diff --git a/books/bookvol10.4.pamphlet b/books/bookvol10.4.pamphlet
index 225eb0869..06805bc8e 100644
--- a/books/bookvol10.4.pamphlet
+++ b/books/bookvol10.4.pamphlet
@@ -63798,6 +63798,10 @@ GaloisGroupFactorizer(UP) : SIG == CODE where
import ModularDistinctDegreeFactorizer(UP)
+\end{chunk}
+ See:
+\href{http://axiom-developer.org/axiom-website/GroupTheoryII/Salomone.html#302.S1}{eisensteinIrreducible?}
+\begin{chunk}{package GALFACT GaloisGroupFactorizer}
eisensteinIrreducible?(f:UP):Boolean ==
rf := reductum f
c: Z := content rf
@@ -96632,22 +96636,16 @@ The computations use lexicographical Groebner bases. The main operations
are lexTriangular and squareFreeLexTriangular. The second one provide
decompositions by means of square-free regular triangular sets.
-Both are based on the lexTriangular method described in
- D. LAZARD "Solving Zero-dimensional Algebraic Systems"
- published in the J. of Symbol. Comput. (1992) 13, 117-131.
+Both are based on the lexTriangular method described in \cite{Laza92}.
-They differ from the algorithm described in
- M. MORENO MAZA and R. RIOBOO "Computations of gcd over
- algebraic towers of simple extensions"
- In proceedings of AAECC11, Paris, 1995.
+They differ from the algorithm described in \cite{Maza95}
by the fact that multiciplities of the roots are not kept. With the
squareFreeLexTriangular operation all multiciplities are removed.
With the other operation some multiciplities may remain. Both operations
- admit an optional argument to produce normalized triangular sets.
+admit an optional argument to produce normalized triangular sets.
The LexTriangularPackage package constructor provides an
-implementation of the lexTriangular algorithm (D. Lazard "Solving
-Zero-dimensional Algebraic Systems", J. of Symbol. Comput., 1992).
+implementation of the lexTriangular algorithm \cite{Laza92}.
This algorithm decomposes a zero-dimensional variety into zero-sets of
regular triangular sets. Thus the input system must have a finite
number of complex solutions. Moreover, this system needs to be a
@@ -96668,9 +96666,7 @@ Groebner bases are needed and the input system may have any dimension
(it may have an infinite number of solutions).
The implementation of the lexTriangular algorithm provided in the
-LexTriangularPackage constructor differs from that reported in
-"Computations of gcd over algebraic towers of simple extensions" by
-M. Moreno Maza and R. Rioboo (in proceedings of AAECC11, Paris, 1995).
+LexTriangularPackage constructor differs from that reported in \cite{Maza95}.
Indeed, the squareFreeLexTriangular operation removes all multiplicities
of the solutions (the computed solutions are pairwise different)
and the lexTriangular operation may keep some multiplicities; this
@@ -96705,10 +96701,8 @@ check whether this requirement holds. There is also a groebner operation
to compute the lexicographical Groebner basis of a set of polynomials
with type NewSparseMultivariatePolynomial(R,V). The elimination ordering
is that given by ls (the greatest variable being the first element
-of ls). This basis is computed by the FLGM algorithm (Faugere et al.
-"Efficient Computation of Zero-Dimensional Groebner Bases by Change
-of Ordering" , J. of Symbol. Comput., 1993) implemented in the
-LinGroebnerPackage package constructor.
+of ls). This basis is computed by the FLGM algorithm \cite{Faug94}
+implemented in the LinGroebnerPackage package constructor.
Once a lexicographical Groebner basis is computed, then one can call
the operations lexTriangular and squareFreeLexTriangular. Note that
@@ -98335,17 +98329,21 @@ o )show LexTriangularPackage
\cross{LEXTRIPK}{zeroSetSplit}
\end{tabular}
+See Lazard\cite{Laza92}, Aubry\cite{Aubr96}\cite{Aubr99}, Maza\cite{Maza95},
+Faugere\cite{Faug94}
+\label{package LEXTRIPK LexTriangularPackage}
\begin{chunk}{package LEXTRIPK LexTriangularPackage}
)abbrev package LEXTRIPK LexTriangularPackage
++ Author: Marc Moreno Maza
++ Date Created: 08/02/1999
++ Date Last Updated: 08/02/1999
++ References:
-++ [1] D. LAZARD "Solving Zero-dimensional Algebraic Systems"
-++ published in the J. of Symbol. Comput. (1992) 13, 117-131.
-++ [2] M. MORENO MAZA and R. RIOBOO "Computations of gcd over
-++ algebraic towers of simple extensions"
-++ In proceedings of AAECC11, Paris, 1995.
+++ Lazard Solving Zero-dimensional Algebraic Systems
+++ Aubry Triangular Sets for Solving Polynomial Systems
+++ Aubry On the Theories of Triangular Sets
+++ Maza Polynomial gcd over towers of algebraic extensions
+++ Faugere Efficient Computation of Zero-Dimensional Groebner Bases by Change
+++ of Ordering
++ Description:
++ A package for solving polynomial systems with finitely many solutions.
++ The decompositions are given by means of regular triangular sets.
@@ -98355,7 +98353,7 @@ o )show LexTriangularPackage
++ means of square-free regular triangular sets.
++ Both are based on the lexTriangular method described in [1].
++ They differ from the algorithm described in [2] by the fact that
-++ multiciplities of the roots are not kept.
+++ multiplicities of the roots are not kept.
++ With the squareFreeLexTriangular operation all multiciplities are removed.
++ With the other operation some multiciplities may remain. Both operations
++ admit an optional argument to produce normalized triangular sets.
@@ -203208,8 +203206,6 @@ o )show PermutationGroupExamples
\cross{PGE}{youngGroup} &&
\end{tabular}
-\href{http://axiom-developer.org/axiom-website/VisualGroupTheory/Macauley.html#1.1}{rubiksGroup}
-
\begin{chunk}{package PGE PermutationGroupExamples}
)abbrev package PGE PermutationGroupExamples
++ Authors: M. Weller, G. Schneider, J. Grabmeier
@@ -203446,6 +203442,10 @@ PermutationGroupExamples() : SIG == CODE where
youngGroup(lambda : Partition):PERMGRP I ==
youngGroup(convert(lambda)$Partition)
+\end{chunk}
+See:
+\href{http://axiom-developer.org/axiom-website/VisualGroupTheory/Macauley.html#1.1}{rubiksGroup}
+\begin{chunk}{package PGE PermutationGroupExamples}
rubiksGroup():PERMGRP I ==
-- each generator represents a 90 degree turn of the appropriate
-- side.
diff --git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index 8baa328d0..ace2698c0 100644
--- a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ -2457,6 +2457,37 @@ when shown in factored form.
\end{chunk}
+\index{Corless, Robert M.}
+\index{Gianni, Patrizia, M.}
+\index{Trager, Barry M.}
+\index{Watt, Stephen M.}
+\begin{chunk}{axiom.bib}
+@inproceedings{Corl95,
+ author = "Corless, Robert M. and Gianni, Patrizia, M. and Trager, Barry M.
+ and Watt, Stephen M.",
+ title = "The Singular Value Decomposition for Polynomial Systems",
+ booktitle = "ISSAC 95",
+ year = "1995",
+ pages = "195-207",
+ publisher = "ACM",
+ abstract =
+ "This paper introduces singular value decomposition (SVD) algorithms
+ for some standard polynomial computations, in the case where the
+ coefficients are inexact or imperfectly known. We first give an
+ algorithm for computing univariate GCD's which gives {\sl exact}
+ results for interesting {\sl nearby} problems, and give efficient
+ algorithms for computing precisely how nearby. We generalize this to
+ multivariate GCD computations. Next, we adapt Lazard's $u$-resultant
+ algorithm for the solution of overdetermined systems of polynomial
+ equations to the inexact-coefficent case. We also briefly discuss an
+ application of the modified Lazard's method to the location of
+ singular points on approximately known projections of algebraic curves.",
+ paper = "Corl95.pdf",
+ keywords = "axiomref",
+}
+
+\end{chunk}
+
\index{Li, Xiaoliang}
\index{Mou, Chenqi}
\index{Wang, Dongming}
@@ -21465,6 +21496,7 @@ TPHOLS 2001, Edinburgh
year = "1984",
url = "http://www-polsys.lip6.fr/~jcf/Papers/FGLM.pdf",
publisher = "Academic Press Limited",
+ algebra = "\newline\refto{package LEXTRIPK LexTriangularPackage}",
abstract = "
We present an efficient algorithm for the transformation of a
Grobner basis of a zero-dimensional ideal with respect to any given
@@ -32922,6 +32954,7 @@ National Physical Laboratory. (1982)
\newline\refto{category RSETCAT RegularTriangularSetCategory}
\newline\refto{category NTSCAT NormalizedTriangularSetCategory}
\newline\refto{category SFRTCAT SquareFreeRegularTriangularSetCategory}
+ \newline\refto{package LEXTRIPK LexTriangularPackage}
\newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
abstract =
"Different notions of triangular sets are presented. The relationship
@@ -32951,6 +32984,7 @@ National Physical Laboratory. (1982)
\newline\refto{category RSETCAT RegularTriangularSetCategory}
\newline\refto{category NTSCAT NormalizedTriangularSetCategory}
\newline\refto{category SFRTCAT SquareFreeRegularTriangularSetCategory}
+ \newline\refto{package LEXTRIPK LexTriangularPackage}
\newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
abstract =
"Four methods for solving polynomial systems by means of triangular
@@ -35462,10 +35496,26 @@ Prentice-Hall. (1974)
\end{chunk}
\index{Lazard, Daniel}
-\begin{chunk}{ignore}
-\bibitem[Lazard92]{Laz92} Lazard, D.
+\begin{chunk}{axiom.bib}
+@article{Laza92,
+ author = "Lazard, Daniel",
title = "Solving Zero-dimensional Algebraic Systems",
-Journal of Symbolic Computation, 1992, 13, 117-131
+ journal = "J. of Symbolic Computation",
+ volume = "13",
+ pages = "117-131",
+ year = "1992",
+ abstract =
+ "It is shown that a good output for a solver of algebraic systems of
+ dimension zero consists of a family of ``triangular sets of
+ polynomials''. Such an output is simple, readable, and consists
+ of all information which may be wanted.
+
+ Different algorithms are described for handling triangular systems
+ and obtaining them from Groebner bases. These algorithms are
+ practicable, and most of them are polynomial in the number of
+ solutions",
+ paper = "Laza92.pdf"
+}
\end{chunk}
@@ -35741,6 +35791,7 @@ Mathematical Surveys. 3 Am. Math. Soc., Providence, RI. (1966)
\newline\refto{category RSETCAT RegularTriangularSetCategory}
\newline\refto{category NTSCAT NormalizedTriangularSetCategory}
\newline\refto{category SFRTCAT SquareFreeRegularTriangularSetCategory}
+ \newline\refto{package LEXTRIPK LexTriangularPackage}
\newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
abstract =
"Some methods for polynomial system solving require efficient
diff --git a/changelog b/changelog
index 403e21498..17be2930c 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,6 @@
+20161030 tpd src/axiom-website/patches.html 20161030.01.tpd.patch
+20161030 tpd books/bookvol10.4 update references
+20161030 tpd books/bookvolbib add references
20161029 tpd src/axiom-website/patches.html 20161029.01.tpd.patch
20161029 tpd books/bookvolbib add Type Inference and Coercion references
20161029 rdj books/bookvol5 Add chapter Type Inference and Coercion
diff --git a/patch b/patch
index b170a950c..1da3c0421 100644
--- a/patch
+++ b/patch
@@ -1,72 +1,59 @@
-books/bookvol5 Add chapter Type Inference and Coercion
+books/bookvol10.4 update references
Goal: Axiom Literate Programming
-\index{Jenks, Richard D.}
+\index{Corless, Robert M.}
+\index{Gianni, Patrizia, M.}
+\index{Trager, Barry M.}
+\index{Watt, Stephen M.}
\begin{chunk}{axiom.bib}
-@techreport{Jenk86c,
- author = "Jenks, Richard D.",
- title = "A History of the SCRATCHPAD Project (1977-1986)",
- institution = "IBM Research",
- year = "1986",
- month = "May",
- type = "Scratchpad II Newsletter",
- volume = "1",
- number = "3",
-}
-
-\end{chunk}
-
-\index{Liskov, Barbara}
-\index{Atkinson, Russ}
-\index{Bloom, Toby}
-\index{Moss, Eliot}
-\index{Schaffert, Craig}
-\index{Scheifler, Bob}
-\index{Snyder, Alan}
-\begin{chunk}{axiom.bib}
-@techreport{Lisk79,
- author = "Liskov, Barbara and Atkinson, Russ and Bloom, Toby and
- Moss, Eliot and Schaffert, Craig and Scheifler, Bob and
- Snyder, Alan",
- title = "CLU Reference Manual",
- institution = "Massachusetts Institute of Technology",
- year = "1979",
- paper = "Lisk79.pdf"
+@inproceedings{Corl95,
+ author = "Corless, Robert M. and Gianni, Patrizia, M. and Trager, Barry M.
+ and Watt, Stephen M.",
+ title = "The Singular Value Decomposition for Polynomial Systems",
+ booktitle = "ISSAC 95",
+ year = "1995",
+ pages = "195-207",
+ publisher = "ACM",
+ abstract =
+ "This paper introduces singular value decomposition (SVD) algorithms
+ for some standard polynomial computations, in the case where the
+
+ coefficients are inexact or imperfectly known. We first give an
+ algorithm for computing univariate GCD's which gives {\sl exact}
+ results for interesting {\sl nearby} problems, and give efficient
+ algorithms for computing precisely how nearby. We generalize this to
+ multivariate GCD computations. Next, we adapt Lazard's $u$-resultant
+ algorithm for the solution of overdetermined systems of polynomial
+ equations to the inexact-coefficent case. We also briefly discuss an
+ application of the modified Lazard's method to the location of
+ singular points on approximately known projections of algebraic curves.",
+ paper = "Corl95.pdf",
+ keywords = "axiomref",
}
\end{chunk}
-\index{Schaffert, C.}
-\index{Cooper, T.}
+\index{Lazard, Daniel}
\begin{chunk}{axiom.bib}
-@article{Scha86,
- author = "Schaffert, C. and Cooper, T.",
- title = "An Introduction to Trellis/Owl",
- journal = "SIGPLAN Notices",
- volume = "21",
- number = "11",
- publisher = "ACM",
- year = "1986",
- pages = "9-16"
+@article{Laza92,
+ author = "Lazard, Daniel",
+ title = "Solving Zero-dimensional Algebraic Systems",
+Journal of Symbolic Computation, 1992, 13, 117-131
+ journal = "J. of Symbolic Computation",
+ volume = "13",
+ pages = "117-131",
+ year = "1992",
+ abstract =
+ "It is shown that a good output for a solver of algebraic systems of
+ dimension zero consists of a family of ``triangular sets of
+ polynomials''. Such an output is simple, readable, and consists
+ of all information which may be wanted.
+
+ Different algorithms are described for handling triangular systems
+ and obtaining them from Groebner bases. These algorithms are
+ practicable, and most of them are polynomial in the number of
+ solutions",
+ paper = "Laza92.pdf"
}
-
-\end{chunk}
-\index{Sweedler, Moss E.}
-\begin{chunk}{axiom.bib}
-@techreport{Swee86,
- author = "Sweedler, Moss E.",
- title = "Typing in Scratchpad II",
- institution = "IBM Research",
- year = "1986",
- month = "January",
- type = "Scratchpad II Newsletter",
- volume = "1",
- number = "2",
-}
-
-\end{chunk}
-
-
-
diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html
index 7580de048..9297c209d 100644
--- a/src/axiom-website/patches.html
+++ b/src/axiom-website/patches.html
@@ -5580,6 +5580,8 @@ Latest Release
books/bookvolbib Finite Fields in Axiom citations fixes
20161029.01.tpd.patch
books/bookvol5 Add chapter Type Inference and Coercion
+20161030.01.tpd.patch
+books/bookvol10.4 update references