % save graphics state for clipping path - - 24 259 256 setDim - maxX maxY 0 0 rectangle clip % set clip path - - globalGC1 256 244 0 244 psDrawLine - globalGC1 128 259 128 0 psDrawLine - globalGC1 11 13 3 3 0 360 12 14 psFillArc - globalGC1 12 14 12 14 psDrawLine - globalGC1 11 13 3 3 0 360 12 14 psFillArc - globalGC1 17 33 12 14 psDrawLine - globalGC1 16 32 3 3 0 360 17 33 psFillArc - globalGC1 22 51 17 33 psDrawLine - globalGC1 21 50 3 3 0 360 22 51 psFillArc - globalGC1 27 68 22 51 psDrawLine - globalGC1 26 67 3 3 0 360 27 68 psFillArc - globalGC1 32 84 27 68 psDrawLine - globalGC1 31 83 3 3 0 360 32 84 psFillArc - globalGC1 36 100 32 84 psDrawLine - globalGC1 35 99 3 3 0 360 36 100 psFillArc - globalGC1 41 115 36 100 psDrawLine - globalGC1 40 114 3 3 0 360 41 115 psFillArc - globalGC1 46 129 41 115 psDrawLine - globalGC1 45 128 3 3 0 360 46 129 psFillArc - globalGC1 51 142 46 129 psDrawLine - globalGC1 50 141 3 3 0 360 51 142 psFillArc - globalGC1 56 154 51 142 psDrawLine - globalGC1 55 153 3 3 0 360 56 154 psFillArc - globalGC1 60 166 56 154 psDrawLine - globalGC1 59 165 3 3 0 360 60 166 psFillArc - globalGC1 65 177 60 166 psDrawLine - globalGC1 64 176 3 3 0 360 65 177 psFillArc - globalGC1 70 187 65 177 psDrawLine - globalGC1 69 186 3 3 0 360 70 187 psFillArc - globalGC1 75 196 70 187 psDrawLine - globalGC1 74 195 3 3 0 360 75 196 psFillArc - globalGC1 80 204 75 196 psDrawLine - globalGC1 79 203 3 3 0 360 80 204 psFillArc - globalGC1 84 212 80 204 psDrawLine - globalGC1 83 211 3 3 0 360 84 212 psFillArc - globalGC1 89 219 84 212 psDrawLine - globalGC1 88 218 3 3 0 360 89 219 psFillArc - globalGC1 94 225 89 219 psDrawLine - globalGC1 93 224 3 3 0 360 94 225 psFillArc - globalGC1 99 230 94 225 psDrawLine - globalGC1 98 229 3 3 0 360 99 230 psFillArc - globalGC1 104 234 99 230 psDrawLine - globalGC1 103 233 3 3 0 360 104 234 psFillArc - globalGC1 108 238 104 234 psDrawLine - globalGC1 107 237 3 3 0 360 108 238 psFillArc - globalGC1 113 241 108 238 psDrawLine - globalGC1 112 240 3 3 0 360 113 241 psFillArc - globalGC1 118 243 113 241 psDrawLine - globalGC1 117 242 3 3 0 360 118 243 psFillArc - globalGC1 123 244 118 243 psDrawLine - globalGC1 122 243 3 3 0 360 123 244 psFillArc - globalGC1 127 244 123 244 psDrawLine - globalGC1 126 243 3 3 0 360 127 244 psFillArc - globalGC1 132 244 127 244 psDrawLine - globalGC1 131 243 3 3 0 360 132 244 psFillArc - globalGC1 137 243 132 244 psDrawLine - globalGC1 136 242 3 3 0 360 137 243 psFillArc - globalGC1 142 241 137 243 psDrawLine - globalGC1 141 240 3 3 0 360 142 241 psFillArc - globalGC1 147 238 142 241 psDrawLine - globalGC1 146 237 3 3 0 360 147 238 psFillArc - globalGC1 151 234 147 238 psDrawLine - globalGC1 150 233 3 3 0 360 151 234 psFillArc - globalGC1 156 230 151 234 psDrawLine - globalGC1 155 229 3 3 0 360 156 230 psFillArc - globalGC1 161 225 156 230 psDrawLine - globalGC1 160 224 3 3 0 360 161 225 psFillArc - globalGC1 166 219 161 225 psDrawLine - globalGC1 165 218 3 3 0 360 166 219 psFillArc - globalGC1 171 212 166 219 psDrawLine - globalGC1 170 211 3 3 0 360 171 212 psFillArc - globalGC1 175 204 171 212 psDrawLine - globalGC1 174 203 3 3 0 360 175 204 psFillArc - globalGC1 180 196 175 204 psDrawLine - globalGC1 179 195 3 3 0 360 180 196 psFillArc - globalGC1 185 187 180 196 psDrawLine - globalGC1 184 186 3 3 0 360 185 187 psFillArc - globalGC1 190 177 185 187 psDrawLine - globalGC1 189 176 3 3 0 360 190 177 psFillArc - globalGC1 195 166 190 177 psDrawLine - globalGC1 194 165 3 3 0 360 195 166 psFillArc - globalGC1 199 154 195 166 psDrawLine - globalGC1 198 153 3 3 0 360 199 154 psFillArc - globalGC1 204 142 199 154 psDrawLine - globalGC1 203 141 3 3 0 360 204 142 psFillArc - globalGC1 209 129 204 142 psDrawLine - globalGC1 208 128 3 3 0 360 209 129 psFillArc - globalGC1 214 115 209 129 psDrawLine - globalGC1 213 114 3 3 0 360 214 115 psFillArc - globalGC1 219 100 214 115 psDrawLine - globalGC1 218 99 3 3 0 360 219 100 psFillArc - globalGC1 223 84 219 100 psDrawLine - globalGC1 222 83 3 3 0 360 223 84 psFillArc - globalGC1 228 68 223 84 psDrawLine - globalGC1 227 67 3 3 0 360 228 68 psFillArc - globalGC1 233 51 228 68 psDrawLine - globalGC1 232 50 3 3 0 360 233 51 psFillArc - globalGC1 238 33 233 51 psDrawLine - globalGC1 237 32 3 3 0 360 238 33 psFillArc - globalGC1 243 14 238 33 psDrawLine - globalGC1 242 13 3 3 0 360 243 14 psFillArc - - grestore % restore graphics state - - - cleartomark %% clearing operand stack - -end %% pops mainDict from dictionary stack - -showpage - -%-------------------------- end --------------------------% diff --git a/books/ps/23dcolb.eps b/books/ps/23dcolb.eps new file mode 100644 index 0000000..4d79d67 --- /dev/null +++ b/books/ps/23dcolb.eps @@ -0,0 +1,1100 @@ +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: GIMP PostScript file plugin V 1.17 by Peter Kirchgessner +%%Title: 23dcolb.eps +%%CreationDate: Thu Mar 28 17:51:53 2013 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%Pages: 1 +%%BoundingBox: 14 14 270 270 +%%EndComments +%%BeginProlog +% Use own dictionary to avoid conflicts +10 dict begin +%%EndProlog +%%Page: 1 1 +% Translate for offset +14.173228346456694 14.173228346456694 translate +% Translate to begin of first scanline +0 254.88 translate +254.88 -254.88 scale +% Image geometry +354 354 8 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-%!IBM Personal Pageprinter (4216) Adapter Program V1.0 -%%DocumentFonts: Times-Roman -%%Creator: Axiom -%%CreationDate: today -%%Pages: 1 -%%processing (hard) limit: 250 pts or 500 values for the operand stack. -%%EndComments - -%------------------------------- prologue -------------------------------% -%-------------------------- support procedures --------------------------% - -%--------- first create user dictionary with 100 entries max ------------% -% (number can be changed to accomodate definitions) % - -100 dict begin %% using 100 entries in top level dictionary - -/FontHeight 12 def - -/inch - { 72 mul } - def - -% yVal and hVal are necessary because the Xwindow display origin -% is at the upper left corner, while the postscript display -% origin is at the lower left hand corner. - -/yVal %% get Y value -- make upper left corner origin - { maxY sub abs } %% maxY is viewWindow height - def - -/hVal %% get H value -- used for displaying title text - { maxH sub abs } %% maxH is viewWindow height+titleWindow height - def - -% loads in the font - -/loadFont - { /Times-Roman findfont FontHeight scalefont setfont } - def - -% draws a rectangle with input operand: -% height -% width -% notice that this function does not "draw" or ink the rectangle. -/drawRect - { 1 index 1 add 0 rlineto %% draw first side - 0 exch 1 add neg rlineto %% draw second side - 1 add neg 0 rlineto %% draw third side - closepath } %% draw fourth side - def - -% create a rectangle with input operand in the view window: -% y -% x -% height -% width -% notice that this function does not "draw" or ink the rectangle. -/rectangle - { yVal moveto %% set currentpoint for line - drawRect } %% draws the rectangle - def - -% These are global variables that every draw procedure uses -% THe operand should be as follows: -% viewWindow width -% viewWindow height -% title height -/setDim - { /maxX exch def %% width of display - /maxY exch def %% height of display - /titleH exch def %% height of title - /maxH maxY titleH add def %% height of display + title - } def - -%-------------------------- major procedures --------------------------% - -/title %% draws a rectangle around the title of picture - { gsave - newpath - moveto %% lower left of title - titleH 1 add 0 exch rlineto %% draw first side - 1 add 0 rlineto %% draw second side - 1 add neg 0 exch rlineto - begin installGC stroke end %% draw third side - grestore } - def - -/drawFrame %% draw display frame - { gsave - newpath - maxX maxY 0 0 rectangle - begin installGC stroke end - grestore } - def - -% updates the foreground color of existing graphics-context dictionary: -% foreground color -% dictionary name -/setForeground - { /FGcolor exch put } - def - -% updates the background color of existing graphics-context dictionary: -% background color -% dictionary name -/setBackground - { /BGcolor exch put } - def - -% updates the line width, line style, cap style, join style of -% existing graphics-context dictionary: -% dictionary name -% join style -% cap style -% line width -/setLineAttributes - { begin - /JoinStyle exch def - /CapStyle exch def - /LineWidth exch def - end } - def - -% creates a graphics context dictionary with the following information: -% /dictionary name -% foreground color -% background color -% line width -% cap style -% join style -% this creates different graphical contexts for different drawing functions. -/makeDict - { 5 dict 2 copy def begin pop %% with dict name on top of stack - /FGcolor exch def %% define drawing attributes - /BGcolor exch def %% not heavily used - /LineWidth exch def - /CapStyle exch def - /JoinStyle exch def - end } - def - -% makes the current dictionary attributes effective -% this function takes the values in the current dictionary to set the context -% these are the values currently being used: foreground, cap, join, and width -/installGC - { - FGcolor currentgray ne - {FGcolor setgray} if %% foreground color - CapStyle currentlinecap ne - {CapStyle setlinecap} if %% cap style - JoinStyle currentlinejoin ne - {JoinStyle setlinejoin} if %% join style - LineWidth currentlinewidth ne - {LineWidth setlinewidth} if } %% line width - def - -% operand stack configuration in order to use psDrawLine: -% psDrawLine -% y0 -% x0 -% y1 -% x1 -% graphics-context dictionary -% this draws a line from (x0, y0) to (x1, y1). - -/psDrawLine - { gsave - newpath - yVal moveto - yVal lineto - begin installGC stroke end - grestore } - def - -% operand stack configuration in order to use psFillArc: -% psFillArc -% y center of rectangle -% x center of rectangle -% angle2 -% angle1 -% width -% height -% y -% x -% graphics-context dictionary -% this draws and fills an arc whose origin is at x, y, and whose width -% and height specifies the rectangle which encases the arc. -% Origin is at upper left corner of rectangle. -% This function uses "scale" to make cricles and ellipses. -/psFillArc - { gsave - newpath - yVal moveto - /sfactor 4 index 4 index div def - 1 sfactor scale - 6 5 roll %% x on top of stack - 3 index 2 div add %% define x origin - 6 5 roll %% y on top of stack - 6 5 roll %% h on top of stack - 2 div add yVal sfactor div %% define y origin - 5 4 roll %% w on top of stack - 2 div %% define radius - 5 3 roll %% a1 a2 now on top - 1 index add - arcn %% draw clockwise arc - begin installGC fill end %% fills with foreground color - grestore } - def - -%-------------------------- script --------------------------% - -% 1 inch 1 inch translate - - mark %% mark bottom of our stack - - 0 0 1 - 1072693248 0 /globalGC1 makeDict - 0 0 1 - 1072693248 0 /globalGC2 makeDict - 0 0 1 - 1072693248 0 /trashGC makeDict - 0 0 1 - 1072693248 0 /globGC makeDict - 0 0 1 - 1072693248 0 /anotherGC makeDict - 0 0 1 - 1072693248 0 /graphGC makeDict - 0 0 1 - 1072693248 0 /unitGC makeDict - - gsave % save graphics state for clipping path - - 24 259 256 setDim - maxX maxY 0 0 rectangle clip % set clip path - - globalGC1 256 244 0 244 psDrawLine - globalGC1 128 259 128 0 psDrawLine - globalGC1 11 13 3 3 0 360 12 14 psFillArc - globalGC1 12 14 12 14 psDrawLine - globalGC1 11 13 3 3 0 360 12 14 psFillArc - globalGC1 17 33 12 14 psDrawLine - globalGC1 16 32 3 3 0 360 17 33 psFillArc - globalGC1 22 51 17 33 psDrawLine - globalGC1 21 50 3 3 0 360 22 51 psFillArc - globalGC1 27 68 22 51 psDrawLine - globalGC1 26 67 3 3 0 360 27 68 psFillArc - globalGC1 32 84 27 68 psDrawLine - globalGC1 31 83 3 3 0 360 32 84 psFillArc - globalGC1 36 100 32 84 psDrawLine - globalGC1 35 99 3 3 0 360 36 100 psFillArc - globalGC1 41 115 36 100 psDrawLine - globalGC1 40 114 3 3 0 360 41 115 psFillArc - globalGC1 46 129 41 115 psDrawLine - globalGC1 45 128 3 3 0 360 46 129 psFillArc - globalGC1 51 142 46 129 psDrawLine - globalGC1 50 141 3 3 0 360 51 142 psFillArc - globalGC1 56 154 51 142 psDrawLine - globalGC1 55 153 3 3 0 360 56 154 psFillArc - globalGC1 60 166 56 154 psDrawLine - globalGC1 59 165 3 3 0 360 60 166 psFillArc - globalGC1 65 177 60 166 psDrawLine - globalGC1 64 176 3 3 0 360 65 177 psFillArc - globalGC1 70 187 65 177 psDrawLine - globalGC1 69 186 3 3 0 360 70 187 psFillArc - globalGC1 75 196 70 187 psDrawLine - globalGC1 74 195 3 3 0 360 75 196 psFillArc - globalGC1 80 204 75 196 psDrawLine - globalGC1 79 203 3 3 0 360 80 204 psFillArc - globalGC1 84 212 80 204 psDrawLine - globalGC1 83 211 3 3 0 360 84 212 psFillArc - globalGC1 89 219 84 212 psDrawLine - globalGC1 88 218 3 3 0 360 89 219 psFillArc - globalGC1 94 225 89 219 psDrawLine - globalGC1 93 224 3 3 0 360 94 225 psFillArc - globalGC1 99 230 94 225 psDrawLine - globalGC1 98 229 3 3 0 360 99 230 psFillArc - globalGC1 104 234 99 230 psDrawLine - globalGC1 103 233 3 3 0 360 104 234 psFillArc - globalGC1 108 238 104 234 psDrawLine - globalGC1 107 237 3 3 0 360 108 238 psFillArc - globalGC1 113 241 108 238 psDrawLine - globalGC1 112 240 3 3 0 360 113 241 psFillArc - globalGC1 118 243 113 241 psDrawLine - globalGC1 117 242 3 3 0 360 118 243 psFillArc - globalGC1 123 244 118 243 psDrawLine - globalGC1 122 243 3 3 0 360 123 244 psFillArc - globalGC1 127 244 123 244 psDrawLine - globalGC1 126 243 3 3 0 360 127 244 psFillArc - globalGC1 132 244 127 244 psDrawLine - globalGC1 131 243 3 3 0 360 132 244 psFillArc - globalGC1 137 243 132 244 psDrawLine - globalGC1 136 242 3 3 0 360 137 243 psFillArc - globalGC1 142 241 137 243 psDrawLine - globalGC1 141 240 3 3 0 360 142 241 psFillArc - globalGC1 147 238 142 241 psDrawLine - globalGC1 146 237 3 3 0 360 147 238 psFillArc - globalGC1 151 234 147 238 psDrawLine - globalGC1 150 233 3 3 0 360 151 234 psFillArc - globalGC1 156 230 151 234 psDrawLine - globalGC1 155 229 3 3 0 360 156 230 psFillArc - globalGC1 161 225 156 230 psDrawLine - globalGC1 160 224 3 3 0 360 161 225 psFillArc - globalGC1 166 219 161 225 psDrawLine - globalGC1 165 218 3 3 0 360 166 219 psFillArc - globalGC1 171 212 166 219 psDrawLine - globalGC1 170 211 3 3 0 360 171 212 psFillArc - globalGC1 175 204 171 212 psDrawLine - globalGC1 174 203 3 3 0 360 175 204 psFillArc - globalGC1 180 196 175 204 psDrawLine - globalGC1 179 195 3 3 0 360 180 196 psFillArc - globalGC1 185 187 180 196 psDrawLine - globalGC1 184 186 3 3 0 360 185 187 psFillArc - globalGC1 190 177 185 187 psDrawLine - globalGC1 189 176 3 3 0 360 190 177 psFillArc - globalGC1 195 166 190 177 psDrawLine - globalGC1 194 165 3 3 0 360 195 166 psFillArc - globalGC1 199 154 195 166 psDrawLine - globalGC1 198 153 3 3 0 360 199 154 psFillArc - globalGC1 204 142 199 154 psDrawLine - globalGC1 203 141 3 3 0 360 204 142 psFillArc - globalGC1 209 129 204 142 psDrawLine - globalGC1 208 128 3 3 0 360 209 129 psFillArc - globalGC1 214 115 209 129 psDrawLine - globalGC1 213 114 3 3 0 360 214 115 psFillArc - globalGC1 219 100 214 115 psDrawLine - globalGC1 218 99 3 3 0 360 219 100 psFillArc - globalGC1 223 84 219 100 psDrawLine - globalGC1 222 83 3 3 0 360 223 84 psFillArc - globalGC1 228 68 223 84 psDrawLine - globalGC1 227 67 3 3 0 360 228 68 psFillArc - globalGC1 233 51 228 68 psDrawLine - globalGC1 232 50 3 3 0 360 233 51 psFillArc - globalGC1 238 33 233 51 psDrawLine - globalGC1 237 32 3 3 0 360 238 33 psFillArc - globalGC1 243 14 238 33 psDrawLine - globalGC1 242 13 3 3 0 360 243 14 psFillArc - - grestore % restore graphics state - - - cleartomark %% clearing operand stack - -end %% pops mainDict from dictionary stack - -showpage - -%-------------------------- end --------------------------% diff --git a/books/ps/23dpal.eps b/books/ps/23dpal.eps new file mode 100644 index 0000000..180f781 --- /dev/null +++ b/books/ps/23dpal.eps @@ -0,0 +1,1091 @@ +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: GIMP PostScript file plugin V 1.17 by Peter Kirchgessner +%%Title: 23dpal.eps +%%CreationDate: Thu Mar 28 18:02:32 2013 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%Pages: 1 +%%BoundingBox: 14 14 265 267 +%%EndComments +%%BeginProlog +% Use own dictionary to avoid conflicts +10 dict begin +%%EndProlog +%%Page: 1 1 +% Translate for offset 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+JcF4!!!%TMeGk%~> +%%EndData +showpage +%%Trailer +end +%%EOF diff --git a/books/ps/23dpal.ps b/books/ps/23dpal.ps deleted file mode 100644 index e4dc23e..0000000 --- a/books/ps/23dpal.ps +++ /dev/null @@ -1,347 +0,0 @@ -%!IBM Personal Pageprinter (4216) Adapter Program V1.0 -%%DocumentFonts: Times-Roman -%%Creator: Axiom -%%CreationDate: today -%%Pages: 1 -%%processing (hard) limit: 250 pts or 500 values for the operand stack. -%%EndComments - -%------------------------------- prologue -------------------------------% -%-------------------------- support procedures --------------------------% - -%--------- first create user dictionary with 100 entries max ------------% -% (number can be changed to accomodate definitions) % - -100 dict begin %% using 100 entries in top level dictionary - -/FontHeight 12 def - -/inch - { 72 mul } - def - -% yVal and hVal are necessary because the Xwindow display origin -% is at the upper left corner, while the postscript display -% origin is at the lower left hand corner. - -/yVal %% get Y value -- make upper left corner origin - { maxY sub abs } %% maxY is viewWindow height - def - -/hVal %% get H value -- used for displaying title text - { maxH sub abs } %% maxH is viewWindow height+titleWindow height - def - -% loads in the font - -/loadFont - { /Times-Roman findfont FontHeight scalefont setfont } - def - -% draws a rectangle with input operand: -% height -% width -% notice that this function does not "draw" or ink the rectangle. -/drawRect - { 1 index 1 add 0 rlineto %% draw first side - 0 exch 1 add neg rlineto %% draw second side - 1 add neg 0 rlineto %% draw third side - closepath } %% draw fourth side - def - -% create a rectangle with input operand in the view window: -% y -% x -% height -% width -% notice that this function does not "draw" or ink the rectangle. -/rectangle - { yVal moveto %% set currentpoint for line - drawRect } %% draws the rectangle - def - -% These are global variables that every draw procedure uses -% THe operand should be as follows: -% viewWindow width -% viewWindow height -% title height -/setDim - { /maxX exch def %% width of display - /maxY exch def %% height of display - /titleH exch def %% height of title - /maxH maxY titleH add def %% height of display + title - } def - -%-------------------------- major procedures --------------------------% - -/title %% draws a rectangle around the title of picture - { gsave - newpath - moveto %% lower left of title - titleH 1 add 0 exch rlineto %% draw first side - 1 add 0 rlineto %% draw second side - 1 add neg 0 exch rlineto - begin installGC stroke end %% draw third side - grestore } - def - -/drawFrame %% draw display frame - { gsave - newpath - maxX maxY 0 0 rectangle - begin installGC stroke end - grestore } - def - -% updates the foreground color of existing graphics-context dictionary: -% foreground color -% dictionary name -/setForeground - { /FGcolor exch put } - def - -% updates the background color of existing graphics-context dictionary: -% background color -% dictionary name -/setBackground - { /BGcolor exch put } - def - -% updates the line width, line style, cap style, join style of -% existing graphics-context dictionary: -% dictionary name -% join style -% cap style -% line width -/setLineAttributes - { begin - /JoinStyle exch def - /CapStyle exch def - /LineWidth exch def - end } - def - -% creates a graphics context dictionary with the following information: -% /dictionary name -% foreground color -% background color -% line width -% cap style -% join style -% this creates different graphical contexts for different drawing functions. -/makeDict - { 5 dict 2 copy def begin pop %% with dict name on top of stack - /FGcolor exch def %% define drawing attributes - /BGcolor exch def %% not heavily used - /LineWidth exch def - /CapStyle exch def - /JoinStyle exch def - end } - def - -% makes the current dictionary attributes effective -% this function takes the values in the current dictionary to set the context -% these are the values currently being used: foreground, cap, join, and width -/installGC - { - FGcolor currentgray ne - {FGcolor setgray} if %% foreground color - CapStyle currentlinecap ne - {CapStyle setlinecap} if %% cap style - JoinStyle currentlinejoin ne - {JoinStyle setlinejoin} if %% join style - LineWidth currentlinewidth ne - {LineWidth setlinewidth} if } %% line width - def - -% operand stack configuration in order to use psDrawLine: -% psDrawLine -% y0 -% x0 -% y1 -% x1 -% graphics-context dictionary -% this draws a line from (x0, y0) to (x1, y1). - -/psDrawLine - { gsave - newpath - yVal moveto - yVal lineto - begin installGC stroke end - grestore } - def - -% operand stack configuration in order to use psFillArc: -% psFillArc -% y center of rectangle -% x center of rectangle -% angle2 -% angle1 -% width -% height -% y -% x -% graphics-context dictionary -% this draws and fills an arc whose origin is at x, y, and whose width -% and height specifies the rectangle which encases the arc. -% Origin is at upper left corner of rectangle. -% This function uses "scale" to make cricles and ellipses. -/psFillArc - { gsave - newpath - yVal moveto - /sfactor 4 index 4 index div def - 1 sfactor scale - 6 5 roll %% x on top of stack - 3 index 2 div add %% define x origin - 6 5 roll %% y on top of stack - 6 5 roll %% h on top of stack - 2 div add yVal sfactor div %% define y origin - 5 4 roll %% w on top of stack - 2 div %% define radius - 5 3 roll %% a1 a2 now on top - 1 index add - arcn %% draw clockwise arc - begin installGC fill end %% fills with foreground color - grestore } - def - -%-------------------------- script --------------------------% - -% 1 inch 1 inch translate - - mark %% mark bottom of our stack - - 0 0 1 - 1072693248 0 /globalGC1 makeDict - 0 0 1 - 1072693248 0 /globalGC2 makeDict - 0 0 1 - 1072693248 0 /trashGC makeDict - 0 0 1 - 1072693248 0 /globGC makeDict - 0 0 1 - 1072693248 0 /anotherGC makeDict - 0 0 1 - 1072693248 0 /graphGC makeDict - 0 0 1 - 1072693248 0 /unitGC makeDict - - gsave % save graphics state for clipping path - - 24 259 256 setDim - maxX maxY 0 0 rectangle clip % set clip path - - globalGC1 256 244 0 244 psDrawLine - globalGC1 128 259 128 0 psDrawLine - globalGC1 11 13 3 3 0 360 12 14 psFillArc - globalGC1 12 14 12 14 psDrawLine - globalGC1 11 13 3 3 0 360 12 14 psFillArc - globalGC1 17 33 12 14 psDrawLine - globalGC1 16 32 3 3 0 360 17 33 psFillArc - globalGC1 22 51 17 33 psDrawLine - globalGC1 21 50 3 3 0 360 22 51 psFillArc - globalGC1 27 68 22 51 psDrawLine - globalGC1 26 67 3 3 0 360 27 68 psFillArc - globalGC1 32 84 27 68 psDrawLine - globalGC1 31 83 3 3 0 360 32 84 psFillArc - globalGC1 36 100 32 84 psDrawLine - globalGC1 35 99 3 3 0 360 36 100 psFillArc - globalGC1 41 115 36 100 psDrawLine - globalGC1 40 114 3 3 0 360 41 115 psFillArc - globalGC1 46 129 41 115 psDrawLine - globalGC1 45 128 3 3 0 360 46 129 psFillArc - globalGC1 51 142 46 129 psDrawLine - globalGC1 50 141 3 3 0 360 51 142 psFillArc - globalGC1 56 154 51 142 psDrawLine - globalGC1 55 153 3 3 0 360 56 154 psFillArc - globalGC1 60 166 56 154 psDrawLine - globalGC1 59 165 3 3 0 360 60 166 psFillArc - globalGC1 65 177 60 166 psDrawLine - globalGC1 64 176 3 3 0 360 65 177 psFillArc - globalGC1 70 187 65 177 psDrawLine - globalGC1 69 186 3 3 0 360 70 187 psFillArc - globalGC1 75 196 70 187 psDrawLine - globalGC1 74 195 3 3 0 360 75 196 psFillArc - globalGC1 80 204 75 196 psDrawLine - globalGC1 79 203 3 3 0 360 80 204 psFillArc - globalGC1 84 212 80 204 psDrawLine - globalGC1 83 211 3 3 0 360 84 212 psFillArc - globalGC1 89 219 84 212 psDrawLine - globalGC1 88 218 3 3 0 360 89 219 psFillArc - globalGC1 94 225 89 219 psDrawLine - globalGC1 93 224 3 3 0 360 94 225 psFillArc - globalGC1 99 230 94 225 psDrawLine - globalGC1 98 229 3 3 0 360 99 230 psFillArc - globalGC1 104 234 99 230 psDrawLine - globalGC1 103 233 3 3 0 360 104 234 psFillArc - globalGC1 108 238 104 234 psDrawLine - globalGC1 107 237 3 3 0 360 108 238 psFillArc - globalGC1 113 241 108 238 psDrawLine - globalGC1 112 240 3 3 0 360 113 241 psFillArc - globalGC1 118 243 113 241 psDrawLine - globalGC1 117 242 3 3 0 360 118 243 psFillArc - globalGC1 123 244 118 243 psDrawLine - globalGC1 122 243 3 3 0 360 123 244 psFillArc - globalGC1 127 244 123 244 psDrawLine - globalGC1 126 243 3 3 0 360 127 244 psFillArc - globalGC1 132 244 127 244 psDrawLine - globalGC1 131 243 3 3 0 360 132 244 psFillArc - globalGC1 137 243 132 244 psDrawLine - globalGC1 136 242 3 3 0 360 137 243 psFillArc - globalGC1 142 241 137 243 psDrawLine - globalGC1 141 240 3 3 0 360 142 241 psFillArc - globalGC1 147 238 142 241 psDrawLine - globalGC1 146 237 3 3 0 360 147 238 psFillArc - globalGC1 151 234 147 238 psDrawLine - globalGC1 150 233 3 3 0 360 151 234 psFillArc - globalGC1 156 230 151 234 psDrawLine - globalGC1 155 229 3 3 0 360 156 230 psFillArc - globalGC1 161 225 156 230 psDrawLine - globalGC1 160 224 3 3 0 360 161 225 psFillArc - globalGC1 166 219 161 225 psDrawLine - globalGC1 165 218 3 3 0 360 166 219 psFillArc - globalGC1 171 212 166 219 psDrawLine - globalGC1 170 211 3 3 0 360 171 212 psFillArc - globalGC1 175 204 171 212 psDrawLine - globalGC1 174 203 3 3 0 360 175 204 psFillArc - globalGC1 180 196 175 204 psDrawLine - globalGC1 179 195 3 3 0 360 180 196 psFillArc - globalGC1 185 187 180 196 psDrawLine - globalGC1 184 186 3 3 0 360 185 187 psFillArc - globalGC1 190 177 185 187 psDrawLine - globalGC1 189 176 3 3 0 360 190 177 psFillArc - globalGC1 195 166 190 177 psDrawLine - globalGC1 194 165 3 3 0 360 195 166 psFillArc - globalGC1 199 154 195 166 psDrawLine - globalGC1 198 153 3 3 0 360 199 154 psFillArc - globalGC1 204 142 199 154 psDrawLine - globalGC1 203 141 3 3 0 360 204 142 psFillArc - globalGC1 209 129 204 142 psDrawLine - globalGC1 208 128 3 3 0 360 209 129 psFillArc - globalGC1 214 115 209 129 psDrawLine - globalGC1 213 114 3 3 0 360 214 115 psFillArc - globalGC1 219 100 214 115 psDrawLine - globalGC1 218 99 3 3 0 360 219 100 psFillArc - globalGC1 223 84 219 100 psDrawLine - globalGC1 222 83 3 3 0 360 223 84 psFillArc - globalGC1 228 68 223 84 psDrawLine - globalGC1 227 67 3 3 0 360 228 68 psFillArc - globalGC1 233 51 228 68 psDrawLine - globalGC1 232 50 3 3 0 360 233 51 psFillArc - globalGC1 238 33 233 51 psDrawLine - globalGC1 237 32 3 3 0 360 238 33 psFillArc - globalGC1 243 14 238 33 psDrawLine - globalGC1 242 13 3 3 0 360 243 14 psFillArc - - grestore % restore graphics state - - - cleartomark %% clearing operand stack - -end %% pops mainDict from dictionary stack - -showpage - -%-------------------------- end --------------------------% diff --git a/books/ps/2d1vara.eps b/books/ps/2d1vara.eps new file mode 100644 index 0000000..3457778 --- /dev/null +++ b/books/ps/2d1vara.eps @@ -0,0 +1,1235 @@ +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: GIMP PostScript file plugin V 1.17 by Peter Kirchgessner +%%Title: 2d1vara.eps +%%CreationDate: Thu Mar 28 03:57:00 2013 +%%DocumentData: 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first create user dictionary with 100 entries max ------------% -% (number can be changed to accomodate definitions) % - -100 dict begin %% using 100 entries in top level dictionary - -/FontHeight 12 def - -/inch - { 72 mul } - def - -% yVal and hVal are necessary because the Xwindow display origin -% is at the upper left corner, while the postscript display -% origin is at the lower left hand corner. - -/yVal %% get Y value -- make upper left corner origin - { maxY sub abs } %% maxY is viewWindow height - def - -/hVal %% get H value -- used for displaying title text - { maxH sub abs } %% maxH is viewWindow height+titleWindow height - def - -% loads in the font - -/loadFont - { /Times-Roman findfont FontHeight scalefont setfont } - def - -% draws a rectangle with input operand: -% height -% width -% notice that this function does not "draw" or ink the rectangle. -/drawRect - { 1 index 1 add 0 rlineto %% draw first side - 0 exch 1 add neg rlineto %% draw second side - 1 add neg 0 rlineto %% draw third side - closepath } %% draw fourth side - def - -% create a rectangle with input operand in the view window: -% y -% x -% height -% width -% notice that this function does not "draw" or ink the rectangle. -/rectangle - { yVal moveto %% set currentpoint for line - drawRect } %% draws the rectangle - def - -% These are global variables that every draw procedure uses -% THe operand should be as follows: -% viewWindow width -% viewWindow height -% title height -/setDim - { /maxX exch def %% width of display - /maxY exch def %% height of display - /titleH exch def %% height of title - /maxH maxY titleH add def %% height of display + title - } def - -%-------------------------- major procedures --------------------------% - -/title %% draws a rectangle around the title of picture - { gsave - newpath - moveto %% lower left of title - titleH 1 add 0 exch rlineto %% draw first side - 1 add 0 rlineto %% draw second side - 1 add neg 0 exch rlineto - begin installGC stroke end %% draw third side - grestore } - def - -/drawFrame %% draw display frame - { gsave - newpath - maxX maxY 0 0 rectangle - begin installGC stroke end - grestore } - def - -% updates the foreground color of existing graphics-context dictionary: -% foreground color -% dictionary name -/setForeground - { /FGcolor exch put } - def - -% updates the background color of existing graphics-context dictionary: -% background color -% dictionary name -/setBackground - { /BGcolor exch put } - def - -% updates the line width, line style, cap style, join style of -% existing graphics-context dictionary: -% dictionary name -% join style -% cap style -% line width -/setLineAttributes - { begin - /JoinStyle exch def - /CapStyle exch def - /LineWidth exch def - end } - def - -% creates a graphics context dictionary with the following information: -% /dictionary name -% foreground color -% background color -% line width -% cap style -% join style -% this creates different graphical contexts for different drawing functions. -/makeDict - { 5 dict 2 copy def begin pop %% with dict name on top of stack - /FGcolor exch def %% define drawing attributes - /BGcolor exch def %% not heavily used - /LineWidth exch def - /CapStyle exch def - /JoinStyle exch def - end } - def - -% makes the current dictionary attributes effective -% this function takes the values in the current dictionary to set the context -% these are the values currently being used: foreground, cap, join, and width -/installGC - { - FGcolor currentgray ne - {FGcolor setgray} if %% foreground color - CapStyle currentlinecap ne - {CapStyle setlinecap} if %% cap style - JoinStyle currentlinejoin ne - {JoinStyle setlinejoin} if %% join style - LineWidth currentlinewidth ne - {LineWidth setlinewidth} if } %% line width - def - -% operand stack configuration in order to use psDrawLine: -% psDrawLine -% y0 -% x0 -% y1 -% x1 -% graphics-context dictionary -% this draws a line from (x0, y0) to (x1, y1). - -/psDrawLine - { gsave - newpath - yVal moveto - yVal lineto - begin installGC stroke end - grestore } - def - -% operand stack configuration in order to use psFillArc: -% psFillArc -% y center of rectangle -% x center of rectangle -% angle2 -% angle1 -% width -% height -% y -% x -% graphics-context dictionary -% this draws and fills an arc whose origin is at x, y, and whose width -% and height specifies the rectangle which encases the arc. -% Origin is at upper left corner of rectangle. -% This function uses "scale" to make cricles and ellipses. -/psFillArc - { gsave - newpath - yVal moveto - /sfactor 4 index 4 index div def - 1 sfactor scale - 6 5 roll %% x on top of stack - 3 index 2 div add %% define x origin - 6 5 roll %% y on top of stack - 6 5 roll %% h on top of stack - 2 div add yVal sfactor div %% define y origin - 5 4 roll %% w on top of stack - 2 div %% define radius - 5 3 roll %% a1 a2 now on top - 1 index add - arcn %% draw clockwise arc - begin installGC fill end %% fills with foreground color - grestore } - def - -%-------------------------- script --------------------------% - -% 1 inch 1 inch translate - - mark %% mark bottom of our stack - - 0 0 1 - 1072693248 0 /globalGC1 makeDict - 0 0 1 - 1072693248 0 /globalGC2 makeDict - 0 0 1 - 1072693248 0 /trashGC makeDict - 0 0 1 - 1072693248 0 /globGC makeDict - 0 0 1 - 1072693248 0 /anotherGC makeDict - 0 0 1 - 1072693248 0 /graphGC makeDict - 0 0 1 - 1072693248 0 /unitGC makeDict - - gsave % save graphics state for clipping path - - 24 259 256 setDim - maxX maxY 0 0 rectangle clip % set clip path - - globalGC1 256 129 0 129 psDrawLine - globalGC1 12 259 12 0 psDrawLine - globalGC1 11 128 3 3 0 360 12 129 psFillArc - globalGC1 12 129 12 129 psDrawLine - globalGC1 11 128 3 3 0 360 12 129 psFillArc - globalGC1 17 129 12 129 psDrawLine - globalGC1 16 128 3 3 0 360 17 129 psFillArc - globalGC1 22 129 17 129 psDrawLine - globalGC1 21 128 3 3 0 360 22 129 psFillArc - globalGC1 27 129 22 129 psDrawLine - globalGC1 26 128 3 3 0 360 27 129 psFillArc - globalGC1 32 129 27 129 psDrawLine - globalGC1 31 128 3 3 0 360 32 129 psFillArc - globalGC1 36 129 32 129 psDrawLine - globalGC1 35 128 3 3 0 360 36 129 psFillArc - globalGC1 41 129 36 129 psDrawLine - globalGC1 40 128 3 3 0 360 41 129 psFillArc - globalGC1 43 130 41 129 psDrawLine - globalGC1 42 129 3 3 0 360 43 130 psFillArc - globalGC1 46 131 43 130 psDrawLine - globalGC1 45 130 3 3 0 360 46 131 psFillArc - globalGC1 47 131 46 131 psDrawLine - globalGC1 46 130 3 3 0 360 47 131 psFillArc - globalGC1 48 132 47 131 psDrawLine - globalGC1 47 131 3 3 0 360 48 132 psFillArc - globalGC1 50 133 48 132 psDrawLine - globalGC1 49 132 3 3 0 360 50 133 psFillArc - globalGC1 51 134 50 133 psDrawLine - globalGC1 50 133 3 3 0 360 51 134 psFillArc - globalGC1 53 139 51 134 psDrawLine - globalGC1 52 138 3 3 0 360 53 139 psFillArc - globalGC1 56 147 53 139 psDrawLine - globalGC1 55 146 3 3 0 360 56 147 psFillArc - globalGC1 58 161 56 147 psDrawLine - globalGC1 57 160 3 3 0 360 58 161 psFillArc - globalGC1 59 172 58 161 psDrawLine - globalGC1 58 171 3 3 0 360 59 172 psFillArc - globalGC1 60 186 59 172 psDrawLine - globalGC1 59 185 3 3 0 360 60 186 psFillArc - globalGC1 62 203 60 186 psDrawLine - globalGC1 61 202 3 3 0 360 62 203 psFillArc - globalGC1 63 221 62 203 psDrawLine - globalGC1 62 220 3 3 0 360 63 221 psFillArc - globalGC1 63 230 63 221 psDrawLine - globalGC1 62 229 3 3 0 360 63 230 psFillArc - globalGC1 64 237 63 230 psDrawLine - globalGC1 63 236 3 3 0 360 64 237 psFillArc - globalGC1 64 240 64 237 psDrawLine - globalGC1 63 239 3 3 0 360 64 240 psFillArc - globalGC1 65 241 64 240 psDrawLine - globalGC1 64 240 3 3 0 360 65 241 psFillArc - globalGC1 65 241 65 241 psDrawLine - globalGC1 64 240 3 3 0 360 65 241 psFillArc - globalGC1 65 241 65 241 psDrawLine - globalGC1 64 240 3 3 0 360 65 241 psFillArc - globalGC1 65 240 65 241 psDrawLine - globalGC1 64 239 3 3 0 360 65 240 psFillArc - globalGC1 65 239 65 240 psDrawLine - globalGC1 64 238 3 3 0 360 65 239 psFillArc - globalGC1 66 229 65 239 psDrawLine - globalGC1 65 228 3 3 0 360 66 229 psFillArc - globalGC1 66 209 66 229 psDrawLine - globalGC1 65 208 3 3 0 360 66 209 psFillArc - globalGC1 67 181 66 209 psDrawLine - globalGC1 66 180 3 3 0 360 67 181 psFillArc - globalGC1 67 167 67 181 psDrawLine - globalGC1 66 166 3 3 0 360 67 167 psFillArc - globalGC1 68 156 67 167 psDrawLine - globalGC1 67 155 3 3 0 360 68 156 psFillArc - globalGC1 68 153 68 156 psDrawLine - globalGC1 67 152 3 3 0 360 68 153 psFillArc - globalGC1 68 153 68 153 psDrawLine - globalGC1 67 152 3 3 0 360 68 153 psFillArc - globalGC1 68 153 68 153 psDrawLine - globalGC1 67 152 3 3 0 360 68 153 psFillArc - globalGC1 68 154 68 153 psDrawLine - globalGC1 67 153 3 3 0 360 68 154 psFillArc - globalGC1 68 155 68 154 psDrawLine - globalGC1 67 154 3 3 0 360 68 155 psFillArc - globalGC1 68 161 68 155 psDrawLine - globalGC1 67 160 3 3 0 360 68 161 psFillArc - globalGC1 68 182 68 161 psDrawLine - globalGC1 67 181 3 3 0 360 68 182 psFillArc - globalGC1 69 213 68 182 psDrawLine - globalGC1 68 212 3 3 0 360 69 213 psFillArc - globalGC1 69 229 69 213 psDrawLine - globalGC1 68 228 3 3 0 360 69 229 psFillArc - globalGC1 69 240 69 229 psDrawLine - globalGC1 68 239 3 3 0 360 69 240 psFillArc - globalGC1 69 243 69 240 psDrawLine - globalGC1 68 242 3 3 0 360 69 243 psFillArc - globalGC1 69 243 69 243 psDrawLine - globalGC1 68 242 3 3 0 360 69 243 psFillArc - globalGC1 69 244 69 243 psDrawLine - globalGC1 68 243 3 3 0 360 69 244 psFillArc - globalGC1 69 243 69 244 psDrawLine - globalGC1 68 242 3 3 0 360 69 243 psFillArc - globalGC1 69 242 69 243 psDrawLine - globalGC1 68 241 3 3 0 360 69 242 psFillArc - globalGC1 69 237 69 242 psDrawLine - globalGC1 68 236 3 3 0 360 69 237 psFillArc - globalGC1 69 219 69 237 psDrawLine - globalGC1 68 218 3 3 0 360 69 219 psFillArc - globalGC1 70 193 69 219 psDrawLine - globalGC1 69 192 3 3 0 360 70 193 psFillArc - globalGC1 70 167 70 193 psDrawLine - globalGC1 69 166 3 3 0 360 70 167 psFillArc - globalGC1 70 158 70 167 psDrawLine - globalGC1 69 157 3 3 0 360 70 158 psFillArc - globalGC1 70 155 70 158 psDrawLine - globalGC1 69 154 3 3 0 360 70 155 psFillArc - globalGC1 70 154 70 155 psDrawLine - globalGC1 69 153 3 3 0 360 70 154 psFillArc - globalGC1 70 154 70 154 psDrawLine - globalGC1 69 153 3 3 0 360 70 154 psFillArc - globalGC1 70 157 70 154 psDrawLine - globalGC1 69 156 3 3 0 360 70 157 psFillArc - globalGC1 70 167 70 157 psDrawLine - globalGC1 69 166 3 3 0 360 70 167 psFillArc - globalGC1 70 184 70 167 psDrawLine - globalGC1 69 183 3 3 0 360 70 184 psFillArc - globalGC1 70 206 70 184 psDrawLine - globalGC1 69 205 3 3 0 360 70 206 psFillArc - globalGC1 70 226 70 206 psDrawLine - globalGC1 69 225 3 3 0 360 70 226 psFillArc - globalGC1 70 241 70 226 psDrawLine - globalGC1 69 240 3 3 0 360 70 241 psFillArc - globalGC1 70 243 70 241 psDrawLine - globalGC1 69 242 3 3 0 360 70 243 psFillArc - globalGC1 70 244 70 243 psDrawLine - globalGC1 69 243 3 3 0 360 70 244 psFillArc - globalGC1 70 244 70 244 psDrawLine - globalGC1 69 243 3 3 0 360 70 244 psFillArc - globalGC1 70 243 70 244 psDrawLine - globalGC1 69 242 3 3 0 360 70 243 psFillArc - globalGC1 70 238 70 243 psDrawLine - globalGC1 69 237 3 3 0 360 70 238 psFillArc - globalGC1 71 229 70 238 psDrawLine - globalGC1 70 228 3 3 0 360 71 229 psFillArc - globalGC1 71 202 71 229 psDrawLine - globalGC1 70 201 3 3 0 360 71 202 psFillArc - globalGC1 71 172 71 202 psDrawLine - globalGC1 70 171 3 3 0 360 71 172 psFillArc - globalGC1 71 161 71 172 psDrawLine - globalGC1 70 160 3 3 0 360 71 161 psFillArc - globalGC1 71 157 71 161 psDrawLine - globalGC1 70 156 3 3 0 360 71 157 psFillArc - globalGC1 71 154 71 157 psDrawLine - globalGC1 70 153 3 3 0 360 71 154 psFillArc - globalGC1 71 154 71 154 psDrawLine - globalGC1 70 153 3 3 0 360 71 154 psFillArc - globalGC1 71 155 71 154 psDrawLine - globalGC1 70 154 3 3 0 360 71 155 psFillArc - globalGC1 71 164 71 155 psDrawLine - globalGC1 70 163 3 3 0 360 71 164 psFillArc - globalGC1 71 180 71 164 psDrawLine - globalGC1 70 179 3 3 0 360 71 180 psFillArc - globalGC1 71 200 71 180 psDrawLine - globalGC1 70 199 3 3 0 360 71 200 psFillArc - globalGC1 71 221 71 200 psDrawLine - globalGC1 70 220 3 3 0 360 71 221 psFillArc - globalGC1 71 237 71 221 psDrawLine - globalGC1 70 236 3 3 0 360 71 237 psFillArc - globalGC1 71 242 71 237 psDrawLine - globalGC1 70 241 3 3 0 360 71 242 psFillArc - globalGC1 71 244 71 242 psDrawLine - globalGC1 70 243 3 3 0 360 71 244 psFillArc - globalGC1 71 243 71 244 psDrawLine - globalGC1 70 242 3 3 0 360 71 243 psFillArc - globalGC1 71 238 71 243 psDrawLine - globalGC1 70 237 3 3 0 360 71 238 psFillArc - globalGC1 71 219 71 238 psDrawLine - globalGC1 70 218 3 3 0 360 71 219 psFillArc - globalGC1 71 193 71 219 psDrawLine - globalGC1 70 192 3 3 0 360 71 193 psFillArc - globalGC1 71 167 71 193 psDrawLine - globalGC1 70 166 3 3 0 360 71 167 psFillArc - globalGC1 71 159 71 167 psDrawLine - globalGC1 70 158 3 3 0 360 71 159 psFillArc - globalGC1 71 154 71 159 psDrawLine - globalGC1 70 153 3 3 0 360 71 154 psFillArc - globalGC1 71 155 71 154 psDrawLine - globalGC1 70 154 3 3 0 360 71 155 psFillArc - globalGC1 71 162 71 155 psDrawLine - globalGC1 70 161 3 3 0 360 71 162 psFillArc - globalGC1 71 189 71 162 psDrawLine - globalGC1 70 188 3 3 0 360 71 189 psFillArc - globalGC1 71 223 71 189 psDrawLine - globalGC1 70 222 3 3 0 360 71 223 psFillArc - globalGC1 71 236 71 223 psDrawLine - globalGC1 70 235 3 3 0 360 71 236 psFillArc - globalGC1 71 243 71 236 psDrawLine - globalGC1 70 242 3 3 0 360 71 243 psFillArc - globalGC1 71 243 71 243 psDrawLine - globalGC1 70 242 3 3 0 360 71 243 psFillArc - globalGC1 71 233 71 243 psDrawLine - globalGC1 70 232 3 3 0 360 71 233 psFillArc - globalGC1 71 216 71 233 psDrawLine - globalGC1 70 215 3 3 0 360 71 216 psFillArc - globalGC1 71 195 71 216 psDrawLine - globalGC1 70 194 3 3 0 360 71 195 psFillArc - globalGC1 71 174 71 195 psDrawLine - globalGC1 70 173 3 3 0 360 71 174 psFillArc - globalGC1 71 159 71 174 psDrawLine - globalGC1 70 158 3 3 0 360 71 159 psFillArc - globalGC1 71 154 71 159 psDrawLine - globalGC1 70 153 3 3 0 360 71 154 psFillArc - globalGC1 71 161 71 154 psDrawLine - globalGC1 70 160 3 3 0 360 71 161 psFillArc - globalGC1 71 180 71 161 psDrawLine - globalGC1 70 179 3 3 0 360 71 180 psFillArc - globalGC1 72 206 71 180 psDrawLine - globalGC1 71 205 3 3 0 360 72 206 psFillArc - globalGC1 72 230 72 206 psDrawLine - globalGC1 71 229 3 3 0 360 72 230 psFillArc - globalGC1 72 238 72 230 psDrawLine - globalGC1 71 237 3 3 0 360 72 238 psFillArc - globalGC1 72 243 72 238 psDrawLine - globalGC1 71 242 3 3 0 360 72 243 psFillArc - globalGC1 72 240 72 243 psDrawLine - globalGC1 71 239 3 3 0 360 72 240 psFillArc - globalGC1 72 219 72 240 psDrawLine - globalGC1 71 218 3 3 0 360 72 219 psFillArc - globalGC1 72 189 72 219 psDrawLine - globalGC1 71 188 3 3 0 360 72 189 psFillArc - globalGC1 72 163 72 189 psDrawLine - globalGC1 71 162 3 3 0 360 72 163 psFillArc - globalGC1 72 154 72 163 psDrawLine - globalGC1 71 153 3 3 0 360 72 154 psFillArc - globalGC1 72 171 72 154 psDrawLine - globalGC1 71 170 3 3 0 360 72 171 psFillArc - globalGC1 72 204 72 171 psDrawLine - globalGC1 71 203 3 3 0 360 72 204 psFillArc - globalGC1 72 236 72 204 psDrawLine - globalGC1 71 235 3 3 0 360 72 236 psFillArc - globalGC1 72 243 72 236 psDrawLine - globalGC1 71 242 3 3 0 360 72 243 psFillArc - globalGC1 72 217 72 243 psDrawLine - globalGC1 71 216 3 3 0 360 72 217 psFillArc - globalGC1 72 176 72 217 psDrawLine - globalGC1 71 175 3 3 0 360 72 176 psFillArc - globalGC1 72 154 72 176 psDrawLine - globalGC1 71 153 3 3 0 360 72 154 psFillArc - globalGC1 72 175 72 154 psDrawLine - globalGC1 71 174 3 3 0 360 72 175 psFillArc - globalGC1 72 221 72 175 psDrawLine - globalGC1 71 220 3 3 0 360 72 221 psFillArc - globalGC1 72 244 72 221 psDrawLine - globalGC1 71 243 3 3 0 360 72 244 psFillArc - globalGC1 72 213 72 244 psDrawLine - globalGC1 71 212 3 3 0 360 72 213 psFillArc - globalGC1 72 163 72 213 psDrawLine - globalGC1 71 162 3 3 0 360 72 163 psFillArc - globalGC1 72 164 72 163 psDrawLine - globalGC1 71 163 3 3 0 360 72 164 psFillArc - globalGC1 72 221 72 164 psDrawLine - globalGC1 71 220 3 3 0 360 72 221 psFillArc - globalGC1 72 241 72 221 psDrawLine - globalGC1 71 240 3 3 0 360 72 241 psFillArc - globalGC1 72 184 72 241 psDrawLine - globalGC1 71 183 3 3 0 360 72 184 psFillArc - globalGC1 72 158 72 184 psDrawLine - globalGC1 71 157 3 3 0 360 72 158 psFillArc - globalGC1 72 223 72 158 psDrawLine - globalGC1 71 222 3 3 0 360 72 223 psFillArc - globalGC1 72 230 72 223 psDrawLine - globalGC1 71 229 3 3 0 360 72 230 psFillArc - globalGC1 72 157 72 230 psDrawLine - globalGC1 71 156 3 3 0 360 72 157 psFillArc - globalGC1 72 204 72 157 psDrawLine - globalGC1 71 203 3 3 0 360 72 204 psFillArc - globalGC1 72 232 72 204 psDrawLine - globalGC1 71 231 3 3 0 360 72 232 psFillArc - globalGC1 72 154 72 232 psDrawLine - globalGC1 71 153 3 3 0 360 72 154 psFillArc - globalGC1 72 235 72 154 psDrawLine - globalGC1 71 234 3 3 0 360 72 235 psFillArc - globalGC1 72 179 72 235 psDrawLine - globalGC1 71 178 3 3 0 360 72 179 psFillArc - globalGC1 72 210 72 179 psDrawLine - globalGC1 71 209 3 3 0 360 72 210 psFillArc - globalGC1 72 187 72 210 psDrawLine - globalGC1 71 186 3 3 0 360 72 187 psFillArc - globalGC1 72 222 72 187 psDrawLine - globalGC1 71 221 3 3 0 360 72 222 psFillArc - globalGC1 72 159 72 222 psDrawLine - globalGC1 71 158 3 3 0 360 72 159 psFillArc - globalGC1 72 240 72 159 psDrawLine - globalGC1 71 239 3 3 0 360 72 240 psFillArc - globalGC1 72 207 72 240 psDrawLine - globalGC1 71 206 3 3 0 360 72 207 psFillArc - globalGC1 72 157 72 207 psDrawLine - globalGC1 71 156 3 3 0 360 72 157 psFillArc - globalGC1 72 161 72 157 psDrawLine - globalGC1 71 160 3 3 0 360 72 161 psFillArc - globalGC1 72 169 72 161 psDrawLine - globalGC1 71 168 3 3 0 360 72 169 psFillArc - globalGC1 72 158 72 169 psDrawLine - globalGC1 71 157 3 3 0 360 72 158 psFillArc - globalGC1 72 169 72 158 psDrawLine - globalGC1 71 168 3 3 0 360 72 169 psFillArc - globalGC1 72 244 72 169 psDrawLine - globalGC1 71 243 3 3 0 360 72 244 psFillArc - globalGC1 72 156 72 244 psDrawLine - globalGC1 71 155 3 3 0 360 72 156 psFillArc - globalGC1 72 175 72 156 psDrawLine - globalGC1 71 174 3 3 0 360 72 175 psFillArc - globalGC1 72 158 72 175 psDrawLine - globalGC1 71 157 3 3 0 360 72 158 psFillArc - globalGC1 72 237 72 158 psDrawLine - globalGC1 71 236 3 3 0 360 72 237 psFillArc - globalGC1 72 231 72 237 psDrawLine - globalGC1 71 230 3 3 0 360 72 231 psFillArc - globalGC1 72 154 72 231 psDrawLine - globalGC1 71 153 3 3 0 360 72 154 psFillArc - globalGC1 72 243 72 154 psDrawLine - globalGC1 71 242 3 3 0 360 72 243 psFillArc - globalGC1 72 231 72 243 psDrawLine - globalGC1 71 230 3 3 0 360 72 231 psFillArc - globalGC1 73 174 72 231 psDrawLine - globalGC1 72 173 3 3 0 360 73 174 psFillArc - globalGC1 73 157 73 174 psDrawLine - globalGC1 72 156 3 3 0 360 73 157 psFillArc - globalGC1 73 239 73 157 psDrawLine - globalGC1 72 238 3 3 0 360 73 239 psFillArc - globalGC1 73 205 73 239 psDrawLine - globalGC1 72 204 3 3 0 360 73 205 psFillArc - globalGC1 73 244 73 205 psDrawLine - globalGC1 72 243 3 3 0 360 73 244 psFillArc - globalGC1 73 213 73 244 psDrawLine - globalGC1 72 212 3 3 0 360 73 213 psFillArc - globalGC1 73 229 73 213 psDrawLine - globalGC1 72 228 3 3 0 360 73 229 psFillArc - globalGC1 73 200 73 229 psDrawLine - globalGC1 72 199 3 3 0 360 73 200 psFillArc - globalGC1 73 244 73 200 psDrawLine - globalGC1 72 243 3 3 0 360 73 244 psFillArc - globalGC1 73 240 73 244 psDrawLine - globalGC1 72 239 3 3 0 360 73 240 psFillArc - globalGC1 73 242 73 240 psDrawLine - globalGC1 72 241 3 3 0 360 73 242 psFillArc - globalGC1 73 219 73 242 psDrawLine - globalGC1 72 218 3 3 0 360 73 219 psFillArc - globalGC1 73 198 73 219 psDrawLine - globalGC1 72 197 3 3 0 360 73 198 psFillArc - globalGC1 73 171 73 198 psDrawLine - globalGC1 72 170 3 3 0 360 73 171 psFillArc - globalGC1 73 234 73 171 psDrawLine - globalGC1 72 233 3 3 0 360 73 234 psFillArc - globalGC1 73 214 73 234 psDrawLine - globalGC1 72 213 3 3 0 360 73 214 psFillArc - globalGC1 73 244 73 214 psDrawLine - globalGC1 72 243 3 3 0 360 73 244 psFillArc - globalGC1 73 155 73 244 psDrawLine - globalGC1 72 154 3 3 0 360 73 155 psFillArc - globalGC1 73 234 73 155 psDrawLine - globalGC1 72 233 3 3 0 360 73 234 psFillArc - globalGC1 73 238 73 234 psDrawLine - globalGC1 72 237 3 3 0 360 73 238 psFillArc - globalGC1 73 225 73 238 psDrawLine - globalGC1 72 224 3 3 0 360 73 225 psFillArc - globalGC1 73 235 73 225 psDrawLine - globalGC1 72 234 3 3 0 360 73 235 psFillArc - globalGC1 73 243 73 235 psDrawLine - globalGC1 72 242 3 3 0 360 73 243 psFillArc - globalGC1 73 195 73 243 psDrawLine - globalGC1 72 194 3 3 0 360 73 195 psFillArc - globalGC1 73 157 73 195 psDrawLine - globalGC1 72 156 3 3 0 360 73 157 psFillArc - globalGC1 73 238 73 157 psDrawLine - globalGC1 72 237 3 3 0 360 73 238 psFillArc - globalGC1 73 179 73 238 psDrawLine - globalGC1 72 178 3 3 0 360 73 179 psFillArc - globalGC1 73 208 73 179 psDrawLine - globalGC1 72 207 3 3 0 360 73 208 psFillArc - globalGC1 73 190 73 208 psDrawLine - globalGC1 72 189 3 3 0 360 73 190 psFillArc - globalGC1 73 218 73 190 psDrawLine - globalGC1 72 217 3 3 0 360 73 218 psFillArc - globalGC1 73 165 73 218 psDrawLine - globalGC1 72 164 3 3 0 360 73 165 psFillArc - globalGC1 73 244 73 165 psDrawLine - globalGC1 72 243 3 3 0 360 73 244 psFillArc - globalGC1 73 165 73 244 psDrawLine - globalGC1 72 164 3 3 0 360 73 165 psFillArc - globalGC1 73 196 73 165 psDrawLine - globalGC1 72 195 3 3 0 360 73 196 psFillArc - globalGC1 73 240 73 196 psDrawLine - globalGC1 72 239 3 3 0 360 73 240 psFillArc - globalGC1 73 167 73 240 psDrawLine - globalGC1 72 166 3 3 0 360 73 167 psFillArc - globalGC1 73 177 73 167 psDrawLine - globalGC1 72 176 3 3 0 360 73 177 psFillArc - globalGC1 73 241 73 177 psDrawLine - globalGC1 72 240 3 3 0 360 73 241 psFillArc - globalGC1 73 213 73 241 psDrawLine - globalGC1 72 212 3 3 0 360 73 213 psFillArc - globalGC1 73 157 73 213 psDrawLine - globalGC1 72 156 3 3 0 360 73 157 psFillArc - globalGC1 73 179 73 157 psDrawLine - globalGC1 72 178 3 3 0 360 73 179 psFillArc - globalGC1 73 235 73 179 psDrawLine - globalGC1 72 234 3 3 0 360 73 235 psFillArc - globalGC1 73 235 73 235 psDrawLine - globalGC1 72 234 3 3 0 360 73 235 psFillArc - globalGC1 73 184 73 235 psDrawLine - globalGC1 72 183 3 3 0 360 73 184 psFillArc - globalGC1 73 154 73 184 psDrawLine - globalGC1 72 153 3 3 0 360 73 154 psFillArc - globalGC1 73 178 73 154 psDrawLine - globalGC1 72 177 3 3 0 360 73 178 psFillArc - globalGC1 73 224 73 178 psDrawLine - globalGC1 72 223 3 3 0 360 73 224 psFillArc - globalGC1 73 244 73 224 psDrawLine - globalGC1 72 243 3 3 0 360 73 244 psFillArc - globalGC1 73 222 73 244 psDrawLine - globalGC1 72 221 3 3 0 360 73 222 psFillArc - globalGC1 74 181 73 222 psDrawLine - globalGC1 73 180 3 3 0 360 74 181 psFillArc - globalGC1 74 155 74 181 psDrawLine - globalGC1 73 154 3 3 0 360 74 155 psFillArc - globalGC1 74 163 74 155 psDrawLine - globalGC1 73 162 3 3 0 360 74 163 psFillArc - globalGC1 74 194 74 163 psDrawLine - globalGC1 73 193 3 3 0 360 74 194 psFillArc - globalGC1 74 228 74 194 psDrawLine - globalGC1 73 227 3 3 0 360 74 228 psFillArc - globalGC1 74 244 74 228 psDrawLine - globalGC1 73 243 3 3 0 360 74 244 psFillArc - globalGC1 74 235 74 244 psDrawLine - globalGC1 73 234 3 3 0 360 74 235 psFillArc - globalGC1 74 209 74 235 psDrawLine - globalGC1 73 208 3 3 0 360 74 209 psFillArc - globalGC1 74 178 74 209 psDrawLine - globalGC1 73 177 3 3 0 360 74 178 psFillArc - globalGC1 74 158 74 178 psDrawLine - globalGC1 73 157 3 3 0 360 74 158 psFillArc - globalGC1 74 155 74 158 psDrawLine - globalGC1 73 154 3 3 0 360 74 155 psFillArc - globalGC1 74 169 74 155 psDrawLine - globalGC1 73 168 3 3 0 360 74 169 psFillArc - globalGC1 74 193 74 169 psDrawLine - globalGC1 73 192 3 3 0 360 74 193 psFillArc - globalGC1 74 218 74 193 psDrawLine - globalGC1 73 217 3 3 0 360 74 218 psFillArc - globalGC1 74 237 74 218 psDrawLine - globalGC1 73 236 3 3 0 360 74 237 psFillArc - globalGC1 74 244 74 237 psDrawLine - globalGC1 73 243 3 3 0 360 74 244 psFillArc - globalGC1 74 239 74 244 psDrawLine - globalGC1 73 238 3 3 0 360 74 239 psFillArc - globalGC1 74 223 74 239 psDrawLine - globalGC1 73 222 3 3 0 360 74 223 psFillArc - globalGC1 74 203 74 223 psDrawLine - globalGC1 73 202 3 3 0 360 74 203 psFillArc - globalGC1 74 182 74 203 psDrawLine - globalGC1 73 181 3 3 0 360 74 182 psFillArc - globalGC1 74 165 74 182 psDrawLine - globalGC1 73 164 3 3 0 360 74 165 psFillArc - globalGC1 74 156 74 165 psDrawLine - globalGC1 73 155 3 3 0 360 74 156 psFillArc - globalGC1 74 155 74 156 psDrawLine - globalGC1 73 154 3 3 0 360 74 155 psFillArc - globalGC1 74 162 74 155 psDrawLine - globalGC1 73 161 3 3 0 360 74 162 psFillArc - globalGC1 74 175 74 162 psDrawLine - globalGC1 73 174 3 3 0 360 74 175 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+JcC<$OT0h~> +%%EndData +showpage +%%Trailer +end +%%EOF diff --git a/books/ps/2d1varb.ps b/books/ps/2d1varb.ps deleted file mode 100644 index 880f01f..0000000 --- a/books/ps/2d1varb.ps +++ /dev/null @@ -1,1527 +0,0 @@ -%!IBM Personal Pageprinter (4216) Adapter Program V1.0 -%%DocumentFonts: Times-Roman -%%Creator: Axiom -%%CreationDate: today -%%Pages: 1 -%%processing (hard) limit: 250 pts or 500 values for the operand stack. -%%EndComments - -%------------------------------- prologue -------------------------------% -%-------------------------- support procedures --------------------------% - -%--------- first create user dictionary with 100 entries max ------------% -% (number can be changed to accomodate definitions) % - -100 dict begin %% using 100 entries in top level dictionary - -/FontHeight 12 def - -/inch - { 72 mul } - def - -% yVal and hVal are necessary because the Xwindow display origin -% is at the upper left corner, while the postscript display -% origin is at the lower left hand corner. - -/yVal %% get Y value -- make upper left corner origin - { maxY sub abs } %% maxY is viewWindow height - def - -/hVal %% get H value -- used for displaying title text - { maxH sub abs } %% maxH is viewWindow height+titleWindow height - def - -% loads in the font - -/loadFont - { /Times-Roman findfont FontHeight scalefont setfont } - def - -% draws a rectangle with input operand: -% height -% width -% notice that this function does not "draw" or ink the rectangle. -/drawRect - { 1 index 1 add 0 rlineto %% draw first side - 0 exch 1 add neg rlineto %% draw second side - 1 add neg 0 rlineto %% draw third side - closepath } %% draw fourth side - def - -% create a rectangle with input operand in the view window: -% y -% x -% height -% width -% notice that this function does not "draw" or ink the rectangle. -/rectangle - { yVal moveto %% set currentpoint for line - drawRect } %% draws the rectangle - def - -% These are global variables that every draw procedure uses -% THe operand should be as follows: -% viewWindow width -% viewWindow height -% title height -/setDim - { /maxX exch def %% width of display - /maxY exch def %% height of display - /titleH exch def %% height of title - /maxH maxY titleH add def %% height of display + title - } def - -%-------------------------- major procedures --------------------------% - -/title %% draws a rectangle around the title of picture - { gsave - newpath - moveto %% lower left of title - titleH 1 add 0 exch rlineto %% draw first side - 1 add 0 rlineto %% draw second side - 1 add neg 0 exch rlineto - begin installGC stroke end %% draw third side - grestore } - def - -/drawFrame %% draw display frame - { gsave - newpath - maxX maxY 0 0 rectangle - begin installGC stroke end - grestore } - def - -% updates the foreground color of existing graphics-context dictionary: -% foreground color -% dictionary name -/setForeground - { /FGcolor exch put } - def - -% updates the background color of existing graphics-context dictionary: -% background color -% dictionary name -/setBackground - { /BGcolor exch put } - def - -% updates the line width, line style, cap style, join style of -% existing graphics-context dictionary: -% dictionary name -% join style -% cap style -% line width -/setLineAttributes - { begin - /JoinStyle exch def - /CapStyle exch def - /LineWidth exch def - end } - def - -% creates a graphics context dictionary with the following information: -% /dictionary name -% foreground color -% background color -% line width -% cap style -% join style -% this creates different graphical contexts for different drawing functions. -/makeDict - { 5 dict 2 copy def begin pop %% with dict name on top of stack - /FGcolor exch def %% define drawing attributes - /BGcolor exch def %% not heavily used - /LineWidth exch def - /CapStyle exch def - /JoinStyle exch def - end } - def - -% makes the current dictionary attributes effective -% this function takes the values in the current dictionary to set the context -% these are the values currently being used: foreground, cap, join, and width -/installGC - { - FGcolor currentgray ne - {FGcolor setgray} if %% foreground color - CapStyle currentlinecap ne - {CapStyle setlinecap} if %% cap style - JoinStyle currentlinejoin ne - {JoinStyle setlinejoin} if %% join style - LineWidth currentlinewidth ne - {LineWidth setlinewidth} if } %% line width - def - -% operand stack configuration in order to use psDrawLine: -% psDrawLine -% y0 -% x0 -% y1 -% x1 -% graphics-context dictionary -% this draws a line from (x0, y0) to (x1, y1). - -/psDrawLine - { gsave - newpath - yVal moveto - yVal lineto - begin installGC stroke end - grestore } - def - -% operand stack configuration in order to use psFillArc: -% psFillArc -% y center of rectangle -% x center of rectangle -% angle2 -% angle1 -% width -% height -% y -% x -% graphics-context dictionary -% this draws and fills an arc whose origin is at x, y, and whose width -% and height specifies the rectangle which encases the arc. -% Origin is at upper left corner of rectangle. -% This function uses "scale" to make cricles and ellipses. -/psFillArc - { gsave - newpath - yVal moveto - /sfactor 4 index 4 index div def - 1 sfactor scale - 6 5 roll %% x on top of stack - 3 index 2 div add %% define x origin - 6 5 roll %% y on top of stack - 6 5 roll %% h on top of stack - 2 div add yVal sfactor div %% define y origin - 5 4 roll %% w on top of stack - 2 div %% define radius - 5 3 roll %% a1 a2 now on top - 1 index add - arcn %% draw clockwise arc - begin installGC fill end %% fills with foreground color - grestore } - def - -%-------------------------- script --------------------------% - -% 1 inch 1 inch translate - - mark %% mark bottom of our stack - - 0 0 1 - 1072693248 0 /globalGC1 makeDict - 0 0 1 - 1072693248 0 /globalGC2 makeDict - 0 0 1 - 1072693248 0 /trashGC makeDict - 0 0 1 - 1072693248 0 /globGC makeDict - 0 0 1 - 1072693248 0 /anotherGC makeDict - 0 0 1 - 1072693248 0 /graphGC makeDict - 0 0 1 - 1072693248 0 /unitGC makeDict - - gsave % save graphics state for clipping path - - 24 259 256 setDim - maxX maxY 0 0 rectangle clip % set clip path - - globalGC1 256 129 0 129 psDrawLine - globalGC1 -371 259 -371 0 psDrawLine - globalGC1 11 74 3 3 0 360 12 75 psFillArc - globalGC1 12 75 12 75 psDrawLine - globalGC1 11 74 3 3 0 360 12 75 psFillArc - globalGC1 17 62 12 75 psDrawLine - globalGC1 16 61 3 3 0 360 17 62 psFillArc - globalGC1 22 49 17 62 psDrawLine - globalGC1 21 48 3 3 0 360 22 49 psFillArc - globalGC1 24 42 22 49 psDrawLine - globalGC1 23 41 3 3 0 360 24 42 psFillArc - globalGC1 27 37 24 42 psDrawLine - globalGC1 26 36 3 3 0 360 27 37 psFillArc - globalGC1 28 35 27 37 psDrawLine - globalGC1 27 34 3 3 0 360 28 35 psFillArc - globalGC1 29 33 28 35 psDrawLine - globalGC1 28 32 3 3 0 360 29 33 psFillArc - globalGC1 30 32 29 33 psDrawLine - globalGC1 29 31 3 3 0 360 30 32 psFillArc - globalGC1 32 31 30 32 psDrawLine - globalGC1 31 30 3 3 0 360 32 31 psFillArc - globalGC1 32 31 32 31 psDrawLine - globalGC1 31 30 3 3 0 360 32 31 psFillArc - globalGC1 33 32 32 31 psDrawLine - globalGC1 32 31 3 3 0 360 33 32 psFillArc - globalGC1 33 33 33 32 psDrawLine - globalGC1 32 32 3 3 0 360 33 33 psFillArc - globalGC1 34 34 33 33 psDrawLine - globalGC1 33 33 3 3 0 360 34 34 psFillArc - globalGC1 35 38 34 34 psDrawLine - globalGC1 34 37 3 3 0 360 35 38 psFillArc - globalGC1 36 44 35 38 psDrawLine - globalGC1 35 43 3 3 0 360 36 44 psFillArc - globalGC1 39 66 36 44 psDrawLine - globalGC1 38 65 3 3 0 360 39 66 psFillArc - globalGC1 40 81 39 66 psDrawLine - globalGC1 39 80 3 3 0 360 40 81 psFillArc - globalGC1 41 97 40 81 psDrawLine - globalGC1 40 96 3 3 0 360 41 97 psFillArc - globalGC1 42 103 41 97 psDrawLine - globalGC1 41 102 3 3 0 360 42 103 psFillArc - globalGC1 42 106 42 103 psDrawLine - globalGC1 41 105 3 3 0 360 42 106 psFillArc - globalGC1 42 107 42 106 psDrawLine - globalGC1 41 106 3 3 0 360 42 107 psFillArc - globalGC1 43 107 42 107 psDrawLine - globalGC1 42 106 3 3 0 360 43 107 psFillArc - globalGC1 43 105 43 107 psDrawLine - globalGC1 42 104 3 3 0 360 43 105 psFillArc - globalGC1 43 96 43 105 psDrawLine - globalGC1 42 95 3 3 0 360 43 96 psFillArc - globalGC1 44 77 43 96 psDrawLine - globalGC1 43 76 3 3 0 360 44 77 psFillArc - globalGC1 45 49 44 77 psDrawLine - globalGC1 44 48 3 3 0 360 45 49 psFillArc - globalGC1 45 22 45 49 psDrawLine - globalGC1 44 21 3 3 0 360 45 22 psFillArc - globalGC1 45 18 45 22 psDrawLine - globalGC1 44 17 3 3 0 360 45 18 psFillArc - globalGC1 46 16 45 18 psDrawLine - globalGC1 45 15 3 3 0 360 46 16 psFillArc - globalGC1 46 15 46 16 psDrawLine - globalGC1 45 14 3 3 0 360 46 15 psFillArc - globalGC1 46 15 46 15 psDrawLine - globalGC1 45 14 3 3 0 360 46 15 psFillArc - globalGC1 46 15 46 15 psDrawLine - globalGC1 45 14 3 3 0 360 46 15 psFillArc - globalGC1 46 18 46 15 psDrawLine - globalGC1 45 17 3 3 0 360 46 18 psFillArc - globalGC1 46 35 46 18 psDrawLine - globalGC1 45 34 3 3 0 360 46 35 psFillArc - 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psDrawLine - globalGC1 47 14 3 3 0 360 48 15 psFillArc - globalGC1 48 14 48 15 psDrawLine - globalGC1 47 13 3 3 0 360 48 14 psFillArc - globalGC1 48 15 48 14 psDrawLine - globalGC1 47 14 3 3 0 360 48 15 psFillArc - globalGC1 48 17 48 15 psDrawLine - globalGC1 47 16 3 3 0 360 48 17 psFillArc - globalGC1 48 22 48 17 psDrawLine - globalGC1 47 21 3 3 0 360 48 22 psFillArc - globalGC1 48 36 48 22 psDrawLine - globalGC1 47 35 3 3 0 360 48 36 psFillArc - globalGC1 48 55 48 36 psDrawLine - globalGC1 47 54 3 3 0 360 48 55 psFillArc - globalGC1 48 77 48 55 psDrawLine - globalGC1 47 76 3 3 0 360 48 77 psFillArc - globalGC1 48 95 48 77 psDrawLine - globalGC1 47 94 3 3 0 360 48 95 psFillArc - globalGC1 48 101 48 95 psDrawLine - globalGC1 47 100 3 3 0 360 48 101 psFillArc - globalGC1 48 103 48 101 psDrawLine - globalGC1 47 102 3 3 0 360 48 103 psFillArc - globalGC1 48 104 48 103 psDrawLine - globalGC1 47 103 3 3 0 360 48 104 psFillArc - globalGC1 48 103 48 104 psDrawLine - globalGC1 47 102 3 3 0 360 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-%-------------------------- support procedures --------------------------% - -%--------- first create user dictionary with 100 entries max ------------% -% (number can be changed to accomodate definitions) % - -100 dict begin %% using 100 entries in top level dictionary - -/FontHeight 12 def - -/inch - { 72 mul } - def - -% yVal and hVal are necessary because the Xwindow display origin -% is at the upper left corner, while the postscript display -% origin is at the lower left hand corner. - -/yVal %% get Y value -- make upper left corner origin - { maxY sub abs } %% maxY is viewWindow height - def - -/hVal %% get H value -- used for displaying title text - { maxH sub abs } %% maxH is viewWindow height+titleWindow height - def - -% loads in the font - -/loadFont - { /Times-Roman findfont FontHeight scalefont setfont } - def - -% draws a rectangle with input operand: -% height -% width -% notice that this function does not "draw" or ink the rectangle. -/drawRect - { 1 index 1 add 0 rlineto %% draw first side - 0 exch 1 add neg rlineto %% draw second side - 1 add neg 0 rlineto %% draw third side - closepath } %% draw fourth side - def - -% create a rectangle with input operand in the view window: -% y -% x -% height -% width -% notice that this function does not "draw" or ink the rectangle. -/rectangle - { yVal moveto %% set currentpoint for line - drawRect } %% draws the rectangle - def - -% These are global variables that every draw procedure uses -% THe operand should be as follows: -% viewWindow width -% viewWindow height -% title height -/setDim - { /maxX exch def %% width of display - /maxY exch def %% height of display - /titleH exch def %% height of title - /maxH maxY titleH add def %% height of display + title - } def - -%-------------------------- major procedures --------------------------% - -/title %% draws a rectangle around the title of picture - { gsave - newpath - moveto %% lower left of title - titleH 1 add 0 exch rlineto %% draw first side - 1 add 0 rlineto %% draw second side - 1 add neg 0 exch rlineto - begin installGC stroke end %% draw third side - grestore } - def - -/drawFrame %% draw display frame - { gsave - newpath - maxX maxY 0 0 rectangle - begin installGC stroke end - grestore } - def - -% updates the foreground color of existing graphics-context dictionary: -% foreground color -% dictionary name -/setForeground - { /FGcolor exch put } - def - -% updates the background color of existing graphics-context dictionary: -% background color -% dictionary name -/setBackground - { /BGcolor exch put } - def - -% updates the line width, line style, cap style, join style of -% existing graphics-context dictionary: -% dictionary name -% join style -% cap style -% line width -/setLineAttributes - { begin - /JoinStyle exch def - /CapStyle exch def - /LineWidth exch def - end } - def - -% creates a graphics context dictionary with the following information: -% /dictionary name -% foreground color -% background color -% line width -% cap style -% join style -% this creates different graphical contexts for different drawing functions. -/makeDict - { 5 dict 2 copy def begin pop %% with dict name on top of stack - /FGcolor exch def %% define drawing attributes - /BGcolor exch def %% not heavily used - /LineWidth exch def - /CapStyle exch def - /JoinStyle exch def - end } - def - -% makes the current dictionary attributes effective -% this function takes the values in the current dictionary to set the context -% these are the values currently being used: foreground, cap, join, and width -/installGC - { - FGcolor currentgray ne - {FGcolor setgray} if %% foreground color - CapStyle currentlinecap ne - {CapStyle setlinecap} if %% cap style - JoinStyle currentlinejoin ne - {JoinStyle setlinejoin} if %% join style - LineWidth currentlinewidth ne - {LineWidth setlinewidth} if } %% line width - def - -% operand stack configuration in order to use psDrawLine: -% psDrawLine -% y0 -% x0 -% y1 -% x1 -% graphics-context dictionary -% this draws a line from (x0, y0) to (x1, y1). - -/psDrawLine - { gsave - newpath - yVal moveto - yVal lineto - begin installGC stroke end - grestore } - def - -% operand stack configuration in order to use psDrawIStr: -% psDrawIStr -% window type: title or window -% string -% y -% x -% graphics-context dictionary -% it draws a text string in foreground color on top of bounding box of -% string, which is in background color. - -/psDrawIStr - { gsave - newpath %% for rectangle - loadFont - - /window exch def %% get window type - - %% draw bounding box with background color - /str exch def %% get text string - str stringwidth pop 1 sub %% width - FontHeight 1 sub %% height - currentfont begin %% get font height - FontBBox - end - /ypos exch def pop %% define ypos - neg ypos add /offset exch def pop - /offset ypos offset div FontHeight mul def %% define offset - /h exch def /w exch def %% define h - /y0 exch def %% define y0 - /x0 exch def %% define x0 - w h x0 y0 offset sub - window (title) eq - {hVal moveto drawRect} %% draws in title window - {rectangle} ifelse %% draws in view window - begin - BGcolor setgray fill %% set background box color - - x0 y0 - window (title) eq - {hVal} %% print title text - {yVal} ifelse %% print window text - moveto str - FGcolor setgray show %% set text color - end - grestore } - def - -% operand stack configuration in order to use psFillArc: -% psFillArc -% y center of rectangle -% x center of rectangle -% angle2 -% angle1 -% width -% height -% y -% x -% graphics-context dictionary -% this draws and fills an arc whose origin is at x, y, and whose width -% and height specifies the rectangle which encases the arc. -% Origin is at upper left corner of rectangle. -% This function uses "scale" to make cricles and ellipses. -/psFillArc - { gsave - newpath - yVal moveto - /sfactor 4 index 4 index div def - 1 sfactor scale - 6 5 roll %% x on top of stack - 3 index 2 div add %% define x origin - 6 5 roll %% y on top of stack - 6 5 roll %% h on top of stack - 2 div add yVal sfactor div %% define y origin - 5 4 roll %% w on top of stack - 2 div %% define radius - 5 3 roll %% a1 a2 now on top - 1 index add - arcn %% draw clockwise arc - begin installGC fill end %% fills with foreground color - grestore } - def - -%-------------------------- script --------------------------% - -% 1 inch 1 inch translate - - mark %% mark bottom of our stack - - 0 0 1 - 1072693248 0 /globalGC1 makeDict - 0 0 1 - 1072693248 0 /globalGC2 makeDict - 0 0 1 - 1072693248 0 /trashGC makeDict - 0 0 1 - 1072693248 0 /globGC makeDict - 0 0 1 - 1072693248 0 /anotherGC makeDict - 0 0 1 - 1072693248 0 /graphGC makeDict - 0 0 1 - 1072693248 0 /unitGC makeDict - - gsave % save graphics state for clipping path - - 1.000000 1.000000 scale - - 24 303 300 setDim - maxX maxY 0 0 rectangle clip % set clip path - - globalGC1 300 151 0 151 psDrawLine - globalGC1 6 303 6 0 psDrawLine - unitGC 62 153 62 149 psDrawLine - unitGC 50 166 (0.80) (window) psDrawIStr - unitGC 118 153 118 149 psDrawLine - unitGC 106 166 (1.60) (window) psDrawIStr - unitGC 174 153 174 149 psDrawLine - unitGC 162 166 (2.40) (window) psDrawIStr - unitGC 230 153 230 149 psDrawLine - unitGC 218 166 (3.20) (window) psDrawIStr - unitGC 286 153 286 149 psDrawLine - unitGC 274 166 (4.00) (window) psDrawIStr - unitGC 8 94 4 94 psDrawLine - unitGC -30 99 (2.40) (window) psDrawIStr - unitGC 8 37 4 37 psDrawLine - unitGC -30 42 (4.80) (window) psDrawIStr - unitGC 8 207 4 207 psDrawLine - unitGC -39 212 (-2.40) (window) psDrawIStr - unitGC 8 263 4 263 psDrawLine - unitGC -39 268 (-4.80) (window) psDrawIStr - globalGC1 5 290 3 3 0 360 6 291 psFillArc - globalGC1 6 291 6 291 psDrawLine - globalGC1 5 290 3 3 0 360 6 291 psFillArc - globalGC1 12 271 6 291 psDrawLine - globalGC1 11 270 3 3 0 360 12 271 psFillArc - globalGC1 18 252 12 271 psDrawLine - globalGC1 17 251 3 3 0 360 18 252 psFillArc - globalGC1 23 235 18 252 psDrawLine - globalGC1 22 234 3 3 0 360 23 235 psFillArc - globalGC1 29 220 23 235 psDrawLine - globalGC1 28 219 3 3 0 360 29 220 psFillArc - globalGC1 35 207 29 220 psDrawLine - globalGC1 34 206 3 3 0 360 35 207 psFillArc - globalGC1 41 195 35 207 psDrawLine - globalGC1 40 194 3 3 0 360 41 195 psFillArc - globalGC1 47 184 41 195 psDrawLine - globalGC1 46 183 3 3 0 360 47 184 psFillArc - globalGC1 53 175 47 184 psDrawLine - globalGC1 52 174 3 3 0 360 53 175 psFillArc - globalGC1 59 167 53 175 psDrawLine - globalGC1 58 166 3 3 0 360 59 167 psFillArc - globalGC1 64 161 59 167 psDrawLine - globalGC1 63 160 3 3 0 360 64 161 psFillArc - globalGC1 70 155 64 161 psDrawLine - globalGC1 69 154 3 3 0 360 70 155 psFillArc - globalGC1 76 151 70 155 psDrawLine - globalGC1 75 150 3 3 0 360 76 151 psFillArc - globalGC1 82 148 76 151 psDrawLine - globalGC1 81 147 3 3 0 360 82 148 psFillArc - globalGC1 88 145 82 148 psDrawLine - globalGC1 87 144 3 3 0 360 88 145 psFillArc - globalGC1 94 143 88 145 psDrawLine - globalGC1 93 142 3 3 0 360 94 143 psFillArc - globalGC1 99 142 94 143 psDrawLine - globalGC1 98 141 3 3 0 360 99 142 psFillArc - globalGC1 105 142 99 142 psDrawLine - globalGC1 104 141 3 3 0 360 105 142 psFillArc - globalGC1 111 142 105 142 psDrawLine - globalGC1 110 141 3 3 0 360 111 142 psFillArc - globalGC1 117 143 111 142 psDrawLine - globalGC1 116 142 3 3 0 360 117 143 psFillArc - globalGC1 123 144 117 143 psDrawLine - globalGC1 122 143 3 3 0 360 123 144 psFillArc - globalGC1 129 145 123 144 psDrawLine - globalGC1 128 144 3 3 0 360 129 145 psFillArc - globalGC1 135 147 129 145 psDrawLine - globalGC1 134 146 3 3 0 360 135 147 psFillArc - globalGC1 140 149 135 147 psDrawLine - globalGC1 139 148 3 3 0 360 140 149 psFillArc - globalGC1 146 151 140 149 psDrawLine - globalGC1 145 150 3 3 0 360 146 151 psFillArc - globalGC1 152 153 146 151 psDrawLine - globalGC1 151 152 3 3 0 360 152 153 psFillArc - globalGC1 158 155 152 153 psDrawLine - globalGC1 157 154 3 3 0 360 158 155 psFillArc - globalGC1 164 156 158 155 psDrawLine - globalGC1 163 155 3 3 0 360 164 156 psFillArc - globalGC1 170 158 164 156 psDrawLine - globalGC1 169 157 3 3 0 360 170 158 psFillArc - globalGC1 176 159 170 158 psDrawLine - globalGC1 175 158 3 3 0 360 176 159 psFillArc - globalGC1 181 160 176 159 psDrawLine - globalGC1 180 159 3 3 0 360 181 160 psFillArc - globalGC1 187 160 181 160 psDrawLine - globalGC1 186 159 3 3 0 360 187 160 psFillArc - globalGC1 193 160 187 160 psDrawLine - globalGC1 192 159 3 3 0 360 193 160 psFillArc - globalGC1 199 159 193 160 psDrawLine - globalGC1 198 158 3 3 0 360 199 159 psFillArc - globalGC1 205 157 199 159 psDrawLine - globalGC1 204 156 3 3 0 360 205 157 psFillArc - globalGC1 211 154 205 157 psDrawLine - globalGC1 210 153 3 3 0 360 211 154 psFillArc - globalGC1 217 151 211 154 psDrawLine - globalGC1 216 150 3 3 0 360 217 151 psFillArc - globalGC1 222 147 217 151 psDrawLine - globalGC1 221 146 3 3 0 360 222 147 psFillArc - globalGC1 228 141 222 147 psDrawLine - globalGC1 227 140 3 3 0 360 228 141 psFillArc - globalGC1 234 135 228 141 psDrawLine - globalGC1 233 134 3 3 0 360 234 135 psFillArc - globalGC1 240 127 234 135 psDrawLine - globalGC1 239 126 3 3 0 360 240 127 psFillArc - globalGC1 246 118 240 127 psDrawLine - globalGC1 245 117 3 3 0 360 246 118 psFillArc - globalGC1 252 107 246 118 psDrawLine - globalGC1 251 106 3 3 0 360 252 107 psFillArc - globalGC1 257 95 252 107 psDrawLine - globalGC1 256 94 3 3 0 360 257 95 psFillArc - globalGC1 263 82 257 95 psDrawLine - globalGC1 262 81 3 3 0 360 263 82 psFillArc - globalGC1 269 67 263 82 psDrawLine - globalGC1 268 66 3 3 0 360 269 67 psFillArc - globalGC1 275 50 269 67 psDrawLine - globalGC1 274 49 3 3 0 360 275 50 psFillArc - globalGC1 281 31 275 50 psDrawLine - globalGC1 280 30 3 3 0 360 281 31 psFillArc - globalGC1 287 11 281 31 psDrawLine - globalGC1 286 10 3 3 0 360 287 11 psFillArc - - grestore % restore graphics state - - - cleartomark %% clearing operand stack - -end %% pops mainDict from dictionary stack - -showpage - 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--- a/books/ps/2dctrl.ps +++ /dev/null @@ -1,722 +0,0 @@ -%!PS-Adobe-2.0 EPSF-1.2 -%%BoundingBox: 127.588757 104.120003 484.411243 718.120003 -%%Creator: xwd2ps -%%CreationDate: Sun Dec 1 15:51:11 1991 -%%Title: standard input -%%EndComments -% xwd2ps -- program written by Robert C. Tatar and Craig A. McGowan. -% The command used to create this file (missing quotes on strings): -% xwd2ps -% by pi.watson.ibm.com:jonms () -% Information from XWD rasterfile header: -% width = 258, height = 445, depth = 8 -% file_version = 7, pixmap_format = 2, byte_order = 1 -% bitmap_unit = 32, bitmap_bit_order = 1, bitmap_pad = 32 -% bits_per_pixel = 8, bytes_per_line = 260, visual_class = 3 -% bits/rgb = 8, colormap entries = 256, ncolors = 256 -% Portion of raster image in this file: -% starting line = 1 -% ending line = 445 -% starting column = 1 -% ending column = 258 -gsave -/inch {72 mul} def -/buffer 2 string def -/rgbmap 768 string def -/rgb (000) def -/pixels 768 string def -%%Title: colorimage.ps -% Written 11-4-88 by Bob Tatar -% U.S. Mail: GE-CRD, PO Box 8, KW-C214, Schenectady, NY 12301 -% E-Mail: tatar@crd.ge.com -% colorimage procedure to be used on monochrome printers -% or when the colorimage procedure is not available -% NOTE: Only 1 color mode is supported: single proc. & RGB - -systemdict /colorimage known not { % only create if not in systemdict - % Utility procedure for colorimage operator. This procedure takes a - % string of rgb encoded values and creates a string 1/3 as long with - % monochrome values. This procedure assumes 8 bits/color (i.e. - % 1 character/color) - % storage format for input string: (r1 g1 b1 r2 g2 b2 r3 g3 b3 ... ) - % storage format for output string: (g1 g2 g3 ... ) - - /colortograyscale { %def % (string) - dup /rgbdata exch store % (string) - length 3 idiv % Ns/3 - /npixls exch store % ; npixls => Ns/3 - /indx 0 store % ; indx => 0 - /pixls npixls string store % ; pixls => (....) - 0 1 npixls -1 add { % counter - pixls exch % pixls counter - rgbdata indx get .3 mul % pixls counter .3*rgbdata(ind) - rgbdata indx 1 add get .59 mul add % pixls counter .3*rgbdata(ind) + - % .59*rgbdata(ind+1) - rgbdata indx 2 add get .11 mul add % pixls counter .3*rgbdata(ind) + .59 - % *rgbdata(ind+1)+.11*rgbdata(ind+2) - cvi % pixls counter - put % - /indx indx 3 add store % ; /ind => ind+3 - } for % repeat for each rgb value - pixls % (pixls) - } bind def % ; /colortograyscale -> dictionary - - % Utility procedure for colorimage operator. This procedure takes two - % procedures off the stack and merges them into a single procedure. - - /mergeprocs { %def % {proc1} {proc2} - dup length % {proc1} {proc2} N2 - 3 -1 roll % {proc2} N2 {proc1} - dup % {proc2} N2 {proc1} {proc1} - length % {proc2} N2 {proc1} N1 - dup % {proc2} N2 {proc1} N1 N1 - 5 1 roll % N1 {proc2} N2 {proc1} N1 - 3 -1 roll % N1 {proc2} {proc1} N1 N2 - add % N1 {proc2} {proc1} N1+N2 - array cvx % N1 {proc2} {proc1} { ... } - dup % N1 {proc2} {proc1} { ... } { ... } - 3 -1 roll % N1 {proc2} { ... } { ... } {proc1} - 0 exch % N1 {proc2} { ... } { ... } 0 {proc1} - putinterval % N1 {proc2} { <<{proc1}>> ... } - dup % N1 {proc2} { <<{proc1}>> ... } { <<{proc1}>> ... } - 4 2 roll % { <<{proc1}>> ... } { <<{proc1}>> ... } N1 {proc2} - putinterval % { <<{proc1}>> <<{proc2}>> } - } bind def % ; /mergeprocs => dictionary - - /colorimage { %def % {imageproc} multiproc ncolors - pop % {imageproc} multiproc ; assume 3 colors - pop % {imageproc} ; assume false - {colortograyscale} % {imageproc} {colortograyscale} - mergeprocs % {imageproc colortograyscale} - image % construct monochrome image - } bind def % ; /colorimage => dictionary -} if % only create if it doesn't already exist -/drawcolorimage { - 258 445 8 - [258 0 0 -445 0 445] - {currentfile buffer readhexstring pop pop % get run length & color info - /npixels buffer 0 get 1 add 3 mul store % number of pixels (run length) - /color buffer 1 get 3 mul store % color of pixels - % /pixels npixels string store % create string to hold colors - /rgb rgbmap color 3 getinterval store % get rgb value - 0 3 npixels -1 add { - pixels exch rgb putinterval - } for - pixels 0 npixels getinterval % Return color values - } - false 3 - colorimage -} bind def -matrix currentmatrix -2.03 inch 3.5 inch scale - -% get rgb color table -currentfile rgbmap readhexstring pop pop -000000 -ffffff -dbdb70 -2f4f4f -d4d8e8 -23238e -d3d3d3 -ff0000 -757780 -46474d -b4b8c5 -236b8e -238e6b -2f2f4f -600808 -931c1c 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limit: 250 pts or 500 values for the operand stack. -%%EndComments - -%------------------------------- prologue -------------------------------% -%-------------------------- support procedures --------------------------% - -%--------- first create user dictionary with 100 entries max ------------% -% (number can be changed to accomodate definitions) % - -100 dict begin %% using 100 entries in top level dictionary - -/FontHeight 12 def - -/inch - { 72 mul } - def - -% yVal and hVal are necessary because the Xwindow display origin -% is at the upper left corner, while the postscript display -% origin is at the lower left hand corner. - -/yVal %% get Y value -- make upper left corner origin - { maxY sub abs } %% maxY is viewWindow height - def - -/hVal %% get H value -- used for displaying title text - { maxH sub abs } %% maxH is viewWindow height+titleWindow height - def - -% loads in the font - -/loadFont - { /Times-Roman findfont FontHeight scalefont setfont } - def - -% draws a rectangle with input operand: -% height -% width -% notice that this function does not "draw" or ink the rectangle. -/drawRect - { 1 index 1 add 0 rlineto %% draw first side - 0 exch 1 add neg rlineto %% draw second side - 1 add neg 0 rlineto %% draw third side - closepath } %% draw fourth side - def - -% create a rectangle with input operand in the view window: -% y -% x -% height -% width -% notice that this function does not "draw" or ink the rectangle. -/rectangle - { yVal moveto %% set currentpoint for line - drawRect } %% draws the rectangle - def - -% These are global variables that every draw procedure uses -% THe operand should be as follows: -% viewWindow width -% viewWindow height -% title height -/setDim - { /maxX exch def %% width of display - /maxY exch def %% height of display - /titleH exch def %% height of title - /maxH maxY titleH add def %% height of display + title - } def - -%-------------------------- major procedures --------------------------% - -/title %% draws a rectangle around the title of picture - { gsave - newpath - moveto %% lower left of title - titleH 1 add 0 exch rlineto %% draw first side - 1 add 0 rlineto %% draw second side - 1 add neg 0 exch rlineto - begin installGC stroke end %% draw third side - grestore } - def - -/drawFrame %% draw display frame - { gsave - newpath - maxX maxY 0 0 rectangle - begin installGC stroke end - grestore } - def - -% updates the foreground color of existing graphics-context dictionary: -% foreground color -% dictionary name -/setForeground - { /FGcolor exch put } - def - -% updates the background color of existing graphics-context dictionary: -% background color -% dictionary name -/setBackground - { /BGcolor exch put } - def - -% updates the line width, line style, cap style, join style of -% existing graphics-context dictionary: -% dictionary name -% join style -% cap style -% line width -/setLineAttributes - { begin - /JoinStyle exch def - /CapStyle exch def - /LineWidth exch def - end } - def - -% creates a graphics context dictionary with the following information: -% /dictionary name -% foreground color -% background color -% line width -% cap style -% join style -% this creates different graphical contexts for different drawing functions. -/makeDict - { 5 dict 2 copy def begin pop %% with dict name on top of stack - /FGcolor exch def %% define drawing attributes - /BGcolor exch def %% not heavily used - /LineWidth exch def - /CapStyle exch def - /JoinStyle exch def - end } - def - -% makes the current dictionary attributes effective -% this function takes the values in the current dictionary to set the context -% these are the values currently being used: foreground, cap, join, and width -/installGC - { - FGcolor currentgray ne - {FGcolor setgray} if %% foreground color - CapStyle currentlinecap ne - {CapStyle setlinecap} if %% cap style - JoinStyle currentlinejoin ne - {JoinStyle setlinejoin} if %% join style - LineWidth currentlinewidth ne - {LineWidth setlinewidth} if } %% line width - def - -% operand stack configuration in order to use psDrawLine: -% psDrawLine -% y0 -% x0 -% y1 -% x1 -% graphics-context dictionary -% this draws a line from (x0, y0) to (x1, y1). - -/psDrawLine - { gsave - newpath - yVal moveto - yVal lineto - begin installGC stroke end - grestore } - def - -% operand stack configuration in order to use psFillArc: -% psFillArc -% y center of rectangle -% x center of rectangle -% angle2 -% angle1 -% width -% height -% y -% x -% graphics-context dictionary -% this draws and fills an arc whose origin is at x, y, and whose width -% and height specifies the rectangle which encases the arc. -% Origin is at upper left corner of rectangle. -% This function uses "scale" to make cricles and ellipses. -/psFillArc - { gsave - newpath - yVal moveto - /sfactor 4 index 4 index div def - 1 sfactor scale - 6 5 roll %% x on top of stack - 3 index 2 div add %% define x origin - 6 5 roll %% y on top of stack - 6 5 roll %% h on top of stack - 2 div add yVal sfactor div %% define y origin - 5 4 roll %% w on top of stack - 2 div %% define radius - 5 3 roll %% a1 a2 now on top - 1 index add - arcn %% draw clockwise arc - begin installGC fill end %% fills with foreground color - grestore } - def - -%-------------------------- script --------------------------% - -% 1 inch 1 inch translate - - mark %% mark bottom of our stack - - 0 0 1 - 1072693248 0 /globalGC1 makeDict - 0 0 1 - 1072693248 0 /globalGC2 makeDict - 0 0 1 - 1072693248 0 /trashGC makeDict - 0 0 1 - 1072693248 0 /globGC makeDict - 0 0 1 - 1072693248 0 /anotherGC makeDict - 0 0 1 - 1072693248 0 /graphGC makeDict - 0 0 1 - 1072693248 0 /unitGC makeDict - - gsave % save graphics state for clipping path - - 24 259 256 setDim - maxX maxY 0 0 rectangle clip % set clip path - - globalGC1 256 129 0 129 psDrawLine - globalGC1 127 259 127 0 psDrawLine - globalGC1 11 147 3 3 0 360 12 148 psFillArc - globalGC1 12 148 12 148 psDrawLine - globalGC1 11 147 3 3 0 360 12 148 psFillArc - 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globalGC1 75 170 70 167 psDrawLine - globalGC1 74 169 3 3 0 360 75 170 psFillArc - globalGC1 80 174 75 170 psDrawLine - globalGC1 79 173 3 3 0 360 80 174 psFillArc - globalGC1 84 179 80 174 psDrawLine - globalGC1 83 178 3 3 0 360 84 179 psFillArc - globalGC1 89 184 84 179 psDrawLine - globalGC1 88 183 3 3 0 360 89 184 psFillArc - globalGC1 94 192 89 184 psDrawLine - globalGC1 93 191 3 3 0 360 94 192 psFillArc - globalGC1 99 201 94 192 psDrawLine - globalGC1 98 200 3 3 0 360 99 201 psFillArc - globalGC1 104 212 99 201 psDrawLine - globalGC1 103 211 3 3 0 360 104 212 psFillArc - globalGC1 108 227 104 212 psDrawLine - globalGC1 107 226 3 3 0 360 108 227 psFillArc - globalGC1 113 244 108 227 psDrawLine - globalGC1 112 243 3 3 0 360 113 244 psFillArc - globalGC1 118 243 113 244 psDrawLine - globalGC1 117 242 3 3 0 360 118 243 psFillArc - globalGC1 123 53 118 243 psDrawLine - globalGC1 122 52 3 3 0 360 123 53 psFillArc - globalGC1 127 35 123 53 psDrawLine - globalGC1 126 34 3 3 0 360 127 35 psFillArc - globalGC1 132 205 127 35 psDrawLine - globalGC1 131 204 3 3 0 360 132 205 psFillArc - globalGC1 137 15 132 205 psDrawLine - globalGC1 136 14 3 3 0 360 137 15 psFillArc - globalGC1 142 14 137 15 psDrawLine - globalGC1 141 13 3 3 0 360 142 14 psFillArc - globalGC1 147 31 142 14 psDrawLine - globalGC1 146 30 3 3 0 360 147 31 psFillArc - globalGC1 151 46 147 31 psDrawLine - globalGC1 150 45 3 3 0 360 151 46 psFillArc - globalGC1 156 57 151 46 psDrawLine - globalGC1 155 56 3 3 0 360 156 57 psFillArc - globalGC1 161 66 156 57 psDrawLine - globalGC1 160 65 3 3 0 360 161 66 psFillArc - globalGC1 166 74 161 66 psDrawLine - globalGC1 165 73 3 3 0 360 166 74 psFillArc - globalGC1 171 79 166 74 psDrawLine - globalGC1 170 78 3 3 0 360 171 79 psFillArc - globalGC1 175 84 171 79 psDrawLine - globalGC1 174 83 3 3 0 360 175 84 psFillArc - globalGC1 180 88 175 84 psDrawLine - globalGC1 179 87 3 3 0 360 180 88 psFillArc - globalGC1 185 91 180 88 psDrawLine - globalGC1 184 90 3 3 0 360 185 91 psFillArc - globalGC1 190 94 185 91 psDrawLine - globalGC1 189 93 3 3 0 360 190 94 psFillArc - globalGC1 195 97 190 94 psDrawLine - globalGC1 194 96 3 3 0 360 195 97 psFillArc - globalGC1 199 99 195 97 psDrawLine - globalGC1 198 98 3 3 0 360 199 99 psFillArc - globalGC1 204 100 199 99 psDrawLine - globalGC1 203 99 3 3 0 360 204 100 psFillArc - globalGC1 209 102 204 100 psDrawLine - globalGC1 208 101 3 3 0 360 209 102 psFillArc - globalGC1 214 104 209 102 psDrawLine - globalGC1 213 103 3 3 0 360 214 104 psFillArc - globalGC1 219 105 214 104 psDrawLine - globalGC1 218 104 3 3 0 360 219 105 psFillArc - globalGC1 223 106 219 105 psDrawLine - globalGC1 222 105 3 3 0 360 223 106 psFillArc - globalGC1 228 107 223 106 psDrawLine - globalGC1 227 106 3 3 0 360 228 107 psFillArc - globalGC1 233 108 228 107 psDrawLine - globalGC1 232 107 3 3 0 360 233 108 psFillArc - globalGC1 238 109 233 108 psDrawLine - globalGC1 237 108 3 3 0 360 238 109 psFillArc - globalGC1 243 110 238 109 psDrawLine - 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procedures --------------------------% - -%--------- first create user dictionary with 100 entries max ------------% -% (number can be changed to accomodate definitions) % - -100 dict begin %% using 100 entries in top level dictionary - -/FontHeight 12 def - -/inch - { 72 mul } - def - -% yVal and hVal are necessary because the Xwindow display origin -% is at the upper left corner, while the postscript display -% origin is at the lower left hand corner. - -/yVal %% get Y value -- make upper left corner origin - { maxY sub abs } %% maxY is viewWindow height - def - -/hVal %% get H value -- used for displaying title text - { maxH sub abs } %% maxH is viewWindow height+titleWindow height - def - -% loads in the font - -/loadFont - { /Times-Roman findfont FontHeight scalefont setfont } - def - -% draws a rectangle with input operand: -% height -% width -% notice that this function does not "draw" or ink the rectangle. -/drawRect - { 1 index 1 add 0 rlineto %% draw first side - 0 exch 1 add neg rlineto %% draw second side - 1 add neg 0 rlineto %% draw third side - closepath } %% draw fourth side - def - -% create a rectangle with input operand in the view window: -% y -% x -% height -% width -% notice that this function does not "draw" or ink the rectangle. -/rectangle - { yVal moveto %% set currentpoint for line - drawRect } %% draws the rectangle - def - -% These are global variables that every draw procedure uses -% THe operand should be as follows: -% viewWindow width -% viewWindow height -% title height -/setDim - { /maxX exch def %% width of display - /maxY exch def %% height of display - /titleH exch def %% height of title - /maxH maxY titleH add def %% height of display + title - } def - -%-------------------------- major procedures --------------------------% - -/title %% draws a rectangle around the title of picture - { gsave - newpath - moveto %% lower left of title - titleH 1 add 0 exch rlineto %% draw first side - 1 add 0 rlineto %% draw second side - 1 add neg 0 exch rlineto - begin installGC stroke end %% draw third side - grestore } - def - -/drawFrame %% draw display frame - { gsave - newpath - maxX maxY 0 0 rectangle - begin installGC stroke end - grestore } - def - -% updates the foreground color of existing graphics-context dictionary: -% foreground color -% dictionary name -/setForeground - { /FGcolor exch put } - def - -% updates the background color of existing graphics-context dictionary: -% background color -% dictionary name -/setBackground - { /BGcolor exch put } - def - -% updates the line width, line style, cap style, join style of -% existing graphics-context dictionary: -% dictionary name -% join style -% cap style -% line width -/setLineAttributes - { begin - /JoinStyle exch def - /CapStyle exch def - /LineWidth exch def - end } - def - -% creates a graphics context dictionary with the following information: -% /dictionary name -% foreground color -% background color -% line width -% cap style -% join style -% this creates different graphical contexts for different drawing functions. -/makeDict - { 5 dict 2 copy def begin pop %% with dict name on top of stack - /FGcolor exch def %% define drawing attributes - /BGcolor exch def %% not heavily used - /LineWidth exch def - /CapStyle exch def - /JoinStyle exch def - end } - def - -% makes the current dictionary attributes effective -% this function takes the values in the current dictionary to set the context -% these are the values currently being used: foreground, cap, join, and width -/installGC - { - FGcolor currentgray ne - {FGcolor setgray} if %% foreground color - CapStyle currentlinecap ne - {CapStyle setlinecap} if %% cap style - JoinStyle currentlinejoin ne - {JoinStyle setlinejoin} if %% join style - LineWidth currentlinewidth ne - {LineWidth setlinewidth} if } %% line width - def - -% operand stack configuration in order to use psDrawLine: -% psDrawLine -% y0 -% x0 -% y1 -% x1 -% graphics-context dictionary -% this draws a line from (x0, y0) to (x1, y1). - -/psDrawLine - { gsave - newpath - yVal moveto - yVal lineto - begin installGC stroke end - grestore } - def - -% operand stack configuration in order to use psFillArc: -% psFillArc -% y center of rectangle -% x center of rectangle -% angle2 -% angle1 -% width -% height -% y -% x -% graphics-context dictionary -% this draws and fills an arc whose origin is at x, y, and whose width -% and height specifies the rectangle which encases the arc. -% Origin is at upper left corner of rectangle. -% This function uses "scale" to make cricles and ellipses. -/psFillArc - { gsave - newpath - yVal moveto - /sfactor 4 index 4 index div def - 1 sfactor scale - 6 5 roll %% x on top of stack - 3 index 2 div add %% define x origin - 6 5 roll %% y on top of stack - 6 5 roll %% h on top of stack - 2 div add yVal sfactor div %% define y origin - 5 4 roll %% w on top of stack - 2 div %% define radius - 5 3 roll %% a1 a2 now on top - 1 index add - arcn %% draw clockwise arc - begin installGC fill end %% fills with foreground color - grestore } - def - -%-------------------------- script --------------------------% - -% 1 inch 1 inch translate - - mark %% mark bottom of our stack - - 0 0 1 - 1072693248 0 /globalGC1 makeDict - 0 0 1 - 1072693248 0 /globalGC2 makeDict - 0 0 1 - 1072693248 0 /trashGC makeDict - 0 0 1 - 1072693248 0 /globGC makeDict - 0 0 1 - 1072693248 0 /anotherGC makeDict - 0 0 1 - 1072693248 0 /graphGC makeDict - 0 0 1 - 1072693248 0 /unitGC makeDict - - gsave % save graphics state for clipping path - - 24 259 256 setDim - maxX maxY 0 0 rectangle clip % set clip path - - globalGC1 256 129 0 129 psDrawLine - globalGC1 127 259 127 0 psDrawLine - globalGC1 213 243 3 3 0 360 214 244 psFillArc - globalGC1 214 244 214 244 psDrawLine - globalGC1 213 243 3 3 0 360 214 244 psFillArc - globalGC1 214 213 214 244 psDrawLine - globalGC1 213 212 3 3 0 360 214 213 psFillArc - globalGC1 214 192 214 213 psDrawLine - globalGC1 213 191 3 3 0 360 214 192 psFillArc - globalGC1 214 171 214 192 psDrawLine - globalGC1 213 170 3 3 0 360 214 171 psFillArc - globalGC1 214 160 214 171 psDrawLine - globalGC1 213 159 3 3 0 360 214 160 psFillArc - globalGC1 214 150 214 160 psDrawLine - globalGC1 213 149 3 3 0 360 214 150 psFillArc - globalGC1 214 145 214 150 psDrawLine - globalGC1 213 144 3 3 0 360 214 145 psFillArc - globalGC1 215 139 214 145 psDrawLine - globalGC1 214 138 3 3 0 360 215 139 psFillArc - globalGC1 215 137 215 139 psDrawLine - globalGC1 214 136 3 3 0 360 215 137 psFillArc - globalGC1 216 134 215 137 psDrawLine - globalGC1 215 133 3 3 0 360 216 134 psFillArc - globalGC1 216 133 216 134 psDrawLine - globalGC1 215 132 3 3 0 360 216 133 psFillArc - globalGC1 217 132 216 133 psDrawLine - globalGC1 216 131 3 3 0 360 217 132 psFillArc - globalGC1 219 131 217 132 psDrawLine - globalGC1 218 130 3 3 0 360 219 131 psFillArc - globalGC1 221 130 219 131 psDrawLine - globalGC1 220 129 3 3 0 360 221 130 psFillArc - globalGC1 223 130 221 130 psDrawLine - globalGC1 222 129 3 3 0 360 223 130 psFillArc - globalGC1 228 129 223 130 psDrawLine - globalGC1 227 128 3 3 0 360 228 129 psFillArc - globalGC1 233 129 228 129 psDrawLine - globalGC1 232 128 3 3 0 360 233 129 psFillArc - globalGC1 238 129 233 129 psDrawLine - globalGC1 237 128 3 3 0 360 238 129 psFillArc - globalGC1 243 129 238 129 psDrawLine - globalGC1 242 128 3 3 0 360 243 129 psFillArc - globalGC1 155 243 3 3 0 360 156 244 psFillArc - globalGC1 156 244 156 244 psDrawLine - globalGC1 155 243 3 3 0 360 156 244 psFillArc - globalGC1 156 213 156 244 psDrawLine - globalGC1 155 212 3 3 0 360 156 213 psFillArc - globalGC1 156 192 156 213 psDrawLine - globalGC1 155 191 3 3 0 360 156 192 psFillArc - globalGC1 157 171 156 192 psDrawLine - globalGC1 156 170 3 3 0 360 157 171 psFillArc - globalGC1 157 160 157 171 psDrawLine - globalGC1 156 159 3 3 0 360 157 160 psFillArc - globalGC1 157 150 157 160 psDrawLine - globalGC1 156 149 3 3 0 360 157 150 psFillArc - globalGC1 157 145 157 150 psDrawLine - globalGC1 156 144 3 3 0 360 157 145 psFillArc - globalGC1 157 139 157 145 psDrawLine - globalGC1 156 138 3 3 0 360 157 139 psFillArc - globalGC1 157 137 157 139 psDrawLine - globalGC1 156 136 3 3 0 360 157 137 psFillArc - globalGC1 158 134 157 137 psDrawLine - globalGC1 157 133 3 3 0 360 158 134 psFillArc - globalGC1 159 133 158 134 psDrawLine - globalGC1 158 132 3 3 0 360 159 133 psFillArc - globalGC1 160 132 159 133 psDrawLine - globalGC1 159 131 3 3 0 360 160 132 psFillArc - globalGC1 161 131 160 132 psDrawLine - globalGC1 160 130 3 3 0 360 161 131 psFillArc - globalGC1 163 130 161 131 psDrawLine - globalGC1 162 129 3 3 0 360 163 130 psFillArc - globalGC1 166 130 163 130 psDrawLine - globalGC1 165 129 3 3 0 360 166 130 psFillArc - globalGC1 171 129 166 130 psDrawLine - globalGC1 170 128 3 3 0 360 171 129 psFillArc - globalGC1 175 129 171 129 psDrawLine - globalGC1 174 128 3 3 0 360 175 129 psFillArc - globalGC1 180 129 175 129 psDrawLine - globalGC1 179 128 3 3 0 360 180 129 psFillArc - globalGC1 185 129 180 129 psDrawLine - globalGC1 184 128 3 3 0 360 185 129 psFillArc - globalGC1 190 129 185 129 psDrawLine - globalGC1 189 128 3 3 0 360 190 129 psFillArc - globalGC1 195 129 190 129 psDrawLine - globalGC1 194 128 3 3 0 360 195 129 psFillArc - globalGC1 199 128 195 129 psDrawLine - globalGC1 198 127 3 3 0 360 199 128 psFillArc - globalGC1 204 128 199 128 psDrawLine - globalGC1 203 127 3 3 0 360 204 128 psFillArc - globalGC1 207 128 204 128 psDrawLine - globalGC1 206 127 3 3 0 360 207 128 psFillArc - globalGC1 209 127 207 128 psDrawLine - globalGC1 208 126 3 3 0 360 209 127 psFillArc - globalGC1 210 126 209 127 psDrawLine - globalGC1 209 125 3 3 0 360 210 126 psFillArc - globalGC1 211 125 210 126 psDrawLine - globalGC1 210 124 3 3 0 360 211 125 psFillArc - globalGC1 212 124 211 125 psDrawLine - globalGC1 211 123 3 3 0 360 212 124 psFillArc - globalGC1 213 121 212 124 psDrawLine - globalGC1 212 120 3 3 0 360 213 121 psFillArc - globalGC1 213 119 213 121 psDrawLine - globalGC1 212 118 3 3 0 360 213 119 psFillArc - globalGC1 213 113 213 119 psDrawLine - globalGC1 212 112 3 3 0 360 213 113 psFillArc - globalGC1 213 108 213 113 psDrawLine - globalGC1 212 107 3 3 0 360 213 108 psFillArc - globalGC1 214 98 213 108 psDrawLine - globalGC1 213 97 3 3 0 360 214 98 psFillArc - globalGC1 214 87 214 98 psDrawLine - globalGC1 213 86 3 3 0 360 214 87 psFillArc - globalGC1 214 66 214 87 psDrawLine - globalGC1 213 65 3 3 0 360 214 66 psFillArc - globalGC1 214 45 214 66 psDrawLine - globalGC1 213 44 3 3 0 360 214 45 psFillArc - globalGC1 214 14 214 45 psDrawLine - globalGC1 213 13 3 3 0 360 214 14 psFillArc - globalGC1 98 243 3 3 0 360 99 244 psFillArc - globalGC1 99 244 99 244 psDrawLine - globalGC1 98 243 3 3 0 360 99 244 psFillArc - globalGC1 99 213 99 244 psDrawLine - globalGC1 98 212 3 3 0 360 99 213 psFillArc - globalGC1 99 192 99 213 psDrawLine - globalGC1 98 191 3 3 0 360 99 192 psFillArc - globalGC1 99 171 99 192 psDrawLine - globalGC1 98 170 3 3 0 360 99 171 psFillArc - globalGC1 99 160 99 171 psDrawLine - globalGC1 98 159 3 3 0 360 99 160 psFillArc - globalGC1 99 150 99 160 psDrawLine - globalGC1 98 149 3 3 0 360 99 150 psFillArc - globalGC1 99 145 99 150 psDrawLine - globalGC1 98 144 3 3 0 360 99 145 psFillArc - globalGC1 100 139 99 145 psDrawLine - globalGC1 99 138 3 3 0 360 100 139 psFillArc - globalGC1 100 137 100 139 psDrawLine - globalGC1 99 136 3 3 0 360 100 137 psFillArc - globalGC1 101 134 100 137 psDrawLine - globalGC1 100 133 3 3 0 360 101 134 psFillArc - globalGC1 101 133 101 134 psDrawLine - globalGC1 100 132 3 3 0 360 101 133 psFillArc - globalGC1 102 132 101 133 psDrawLine - globalGC1 101 131 3 3 0 360 102 132 psFillArc - globalGC1 104 131 102 132 psDrawLine - globalGC1 103 130 3 3 0 360 104 131 psFillArc - globalGC1 106 130 104 131 psDrawLine - globalGC1 105 129 3 3 0 360 106 130 psFillArc - globalGC1 108 130 106 130 psDrawLine - globalGC1 107 129 3 3 0 360 108 130 psFillArc - globalGC1 113 129 108 130 psDrawLine - globalGC1 112 128 3 3 0 360 113 129 psFillArc - globalGC1 118 129 113 129 psDrawLine - globalGC1 117 128 3 3 0 360 118 129 psFillArc - globalGC1 123 129 118 129 psDrawLine - globalGC1 122 128 3 3 0 360 123 129 psFillArc - globalGC1 127 129 123 129 psDrawLine - globalGC1 126 128 3 3 0 360 127 129 psFillArc - globalGC1 132 129 127 129 psDrawLine - globalGC1 131 128 3 3 0 360 132 129 psFillArc - globalGC1 137 129 132 129 psDrawLine - globalGC1 136 128 3 3 0 360 137 129 psFillArc - globalGC1 142 128 137 129 psDrawLine - globalGC1 141 127 3 3 0 360 142 128 psFillArc - globalGC1 147 128 142 128 psDrawLine - globalGC1 146 127 3 3 0 360 147 128 psFillArc - globalGC1 149 128 147 128 psDrawLine - globalGC1 148 127 3 3 0 360 149 128 psFillArc - globalGC1 151 127 149 128 psDrawLine - globalGC1 150 126 3 3 0 360 151 127 psFillArc - globalGC1 153 126 151 127 psDrawLine - globalGC1 152 125 3 3 0 360 153 126 psFillArc - globalGC1 154 125 153 126 psDrawLine - globalGC1 153 124 3 3 0 360 154 125 psFillArc - globalGC1 154 124 154 125 psDrawLine - globalGC1 153 123 3 3 0 360 154 124 psFillArc - globalGC1 155 121 154 124 psDrawLine - globalGC1 154 120 3 3 0 360 155 121 psFillArc - globalGC1 155 119 155 121 psDrawLine - globalGC1 154 118 3 3 0 360 155 119 psFillArc - globalGC1 156 113 155 119 psDrawLine - globalGC1 155 112 3 3 0 360 156 113 psFillArc - globalGC1 156 108 156 113 psDrawLine - globalGC1 155 107 3 3 0 360 156 108 psFillArc - globalGC1 156 98 156 108 psDrawLine - globalGC1 155 97 3 3 0 360 156 98 psFillArc - globalGC1 156 87 156 98 psDrawLine - globalGC1 155 86 3 3 0 360 156 87 psFillArc - globalGC1 156 66 156 87 psDrawLine - globalGC1 155 65 3 3 0 360 156 66 psFillArc - globalGC1 156 45 156 66 psDrawLine - globalGC1 155 44 3 3 0 360 156 45 psFillArc - globalGC1 156 14 156 45 psDrawLine - globalGC1 155 13 3 3 0 360 156 14 psFillArc - globalGC1 40 243 3 3 0 360 41 244 psFillArc - globalGC1 41 244 41 244 psDrawLine - globalGC1 40 243 3 3 0 360 41 244 psFillArc - globalGC1 41 213 41 244 psDrawLine - globalGC1 40 212 3 3 0 360 41 213 psFillArc - globalGC1 41 192 41 213 psDrawLine - globalGC1 40 191 3 3 0 360 41 192 psFillArc - globalGC1 41 171 41 192 psDrawLine - globalGC1 40 170 3 3 0 360 41 171 psFillArc - globalGC1 41 160 41 171 psDrawLine - globalGC1 40 159 3 3 0 360 41 160 psFillArc - globalGC1 42 150 41 160 psDrawLine - globalGC1 41 149 3 3 0 360 42 150 psFillArc - globalGC1 42 145 42 150 psDrawLine - globalGC1 41 144 3 3 0 360 42 145 psFillArc - globalGC1 42 139 42 145 psDrawLine - globalGC1 41 138 3 3 0 360 42 139 psFillArc - globalGC1 42 137 42 139 psDrawLine - globalGC1 41 136 3 3 0 360 42 137 psFillArc - globalGC1 43 134 42 137 psDrawLine - globalGC1 42 133 3 3 0 360 43 134 psFillArc - globalGC1 44 133 43 134 psDrawLine - globalGC1 43 132 3 3 0 360 44 133 psFillArc - globalGC1 45 132 44 133 psDrawLine - globalGC1 44 131 3 3 0 360 45 132 psFillArc - globalGC1 46 131 45 132 psDrawLine - globalGC1 45 130 3 3 0 360 46 131 psFillArc - globalGC1 48 130 46 131 psDrawLine - globalGC1 47 129 3 3 0 360 48 130 psFillArc - globalGC1 51 130 48 130 psDrawLine - globalGC1 50 129 3 3 0 360 51 130 psFillArc - globalGC1 56 129 51 130 psDrawLine - globalGC1 55 128 3 3 0 360 56 129 psFillArc - globalGC1 60 129 56 129 psDrawLine - globalGC1 59 128 3 3 0 360 60 129 psFillArc - globalGC1 65 129 60 129 psDrawLine - globalGC1 64 128 3 3 0 360 65 129 psFillArc - globalGC1 70 129 65 129 psDrawLine - globalGC1 69 128 3 3 0 360 70 129 psFillArc - globalGC1 75 129 70 129 psDrawLine - globalGC1 74 128 3 3 0 360 75 129 psFillArc - globalGC1 80 129 75 129 psDrawLine - globalGC1 79 128 3 3 0 360 80 129 psFillArc - globalGC1 84 128 80 129 psDrawLine - globalGC1 83 127 3 3 0 360 84 128 psFillArc - globalGC1 89 128 84 128 psDrawLine - globalGC1 88 127 3 3 0 360 89 128 psFillArc - globalGC1 92 128 89 128 psDrawLine - globalGC1 91 127 3 3 0 360 92 128 psFillArc - globalGC1 94 127 92 128 psDrawLine - globalGC1 93 126 3 3 0 360 94 127 psFillArc - globalGC1 95 126 94 127 psDrawLine - globalGC1 94 125 3 3 0 360 95 126 psFillArc - globalGC1 96 125 95 126 psDrawLine - globalGC1 95 124 3 3 0 360 96 125 psFillArc - globalGC1 97 124 96 125 psDrawLine - globalGC1 96 123 3 3 0 360 97 124 psFillArc - globalGC1 97 121 97 124 psDrawLine - globalGC1 96 120 3 3 0 360 97 121 psFillArc - globalGC1 98 119 97 121 psDrawLine - globalGC1 97 118 3 3 0 360 98 119 psFillArc - globalGC1 98 113 98 119 psDrawLine - globalGC1 97 112 3 3 0 360 98 113 psFillArc - globalGC1 98 108 98 113 psDrawLine - globalGC1 97 107 3 3 0 360 98 108 psFillArc - globalGC1 98 98 98 108 psDrawLine - globalGC1 97 97 3 3 0 360 98 98 psFillArc - globalGC1 98 87 98 98 psDrawLine - globalGC1 97 86 3 3 0 360 98 87 psFillArc - globalGC1 99 66 98 87 psDrawLine - globalGC1 98 65 3 3 0 360 99 66 psFillArc - globalGC1 99 45 99 66 psDrawLine - globalGC1 98 44 3 3 0 360 99 45 psFillArc - globalGC1 99 14 99 45 psDrawLine - globalGC1 98 13 3 3 0 360 99 14 psFillArc - globalGC1 11 128 3 3 0 360 12 129 psFillArc - globalGC1 12 129 12 129 psDrawLine - globalGC1 11 128 3 3 0 360 12 129 psFillArc - globalGC1 17 129 12 129 psDrawLine - globalGC1 16 128 3 3 0 360 17 129 psFillArc - globalGC1 22 129 17 129 psDrawLine - globalGC1 21 128 3 3 0 360 22 129 psFillArc - globalGC1 27 128 22 129 psDrawLine - globalGC1 26 127 3 3 0 360 27 128 psFillArc - globalGC1 32 128 27 128 psDrawLine - globalGC1 31 127 3 3 0 360 32 128 psFillArc - globalGC1 34 128 32 128 psDrawLine - globalGC1 33 127 3 3 0 360 34 128 psFillArc - globalGC1 36 127 34 128 psDrawLine - globalGC1 35 126 3 3 0 360 36 127 psFillArc - globalGC1 38 126 36 127 psDrawLine - globalGC1 37 125 3 3 0 360 38 126 psFillArc - globalGC1 39 125 38 126 psDrawLine - globalGC1 38 124 3 3 0 360 39 125 psFillArc - globalGC1 39 124 39 125 psDrawLine - globalGC1 38 123 3 3 0 360 39 124 psFillArc - globalGC1 40 121 39 124 psDrawLine - globalGC1 39 120 3 3 0 360 40 121 psFillArc - globalGC1 40 119 40 121 psDrawLine - globalGC1 39 118 3 3 0 360 40 119 psFillArc - globalGC1 41 113 40 119 psDrawLine - globalGC1 40 112 3 3 0 360 41 113 psFillArc - globalGC1 41 108 41 113 psDrawLine - globalGC1 40 107 3 3 0 360 41 108 psFillArc - globalGC1 41 98 41 108 psDrawLine - globalGC1 40 97 3 3 0 360 41 98 psFillArc - globalGC1 41 87 41 98 psDrawLine - globalGC1 40 86 3 3 0 360 41 87 psFillArc - globalGC1 41 66 41 87 psDrawLine - globalGC1 40 65 3 3 0 360 41 66 psFillArc - globalGC1 41 45 41 66 psDrawLine - globalGC1 40 44 3 3 0 360 41 45 psFillArc - globalGC1 41 14 41 45 psDrawLine - globalGC1 40 13 3 3 0 360 41 14 psFillArc - - grestore % restore graphics state - - - cleartomark %% clearing operand stack - -end %% pops mainDict from dictionary stack - -showpage - -%-------------------------- end --------------------------% diff --git a/books/ps/2doptcpr.eps b/books/ps/2doptcpr.eps new file mode 100644 index 0000000..dd8d407 --- /dev/null +++ b/books/ps/2doptcpr.eps @@ -0,0 +1,1352 @@ +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: GIMP PostScript 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a/books/ps/2doptcpr.ps +++ /dev/null @@ -1,434 +0,0 @@ -%!PS-Adobe-2.0 -%%DocumentFonts: Times-Roman -%%Creator: Axiom -%%CreationDate: today -%%Pages: 1 -%%processing (hard) limit: 250 pts or 500 values for the operand stack. -%%EndComments - -%------------------------------- prologue -------------------------------% -%-------------------------- support procedures --------------------------% - -%--------- first create user dictionary with 100 entries max ------------% -% (number can be changed to accomodate definitions) % - -100 dict begin %% using 100 entries in top level dictionary - -/FontHeight 12 def - -/inch - { 72 mul } - def - -% yVal and hVal are necessary because the Xwindow display origin -% is at the upper left corner, while the postscript display -% origin is at the lower left hand corner. - -/yVal %% get Y value -- make upper left corner origin - { maxY sub abs } %% maxY is viewWindow height - def - -/hVal %% get H value -- used for displaying title text - { maxH sub abs } %% maxH is viewWindow height+titleWindow height - def - -% loads in the font - -/loadFont - { /Times-Roman findfont FontHeight scalefont setfont } - def - -% draws a rectangle with input operand: -% height -% width -% notice that this function does not "draw" or ink the rectangle. -/drawRect - { 1 index 1 add 0 rlineto %% draw first side - 0 exch 1 add neg rlineto %% draw second side - 1 add neg 0 rlineto %% draw third side - closepath } %% draw fourth side - def - -% create a rectangle with input operand in the view window: -% y -% x -% height -% width -% notice that this function does not "draw" or ink the rectangle. -/rectangle - { yVal moveto %% set currentpoint for line - drawRect } %% draws the rectangle - def - -% These are global variables that every draw procedure uses -% THe operand should be as follows: -% viewWindow width -% viewWindow height -% title height -/setDim - { /maxX exch def %% width of display - /maxY exch def %% height of display - /titleH exch def %% height of title - /maxH maxY titleH add def %% height of display + title - } def - -%-------------------------- major procedures --------------------------% - -/title %% draws a rectangle around the title of picture - { gsave - newpath - moveto %% lower left of title - titleH 1 add 0 exch rlineto %% draw first side - 1 add 0 rlineto %% draw second side - 1 add neg 0 exch rlineto - begin installGC stroke end %% draw third side - grestore } - def - -/drawFrame %% draw display frame - { gsave - newpath - maxX maxY 0 0 rectangle - begin installGC stroke end - grestore } - def - -% updates the foreground color of existing graphics-context dictionary: -% foreground color -% dictionary name -/setForeground - { /FGcolor exch put } - def - -% updates the background color of existing graphics-context dictionary: -% background color -% dictionary name -/setBackground - { /BGcolor exch put } - def - -% updates the line width, line style, cap style, join style of -% existing graphics-context dictionary: -% dictionary name -% join style -% cap style -% line width -/setLineAttributes - { begin - /JoinStyle exch def - /CapStyle exch def - /LineWidth exch def - end } - def - -% creates a graphics context dictionary with the following information: -% /dictionary name -% foreground color -% background color -% line width -% cap style -% join style -% this creates different graphical contexts for different drawing functions. -/makeDict - { 5 dict 2 copy def begin pop %% with dict name on top of stack - /FGcolor exch def %% define drawing attributes - /BGcolor exch def %% not heavily used - /LineWidth exch def - /CapStyle exch def - /JoinStyle exch def - end } - def - -% makes the current dictionary attributes effective -% this function takes the values in the current dictionary to set the context -% these are the values currently being used: foreground, cap, join, and width -/installGC - { - FGcolor currentgray ne - {FGcolor setgray} if %% foreground color - CapStyle currentlinecap ne - {CapStyle setlinecap} if %% cap style - JoinStyle currentlinejoin ne - {JoinStyle setlinejoin} if %% join style - LineWidth currentlinewidth ne - {LineWidth setlinewidth} if } %% line width - def - -% operand stack configuration in order to use psDrawLine: -% psDrawLine -% y0 -% x0 -% y1 -% x1 -% graphics-context dictionary -% this draws a line from (x0, y0) to (x1, y1). - -/psDrawLine - { gsave - newpath - yVal moveto - yVal lineto - begin installGC stroke end - grestore } - def - -% operand stack configuration in order to use psDrawIStr: -% psDrawIStr -% window type: title or window -% string -% y -% x -% graphics-context dictionary -% it draws a text string in foreground color on top of bounding box of -% string, which is in background color. - -/psDrawIStr - { gsave - newpath %% for rectangle - loadFont - - /window exch def %% get window type - - %% draw bounding box with background color - /str exch def %% get text string - str stringwidth pop 1 sub %% width - FontHeight 1 sub %% height - currentfont begin %% get font height - FontBBox - end - /ypos exch def pop %% define ypos - neg ypos add /offset exch def pop - /offset ypos offset div FontHeight mul def %% define offset - /h exch def /w exch def %% define h - /y0 exch def %% define y0 - /x0 exch def %% define x0 - w h x0 y0 offset sub - window (title) eq - {hVal moveto drawRect} %% draws in title window - {rectangle} ifelse %% draws in view window - begin - BGcolor setgray fill %% set background box color - - x0 y0 - window (title) eq - {hVal} %% print title text - {yVal} ifelse %% print window text - moveto str - FGcolor setgray show %% set text color - end - grestore } - def - -% operand stack configuration in order to use psFillArc: -% psFillArc -% y center of rectangle -% x center of rectangle -% angle2 -% angle1 -% width -% height -% y -% x -% graphics-context dictionary -% this draws and fills an arc whose origin is at x, y, and whose width -% and height specifies the rectangle which encases the arc. -% Origin is at upper left corner of rectangle. -% This function uses "scale" to make cricles and ellipses. -/psFillArc - { gsave - newpath - yVal moveto - /sfactor 4 index 4 index div def - 1 sfactor scale - 6 5 roll %% x on top of stack - 3 index 2 div add %% define x origin - 6 5 roll %% y on top of stack - 6 5 roll %% h on top of stack - 2 div add yVal sfactor div %% define y origin - 5 4 roll %% w on top of stack - 2 div %% define radius - 5 3 roll %% a1 a2 now on top - 1 index add - arcn %% draw clockwise arc - begin installGC fill end %% fills with foreground color - grestore } - def - -%-------------------------- script --------------------------% - -% 1 inch 1 inch translate - - mark %% mark bottom of our stack - - 0 0 1 - 1072693248 0 /globalGC1 makeDict - 0 0 1 - 1072693248 0 /globalGC2 makeDict - 0 0 1 - 1072693248 0 /trashGC makeDict - 0 0 1 - 1072693248 0 /globGC makeDict - 0 0 1 - 1072693248 0 /anotherGC makeDict - 0 0 1 - 1072693248 0 /graphGC makeDict - 0 0 1 - 1072693248 0 /unitGC makeDict - - gsave % save graphics state for clipping path - - 1.000000 1.000000 scale - - 24 303 300 setDim - maxX maxY 0 0 rectangle clip % set clip path - - globalGC1 300 151 0 151 psDrawLine - globalGC1 149 303 149 0 psDrawLine - unitGC 150 153 150 149 psDrawLine - unitGC 138 166 (0.00) (window) psDrawIStr - unitGC 190 153 190 149 psDrawLine - unitGC 178 166 (2.00) (window) psDrawIStr - unitGC 230 153 230 149 psDrawLine - unitGC 218 166 (4.00) (window) psDrawIStr - unitGC 270 153 270 149 psDrawLine - unitGC 258 166 (6.00) (window) psDrawIStr - unitGC 106 153 106 149 psDrawLine - unitGC 91 166 (-2.00) (window) psDrawIStr - unitGC 62 153 62 149 psDrawLine - unitGC 47 166 (-4.00) (window) psDrawIStr - unitGC 18 153 18 149 psDrawLine - unitGC 3 166 (-6.00) (window) psDrawIStr - unitGC 151 107 147 107 psDrawLine - unitGC 113 112 (1.00) (window) psDrawIStr - unitGC 151 63 147 63 psDrawLine - unitGC 113 68 (2.00) (window) psDrawIStr - unitGC 151 19 147 19 psDrawLine - unitGC 113 24 (3.00) (window) psDrawIStr - unitGC 151 195 147 195 psDrawLine - unitGC 104 200 (-1.00) (window) psDrawIStr - unitGC 151 238 147 238 psDrawLine - unitGC 104 243 (-2.00) (window) psDrawIStr - unitGC 151 281 147 281 psDrawLine - unitGC 104 286 (-3.00) (window) psDrawIStr - globalGC1 260 12 3 3 0 360 261 13 psFillArc - globalGC1 261 13 261 13 psDrawLine - globalGC1 260 12 3 3 0 360 261 13 psFillArc - globalGC1 262 36 261 13 psDrawLine - globalGC1 261 35 3 3 0 360 262 36 psFillArc - globalGC1 265 63 262 36 psDrawLine - globalGC1 264 62 3 3 0 360 265 63 psFillArc - globalGC1 270 89 265 63 psDrawLine - globalGC1 269 88 3 3 0 360 270 89 psFillArc - globalGC1 276 100 270 89 psDrawLine - globalGC1 275 99 3 3 0 360 276 100 psFillArc - globalGC1 282 105 276 100 psDrawLine - globalGC1 281 104 3 3 0 360 282 105 psFillArc - globalGC1 288 107 282 105 psDrawLine - globalGC1 287 106 3 3 0 360 288 107 psFillArc - globalGC1 190 288 3 3 0 360 191 289 psFillArc - globalGC1 191 289 191 289 psDrawLine - globalGC1 190 288 3 3 0 360 191 289 psFillArc - globalGC1 193 266 191 289 psDrawLine - globalGC1 192 265 3 3 0 360 193 266 psFillArc - globalGC1 196 239 193 266 psDrawLine - globalGC1 195 238 3 3 0 360 196 239 psFillArc - globalGC1 201 213 196 239 psDrawLine - globalGC1 200 212 3 3 0 360 201 213 psFillArc - globalGC1 207 202 201 213 psDrawLine - globalGC1 206 201 3 3 0 360 207 202 psFillArc - globalGC1 213 197 207 202 psDrawLine - globalGC1 212 196 3 3 0 360 213 197 psFillArc - globalGC1 219 195 213 197 psDrawLine - globalGC1 218 194 3 3 0 360 219 195 psFillArc - globalGC1 224 197 219 195 psDrawLine - globalGC1 223 196 3 3 0 360 224 197 psFillArc - globalGC1 230 202 224 197 psDrawLine - globalGC1 229 201 3 3 0 360 230 202 psFillArc - globalGC1 236 213 230 202 psDrawLine - globalGC1 235 212 3 3 0 360 236 213 psFillArc - globalGC1 242 239 236 213 psDrawLine - globalGC1 241 238 3 3 0 360 242 239 psFillArc - globalGC1 244 266 242 239 psDrawLine - globalGC1 243 265 3 3 0 360 244 266 psFillArc - globalGC1 246 289 244 266 psDrawLine - globalGC1 245 288 3 3 0 360 246 289 psFillArc - globalGC1 121 12 3 3 0 360 122 13 psFillArc - globalGC1 122 13 122 13 psDrawLine - globalGC1 121 12 3 3 0 360 122 13 psFillArc - globalGC1 124 36 122 13 psDrawLine - globalGC1 123 35 3 3 0 360 124 36 psFillArc - globalGC1 126 63 124 36 psDrawLine - globalGC1 125 62 3 3 0 360 126 63 psFillArc - globalGC1 132 89 126 63 psDrawLine - globalGC1 131 88 3 3 0 360 132 89 psFillArc - globalGC1 138 100 132 89 psDrawLine - globalGC1 137 99 3 3 0 360 138 100 psFillArc - globalGC1 144 105 138 100 psDrawLine - globalGC1 143 104 3 3 0 360 144 105 psFillArc - globalGC1 149 107 144 105 psDrawLine - globalGC1 148 106 3 3 0 360 149 107 psFillArc - globalGC1 155 105 149 107 psDrawLine - globalGC1 154 104 3 3 0 360 155 105 psFillArc - globalGC1 161 100 155 105 psDrawLine - globalGC1 160 99 3 3 0 360 161 100 psFillArc - globalGC1 167 89 161 100 psDrawLine - globalGC1 166 88 3 3 0 360 167 89 psFillArc - globalGC1 173 63 167 89 psDrawLine - globalGC1 172 62 3 3 0 360 173 63 psFillArc - globalGC1 175 36 173 63 psDrawLine - globalGC1 174 35 3 3 0 360 175 36 psFillArc - globalGC1 177 13 175 36 psDrawLine - globalGC1 176 12 3 3 0 360 177 13 psFillArc - globalGC1 52 288 3 3 0 360 53 289 psFillArc - globalGC1 53 289 53 289 psDrawLine - globalGC1 52 288 3 3 0 360 53 289 psFillArc - globalGC1 55 266 53 289 psDrawLine - globalGC1 54 265 3 3 0 360 55 266 psFillArc - globalGC1 57 239 55 266 psDrawLine - globalGC1 56 238 3 3 0 360 57 239 psFillArc - globalGC1 63 213 57 239 psDrawLine - globalGC1 62 212 3 3 0 360 63 213 psFillArc - globalGC1 69 202 63 213 psDrawLine - globalGC1 68 201 3 3 0 360 69 202 psFillArc - globalGC1 75 197 69 202 psDrawLine - globalGC1 74 196 3 3 0 360 75 197 psFillArc - globalGC1 80 195 75 197 psDrawLine - globalGC1 79 194 3 3 0 360 80 195 psFillArc - globalGC1 86 197 80 195 psDrawLine - globalGC1 85 196 3 3 0 360 86 197 psFillArc - globalGC1 92 202 86 197 psDrawLine - globalGC1 91 201 3 3 0 360 92 202 psFillArc - globalGC1 98 213 92 202 psDrawLine - globalGC1 97 212 3 3 0 360 98 213 psFillArc - globalGC1 103 239 98 213 psDrawLine - globalGC1 102 238 3 3 0 360 103 239 psFillArc - globalGC1 106 266 103 239 psDrawLine - globalGC1 105 265 3 3 0 360 106 266 psFillArc - globalGC1 108 289 106 266 psDrawLine - globalGC1 107 288 3 3 0 360 108 289 psFillArc - globalGC1 10 106 3 3 0 360 11 107 psFillArc - globalGC1 11 107 11 107 psDrawLine - globalGC1 10 106 3 3 0 360 11 107 psFillArc - globalGC1 17 105 11 107 psDrawLine - globalGC1 16 104 3 3 0 360 17 105 psFillArc - globalGC1 23 100 17 105 psDrawLine - globalGC1 22 99 3 3 0 360 23 100 psFillArc - globalGC1 29 89 23 100 psDrawLine - globalGC1 28 88 3 3 0 360 29 89 psFillArc - globalGC1 34 63 29 89 psDrawLine - globalGC1 33 62 3 3 0 360 34 63 psFillArc - globalGC1 37 36 34 63 psDrawLine - globalGC1 36 35 3 3 0 360 37 36 psFillArc - globalGC1 38 13 37 36 psDrawLine - globalGC1 37 12 3 3 0 360 38 13 psFillArc - - grestore % restore graphics state - - - cleartomark %% clearing operand stack - -end %% pops mainDict from dictionary stack - -showpage - -%-------------------------- end --------------------------% diff --git a/books/ps/2doptcvc.eps b/books/ps/2doptcvc.eps new file mode 100644 index 0000000..122c4de --- /dev/null +++ b/books/ps/2doptcvc.eps @@ -0,0 +1,1172 @@ +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: GIMP PostScript file plugin V 1.17 by Peter Kirchgessner +%%Title: 2doptcvc.eps +%%CreationDate: Thu Mar 28 17:02:06 2013 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%Pages: 1 +%%BoundingBox: 14 14 276 287 +%%EndComments +%%BeginProlog +% Use own dictionary to avoid conflicts +10 dict begin +%%EndProlog +%%Page: 1 1 +% Translate for offset +14.173228346456694 14.173228346456694 translate +% Translate to begin of first scanline +0 272.15409644042427 translate +261.35433070866145 -272.15409644042427 scale +% Image geometry +363 378 8 +% Transformation matrix +[ 363 0 0 378 0 0 ] +% 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-%%EndComments - -%------------------------------- prologue -------------------------------% -%-------------------------- support procedures --------------------------% - -%--------- first create user dictionary with 100 entries max ------------% -% (number can be changed to accomodate definitions) % - -100 dict begin %% using 100 entries in top level dictionary - -/FontHeight 12 def - -/inch - { 72 mul } - def - -% yVal and hVal are necessary because the Xwindow display origin -% is at the upper left corner, while the postscript display -% origin is at the lower left hand corner. - -/yVal %% get Y value -- make upper left corner origin - { maxY sub abs } %% maxY is viewWindow height - def - -/hVal %% get H value -- used for displaying title text - { maxH sub abs } %% maxH is viewWindow height+titleWindow height - def - -% loads in the font - -/loadFont - { /Times-Roman findfont FontHeight scalefont setfont } - def - -% draws a rectangle with input operand: -% height -% width -% notice that this function does not "draw" or ink the rectangle. -/drawRect - { 1 index 1 add 0 rlineto %% draw first side - 0 exch 1 add neg rlineto %% draw second side - 1 add neg 0 rlineto %% draw third side - closepath } %% draw fourth side - def - -% create a rectangle with input operand in the view window: -% y -% x -% height -% width -% notice that this function does not "draw" or ink the rectangle. -/rectangle - { yVal moveto %% set currentpoint for line - drawRect } %% draws the rectangle - def - -% These are global variables that every draw procedure uses -% THe operand should be as follows: -% viewWindow width -% viewWindow height -% title height -/setDim - { /maxX exch def %% width of display - /maxY exch def %% height of display - /titleH exch def %% height of title - /maxH maxY titleH add def %% height of display + title - } def - -%-------------------------- major procedures --------------------------% - -/title %% draws a rectangle around the title of picture - { gsave - newpath - moveto %% lower left of title - titleH 1 add 0 exch rlineto %% draw first side - 1 add 0 rlineto %% draw second side - 1 add neg 0 exch rlineto - begin installGC stroke end %% draw third side - grestore } - def - -/drawFrame %% draw display frame - { gsave - newpath - maxX maxY 0 0 rectangle - begin installGC stroke end - grestore } - def - -% updates the foreground color of existing graphics-context dictionary: -% foreground color -% dictionary name -/setForeground - { /FGcolor exch put } - def - -% updates the background color of existing graphics-context dictionary: -% background color -% dictionary name -/setBackground - { /BGcolor exch put } - def - -% updates the line width, line style, cap style, join style of -% existing graphics-context dictionary: -% dictionary name -% join style -% cap style -% line width -/setLineAttributes - { begin - /JoinStyle exch def - /CapStyle exch def - /LineWidth exch def - end } - def - -% creates a graphics context dictionary with the following information: -% /dictionary name -% foreground color -% background color -% line width -% cap style -% join style -% this creates different graphical contexts for different drawing functions. -/makeDict - { 5 dict 2 copy def begin pop %% with dict name on top of stack - /FGcolor exch def %% define drawing attributes - /BGcolor exch def %% not heavily used - /LineWidth exch def - /CapStyle exch def - /JoinStyle exch def - end } - def - -% makes the current dictionary attributes effective -% this function takes the values in the current dictionary to set the context -% these are the values currently being used: foreground, cap, join, and width -/installGC - { - FGcolor currentgray ne - {FGcolor setgray} if %% foreground color - CapStyle currentlinecap ne - {CapStyle setlinecap} if %% cap style - JoinStyle currentlinejoin ne - {JoinStyle setlinejoin} if %% join style - LineWidth currentlinewidth ne - {LineWidth setlinewidth} if } %% line width - def - -% operand stack configuration in order to use psDrawLine: -% psDrawLine -% y0 -% x0 -% y1 -% x1 -% graphics-context dictionary -% this draws a line from (x0, y0) to (x1, y1). - -/psDrawLine - { gsave - newpath - yVal moveto - yVal lineto - begin installGC stroke end - grestore } - def - -% operand stack configuration in order to use psFillArc: -% psFillArc -% y center of rectangle -% x center of rectangle -% angle2 -% angle1 -% width -% height -% y -% x -% graphics-context dictionary -% this draws and fills an arc whose origin is at x, y, and whose width -% and height specifies the rectangle which encases the arc. -% Origin is at upper left corner of rectangle. -% This function uses "scale" to make cricles and ellipses. -/psFillArc - { gsave - newpath - yVal moveto - /sfactor 4 index 4 index div def - 1 sfactor scale - 6 5 roll %% x on top of stack - 3 index 2 div add %% define x origin - 6 5 roll %% y on top of stack - 6 5 roll %% h on top of stack - 2 div add yVal sfactor div %% define y origin - 5 4 roll %% w on top of stack - 2 div %% define radius - 5 3 roll %% a1 a2 now on top - 1 index add - arcn %% draw clockwise arc - begin installGC fill end %% fills with foreground color - grestore } - def - -%-------------------------- script --------------------------% - -% 1 inch 1 inch translate - - mark %% mark bottom of our stack - - 0 0 1 - 1072693248 0 /globalGC1 makeDict - 0 0 1 - 1072693248 0 /globalGC2 makeDict - 0 0 1 - 1072693248 0 /trashGC makeDict - 0 0 1 - 1072693248 0 /globGC makeDict - 0 0 1 - 1072693248 0 /anotherGC makeDict - 0 0 1 - 1072693248 0 /graphGC makeDict - 0 0 1 - 1072693248 0 /unitGC makeDict - - gsave % save graphics state for clipping path - - 24 259 256 setDim - maxX maxY 0 0 rectangle clip % set clip path - - globalGC1 256 129 0 129 psDrawLine - globalGC1 127 259 127 0 psDrawLine - globalGC1 11 128 3 3 0 360 12 129 psFillArc - globalGC1 12 129 12 129 psDrawLine - globalGC1 11 128 3 3 0 360 12 129 psFillArc - globalGC1 17 144 12 129 psDrawLine - globalGC1 16 143 3 3 0 360 17 144 psFillArc - globalGC1 22 159 17 144 psDrawLine - globalGC1 21 158 3 3 0 360 22 159 psFillArc - globalGC1 27 173 22 159 psDrawLine - globalGC1 26 172 3 3 0 360 27 173 psFillArc - globalGC1 32 187 27 173 psDrawLine - globalGC1 31 186 3 3 0 360 32 187 psFillArc - globalGC1 36 199 32 187 psDrawLine - globalGC1 35 198 3 3 0 360 36 199 psFillArc - globalGC1 41 210 36 199 psDrawLine - globalGC1 40 209 3 3 0 360 41 210 psFillArc - globalGC1 46 220 41 210 psDrawLine - globalGC1 45 219 3 3 0 360 46 220 psFillArc - globalGC1 51 229 46 220 psDrawLine - globalGC1 50 228 3 3 0 360 51 229 psFillArc - globalGC1 56 235 51 229 psDrawLine - globalGC1 55 234 3 3 0 360 56 235 psFillArc - globalGC1 60 240 56 235 psDrawLine - globalGC1 59 239 3 3 0 360 60 240 psFillArc - globalGC1 63 242 60 240 psDrawLine - globalGC1 62 241 3 3 0 360 63 242 psFillArc - globalGC1 65 243 63 242 psDrawLine - globalGC1 64 242 3 3 0 360 65 243 psFillArc - globalGC1 68 244 65 243 psDrawLine - globalGC1 67 243 3 3 0 360 68 244 psFillArc - globalGC1 70 244 68 244 psDrawLine - globalGC1 69 243 3 3 0 360 70 244 psFillArc - globalGC1 72 244 70 244 psDrawLine - globalGC1 71 243 3 3 0 360 72 244 psFillArc - globalGC1 75 243 72 244 psDrawLine - globalGC1 74 242 3 3 0 360 75 243 psFillArc - globalGC1 77 242 75 243 psDrawLine - globalGC1 76 241 3 3 0 360 77 242 psFillArc - globalGC1 80 240 77 242 psDrawLine - globalGC1 79 239 3 3 0 360 80 240 psFillArc - globalGC1 84 235 80 240 psDrawLine - globalGC1 83 234 3 3 0 360 84 235 psFillArc - globalGC1 89 229 84 235 psDrawLine - globalGC1 88 228 3 3 0 360 89 229 psFillArc - globalGC1 94 220 89 229 psDrawLine - globalGC1 93 219 3 3 0 360 94 220 psFillArc - globalGC1 99 210 94 220 psDrawLine - globalGC1 98 209 3 3 0 360 99 210 psFillArc - globalGC1 104 199 99 210 psDrawLine - globalGC1 103 198 3 3 0 360 104 199 psFillArc - globalGC1 108 187 104 199 psDrawLine - globalGC1 107 186 3 3 0 360 108 187 psFillArc - globalGC1 113 173 108 187 psDrawLine - globalGC1 112 172 3 3 0 360 113 173 psFillArc - globalGC1 118 159 113 173 psDrawLine - globalGC1 117 158 3 3 0 360 118 159 psFillArc - globalGC1 123 144 118 159 psDrawLine - globalGC1 122 143 3 3 0 360 123 144 psFillArc - globalGC1 127 129 123 144 psDrawLine - globalGC1 126 128 3 3 0 360 127 129 psFillArc - globalGC1 132 114 127 129 psDrawLine - globalGC1 131 113 3 3 0 360 132 114 psFillArc - globalGC1 137 99 132 114 psDrawLine - globalGC1 136 98 3 3 0 360 137 99 psFillArc - globalGC1 142 85 137 99 psDrawLine - globalGC1 141 84 3 3 0 360 142 85 psFillArc - globalGC1 147 71 142 85 psDrawLine - globalGC1 146 70 3 3 0 360 147 71 psFillArc - globalGC1 151 59 147 71 psDrawLine - globalGC1 150 58 3 3 0 360 151 59 psFillArc - globalGC1 156 48 151 59 psDrawLine - globalGC1 155 47 3 3 0 360 156 48 psFillArc - globalGC1 161 38 156 48 psDrawLine - globalGC1 160 37 3 3 0 360 161 38 psFillArc - globalGC1 166 29 161 38 psDrawLine - globalGC1 165 28 3 3 0 360 166 29 psFillArc - globalGC1 171 23 166 29 psDrawLine - globalGC1 170 22 3 3 0 360 171 23 psFillArc - globalGC1 175 18 171 23 psDrawLine - globalGC1 174 17 3 3 0 360 175 18 psFillArc - globalGC1 178 16 175 18 psDrawLine - globalGC1 177 15 3 3 0 360 178 16 psFillArc - globalGC1 180 15 178 16 psDrawLine - globalGC1 179 14 3 3 0 360 180 15 psFillArc - globalGC1 183 14 180 15 psDrawLine - globalGC1 182 13 3 3 0 360 183 14 psFillArc - globalGC1 185 14 183 14 psDrawLine - globalGC1 184 13 3 3 0 360 185 14 psFillArc - globalGC1 187 14 185 14 psDrawLine - globalGC1 186 13 3 3 0 360 187 14 psFillArc - globalGC1 190 15 187 14 psDrawLine - globalGC1 189 14 3 3 0 360 190 15 psFillArc - globalGC1 192 16 190 15 psDrawLine - globalGC1 191 15 3 3 0 360 192 16 psFillArc - globalGC1 195 18 192 16 psDrawLine - globalGC1 194 17 3 3 0 360 195 18 psFillArc - globalGC1 199 23 195 18 psDrawLine - globalGC1 198 22 3 3 0 360 199 23 psFillArc - globalGC1 204 29 199 23 psDrawLine - globalGC1 203 28 3 3 0 360 204 29 psFillArc - globalGC1 209 38 204 29 psDrawLine - globalGC1 208 37 3 3 0 360 209 38 psFillArc - globalGC1 214 48 209 38 psDrawLine - globalGC1 213 47 3 3 0 360 214 48 psFillArc - globalGC1 219 59 214 48 psDrawLine - globalGC1 218 58 3 3 0 360 219 59 psFillArc - globalGC1 223 71 219 59 psDrawLine - globalGC1 222 70 3 3 0 360 223 71 psFillArc - globalGC1 228 85 223 71 psDrawLine - globalGC1 227 84 3 3 0 360 228 85 psFillArc - globalGC1 233 99 228 85 psDrawLine - globalGC1 232 98 3 3 0 360 233 99 psFillArc - globalGC1 238 114 233 99 psDrawLine - globalGC1 237 113 3 3 0 360 238 114 psFillArc - globalGC1 243 129 238 114 psDrawLine - globalGC1 242 128 3 3 0 360 243 129 psFillArc - - grestore % restore graphics state - - - cleartomark %% clearing operand stack - -end %% pops mainDict from dictionary stack - -showpage - -%-------------------------- end --------------------------% diff --git a/books/ps/2doptplr.eps b/books/ps/2doptplr.eps new file mode 100644 index 0000000..7bb04bf --- /dev/null +++ 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+showpage +%%Trailer +end +%%EOF diff --git a/books/ps/2doptplr.ps b/books/ps/2doptplr.ps deleted file mode 100644 index 553c212..0000000 --- a/books/ps/2doptplr.ps +++ /dev/null @@ -1,795 +0,0 @@ -%!IBM Personal Pageprinter (4216) Adapter Program V1.0 -%%DocumentFonts: Times-Roman -%%Creator: Axiom -%%CreationDate: today -%%Pages: 1 -%%processing (hard) limit: 250 pts or 500 values for the operand stack. -%%EndComments - -%------------------------------- prologue -------------------------------% -%-------------------------- support procedures --------------------------% - -%--------- first create user dictionary with 100 entries max ------------% -% (number can be changed to accomodate definitions) % - -100 dict begin %% using 100 entries in top level dictionary - -/FontHeight 12 def - -/inch - { 72 mul } - def - -% yVal and hVal are necessary because the Xwindow display origin -% is at the upper left corner, while the postscript display -% origin is at the lower left hand corner. - -/yVal %% get Y value -- make upper left corner origin - { maxY sub abs } %% maxY is viewWindow height - def - -/hVal %% get H value -- used for displaying title text - { maxH sub abs } %% maxH is viewWindow height+titleWindow height - def - -% loads in the font - -/loadFont - { /Times-Roman findfont FontHeight scalefont setfont } - def - -% draws a rectangle with input operand: -% height -% width -% notice that this function does not "draw" or ink the rectangle. -/drawRect - { 1 index 1 add 0 rlineto %% draw first side - 0 exch 1 add neg rlineto %% draw second side - 1 add neg 0 rlineto %% draw third side - closepath } %% draw fourth side - def - -% create a rectangle with input operand in the view window: -% y -% x -% height -% width -% notice that this function does not "draw" or ink the rectangle. -/rectangle - { yVal moveto %% set currentpoint for line - drawRect } %% draws the rectangle - def - -% These are global variables that every draw procedure uses -% THe operand should be as follows: -% viewWindow width -% viewWindow height -% title height -/setDim - { /maxX exch def %% width of display - /maxY exch def %% height of display - /titleH exch def %% height of title - /maxH maxY titleH add def %% height of display + title - } def - -%-------------------------- major procedures --------------------------% - -/title %% draws a rectangle around the title of picture - { gsave - newpath - moveto %% lower left of title - titleH 1 add 0 exch rlineto %% draw first side - 1 add 0 rlineto %% draw second side - 1 add neg 0 exch rlineto - begin installGC stroke end %% draw third side - grestore } - def - -/drawFrame %% draw display frame - { gsave - newpath - maxX maxY 0 0 rectangle - begin installGC stroke end - grestore } - def - -% updates the foreground color of existing graphics-context dictionary: -% foreground color -% dictionary name -/setForeground - { /FGcolor exch put } - def - -% updates the background color of existing graphics-context dictionary: -% background color -% dictionary name -/setBackground - { /BGcolor exch put } - def - -% updates the line width, line style, cap style, join style of -% existing graphics-context dictionary: -% dictionary name -% join style -% cap style -% line width -/setLineAttributes - { begin - /JoinStyle exch def - /CapStyle exch def - /LineWidth exch def - end } - def - -% creates a graphics context dictionary with the following information: -% /dictionary name -% foreground color -% background color -% line width -% cap style -% join style -% this creates different graphical contexts for different drawing functions. -/makeDict - { 5 dict 2 copy def begin pop %% with dict name on top of stack - /FGcolor exch def %% define drawing attributes - /BGcolor exch def %% not heavily used - /LineWidth exch def - /CapStyle exch def - /JoinStyle exch def - end } - def - -% makes the current dictionary attributes effective -% this function takes the values in the current dictionary to set the context -% these are the values currently being used: foreground, cap, join, and width -/installGC - { - FGcolor currentgray ne - {FGcolor setgray} if %% foreground color - CapStyle currentlinecap ne - {CapStyle setlinecap} if %% cap style - JoinStyle currentlinejoin ne - {JoinStyle setlinejoin} if %% join style - LineWidth currentlinewidth ne - {LineWidth setlinewidth} if } %% line width - def - -% operand stack configuration in order to use psDrawLine: -% psDrawLine -% y0 -% x0 -% y1 -% x1 -% graphics-context dictionary -% this draws a line from (x0, y0) to (x1, y1). - -/psDrawLine - { gsave - newpath - yVal moveto - yVal lineto - begin installGC stroke end - grestore } - def - -% operand stack configuration in order to use psFillArc: -% psFillArc -% y center of rectangle -% x center of rectangle -% angle2 -% angle1 -% width -% height -% y -% x -% graphics-context dictionary -% this draws and fills an arc whose origin is at x, y, and whose width -% and height specifies the rectangle which encases the arc. -% Origin is at upper left corner of rectangle. -% This function uses "scale" to make cricles and ellipses. -/psFillArc - { gsave - newpath - yVal moveto - /sfactor 4 index 4 index div def - 1 sfactor scale - 6 5 roll %% x on top of stack - 3 index 2 div add %% define x origin - 6 5 roll %% y on top of stack - 6 5 roll %% h on top of stack - 2 div add yVal sfactor div %% define y origin - 5 4 roll %% w on top of stack - 2 div %% define radius - 5 3 roll %% a1 a2 now on top - 1 index add - arcn %% draw clockwise arc - begin installGC fill end %% fills with foreground color - grestore } - def - -%-------------------------- script --------------------------% - -% 1 inch 1 inch translate - - mark %% mark bottom of our stack - - 0 0 1 - 1072693248 0 /globalGC1 makeDict - 0 0 1 - 1072693248 0 /globalGC2 makeDict - 0 0 1 - 1072693248 0 /trashGC makeDict - 0 0 1 - 1072693248 0 /globGC makeDict - 0 0 1 - 1072693248 0 /anotherGC makeDict - 0 0 1 - 1072693248 0 /graphGC makeDict - 0 0 1 - 1072693248 0 /unitGC makeDict - - gsave % save graphics state for clipping path - - 24 259 256 setDim - maxX maxY 0 0 rectangle clip % set clip path - - globalGC1 256 141 0 141 psDrawLine - globalGC1 128 259 128 0 psDrawLine - globalGC1 127 140 3 3 0 360 128 141 psFillArc - globalGC1 128 141 128 141 psDrawLine - globalGC1 127 140 3 3 0 360 128 141 psFillArc - globalGC1 147 140 128 141 psDrawLine - globalGC1 146 139 3 3 0 360 147 140 psFillArc - globalGC1 166 138 147 140 psDrawLine - globalGC1 165 137 3 3 0 360 166 138 psFillArc - globalGC1 184 135 166 138 psDrawLine - globalGC1 183 134 3 3 0 360 184 135 psFillArc - globalGC1 200 131 184 135 psDrawLine - globalGC1 199 130 3 3 0 360 200 131 psFillArc - globalGC1 215 126 200 131 psDrawLine - globalGC1 214 125 3 3 0 360 215 126 psFillArc - globalGC1 226 120 215 126 psDrawLine - globalGC1 225 119 3 3 0 360 226 120 psFillArc - globalGC1 235 114 226 120 psDrawLine - globalGC1 234 113 3 3 0 360 235 114 psFillArc - globalGC1 238 112 235 114 psDrawLine - globalGC1 237 111 3 3 0 360 238 112 psFillArc - globalGC1 240 109 238 112 psDrawLine - globalGC1 239 108 3 3 0 360 240 109 psFillArc - globalGC1 242 106 240 109 psDrawLine - globalGC1 241 105 3 3 0 360 242 106 psFillArc - globalGC1 242 105 242 106 psDrawLine - globalGC1 241 104 3 3 0 360 242 105 psFillArc - globalGC1 243 104 242 105 psDrawLine - globalGC1 242 103 3 3 0 360 243 104 psFillArc - globalGC1 243 103 243 104 psDrawLine - globalGC1 242 102 3 3 0 360 243 103 psFillArc - globalGC1 243 102 243 103 psDrawLine - globalGC1 242 101 3 3 0 360 243 102 psFillArc - globalGC1 242 101 243 102 psDrawLine - globalGC1 241 100 3 3 0 360 242 101 psFillArc - globalGC1 242 100 242 101 psDrawLine - globalGC1 241 99 3 3 0 360 242 100 psFillArc - globalGC1 241 99 242 100 psDrawLine - globalGC1 240 98 3 3 0 360 241 99 psFillArc - globalGC1 240 98 241 99 psDrawLine - globalGC1 239 97 3 3 0 360 240 98 psFillArc - globalGC1 238 97 240 98 psDrawLine - globalGC1 237 96 3 3 0 360 238 97 psFillArc - globalGC1 235 96 238 97 psDrawLine - globalGC1 234 95 3 3 0 360 235 96 psFillArc - globalGC1 231 96 235 96 psDrawLine - globalGC1 230 95 3 3 0 360 231 96 psFillArc - globalGC1 221 96 231 96 psDrawLine - globalGC1 220 95 3 3 0 360 221 96 psFillArc - globalGC1 209 98 221 96 psDrawLine - globalGC1 208 97 3 3 0 360 209 98 psFillArc - globalGC1 180 109 209 98 psDrawLine - globalGC1 179 108 3 3 0 360 180 109 psFillArc - globalGC1 164 117 180 109 psDrawLine - globalGC1 163 116 3 3 0 360 164 117 psFillArc - globalGC1 147 127 164 117 psDrawLine - globalGC1 146 126 3 3 0 360 147 127 psFillArc - globalGC1 131 138 147 127 psDrawLine - globalGC1 130 137 3 3 0 360 131 138 psFillArc - globalGC1 115 151 131 138 psDrawLine - globalGC1 114 150 3 3 0 360 115 151 psFillArc - globalGC1 100 164 115 151 psDrawLine - globalGC1 99 163 3 3 0 360 100 164 psFillArc - globalGC1 87 178 100 164 psDrawLine - globalGC1 86 177 3 3 0 360 87 178 psFillArc - globalGC1 76 191 87 178 psDrawLine - globalGC1 75 190 3 3 0 360 76 191 psFillArc - globalGC1 67 204 76 191 psDrawLine - globalGC1 66 203 3 3 0 360 67 204 psFillArc - globalGC1 60 216 67 204 psDrawLine - globalGC1 59 215 3 3 0 360 60 216 psFillArc - globalGC1 56 226 60 216 psDrawLine - globalGC1 55 225 3 3 0 360 56 226 psFillArc - globalGC1 55 231 56 226 psDrawLine - globalGC1 54 230 3 3 0 360 55 231 psFillArc - globalGC1 54 234 55 231 psDrawLine - globalGC1 53 233 3 3 0 360 54 234 psFillArc - globalGC1 54 238 54 234 psDrawLine - globalGC1 53 237 3 3 0 360 54 238 psFillArc - globalGC1 54 239 54 238 psDrawLine - globalGC1 53 238 3 3 0 360 54 239 psFillArc - globalGC1 55 240 54 239 psDrawLine - globalGC1 54 239 3 3 0 360 55 240 psFillArc - globalGC1 55 241 55 240 psDrawLine - globalGC1 54 240 3 3 0 360 55 241 psFillArc - globalGC1 56 242 55 241 psDrawLine - globalGC1 55 241 3 3 0 360 56 242 psFillArc - globalGC1 56 243 56 242 psDrawLine - globalGC1 55 242 3 3 0 360 56 243 psFillArc - globalGC1 57 244 56 243 psDrawLine - globalGC1 56 243 3 3 0 360 57 244 psFillArc - globalGC1 58 244 57 244 psDrawLine - globalGC1 57 243 3 3 0 360 58 244 psFillArc - globalGC1 59 244 58 244 psDrawLine - globalGC1 58 243 3 3 0 360 59 244 psFillArc - globalGC1 60 244 59 244 psDrawLine - globalGC1 59 243 3 3 0 360 60 244 psFillArc - globalGC1 62 244 60 244 psDrawLine - globalGC1 61 243 3 3 0 360 62 244 psFillArc - globalGC1 65 243 62 244 psDrawLine - globalGC1 64 242 3 3 0 360 65 243 psFillArc - globalGC1 68 241 65 243 psDrawLine - globalGC1 67 240 3 3 0 360 68 241 psFillArc - globalGC1 75 236 68 241 psDrawLine - globalGC1 74 235 3 3 0 360 75 236 psFillArc - globalGC1 92 216 75 236 psDrawLine - globalGC1 91 215 3 3 0 360 92 216 psFillArc - globalGC1 101 202 92 216 psDrawLine - globalGC1 100 201 3 3 0 360 101 202 psFillArc - globalGC1 110 185 101 202 psDrawLine - globalGC1 109 184 3 3 0 360 110 185 psFillArc - globalGC1 118 168 110 185 psDrawLine - globalGC1 117 167 3 3 0 360 118 168 psFillArc - globalGC1 125 148 118 168 psDrawLine - globalGC1 124 147 3 3 0 360 125 148 psFillArc - globalGC1 131 129 125 148 psDrawLine - globalGC1 130 128 3 3 0 360 131 129 psFillArc - globalGC1 136 109 131 129 psDrawLine - globalGC1 135 108 3 3 0 360 136 109 psFillArc - globalGC1 139 90 136 109 psDrawLine - globalGC1 138 89 3 3 0 360 139 90 psFillArc - globalGC1 141 71 139 90 psDrawLine - globalGC1 140 70 3 3 0 360 141 71 psFillArc - globalGC1 140 41 141 71 psDrawLine - globalGC1 139 40 3 3 0 360 140 41 psFillArc - globalGC1 138 29 140 41 psDrawLine - globalGC1 137 28 3 3 0 360 138 29 psFillArc - globalGC1 137 25 138 29 psDrawLine - globalGC1 136 24 3 3 0 360 137 25 psFillArc - globalGC1 135 21 137 25 psDrawLine - globalGC1 134 20 3 3 0 360 135 21 psFillArc - globalGC1 133 18 135 21 psDrawLine - globalGC1 132 17 3 3 0 360 133 18 psFillArc - globalGC1 132 17 133 18 psDrawLine - globalGC1 131 16 3 3 0 360 132 17 psFillArc - globalGC1 131 16 132 17 psDrawLine - globalGC1 130 15 3 3 0 360 131 16 psFillArc - globalGC1 130 15 131 16 psDrawLine - globalGC1 129 14 3 3 0 360 130 15 psFillArc - globalGC1 129 14 130 15 psDrawLine - globalGC1 128 13 3 3 0 360 129 14 psFillArc - globalGC1 128 14 129 14 psDrawLine - globalGC1 127 13 3 3 0 360 128 14 psFillArc - globalGC1 128 14 128 14 psDrawLine - globalGC1 127 13 3 3 0 360 128 14 psFillArc - globalGC1 127 14 128 14 psDrawLine - globalGC1 126 13 3 3 0 360 127 14 psFillArc - globalGC1 126 14 127 14 psDrawLine - globalGC1 125 13 3 3 0 360 126 14 psFillArc - globalGC1 125 15 126 14 psDrawLine - globalGC1 124 14 3 3 0 360 125 15 psFillArc - globalGC1 124 16 125 15 psDrawLine - globalGC1 123 15 3 3 0 360 124 16 psFillArc - globalGC1 123 17 124 16 psDrawLine - globalGC1 122 16 3 3 0 360 123 17 psFillArc - globalGC1 122 18 123 17 psDrawLine - globalGC1 121 17 3 3 0 360 122 18 psFillArc - globalGC1 120 21 122 18 psDrawLine - globalGC1 119 20 3 3 0 360 120 21 psFillArc - globalGC1 118 25 120 21 psDrawLine - globalGC1 117 24 3 3 0 360 118 25 psFillArc - globalGC1 117 29 118 25 psDrawLine - globalGC1 116 28 3 3 0 360 117 29 psFillArc - globalGC1 115 41 117 29 psDrawLine - globalGC1 114 40 3 3 0 360 115 41 psFillArc - globalGC1 114 71 115 41 psDrawLine - globalGC1 113 70 3 3 0 360 114 71 psFillArc - globalGC1 116 90 114 71 psDrawLine - globalGC1 115 89 3 3 0 360 116 90 psFillArc - globalGC1 119 109 116 90 psDrawLine - globalGC1 118 108 3 3 0 360 119 109 psFillArc - globalGC1 124 129 119 109 psDrawLine - globalGC1 123 128 3 3 0 360 124 129 psFillArc - globalGC1 130 148 124 129 psDrawLine - globalGC1 129 147 3 3 0 360 130 148 psFillArc - globalGC1 137 168 130 148 psDrawLine - globalGC1 136 167 3 3 0 360 137 168 psFillArc - globalGC1 145 185 137 168 psDrawLine - globalGC1 144 184 3 3 0 360 145 185 psFillArc - globalGC1 154 202 145 185 psDrawLine - globalGC1 153 201 3 3 0 360 154 202 psFillArc - globalGC1 163 216 154 202 psDrawLine - globalGC1 162 215 3 3 0 360 163 216 psFillArc - globalGC1 172 227 163 216 psDrawLine - globalGC1 171 226 3 3 0 360 172 227 psFillArc - globalGC1 180 236 172 227 psDrawLine - globalGC1 179 235 3 3 0 360 180 236 psFillArc - globalGC1 187 241 180 236 psDrawLine - globalGC1 186 240 3 3 0 360 187 241 psFillArc - globalGC1 190 243 187 241 psDrawLine - globalGC1 189 242 3 3 0 360 190 243 psFillArc - globalGC1 193 244 190 243 psDrawLine - globalGC1 192 243 3 3 0 360 193 244 psFillArc - globalGC1 195 244 193 244 psDrawLine - globalGC1 194 243 3 3 0 360 195 244 psFillArc - globalGC1 196 244 195 244 psDrawLine - globalGC1 195 243 3 3 0 360 196 244 psFillArc - globalGC1 197 244 196 244 psDrawLine - globalGC1 196 243 3 3 0 360 197 244 psFillArc - globalGC1 198 244 197 244 psDrawLine - globalGC1 197 243 3 3 0 360 198 244 psFillArc - globalGC1 199 243 198 244 psDrawLine - globalGC1 198 242 3 3 0 360 199 243 psFillArc - globalGC1 199 242 199 243 psDrawLine - globalGC1 198 241 3 3 0 360 199 242 psFillArc - globalGC1 200 241 199 242 psDrawLine - globalGC1 199 240 3 3 0 360 200 241 psFillArc - globalGC1 200 240 200 241 psDrawLine - globalGC1 199 239 3 3 0 360 200 240 psFillArc - globalGC1 201 238 200 240 psDrawLine - globalGC1 200 237 3 3 0 360 201 238 psFillArc - globalGC1 201 234 201 238 psDrawLine - globalGC1 200 233 3 3 0 360 201 234 psFillArc - globalGC1 199 226 201 234 psDrawLine - globalGC1 198 225 3 3 0 360 199 226 psFillArc - globalGC1 188 204 199 226 psDrawLine - globalGC1 187 203 3 3 0 360 188 204 psFillArc - globalGC1 179 191 188 204 psDrawLine - globalGC1 178 190 3 3 0 360 179 191 psFillArc - globalGC1 168 178 179 191 psDrawLine - globalGC1 167 177 3 3 0 360 168 178 psFillArc - globalGC1 155 164 168 178 psDrawLine - globalGC1 154 163 3 3 0 360 155 164 psFillArc - globalGC1 140 151 155 164 psDrawLine - globalGC1 139 150 3 3 0 360 140 151 psFillArc - globalGC1 124 138 140 151 psDrawLine - globalGC1 123 137 3 3 0 360 124 138 psFillArc - globalGC1 108 127 124 138 psDrawLine - globalGC1 107 126 3 3 0 360 108 127 psFillArc - globalGC1 91 117 108 127 psDrawLine - globalGC1 90 116 3 3 0 360 91 117 psFillArc - globalGC1 75 109 91 117 psDrawLine - globalGC1 74 108 3 3 0 360 75 109 psFillArc - globalGC1 46 98 75 109 psDrawLine - globalGC1 45 97 3 3 0 360 46 98 psFillArc - globalGC1 34 96 46 98 psDrawLine - globalGC1 33 95 3 3 0 360 34 96 psFillArc - globalGC1 24 96 34 96 psDrawLine - globalGC1 23 95 3 3 0 360 24 96 psFillArc - globalGC1 20 96 24 96 psDrawLine - globalGC1 19 95 3 3 0 360 20 96 psFillArc - globalGC1 17 97 20 96 psDrawLine - globalGC1 16 96 3 3 0 360 17 97 psFillArc - globalGC1 16 98 17 97 psDrawLine - globalGC1 15 97 3 3 0 360 16 98 psFillArc - globalGC1 15 98 16 98 psDrawLine - globalGC1 14 97 3 3 0 360 15 98 psFillArc - globalGC1 14 99 15 98 psDrawLine - globalGC1 13 98 3 3 0 360 14 99 psFillArc - globalGC1 13 100 14 99 psDrawLine - globalGC1 12 99 3 3 0 360 13 100 psFillArc - globalGC1 13 101 13 100 psDrawLine - globalGC1 12 100 3 3 0 360 13 101 psFillArc - globalGC1 12 102 13 101 psDrawLine - globalGC1 11 101 3 3 0 360 12 102 psFillArc - globalGC1 12 103 12 102 psDrawLine - globalGC1 11 102 3 3 0 360 12 103 psFillArc - globalGC1 12 104 12 103 psDrawLine - globalGC1 11 103 3 3 0 360 12 104 psFillArc - globalGC1 13 106 12 104 psDrawLine - globalGC1 12 105 3 3 0 360 13 106 psFillArc - globalGC1 15 109 13 106 psDrawLine - globalGC1 14 108 3 3 0 360 15 109 psFillArc - globalGC1 20 114 15 109 psDrawLine - globalGC1 19 113 3 3 0 360 20 114 psFillArc - globalGC1 29 120 20 114 psDrawLine - globalGC1 28 119 3 3 0 360 29 120 psFillArc - globalGC1 55 131 29 120 psDrawLine - globalGC1 54 130 3 3 0 360 55 131 psFillArc - globalGC1 71 135 55 131 psDrawLine - globalGC1 70 134 3 3 0 360 71 135 psFillArc - globalGC1 89 138 71 135 psDrawLine - globalGC1 88 137 3 3 0 360 89 138 psFillArc - globalGC1 108 140 89 138 psDrawLine - globalGC1 107 139 3 3 0 360 108 140 psFillArc - globalGC1 128 141 108 140 psDrawLine - globalGC1 127 140 3 3 0 360 128 141 psFillArc - globalGC1 147 140 128 141 psDrawLine - globalGC1 146 139 3 3 0 360 147 140 psFillArc - globalGC1 166 138 147 140 psDrawLine - globalGC1 165 137 3 3 0 360 166 138 psFillArc - globalGC1 184 135 166 138 psDrawLine - globalGC1 183 134 3 3 0 360 184 135 psFillArc - globalGC1 200 131 184 135 psDrawLine - globalGC1 199 130 3 3 0 360 200 131 psFillArc - globalGC1 215 126 200 131 psDrawLine - globalGC1 214 125 3 3 0 360 215 126 psFillArc - globalGC1 226 120 215 126 psDrawLine - globalGC1 225 119 3 3 0 360 226 120 psFillArc - globalGC1 235 114 226 120 psDrawLine - globalGC1 234 113 3 3 0 360 235 114 psFillArc - globalGC1 238 112 235 114 psDrawLine - globalGC1 237 111 3 3 0 360 238 112 psFillArc - globalGC1 240 109 238 112 psDrawLine - globalGC1 239 108 3 3 0 360 240 109 psFillArc - globalGC1 242 106 240 109 psDrawLine - globalGC1 241 105 3 3 0 360 242 106 psFillArc - globalGC1 242 105 242 106 psDrawLine - globalGC1 241 104 3 3 0 360 242 105 psFillArc - globalGC1 243 104 242 105 psDrawLine - globalGC1 242 103 3 3 0 360 243 104 psFillArc - globalGC1 243 103 243 104 psDrawLine - globalGC1 242 102 3 3 0 360 243 103 psFillArc - globalGC1 243 102 243 103 psDrawLine - globalGC1 242 101 3 3 0 360 243 102 psFillArc - globalGC1 242 101 243 102 psDrawLine - globalGC1 241 100 3 3 0 360 242 101 psFillArc - globalGC1 242 100 242 101 psDrawLine - globalGC1 241 99 3 3 0 360 242 100 psFillArc - globalGC1 241 99 242 100 psDrawLine - globalGC1 240 98 3 3 0 360 241 99 psFillArc - globalGC1 240 98 241 99 psDrawLine - globalGC1 239 97 3 3 0 360 240 98 psFillArc - globalGC1 238 97 240 98 psDrawLine - globalGC1 237 96 3 3 0 360 238 97 psFillArc - globalGC1 235 96 238 97 psDrawLine - globalGC1 234 95 3 3 0 360 235 96 psFillArc - globalGC1 231 96 235 96 psDrawLine - globalGC1 230 95 3 3 0 360 231 96 psFillArc - globalGC1 221 96 231 96 psDrawLine - globalGC1 220 95 3 3 0 360 221 96 psFillArc - globalGC1 209 98 221 96 psDrawLine - globalGC1 208 97 3 3 0 360 209 98 psFillArc - globalGC1 180 109 209 98 psDrawLine - globalGC1 179 108 3 3 0 360 180 109 psFillArc - globalGC1 164 117 180 109 psDrawLine - globalGC1 163 116 3 3 0 360 164 117 psFillArc - globalGC1 147 127 164 117 psDrawLine - globalGC1 146 126 3 3 0 360 147 127 psFillArc - globalGC1 131 138 147 127 psDrawLine - globalGC1 130 137 3 3 0 360 131 138 psFillArc - globalGC1 115 151 131 138 psDrawLine - globalGC1 114 150 3 3 0 360 115 151 psFillArc - globalGC1 100 164 115 151 psDrawLine - globalGC1 99 163 3 3 0 360 100 164 psFillArc - globalGC1 87 178 100 164 psDrawLine - globalGC1 86 177 3 3 0 360 87 178 psFillArc - globalGC1 76 191 87 178 psDrawLine - globalGC1 75 190 3 3 0 360 76 191 psFillArc - globalGC1 67 204 76 191 psDrawLine - globalGC1 66 203 3 3 0 360 67 204 psFillArc - globalGC1 60 216 67 204 psDrawLine - globalGC1 59 215 3 3 0 360 60 216 psFillArc - globalGC1 56 226 60 216 psDrawLine - globalGC1 55 225 3 3 0 360 56 226 psFillArc - globalGC1 55 231 56 226 psDrawLine - globalGC1 54 230 3 3 0 360 55 231 psFillArc - globalGC1 54 234 55 231 psDrawLine - globalGC1 53 233 3 3 0 360 54 234 psFillArc - globalGC1 54 238 54 234 psDrawLine - globalGC1 53 237 3 3 0 360 54 238 psFillArc - globalGC1 54 239 54 238 psDrawLine - globalGC1 53 238 3 3 0 360 54 239 psFillArc - globalGC1 55 240 54 239 psDrawLine - globalGC1 54 239 3 3 0 360 55 240 psFillArc - globalGC1 55 241 55 240 psDrawLine - globalGC1 54 240 3 3 0 360 55 241 psFillArc - globalGC1 56 242 55 241 psDrawLine - globalGC1 55 241 3 3 0 360 56 242 psFillArc - globalGC1 56 243 56 242 psDrawLine - globalGC1 55 242 3 3 0 360 56 243 psFillArc - globalGC1 57 244 56 243 psDrawLine - globalGC1 56 243 3 3 0 360 57 244 psFillArc - globalGC1 58 244 57 244 psDrawLine - globalGC1 57 243 3 3 0 360 58 244 psFillArc - globalGC1 59 244 58 244 psDrawLine - globalGC1 58 243 3 3 0 360 59 244 psFillArc - globalGC1 60 244 59 244 psDrawLine - globalGC1 59 243 3 3 0 360 60 244 psFillArc - globalGC1 62 244 60 244 psDrawLine - globalGC1 61 243 3 3 0 360 62 244 psFillArc - globalGC1 65 243 62 244 psDrawLine - globalGC1 64 242 3 3 0 360 65 243 psFillArc - globalGC1 68 241 65 243 psDrawLine - globalGC1 67 240 3 3 0 360 68 241 psFillArc - globalGC1 75 236 68 241 psDrawLine - globalGC1 74 235 3 3 0 360 75 236 psFillArc - globalGC1 92 216 75 236 psDrawLine - globalGC1 91 215 3 3 0 360 92 216 psFillArc - globalGC1 101 202 92 216 psDrawLine - globalGC1 100 201 3 3 0 360 101 202 psFillArc - globalGC1 110 185 101 202 psDrawLine - globalGC1 109 184 3 3 0 360 110 185 psFillArc - globalGC1 118 168 110 185 psDrawLine - globalGC1 117 167 3 3 0 360 118 168 psFillArc - globalGC1 125 148 118 168 psDrawLine - globalGC1 124 147 3 3 0 360 125 148 psFillArc - globalGC1 131 129 125 148 psDrawLine - globalGC1 130 128 3 3 0 360 131 129 psFillArc - globalGC1 136 109 131 129 psDrawLine - globalGC1 135 108 3 3 0 360 136 109 psFillArc - globalGC1 139 90 136 109 psDrawLine - globalGC1 138 89 3 3 0 360 139 90 psFillArc - globalGC1 141 71 139 90 psDrawLine - globalGC1 140 70 3 3 0 360 141 71 psFillArc - globalGC1 140 41 141 71 psDrawLine - globalGC1 139 40 3 3 0 360 140 41 psFillArc - globalGC1 138 29 140 41 psDrawLine - globalGC1 137 28 3 3 0 360 138 29 psFillArc - globalGC1 137 25 138 29 psDrawLine - globalGC1 136 24 3 3 0 360 137 25 psFillArc - globalGC1 135 21 137 25 psDrawLine - globalGC1 134 20 3 3 0 360 135 21 psFillArc - globalGC1 133 18 135 21 psDrawLine - globalGC1 132 17 3 3 0 360 133 18 psFillArc - globalGC1 132 17 133 18 psDrawLine - globalGC1 131 16 3 3 0 360 132 17 psFillArc - globalGC1 131 16 132 17 psDrawLine - globalGC1 130 15 3 3 0 360 131 16 psFillArc - globalGC1 130 15 131 16 psDrawLine - globalGC1 129 14 3 3 0 360 130 15 psFillArc - globalGC1 129 14 130 15 psDrawLine - globalGC1 128 13 3 3 0 360 129 14 psFillArc - globalGC1 128 14 129 14 psDrawLine - globalGC1 127 13 3 3 0 360 128 14 psFillArc - globalGC1 128 14 128 14 psDrawLine - globalGC1 127 13 3 3 0 360 128 14 psFillArc - globalGC1 127 14 128 14 psDrawLine - globalGC1 126 13 3 3 0 360 127 14 psFillArc - globalGC1 126 14 127 14 psDrawLine - globalGC1 125 13 3 3 0 360 126 14 psFillArc - globalGC1 125 15 126 14 psDrawLine - globalGC1 124 14 3 3 0 360 125 15 psFillArc - globalGC1 124 16 125 15 psDrawLine - globalGC1 123 15 3 3 0 360 124 16 psFillArc - globalGC1 123 17 124 16 psDrawLine - globalGC1 122 16 3 3 0 360 123 17 psFillArc - globalGC1 122 18 123 17 psDrawLine - globalGC1 121 17 3 3 0 360 122 18 psFillArc - globalGC1 120 21 122 18 psDrawLine - globalGC1 119 20 3 3 0 360 120 21 psFillArc - globalGC1 118 25 120 21 psDrawLine - globalGC1 117 24 3 3 0 360 118 25 psFillArc - globalGC1 117 29 118 25 psDrawLine - globalGC1 116 28 3 3 0 360 117 29 psFillArc - globalGC1 115 41 117 29 psDrawLine - globalGC1 114 40 3 3 0 360 115 41 psFillArc - globalGC1 114 71 115 41 psDrawLine - globalGC1 113 70 3 3 0 360 114 71 psFillArc - globalGC1 116 90 114 71 psDrawLine - globalGC1 115 89 3 3 0 360 116 90 psFillArc - globalGC1 119 109 116 90 psDrawLine - globalGC1 118 108 3 3 0 360 119 109 psFillArc - globalGC1 124 129 119 109 psDrawLine - globalGC1 123 128 3 3 0 360 124 129 psFillArc - globalGC1 130 148 124 129 psDrawLine - globalGC1 129 147 3 3 0 360 130 148 psFillArc - globalGC1 137 168 130 148 psDrawLine - globalGC1 136 167 3 3 0 360 137 168 psFillArc - globalGC1 145 185 137 168 psDrawLine - globalGC1 144 184 3 3 0 360 145 185 psFillArc - globalGC1 154 202 145 185 psDrawLine - globalGC1 153 201 3 3 0 360 154 202 psFillArc - globalGC1 163 216 154 202 psDrawLine - globalGC1 162 215 3 3 0 360 163 216 psFillArc - globalGC1 172 227 163 216 psDrawLine - globalGC1 171 226 3 3 0 360 172 227 psFillArc - globalGC1 180 236 172 227 psDrawLine - globalGC1 179 235 3 3 0 360 180 236 psFillArc - globalGC1 187 241 180 236 psDrawLine - globalGC1 186 240 3 3 0 360 187 241 psFillArc - globalGC1 190 243 187 241 psDrawLine - globalGC1 189 242 3 3 0 360 190 243 psFillArc - globalGC1 193 244 190 243 psDrawLine - globalGC1 192 243 3 3 0 360 193 244 psFillArc - globalGC1 195 244 193 244 psDrawLine - globalGC1 194 243 3 3 0 360 195 244 psFillArc - globalGC1 196 244 195 244 psDrawLine - globalGC1 195 243 3 3 0 360 196 244 psFillArc - globalGC1 197 244 196 244 psDrawLine - globalGC1 196 243 3 3 0 360 197 244 psFillArc - globalGC1 198 244 197 244 psDrawLine - globalGC1 197 243 3 3 0 360 198 244 psFillArc - globalGC1 199 243 198 244 psDrawLine - globalGC1 198 242 3 3 0 360 199 243 psFillArc - globalGC1 199 242 199 243 psDrawLine - globalGC1 198 241 3 3 0 360 199 242 psFillArc - globalGC1 200 241 199 242 psDrawLine - globalGC1 199 240 3 3 0 360 200 241 psFillArc - globalGC1 200 240 200 241 psDrawLine - globalGC1 199 239 3 3 0 360 200 240 psFillArc - globalGC1 201 238 200 240 psDrawLine - globalGC1 200 237 3 3 0 360 201 238 psFillArc - globalGC1 201 234 201 238 psDrawLine - globalGC1 200 233 3 3 0 360 201 234 psFillArc - globalGC1 199 226 201 234 psDrawLine - globalGC1 198 225 3 3 0 360 199 226 psFillArc - globalGC1 188 204 199 226 psDrawLine - globalGC1 187 203 3 3 0 360 188 204 psFillArc - globalGC1 179 191 188 204 psDrawLine - globalGC1 178 190 3 3 0 360 179 191 psFillArc - globalGC1 168 178 179 191 psDrawLine - globalGC1 167 177 3 3 0 360 168 178 psFillArc - globalGC1 155 164 168 178 psDrawLine - globalGC1 154 163 3 3 0 360 155 164 psFillArc - globalGC1 140 151 155 164 psDrawLine - globalGC1 139 150 3 3 0 360 140 151 psFillArc - globalGC1 124 138 140 151 psDrawLine - globalGC1 123 137 3 3 0 360 124 138 psFillArc - globalGC1 108 127 124 138 psDrawLine - globalGC1 107 126 3 3 0 360 108 127 psFillArc - globalGC1 91 117 108 127 psDrawLine - globalGC1 90 116 3 3 0 360 91 117 psFillArc - globalGC1 75 109 91 117 psDrawLine - globalGC1 74 108 3 3 0 360 75 109 psFillArc - globalGC1 46 98 75 109 psDrawLine - globalGC1 45 97 3 3 0 360 46 98 psFillArc - globalGC1 34 96 46 98 psDrawLine - globalGC1 33 95 3 3 0 360 34 96 psFillArc - globalGC1 24 96 34 96 psDrawLine - globalGC1 23 95 3 3 0 360 24 96 psFillArc - globalGC1 20 96 24 96 psDrawLine - globalGC1 19 95 3 3 0 360 20 96 psFillArc - globalGC1 17 97 20 96 psDrawLine - globalGC1 16 96 3 3 0 360 17 97 psFillArc - globalGC1 16 98 17 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