From 7609525e7fa04fecaf6ea78576e2a07ab7762a8d Mon Sep 17 00:00:00 2001
From: Tim Daly
Date: Mon, 31 Oct 2016 04:12:38 0400
Subject: [PATCH] books/bookvol10.4 update references
Goal: Axiom Literate Programming
\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 = "195207",
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 inexactcoefficent 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{Lazard, Daniel}
\begin{chunk}{axiom.bib}
@article{Laza92,
author = "Lazard, Daniel",
title = "Solving Zerodimensional Algebraic Systems",
Journal of Symbolic Computation, 1992, 13, 117131
journal = "J. of Symbolic Computation",
volume = "13",
pages = "117131",
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"
}

books/bookvol10.4.pamphlet  50 +++++++++
books/bookvolbib.pamphlet  57 ++++++++++++++++++++
changelog  3 +
patch  109 +++++++++++++++++
src/axiomwebsite/patches.html  2 +
5 files changed, 132 insertions(+), 89 deletions()
diff git a/books/bookvol10.4.pamphlet b/books/bookvol10.4.pamphlet
index 225eb08..06805bc 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://axiomdeveloper.org/axiomwebsite/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 squarefree regular triangular sets.
Both are based on the lexTriangular method described in
 D. LAZARD "Solving Zerodimensional Algebraic Systems"
 published in the J. of Symbol. Comput. (1992) 13, 117131.
+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
Zerodimensional Algebraic Systems", J. of Symbol. Comput., 1992).
+implementation of the lexTriangular algorithm \cite{Laza92}.
This algorithm decomposes a zerodimensional variety into zerosets 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 ZeroDimensional 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 Zerodimensional Algebraic Systems"
++ published in the J. of Symbol. Comput. (1992) 13, 117131.
++ [2] M. MORENO MAZA and R. RIOBOO "Computations of gcd over
++ algebraic towers of simple extensions"
++ In proceedings of AAECC11, Paris, 1995.
+++ Lazard Solving Zerodimensional 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 ZeroDimensional 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 squarefree 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://axiomdeveloper.org/axiomwebsite/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://axiomdeveloper.org/axiomwebsite/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 8baa328..ace2698 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 = "195207",
+ 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 inexactcoefficent 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://wwwpolsys.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 zerodimensional 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 @@ PrenticeHall. (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 Zerodimensional Algebraic Systems",
Journal of Symbolic Computation, 1992, 13, 117131
+ journal = "J. of Symbolic Computation",
+ volume = "13",
+ pages = "117131",
+ 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 403e214..17be293 100644
 a/changelog
+++ b/changelog
@@ 1,3 +1,6 @@
+20161030 tpd src/axiomwebsite/patches.html 20161030.01.tpd.patch
+20161030 tpd books/bookvol10.4 update references
+20161030 tpd books/bookvolbib add references
20161029 tpd src/axiomwebsite/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 b170a95..1da3c04 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 (19771986)",
 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 = "195207",
+ 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 inexactcoefficent 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 = "916"
+@article{Laza92,
+ author = "Lazard, Daniel",
+ title = "Solving Zerodimensional Algebraic Systems",
+Journal of Symbolic Computation, 1992, 13, 117131
+ journal = "J. of Symbolic Computation",
+ volume = "13",
+ pages = "117131",
+ 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/axiomwebsite/patches.html b/src/axiomwebsite/patches.html
index 7580de0..9297c20 100644
 a/src/axiomwebsite/patches.html
+++ b/src/axiomwebsite/patches.html
@@ 5580,6 +5580,8 @@ books/bookvol10.1 Finite Fields in Axiom by Grabmeier
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

1.7.5.4