From 5ca7a8bb97d7a38b6cee1303fc2f98fc4f636400 Mon Sep 17 00:00:00 2001
From: Tim Daly
Date: Fri, 24 Jun 2016 09:50:54 0400
Subject: [PATCH] books/bookvolbib category NTSCAT
NormalizedTriangularSetCategory 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{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",
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."
}
\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}

books/bookvol10.2.pamphlet  23 +++
books/bookvolbib.pamphlet  138 +++++++++++++++++++++++++++++++++++
changelog  3 +
patch  125 +++++++++++++++++++++++++++++++
src/axiomwebsite/patches.html  2 +
5 files changed, 247 insertions(+), 44 deletions()
diff git a/books/bookvol10.2.pamphlet b/books/bookvol10.2.pamphlet
index b48a9d6..ef9bf87 100644
 a/books/bookvol10.2.pamphlet
+++ b/books/bookvol10.2.pamphlet
@@ 41143,14 +41143,15 @@ These exports come from \refto{MonadWithUnit}():
?**? : (%,NonNegativeInteger) > %
\end{verbatim}
+See: Schafer\cite{Scha66}
+\label{category NASRING NonAssociativeRing}
\begin{chunk}{category NASRING NonAssociativeRing}
)abbrev category NASRING NonAssociativeRing
++ Author: J. Grabmeier, R. Wisbauer
++ Date Created: 01 March 1991
++ Date Last Updated: 11 June 1991
++ Reference:
++ R.D. Schafer: An Introduction to Nonassociative Algebras
++ Academic Press, New York, 1966
+++ Scha66 An Introduction to Nonassociative Algebras
++ Description:
++ A NonAssociativeRing is a non associative rng which has a unit,
++ the multiplication is not necessarily commutative or associative.
@@ 41628,22 +41629,20 @@ P:RecursivePolynomialCategory(R,E,V)):
?~=? : (%,%) > Boolean
\end{verbatim}
+See: Lazard\cite{Laza91}, Aubry\cite{Aubr99},
+Morena Maza\cite{Maza95}\cite{Maza97}
+\label{category NTSCAT NormalizedTriangularSetCategory}
\begin{chunk}{category NTSCAT NormalizedTriangularSetCategory}
)abbrev category NTSCAT NormalizedTriangularSetCategory
++ Author: Marc Moreno Maza
++ Date Created: 10/07/1998
++ Date Last Updated: 12/12/1998
++ References :
++ [1] D. LAZARD "A new method for solving algebraic systems of
++ positive dimension" Discr. App. Math. 33:147160,1991
++ [2] P. AUBRY, D. LAZARD and M. MORENO MAZA "On the Theories
++ of Triangular Sets" Journal of Symbol. Comp. (to appear)
++ [3] M. MORENO MAZA and R. RIOBOO "Computations of gcd over
++ algebraic towers of simple extensions" In proceedings of AAECC11
++ Paris, 1995.
++ [4] M. MORENO MAZA "Calculs de pgcd audessus des tours
++ d'extensions simples et resolution des systemes d'equations
++ algebriques" These, Universite P.etM. Curie, Paris, 1997.
+++ Laza91 A new method for solving algebraic systems of positive dimension
+++ Aubr99 On the Theories of Triangular Sets
+++ Maza95 Polynomial Gcd Computations over Towers of Algebraic Extensions
+++ Maza97 Calculs de pgcd audessus des tours d'extensions simples et
+++ resolution des systemes d'equations algebriques
++ Description:
++ The category of normalized triangular sets. A triangular
++ set ts is said normalized if for every algebraic
diff git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index df95e69..f54c98f 100644
 a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ 3920,13 +3920,14 @@ Kelsey, Tom; Martin, Ursula; Owre, Sam
\begin{chunk}{axiom.bib}
@phdthesis{Jack95,
author = "Jackson, Paul Bernard",
 title = "Enhancing the NUPRL Proof Development System and Applying it to Computational Abstract Algebra",
+ title = "Enhancing the NUPRL Proof Development System and Applying it to
+ Computational Abstract Algebra",
school = "Cornell University",
year = "1995",
month = "1",
paper = "Jack95.pdf",
keyword = "axiomref",
 note = {
+ abstract = "
This thesis describes substantial enhancements that were made to the
software tools in the Nuprl system that are used to interactively
guide the production of formal proofs. Over 20,000 lines of code were
@@ 3967,7 +3968,7 @@ Kelsey, Tom; Martin, Ursula; Owre, Sam
This work was all done in Nuprl's constructive type theory. The thesis
discusses the appropriateness of this foundation, and the extent to
 which the work relied on it.}
+ which the work relied on it."
}
\end{chunk}
@@ 11349,6 +11350,31 @@ Academic Press, New York, NY, USA, 1988, ISBN 0122042329
\end{chunk}
\index{Davenport, James H.}
+\begin{chunk}{axiom.bib}
+@techreport{Dave89,
+ author = "Davenport, James H.",
+ title = "Looking at a set of equations",
+ institution = "University of Bath, School of Mathematical Sciences",
+ year = "1989",
+ type = "technical report",
+ paper = "Dave89.pdf",
+ url =
+"http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.261.767\&rep=rep1&type=pdf",
+ abstract =
+ "This working paper describes our experiences with using the
+ Groebnerbasis method [Buchberger, 1985] to solve some related systems
+ of polynomial equations. While we have not yet been able to solve the
+ system that was our primary motivation, we feel that these experiences
+ may prove useful to others investigating Buchberger's algorithm in
+ this context, especially when, as is the case for the system under
+ investigation, the equations are highly structured. We conclude with
+ some examples of the polynomials that we factored in the course of
+ this investigation."
+}
+
+\end{chunk}
+
+\index{Davenport, James H.}
\begin{chunk}{ignore}
\bibitem[Davenport 14]{Dav14} Davenport, James H.
title = "Computer Algebra textbook",
@@ 13195,6 +13221,28 @@ ISSN 07308639
\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}
+
\index{McJones, Paul}
\begin{chunk}{ignore}
\bibitem[McJones 11]{McJ11} McJones, Paul
@@ 14859,7 +14907,8 @@ J. Symbolic Computation 5, 237259 (1988)
url = "http://www.csd.uwo.ca/~moreno/Publications/AubryLazardMorenoMaza1999JSC.pdf",
papers = "Aubr99.pdf",
comment = "\newline\refto{category TSETCAT TriangularSetCategory}
 \newline\refto{category RSETCAT RegularTriangularSetCategory}",
+ \newline\refto{category RSETCAT RegularTriangularSetCategory}
+ \newline\refto{category NTSCAT NormalizedTriangularSetCategory}",
abstract =
"Different notions of triangular sets are presented. The relationship
between these notions are studied. The main result is that four
@@ 16965,10 +17014,25 @@ PrenticeHall. (1974)
\end{chunk}
\index{Lazard, Daniel}
\begin{chunk}{ignore}
\bibitem[Lazard 91]{Laz91} Lazard, D.
+\begin{chunk}{axiom.bib}
+@article{Laza91,
+ author = "Lazard, Daniel",
title = "A new method for solving algebraic systems of positive dimension",
Discr. App. Math. 33:147160,1991
+ 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}
@@ 17228,18 +17292,59 @@ Mathematical Surveys. 3 Am. Math. Soc., Providence, RI. (1966)
\index{Maza, Marc Moreno}
\index{Rioboo, Renaud}
\begin{chunk}{ignore}
\bibitem[Maza 95]{MR95} Maza, M. Moreno; Rioboo, R.
 title = "Computations of gcd over algebraic towers of simple extensions",
In proceedings of AAECC11 Paris, 1995.
+\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",
+ keywords = "axiomref",
+ 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}{ignore}
\bibitem[Maza 97]{Maz97} Maza, M. Moreno
 title = "Calculs de pgcd audessus des tours d'extensions simples et resolution des systemes d'equations algebriques",
These, Universite P.etM. Curie, Paris, 1997.
+\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."
+}
\end{chunk}
@@ 18093,7 +18198,8 @@ Num. Math. 16 205223. (1970)
title = "An Introduction to Nonassociative Algebras",
year = "1966",
publisher = "Academic Press, New York",
 comment = "\newline\refto{category NARNG NonAssociativeRng}",
+ comment = "\newline\refto{category NARNG NonAssociativeRng}
+ \newline\refto{category NASRING NonAssociativeRing}",
comment = "documentation for AlgebraGivenByStructuralConstants"
}
diff git a/changelog b/changelog
index 5af2680..7413678 100644
 a/changelog
+++ b/changelog
@@ 1,3 +1,6 @@
+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
20160624 tpd src/axiomwebsite/patches.html 20160624.01.tpd.patch
20160624 tpd src/input/dave89 Davenport Looking at a set of equations
20160624 tpd src/input/Makefile add dave89.input
diff git a/patch b/patch
index daf41f6..21428b3 100644
 a/patch
+++ b/patch
@@ 1,16 +1,109 @@
src/input/dave89 Davenport Looking at a set of equations

Goal: Axiom Test Suite

These are the equations from Dave89, Davenport's
``Looking at a set of equations'' paper.

"This working paper describes our experiences with using the
Groebnerbasis method [Buchberger, 1985] to solve some related systems
of polynomial equations. While we have not yet been able to solve the
system that was our primary motivation, we feel that these experiences
may prove useful to others investigating Buchberger's algorithm in
this context, especially when, as is the case for the system under
investigation, the equations are highly structured. We conclude with
some examples of the polynomials that we factored in the course of
this investigation."
+books/bookvolbib category NTSCAT NormalizedTriangularSetCategory 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{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",
+ 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."
+}
+
+\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 35542b8..f074e80 100644
 a/src/axiomwebsite/patches.html
+++ b/src/axiomwebsite/patches.html
@@ 5364,6 +5364,8 @@ books/bookvolbib add RISC references
books/bookvolbib category RegularTriangularSetCategory refs
20160624.01.tpd.patch
src/input/dave89 Davenport Looking at a set of equations
+20160624.02.tpd.patch
+books/bookvolbib category NormalizedTriangularSetCategory refs

1.7.5.4