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 = "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{Lazard, Daniel} \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" } --- books/bookvol10.4.pamphlet | 50 +++++++-------- books/bookvolbib.pamphlet | 57 ++++++++++++++++- changelog | 3 + patch | 109 +++++++++++++++------------------ src/axiom-website/patches.html | 2 + 5 files changed, 132 insertions(+), 89 deletions(-) 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