From 0b4354d56ceec16e320afd1377d653015286e939 Mon Sep 17 00:00:00 2001
From: Tim Daly
Date: Fri, 24 Jun 2016 13:07:29 0400
Subject: [PATCH] books/bookvolbib Lamb92 category FMCAT FreeModuleCat
Goal: Axiom Literate Programming
Collect algebra references in the bibliography
\index{Lambe, Larry A.}
\begin{chunk}{axiom.bib}
@article{Lamb92,
author = "Lambe, Larry",
title = "Next Generation Computer Algebra Systems AXIOM and the
Scratchpad Concept: Applications to Research in Algebra",
publisher = "21st Nordic Congress of Mathematicians",
year = "1992",
paper = "Lamb92.pdf",
url = "http://axiomwiki.newsynthesis.org/public/refs/axiom21cong.pdf",
keywords = "axiomref",
comment = "\newline\refto{category FMCAT FreeModuleCat}",
abstract =
"One way in which mathematicians deal with infinite amounts of data is
symbolic representation. A simple example is the quadratic equation
\[x = \frac{b\pm\sqrt{b^24ac}}{2a}\]
a formula which uses symbolic representation to describe the solutions
to an infinite class of equations. Most computer algebra systems can
deal with polynomials with symbolic coefficients, but what if symbolic
exponents are called for (e.g. $1+t^i$)? What if symbolic limits on
summations are also called for, for example
\[1+t+\ldots+t^i=\sum_j{t^j}\]
The ``Scratchpad Concept'' is a theoretical ideal which allows the
implementation of objects at this level of abstraction and beyond in a
mathematically consistent way. The Axiom computer algebra system is an
implementation of a major part of the Scratchpad Concept. Axiom
(formerly called Scratchpad) is a language with extensible
parameterized types and generic operators which is based on the
notions of domains and categories. By examining some aspects of the
Axiom system, the Scratchpad Concept will be illustrated. It will be
shown how some complex problems in homologicial algebra were solved
through the use of this system."
}
\end{chunk}

books/bookvol10.2.pamphlet  23 +++++++
books/bookvolbib.pamphlet  83 ++++++++++++++++++++++++++++++
changelog  3 +
patch  46 +++++++++++++++
src/axiomwebsite/patches.html  2 +
5 files changed, 112 insertions(+), 45 deletions()
diff git a/books/bookvol10.2.pamphlet b/books/bookvol10.2.pamphlet
index ef9bf87..0c002fb 100644
 a/books/bookvol10.2.pamphlet
+++ b/books/bookvol10.2.pamphlet
@@ 43094,18 +43094,18 @@ P:RecursivePolynomialCategory(R,E,V)):
?~=? : (%,%) > Boolean
\end{verbatim}
+See: Lazard\cite{Laza91}, Kalkbrener\cite{Kalk98}, Moreno Maza\cite{Maza98}
+\label{category SFRTCAT SquareFreeRegularTriangularSetCategory}
\begin{chunk}{category SFRTCAT SquareFreeRegularTriangularSetCategory}
)abbrev category SFRTCAT SquareFreeRegularTriangularSetCategory
++ Author: Marc Moreno Maza
++ Date Created: 09/03/1996
++ Date Last Updated: 09/10/1998
++ References :
++ [1] D. LAZARD "A new method for solving algebraic systems of
++ positive dimension" Discr. App. Math. 33:147160,1991
++ [2] M. KALKBRENER "Algorithmic properties of polynomial rings"
++ Habilitation Thesis, ETZH, Zurich, 1995.
++ [3] M. MORENO MAZA "A new algorithm for computing triangular
++ decomposition of algebraic varieties" NAG Tech. Rep. 4/98.
+++ Laza91 A new method for solving algebraic systems of positive dimension
+++ Kalk98 Algorithmic properties of polynomial rings
+++ Maza98 A new algorithm for computing triangular decomposition of
+++ algebraic varieties
++ Description:
++ The category of squarefree regular triangular sets.
++ A regular triangular set \spad{ts} is squarefree if
@@ 47028,12 +47028,16 @@ These exports come from \refto{RetractableTo}(Basis:SetCategory):
retractIfCan : % > Union(Basis,"failed")
\end{verbatim}
+See: Lambe\cite{Lamb92}
+\label{category FMCAT FreeModuleCat}
\begin{chunk}{category FMCAT FreeModuleCat}
)abbrev category FMCAT FreeModuleCat
++ Author: Michel Petitot petitot@lifl.fr
++ Date Created: 91
++ Date Last Updated: 7 Juillet 92
++ Fix History: compilation v 2.1 le 13 dec 98
+++ References:
+++ Lamb92 Next Generation Computer Algebra Systems AXIOM and the
+++ Scratchpad Concept: Applications to Research in Algebra
++ Description:
++ A domain of this category
++ implements formal linear combinations
@@ 49742,14 +49746,15 @@ P:RecursivePolynomialCategory(R,E,V)):
?~=? : (%,%) > Boolean
\end{verbatim}
+See Lazard\cite{Laza91}
+\label{category SNTSCAT SquareFreeNormalizedTriangularSetCategory}
\begin{chunk}{category SNTSCAT SquareFreeNormalizedTriangularSetCategory}
)abbrev category SNTSCAT SquareFreeNormalizedTriangularSetCategory
++ Author: Marc Moreno Maza
++ Date Created: 10/07/1998
++ Date Last Updated: 12/16/1998
++ References :
++ [1] D. LAZARD "A new method for solving algebraic systems of
++ positive dimension" Discr. App. Math. 33:147160,1991
+++ Laza91 A new method for solving algebraic systems of positive dimension
++ Description:
++ The category of squarefree and normalized triangular sets.
++ Thus, up to the primitivity axiom of [1], these sets are Lazard
diff git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index ae03eca..24e0fe7 100644
 a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ 10188,6 +10188,14 @@ Symposium on Symbolic and Algebraic Computation. ACM Press, New York, NY,
\end{chunk}
+\begin{chunk}{axiom.bib}
+@misc{America,
+ keywords = "axiomref",
+ url = "http://america.pink/axiomcomputeralgebrasystem_526647.html"
+}
+
+\end{chunk}
+
\index{Augot, D.}
\index{Charpin, P.}
\index{Sendrier, N.}
@@ 12434,6 +12442,21 @@ Vol. 8 No. 3 pp195210 (2001)
\end{chunk}
+\index{Hereman, Willy}
+\begin{chunk}{axiom.bib}
+@misc{Here96,
+ author = "Hereman, Willy",
+ title = "The Incredible World of Symbolic Mathematics
+ A Review of Computer Algebra Systems",
+ year = "1996",
+ keywords = "axiomref",
+ url =
+"https://inside.mines.edu/~whereman/papers/HeremanPhysicsWorld9March1996.pdf",
+ paper = "Here96.pdf"
+}
+
+\end{chunk}
+
\index{Hodorog, Madalina}
\begin{chunk}{axiom.bib}
@phdthesis{Hodo11,
@@ 12977,14 +13000,19 @@ CODEN JSYCEH ISSN 07477171
\end{chunk}
\index{Lambe, Larry A.}
\begin{chunk}{ignore}
\bibitem[Lambe 92]{Lam92} Lambe, Larry
 title = "Next Generation Computer Algebra Systems AXIOM and the Scratchpad Concept: Applications to Research in Algebra",
$21^{st}$ Nordic Congress of Mathematicians 1992
 paper = "Lam92.pdf",
+\begin{chunk}{axiom.bib}
+@article{Lamb92,
+ author = "Lambe, Larry",
+ title = "Next Generation Computer Algebra Systems AXIOM and the
+ Scratchpad Concept: Applications to Research in Algebra",
+ publisher = "21st Nordic Congress of Mathematicians",
+ year = "1992",
+ paper = "Lamb92.pdf",
+ url = "http://axiomwiki.newsynthesis.org/public/refs/axiom21cong.pdf",
keywords = "axiomref",
 abstract = "
 One way in which mathematicians deal with infinite amounts of data is
+ comment = "\newline\refto{category FMCAT FreeModuleCat}",
+ abstract =
+ "One way in which mathematicians deal with infinite amounts of data is
symbolic representation. A simple example is the quadratic equation
\[x = \frac{b\pm\sqrt{b^24ac}}{2a}\]
a formula which uses symbolic representation to describe the solutions
@@ 13004,6 +13032,7 @@ $21^{st}$ Nordic Congress of Mathematicians 1992
Axiom system, the Scratchpad Concept will be illustrated. It will be
shown how some complex problems in homologicial algebra were solved
through the use of this system."
+}
\end{chunk}
@@ 13920,6 +13949,18 @@ Internal Report 9517, Universit\"at Karlsruhe, Fakult\"at f\"ur Informatik
\end{chunk}
+\index{Senechaud, P.}
+\index{Siebert, F.}
+\index{Villard, Gilles}
+\begin{chunk}{ignore}
+\bibitem[SSV87]{SSV87} Senechaud, P.; Siebert, F.; Villard G.
+ title =
+ "Scratchpad II: Pr{\'e}sentation d'un nouveau langage de calcul formel",
+Technical Report 640M, TIM 3 (IMAG), Grenoble, France, Feb 1987
+ keywords = "axiomref",
+
+\end{chunk}
+
\index{Shannon, D.}
\index{Sweedler, M.}
\begin{chunk}{ignore}
@@ 14017,17 +14058,6 @@ Physics, pp337344, Acireale (Italy), 1992 Kluwer, Dordrecht 1993
\end{chunk}
\index{Senechaud, P.}
\index{Siebert, F.}
\index{Villard, Gilles}
\begin{chunk}{ignore}
\bibitem[SSV87]{SSV87} Senechaud, P.; Siebert, F.; Villard G.
 title = "Scratchpad II: Pr{\'e}sentation d'un nouveau langage de calcul formel",
Technical Report 640M, TIM 3 (IMAG), Grenoble, France, Feb 1987
 keywords = "axiomref",

\end{chunk}

\index{Steele, Guy L.}
\index{Gabriel, Richard P.}
\begin{chunk}{ignore}
@@ 14101,6 +14131,14 @@ IBM Manual, March 1988
\end{chunk}
+\begin{chunk}{axiom.bib}
+@misc{Sympy,
+ keywords = "axiomref",
+ url = "https://github.com/sympy/sympy/wiki/SymPyvs.Axiom"
+}
+
+\end{chunk}
+
\subsection{T} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\index{Thompson, Simon}
@@ 16830,7 +16868,8 @@ Comput. J. 9 281285. (1966)
author = "Kalkbrener, M.",
title = "Algorithmic properties of polynomial rings",
journal = "Journal of Symbolic Computation",
 comment = "\newline\refto{category RSETCAT RegularTriangularSetCategory}",
+ comment = "\newline\refto{category RSETCAT RegularTriangularSetCategory}
+ \newline\refto{category SFRTCAT SquareFreeRegularTriangularSetCategory}",
year = "1998",
paper = "Kalk98.pdf",
abstract =
@@ 17032,7 +17071,8 @@ PrenticeHall. (1974)
year = "1991",
pages = "147160",
paper = "Laza91.pdf",
 comment = "\newline\refto{category NTSCAT NormalizedTriangularSetCategory}",
+ comment = "\newline\refto{category NTSCAT NormalizedTriangularSetCategory}
+ \newline\refto{category SFRTCAT SquareFreeRegularTriangularSetCategory}",
abstract =
"A new algorithm is presented for solving algebraic systems of
equations, which is designed from the structure which is wanted for
@@ 17368,7 +17408,8 @@ Mathematical Surveys. 3 Am. Math. Soc., Providence, RI. (1966)
algebraic varieties",
institution = "Numerical Algorithms Group (NAG)",
comment = "\newline\refto{category RSETCAT RegularTriangularSetCategory}
 \newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
+ \newline\refto{package RSDCMPK RegularSetDecompositionPackage}
+ \newline\refto{category SFRTCAT SquareFreeRegularTriangularSetCategory}",
year = "1998"
}
diff git a/changelog b/changelog
index 818a99d..c0c405e 100644
 a/changelog
+++ b/changelog
@@ 1,3 +1,6 @@
+20160624 tpd src/axiomwebsite/patches.html 20160624.04.tpd.patch
+20160624 tpd books/bookvol10.2 Lamb92 category FMCAT FreeModuleCat
+20160624 tpd books/bookvolbib Lamb92 category FMCAT FreeModuleCat
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
diff git a/patch b/patch
index b8e1d1a..de8703a 100644
 a/patch
+++ b/patch
@@ 1,26 +1,42 @@
books/bookvolbib Aubr96 package DFSFUN DoubleFloatSpecialFunctions refs
+books/bookvolbib Lamb92 category FMCAT FreeModuleCat
Goal: Axiom Literate Programming
Collect algebra references in the bibliography
\index{Aubry, Phillippe}
\index{Maza, Marc Moreno}
+\index{Lambe, Larry A.}
\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}",
+@article{Lamb92,
+ author = "Lambe, Larry",
+ title = "Next Generation Computer Algebra Systems AXIOM and the
+ Scratchpad Concept: Applications to Research in Algebra",
+ publisher = "21st Nordic Congress of Mathematicians",
+ year = "1992",
+ paper = "Lamb92.pdf",
+ url = "http://axiomwiki.newsynthesis.org/public/refs/axiom21cong.pdf",
keywords = "axiomref",
+ comment = "\newline\refto{category FMCAT FreeModuleCat}",
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."
+ "One way in which mathematicians deal with infinite amounts of data is
+ symbolic representation. A simple example is the quadratic equation
+ \[x = \frac{b\pm\sqrt{b^24ac}}{2a}\]
+ a formula which uses symbolic representation to describe the solutions
+ to an infinite class of equations. Most computer algebra systems can
+ deal with polynomials with symbolic coefficients, but what if symbolic
+ exponents are called for (e.g. $1+t^i$)? What if symbolic limits on
+ summations are also called for, for example
+ \[1+t+\ldots+t^i=\sum_j{t^j}\]
+
+ The ``Scratchpad Concept'' is a theoretical ideal which allows the
+ implementation of objects at this level of abstraction and beyond in a
+ mathematically consistent way. The Axiom computer algebra system is an
+ implementation of a major part of the Scratchpad Concept. Axiom
+ (formerly called Scratchpad) is a language with extensible
+ parameterized types and generic operators which is based on the
+ notions of domains and categories. By examining some aspects of the
+ Axiom system, the Scratchpad Concept will be illustrated. It will be
+ shown how some complex problems in homologicial algebra were solved
+ through the use of this system."
}
\end{chunk}
diff git a/src/axiomwebsite/patches.html b/src/axiomwebsite/patches.html
index e6f7801..43f2507 100644
 a/src/axiomwebsite/patches.html
+++ b/src/axiomwebsite/patches.html
@@ 5368,6 +5368,8 @@ src/input/dave89 Davenport Looking at a set of equations
books/bookvolbib category NormalizedTriangularSetCategory refs
20160624.03.tpd.patch
books/bookvolbib Aubr96 package DoubleFloatSpecialFunctions
+20160624.04.tpd.patch
+books/bookvolbib Lamb92 category FMCAT FreeModuleCat

1.7.5.4