From 703a8c19d371a02e40f1c81a8156e375f77054f2 Mon Sep 17 00:00:00 2001
From: Tim Daly
Date: Fri, 24 Jun 2016 12:04:46 0400
Subject: [PATCH] books/bookvolbib Aubr96 package DFSFUN
DoubleFloatSpecialFunctions refs
Goal: Axiom Literate Programming
Collect algebra references in the bibliography
\index{Aubry, Phillippe}
\index{Maza, Marc Moreno}
\begin{chunk}{axiom.bib}
@article{Aubr96,
author = "Aubry, Phillippe and Maza, Marc Moreno",
title = "Triangular Sets for Solving Polynomial Systems:
a Comparison of Four Methods",
url = "http://www.lip6.fr/lip6/reports/1997/lip6.1997.009.ps.gz",
paper = "Aubr96.pdf",
comment = "\newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
keywords = "axiomref",
abstract =
"Four methods for solving polynomial systems by means of triangular
sets are presented and implemented in a unified way. These methods are
those of Wu, Lazard, Kalkbrener, and Wang. They are compared on
various examples with emphasis on efficiency, conciseness and
legibility of the outputs."
}
\end{chunk}

books/bookvol10.4.pamphlet  68 ++++++++++++++++++++++++
books/bookvolbib.pamphlet  43 +++++++++++
changelog  3 +
patch  110 +++++
src/axiomwebsite/patches.html  2 +
5 files changed, 114 insertions(+), 112 deletions()
diff git a/books/bookvol10.4.pamphlet b/books/bookvol10.4.pamphlet
index f98c535..d47da2d 100644
 a/books/bookvol10.4.pamphlet
+++ b/books/bookvol10.4.pamphlet
@@ 23564,11 +23564,20 @@ o )show DoubleFloatSpecialFunctions
\cross{DFSFUN}{polygamma} &&
\end{tabular}
+See: L\"osch\cite{Losc60}, Pearcey\cite{Pear56}, Luke\cite{Luke69a,Luke69b}
+Segletes\cite{Segl98}, Steele\cite{Stee90}, and \cite{WikiG}
+\label{package DFSFUN DoubleFloatSpecialFunctions}
\begin{chunk}{package DFSFUN DoubleFloatSpecialFunctions}
)abbrev package DFSFUN DoubleFloatSpecialFunctions
++ Author: Bruce W. Char, Timothy Daly, Stephen M. Watt
++ Date Created: 1990
++ Date Last Updated: Jan 19, 2008
+++ References:
+++ Losc60 Tables of Higher Functions
+++ Pear56 Pearcey Table of the Fresnel Integral
+++ Luke The Special FUnctions and their Approximations
+++ Segl98 A compact analytical fit to the exponential integral E1(x)
+++ WikiG Gamma Function
++ Description:
++ This package provides special functions for double precision
++ real and complex floating point.
@@ 206165,6 +206174,8 @@ Gathen also notes that for polynomials we should modify the Euclidean
algorithm so {\sl all} remainders are normalized. Without this
constraint the remainders will have huge numerators and denominators.
+See: von zur Gathen\cite{Gath99}
+\label{package PGCD PolynomialGcdPackage}
\begin{chunk}{package PGCD PolynomialGcdPackage}
 impose the right leading condition, check for failure.
@@ 226346,14 +226357,67 @@ o )show RegularSetDecompositionPackage
\cross{RSDCMPK}{upDateBranches} &&
\end{tabular}
+\subsection{The decompose algorithm}
+In Moreno Maza\cite{Maza00} we read:
+\begin{quote}
+
+The algorithm presented in this paper decomposes the variety $V$ by
+means of regular chains. All the zeros of $V$, generic or not, are
+represented. The components are produced in order of decreasing
+dimension allowing good control of the redundent intermediate
+components. Moreover, we show how our algorithm can produce
+Kalkbrener's decompositions or Lazard's regular chaings.
+
+A prelimiary implementation (which does not contain most of the
+improvements given in this paper) is distributed with version 2.2 of
+AXIOM and experiments are reported in [AM99] (\cite{Aubr96}). They
+show that this implementation is comparable in performaces with that
+of Kalkbrener, although our method provides a complete decomposition
+of $V$. Moreover we obtain much better results than with our
+implementation of Lazard's method.
+
+Our decomposition strategy is based on a procedure called {\tt
+decompose} that computes the intersection of a hypersurface with a
+quasicomponent (the set of the generic points associated with a
+regular chain). More precisely, this operation computes the
+quasicomponents with maximal dimension contained in this
+intersection, and the necessary information in order to obtain those
+of lower dimension when they are needed. A toplevel procedure manages
+the calls to the procedure {\tt decompose} such that the output
+quasicomponents are produced in order of decreasing dimension and
+such that the redundant quasicomponents are removed as soon as
+possible, by means of an inclusion test. The procedure {\tt decompose}
+itself relies on a procedure for polynomial gcd computations modulo
+regular chains that produces a {\sl main result} and a way to
+terminate some {\sl degenerated computations} when they are needed.
+
+This strategy leads to the following difficulty. Since we proceed in
+order of decreasing dimension, we cannot use a topdown elimination
+process (eliminating the greatest variables first) as in Wang's
+algorithm or a bottomup construction as in Kalkbrener's algorithm. In
+fact, we need to perform projections into some subspace and then
+reconstructions in the whole space where the algebraic variety $V$ is
+to be decomposed. Lazard's algorithm has to face the same difficulty
+but solves it with the strong properties of Lazard regular
+chains. General regular chains do not have these properties, this
+leads us to establish a lifting theorem for polynomial computations
+modulo regular chains.
+
+\end{quote}
+
+See: Moreno Maza\cite{Maza98}\cite{Maza00}, Aubry\cite{Aubr96}
+\label{package RSDCMPK RegularSetDecompositionPackage}
\begin{chunk}{package RSDCMPK RegularSetDecompositionPackage}
)abbrev package RSDCMPK RegularSetDecompositionPackage
++ Author: Marc Moreno Maza
++ Date Created: 09/16/1998
++ Date Last Updated: 12/16/1998
++ References :
++ [1] M. MORENO MAZA "A new algorithm for computing triangular
++ decomposition of algebraic varieties" NAG Tech. Rep. 4/98.
+++ Maza98 A new algorithm for computing triangular decomposition of
+++ algebraic varieties
+++ Maza00 On Triangular Decompositions of Algebraic Varieties
+++ Aubr96 Triangular Sets for Solving Polynomial Systems:
+++ a Comparison of Four Methods
++ Description:
++ A package providing a new algorithm for solving polynomial systems
++ by means of regular chains. Two ways of solving are proposed:
diff git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index f54c98f..ae03eca 100644
 a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ 3428,6 +3428,7 @@ when shown in factored form.
type = "Technical Report",
number = "ARLTR1758",
paper = "Segl98.pdf",
+ comment = "\newline\refto{package DFSFUN DoubleFloatSpecialFunctions}",
abstract = "
A fourparameter fit is developed for the class of integrals known as
the exponential integral (real branch). Unlike other fits that are
@@ 13234,6 +13235,7 @@ ISSN 07308639
paper = "Maza00.pdf",
url = "http://www.csd.uwo.ca/~moreno//Publications",
keywords = "axiomref",
+ comment = "\newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
abstract =
"Different kinds of triangular decompositions of algebraic varieties
are presented. The main result is an efficient method for obtaining
@@ 14704,7 +14706,8 @@ Software Preservation Group
author = "Wikipedia Authors",
title = "Gamma Function",
year = "2016",
 url = "https://en.wikipedia.org/wiki/Gamma\_function"
+ url = "https://en.wikipedia.org/wiki/Gamma\_function",
+ comment = "\newline\refto{package DFSFUN DoubleFloatSpecialFunctions}"
}
\subsection{Y} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ 14920,17 +14923,22 @@ J. Symbolic Computation 5, 237259 (1988)
\index{Aubry, Phillippe}
\index{Maza, Marc Moreno}
\begin{chunk}{ignore}
\bibitem[Aubry 96]{Aub96} Aubry, Philippe; Maza, Marc Moreno
 title = "Triangular Sets for Solving Polynomial Systems: a Comparison of Four Methods",
+\begin{chunk}{axiom.bib}
+@article{Aubr96,
+ author = "Aubry, Phillippe and Maza, Marc Moreno",
+ title = "Triangular Sets for Solving Polynomial Systems:
+ a Comparison of Four Methods",
url = "http://www.lip6.fr/lip6/reports/1997/lip6.1997.009.ps.gz",
 paper = "Aub96.ps",
 abstract = "
 Four methods for solving polynomial systems by means of triangular
+ paper = "Aubr96.pdf",
+ comment = "\newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
+ keywords = "axiomref",
+ abstract =
+ "Four methods for solving polynomial systems by means of triangular
sets are presented and implemented in a unified way. These methods are
those of Wu, Lazard, Kalkbrener, and Wang. They are compared on
various examples with emphasis on efficiency, conciseness and
legibility of the outputs."
+}
\end{chunk}
@@ 16118,7 +16126,8 @@ Journal of Symbolic Computation (1990) 9, 281299
title = "Modern Computer Algebra",
publisher = "Cambridge University Press",
year = "1999",
 isbn = "0521641764"
+ isbn = "0521641764",
+ comment = "\newline\refto{package PGCD PolynomialGcdPackage}"
}
\end{chunk}
@@ 17185,7 +17194,8 @@ The Benjamin/Cummings Publishing Company, Inc.Menlo Park, California, 1981.
author = {L\"osch, Friedrich},
title = "Tables of Higher Functions",
publisher = "McGrawHill Book Company",
 year = "1960"
+ year = "1960",
+ comment = "\newline\refto{package DFSFUN DoubleFloatSpecialFunctions}"
}
\end{chunk}
@@ 17205,7 +17215,8 @@ The Benjamin/Cummings Publishing Company, Inc.Menlo Park, California, 1981.
volume = "1",
publisher = "Academic Press",
year = "1969",
 booktitle = "Mathematics in Science and Engineering Volume 53I"
+ booktitle = "Mathematics in Science and Engineering Volume 53I",
+ comment = "\newline\refto{package DFSFUN DoubleFloatSpecialFunctions}"
}
\end{chunk}
@@ 17218,7 +17229,8 @@ The Benjamin/Cummings Publishing Company, Inc.Menlo Park, California, 1981.
volume = "2",
publisher = "Academic Press",
year = "1969",
 booktitle = "Mathematics in Science and Engineering Volume 53I"
+ booktitle = "Mathematics in Science and Engineering Volume 53I",
+ comment = "\newline\refto{package DFSFUN DoubleFloatSpecialFunctions}"
}
\end{chunk}
@@ 17355,7 +17367,8 @@ Mathematical Surveys. 3 Am. Math. Soc., Providence, RI. (1966)
title = "A new algorithm for computing triangular decomposition of
algebraic varieties",
institution = "Numerical Algorithms Group (NAG)",
 comment = "\newline\refto{category RSETCAT RegularTriangularSetCategory}",
+ comment = "\newline\refto{category RSETCAT RegularTriangularSetCategory}
+ \newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
year = "1998"
}
@@ 17693,7 +17706,8 @@ Science of Computer Programming V25 No.1 Oct 1995 pp4161 Elesevier
author = "Pearcey, T.",
title = "Table of the Fresnel Integral",
publisher = "Cambridge University Press",
 year = "1956"
+ year = "1956",
+ comment = "\newline\refto{package DFSFUN DoubleFloatSpecialFunctions}"
}
\end{chunk}
@@ 18362,7 +18376,8 @@ The University of Chicago Press. 1974
url = "http://daly.axiomdeveloper.org/clm.pdf",
publisher = "Digital Equipment Corporation",
isbn = "15555580416",
 paper = "Stee90.pdf"
+ paper = "Stee90.pdf",
+ comment = "\newline\refto{package DFSFUN DoubleFloatSpecialFunctions}"
}
\end{chunk}
diff git a/changelog b/changelog
index 7413678..818a99d 100644
 a/changelog
+++ b/changelog
@@ 1,3 +1,6 @@
+20160624 tpd src/axiomwebsite/patches.html 20160624.03.tpd.patch
+20160624 tpd books/bookvol10.4 Aubr96 package DoubleFloatSpecialFunctions
+20160624 tpd books/bookvolbib Aubr96 package DoubleFloatSpecialFunctions
20160624 tpd src/axiomwebsite/patches.html 20160624.02.tpd.patch
20160624 tpd books/bookvol10.2 category NormalizedTriangularSetCategory refs
20160624 tpd books/bookvolbib category NormalizedTriangularSetCategory refs
diff git a/patch b/patch
index 21428b3..b8e1d1a 100644
 a/patch
+++ b/patch
@@ 1,109 +1,27 @@
books/bookvolbib category NTSCAT NormalizedTriangularSetCategory refs
+books/bookvolbib Aubr96 package DFSFUN DoubleFloatSpecialFunctions refs
Goal: Axiom Literate Programming
Collect algebra references in the bibliography
\index{Lazard, Daniel}
\begin{chunk}{axiom.bib}
@article{Laza91,
 author = "Lazard, Daniel",
 title = "A new method for solving algebraic systems of positive dimension",
 journal = "Discrete. Applied. Mathematics",
 volume = "33",
 year = "1991",
 pages = "147160",
 paper = "Laza91.pdf",
 comment = "\newline\refto{category NTSCAT NormalizedTriangularSetCategory}",
 abstract =
 "A new algorithm is presented for solving algebraic systems of
 equations, which is designed from the structure which is wanted for
 the result. This algorithm is not yet implemented; thus technical
 details and proofs are omitted, for emphasising on the relation
 between the algorithm design and a good representation of the
 result. The algorithm is based on a new theorem of decomposition for
 algebraic varieties."
}

\end{chunk}

+\index{Aubry, Phillippe}
\index{Maza, Marc Moreno}
\index{Rioboo, Renaud}
\begin{chunk}{axiom.bib}
@article{Maza95,
 author = "Maza, Marc Moreno and Rioboo, Renaud",
 title = "Polynomial Gcd Computations over Towers of Algebraic Extensions",
 year = "1995",
 journal = "Proceedings of AAECC11",
+@article{Aubr96,
+ author = "Aubry, Phillippe and Maza, Marc Moreno",
+ title = "Triangular Sets for Solving Polynomial Systems:
+ a Comparison of Four Methods",
+ url = "http://www.lip6.fr/lip6/reports/1997/lip6.1997.009.ps.gz",
+ paper = "Aubr96.pdf",
+ comment = "\newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
keywords = "axiomref",
 paper = "Maza95.pdf",
 comment = "\newline\refto{category NTSCAT NormalizedTriangularSetCategory}",
 abstract =
 "Some methods for polynomial system solving require efficient
 techniques for computing univariate polynomial gcd over algebraic
 extensions of a field. Currently used techniques compute {\sl generic}
 univariate polynomial gcd before {\sl specializing} the result using
 algebraic relations in the ring of coefficients. This strategy
 generates very big intermediate data and fails for many problems. We
 present here a new approach which takes permanently into account those
 algebraic relations. It is based on a property of subresultant
 remainder sequences and leads to a great increase of the speed of
 computations and thus the size of accessible systems."
}

\end{chunk}

\index{Maza, Marc Moreno}
\begin{chunk}{axiom.bib}
@phdthesis{Maza97,
 author = "Maza, Marc Moreno",
 title = "Calculs de pgcd audessus des tours d'extensions simples et
 resolution des systemes d'equations algebriques",
 school = "Universite P.etM. Curie",
 year = "1997",
 paper = "Maza97.pdf",
 keyword = "axiomref",
 comment = "\newline\refto{category NTSCAT NormalizedTriangularSetCategory}",
 url =
 "http://www.csd.uwo.ca/~moreno//Publications/MorenoMazaThesis1997.ps.gz",
abstract =
 "This thesis is dedicated to polynomial system solving by means of
 triangular sets. A first prt presents two algorithms to compute
 polynomial gcds over tower of simple extensions. The first one was
 designed by Renaud Rioboo and applies to algebraic towers. The second
 one is a generalization of the previous one to the most general case
 of seperable towers. These algorithms lead to an efficient
 implementation of two methods suggested by Daniel Lazard to solve
 polynomial systems by means of triangular sets. These programs solved
 problems that were previously unreachable. The second method was only
 sketched by its author. So, a second part of this thesis presents the
 necessary developements to describe a right implementation. Moreover,
 a theorecal and unified presentation, together with an experimental
 comparison with similar methods due to Wu WenTsun, Dongming Wang and
 Michael Kalkbrener were realized by Philippe Aubry and are reported in
 a third part of this document."
+ "Four methods for solving polynomial systems by means of triangular
+ sets are presented and implemented in a unified way. These methods are
+ those of Wu, Lazard, Kalkbrener, and Wang. They are compared on
+ various examples with emphasis on efficiency, conciseness and
+ legibility of the outputs."
}
\end{chunk}
\index{Maza, Marc Moreno}
\begin{chunk}{axiom.bib}
@techreport{Maza00,
 author = "Maza, Marc Moreno",
 title = "On Triangular Decompositions of Algebraic Varieties",
 institution = "Numerical Algorithms Group",
 year = "2000",
 month = "June",
 type = "technical report",
 number = "TR 4/99",
 paper = "Maza00.pdf",
 url = "http://www.csd.uwo.ca/~moreno//Publications",
 keywords = "axiomref",
 abstract =
 "Different kinds of triangular decompositions of algebraic varieties
 are presented. The main result is an efficient method for obtaining
 them. Our strategy is based on a lifting theorem for polynomial
 computations module regular chains."
}

\end{chunk}
diff git a/src/axiomwebsite/patches.html b/src/axiomwebsite/patches.html
index f074e80..e6f7801 100644
 a/src/axiomwebsite/patches.html
+++ b/src/axiomwebsite/patches.html
@@ 5366,6 +5366,8 @@ books/bookvolbib category RegularTriangularSetCategory refs
src/input/dave89 Davenport Looking at a set of equations
20160624.02.tpd.patch
books/bookvolbib category NormalizedTriangularSetCategory refs
+20160624.03.tpd.patch
+books/bookvolbib Aubr96 package DoubleFloatSpecialFunctions

1.7.5.4