diff git a/books/bookvol10.1.pamphlet b/books/bookvol10.1.pamphlet
index 68ebfd2..ee89e7a 100644
 a/books/bookvol10.1.pamphlet
+++ b/books/bookvol10.1.pamphlet
@@ 8552,8 +8552,20 @@ Groebner Basis
Greatest Common Divisor
\chapter{Polynomial Factorization}
Polynomial Factorization
+
\chapter{Cylindrical Algebraic Decomposition}
Cylindrical Algebraic Decomposition
+We quote from LaValle \cite{LaVa06}.
+The idea is to develop a sequence of projections that drops the dimension
+of the semialgebraic set by one each time. Initially, the set is defined
+over ${\bf R}^n$, and after one projection, a semialgebraic set is obtained
+in ${\bf R}^{n1}$. Eventually, the projection reaches ${\bf R}$, and a
+univariate polynomial is obtained for which the zeros are at the critical
+places where cell boundaries need to be formed. A cell decomposition of
+1cells (intervals) and 0cells is formed by partitioning ${\bf R}$.
+The sequences is then reversed, and decompositions are formed from ${\bf R}^2$
+up to ${\bf R}^n$. Each iteration starts with a cell decomposition in
+${\bf R}^i$ and lifts it to obtain a cylinder of cells in ${\bf R}^{i+1}$.
+
\chapter{Pade approximant}
Pade approximant
\chapter{SchwartzZippel lemma and testing polynomial identities}
diff git a/books/bookvol10.2.pamphlet b/books/bookvol10.2.pamphlet
index b5a1789..1a62084 100644
 a/books/bookvol10.2.pamphlet
+++ b/books/bookvol10.2.pamphlet
@@ 35164,6 +35164,42 @@ Ring examples
The category of rings with unity, always associative, but not
necessarily commutative.
+Rings have two operations, '+' and '*' and satisfy 5 axioms:
+
+1) (associative addition) a + (b + c) = (a + b) + c
+2) (commutative addition) a + b = b + a
+3) (associative multiplication) a(bc) = (ab)c
+4) (distributive mulitplication) a(b + c) = ab + ac; (b + c)a = ba + ca
+5) (equation solution) a + x = b has a solution in R
+
+examples include
+
+  even integers
+  integers
+  integers module any positive integer
+  rational numbers
+  real numbers
+  complex numbers
+  real quaterions
+  a + b*sqrt(2) where a and b are rational
+  polynomials in real variables with real coefficients
+  real continuous functions in a fixed interval
+  all power series in a real variable convergent on an interval
+  all subsets of an arbitrary set
+  all square matrices with elements from a ring
+
+Rings are not necessarily commutative. For example, square 2x2 matices:
+
+ + + + + + +
+  0 1   0 0  =  1 0 
+  0 0   1 0   0 0 
+ + + + + + +
+
+ + + + + + +
+  0 0   0 1  =  0 0 
+  1 0   0 0   0 1 
+ + + + + + +
+
See Also:
o )show Ring
@@ 47522,12 +47558,32 @@ IntegralDomain examples
====================================================================
The category of commutative integral domains, i.e. commutative
rings with no zero divisors.
+rings with no zero divisors. That means that we can show that
+if ab = 0 then either a or b must be 0.
+
+This does not have to be true. For instance, real 2x2 matrices
+have zero divisors since
+
+ A x B = 0 but neither A nor B is 0:
+ + + + + + +
+  0 1   0 2  =  0 0 
+  0 0   0 0   0 0 
+ + + + + + +
+
+
Conditional attributes:
canonicalUnitNormal  the canonical field is the same for all associates
canonicalsClosed  the product of two canonicals is itself canonical
+ Ring > CommutativeRing > IntegralDomain
+
+1) (associative addition) a + (b + c) = (a + b) + c
+2) (commutative addition) a + b = b + a
+3) (associative multiplication) a(bc) = (ab)c
+4) (distributive mulitplication) a(b + c) = ab + ac; (b + c)a = ba + ca
+5) (equation solution) a + x = b has a solution in R
+
See Also:
o )show IntegralDomain
diff git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index 5dc52ca..4d47901 100644
 a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ 14758,6 +14758,19 @@ Math. Tables Aids Comput. 10 9196. (1956)
\end{chunk}
+\index{LaValle, Steven M.}
+\begin{chunk}{axiom.bib}
+@book{LaVa06,
+ author = "LaValle, Steven M.",
+ title = "Planning Algorithms",
+ year = "2006",
+ publisher = "Cambridge University Press"
+}
+\index{algorithm!cylindrical algebraic decomposition}
+\index{cylindrical algebraic decomposition}
+
+\end{chunk}
+
\eject
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Bibliography}
diff git a/changelog b/changelog
index 9d93127..d26ef4a 100644
 a/changelog
+++ b/changelog
@@ 1,3 +1,7 @@
+20141004 tpd src/axiomwebsite/patches.html 20141004.01.tpd.patch
+20141004 tpd books/bookvol10.2 add documentation for Ring help file
+20141004 tpd books/bookvolbib add LaValle ref for CAD
+20141004 tpd books/bookvol10.1 add documentation for CAD
20141002 tpd src/axiomwebsite/patches.html 20141002.01.tpd.patch
20141002 tpd src/interp/ianaly.lisp fix bug 7260 wrong type on output
20140928 tpd src/axiomwebsite/patches.html 20140928.01.tpd.patch
diff git a/patch b/patch
index 7adea28..10d6bd4 100644
 a/patch
+++ b/patch
@@ 1,4 +1,3 @@
src/interp/ianaly.lisp fix wrong type on output

fix bug 7260: FINITE() Type: Subdomain(Domain)
+books/bookvol10.1, 10.2, bib add documentation
+add documentation to help files and general algebra (CAD)
diff git a/src/axiomwebsite/patches.html b/src/axiomwebsite/patches.html
index 7618a60..1b5da4c 100644
 a/src/axiomwebsite/patches.html
+++ b/src/axiomwebsite/patches.html
@@ 4660,6 +4660,8 @@ books/bookvol10.4 document Sylvester matrix
books/bookvol0.pamphlet add contributor preamble
20141002.01.tpd.patch
src/interp/ianaly.lisp fix wrong type on output
+20141004.01.tpd.patch
+books/bookvol10.1, 10.2, bib add documentation