From ca85e1d817f52e0ec373326f55f9984268d02aa8 Mon Sep 17 00:00:00 2001
From: Tim Daly
Date: Sun, 28 May 2017 16:39:51 -0400
Subject: [PATCH] bookvolbib reference for Cylindrical Algebraic Decomposition
Goal: Axiom Algebra
\index{Arnon, Dennis}
\index{Buchberger, Bruno}
\begin{chunk}{axiom.bib}
@misc{Arno88a,
author = "Arnon, Dennis and Buchberger, Bruno",
title = "Algorithms in Real Algebraic Geometry",
publisher = "Academic Press",
year = "1988",
journal = "Journal of Symbolic Computation"
}
\end{chunk}
\index{Dolzmann, Andreas}
\index{Sturm, Thomas}
\index{Weispfenning, Volker}
\begin{chunk}{axiom.bib}
@techreport{Dolz97a,
author = "Dolzmann, Andreas and Sturm, Thomas and
Weispfenning, Volker",
title = "Real Quantifier Elimination in Practice",
type = "technical report",
institution = "University of Passau",
number = "MIP-9720",
year = "1997",
abstract =
"We give a survey of three implemented real quantifier elimination
methods: partial cylindrical algebraic decomposition, virtual
substituion of test terms, and a combination of Groebner basis
computations with multivariate real root counting. We examine the
scope of these implementations for applications in various fields of
science, engineering, and economics",
paper = "Dolz97a.pdf"
}
\end{chunk}
\index{Dolzmann, Andreas}
\index{Sturm, Thomas}
\begin{chunk}{axiom.bib}
@misc{Dolz97,
author = "Dolzmann, Andreas and Sturm, Thomas",
title = "Guarded Expressions in Practice",
link = "\url{http://redlog.dolzmann.de/papers/pdf/MIP-9702.pdf}",
year = "1997",
abstract =
"Computer algebra systems typically drop some degenerate cases when
evaluating expressions, e.g. $x/x$ becomes 1 dropping the case
$x=0$. We claim that it is feasible in practice to compute also the
degenerate cases yielding {\sl guarded expressions}. We work over real
closed fields but our ideas about handling guarded expressions can be
easily transferred to other situations. Using formulas as guards
provides a powerful tool for heuristically reducing the combinatorial
explosion of cases: equivalent, redundant, tautological, and
contradictive cases can be detected by simplification and quantifier
elimination. Our approach allows to simplify the expressions on the
basis of simplification knowledge on the logical side. The method
described in this paper is implemented in the REDUCE package GUARDIAN,
which is freely available on the WWW.",
paper = "Dolz97.pdf"
}
\end{chunk}
\index{Basu, Saugata}
\index{Pollack, Richard}
\index{Roy, Marie-Francoise}
\begin{chunk}{axiom.bib}
@book{Basu06,
author = "Basu, Saugata and Pollack, Richard and
Roy, Marie-Francoise",
title = "Algorithms in Real Algebraic Geometry",
publisher = "Springer",
year = "2006",
isbn = "978-3-540-33098-1"
}
\end{chunk}
\index{Arnon, Dennis Soul\'e}
\begin{chunk}{axiom.bib}
@phdthesis{Arno81,
author = {Arnon, Dennis Soul\'e},
title = "Algorithms for the Geometry of Semi-algebraic Sets",
institution = "University of Wisconsin-Madison",
year = "1981",
abstract =
"Let A be a set of polynomials in r variables with integer
coefficients. An $A$-invariant cylindrical algebraic decomposition
(cad) of $r$-dimensional Euclidean space (G. Collins, Lect. Notes
Comp. Sci., 33, Springer-Verlag, 1975, pp 134-183) is a certain
cellular decomposition of $r$-space, such that each cell is a
semi-algebraic set, the polynomials of $A$ are sign-invariant on
each cell, and the cells are arranged into cylinders. The cad
algorithm given by Collins provides, among other applications,
the fastest known decision procedure for real closed fields, a
cellular decomposition algorithm for semi-algebraic sets, and a
method of solving nonlinear (polynomial) optimization problems
exactly. The time-consuming calculations with real algebraic
numbers required by the algorithm have been an obstacle to its
implementation and use. The major contribution of this thesis
is a new version of the cad algorithm for $r \le 3$, in which
one works with maximal connected $A$-invariant collections of
cells, in such a way as to often avoid the most time-consuming
algebraic number calculations. Essential to this new cad
algorithm is an algorithm we present for determination of
adjacenies among the cells of a cad. Computer programs for
the cad and adjacency algorithms have been written, providing
the first complete implementation of a cad algorithm. Empirical
data obtained from application of these programs are presented
and analyzed."
}
\end{chunk}
\index{McCallum, Scott}
\begin{chunk}{axiom.bib}
@phdthesis{Mcca84,
author = "McCallum, Scott",
title = "An Improved Projection Operator for Cylindrical
Algebraic Decomposition",
institution = "University of Wisconsin-Madison",
year = "1984",
comment = "Computer Sciences Technical Report \#578",
link = "\url{ftp://ftp.cs.wisc.edu/pub/techreports/1985/TR578.pdf}",
abstract =
"A fundamental algorithm pertaining to the solution of polynomial
equations in several variables is the {\sl cylindrical algebraic
decomposition (cad)} algorithm due to G.E. Collins. Given as input
a set $A$ of integral polynomials in $r$ variables, the cad
algorithm produces a decomposition of the euclidean space of $r$
dimensions into cells, such that each polynomial in $A$ is
invariant in sign throughout each of the cells in the decomposition.
A key component of the cad algorithm is the projection operation:
the {\sl projection} of a set $A$ of $r$-variate polynomials is
defined to be a certain set $P$ of $(r-1)$-variate polynomials.
The solution set, or variety, of the polynomials in $P$ comprises
a projection in the geometric sense of the variety of $A$. The cad
algorithm proceeds by forming successive projections of the input
set $A$, each projection resulting in the elimination of one
variable.
This thesis is concerned with a refinement to the cad algorithm,
and to its projection operation in particular. It is shown, using
a theorem from real algebraic geometry, that the original
projection set that Collins used can be substantially reduced in
size, without affecting its essential properties. The results of
theoretical analysis and empirical observations suggest that the
reduction in the projection set size leads to an overall decrease
in the computing time of the cad algorithm.",
paper = "Mcca84.pdf"
}
\end{chunk}
---
books/bookvolbib.pamphlet | 154 ++++++++++++++++++++++++++++++++++++++--
changelog | 2 +
patch | 157 ++++++++++++++++++++++++++++++++++++++--
src/axiom-website/patches.html | 2 +
4 files changed, 304 insertions(+), 11 deletions(-)
diff --git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index ce8dbdb..2c0a27b 100644
--- a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ -1639,7 +1639,7 @@ when shown in factored form.
\index{Brown, W. S.}
\begin{chunk}{axiom.bib}
-@articla{Brow78,
+@article{Brow78,
author = "Brown, W. S.",
title = "The Subresultant PRS Algorithm",
journal = "ACM Transactions on Mathematical Software",
@@ -6985,12 +6985,14 @@ England, Matthew; Wilson, David
\index{Dolzmann, Andreas}
\index{Sturm, Thomas}
-\begin{chunk}{ignore}
-\bibitem[Dolzmann 97]{Dolz97} Dolzmann, Andreas; Sturm, Thomas
+\begin{chunk}{axiom.bib}
+@misc{Dolz97,
+ author = "Dolzmann, Andreas and Sturm, Thomas",
title = "Guarded Expressions in Practice",
link = "\url{http://redlog.dolzmann.de/papers/pdf/MIP-9702.pdf}",
- abstract = "
- Computer algebra systems typically drop some degenerate cases when
+ year = "1997",
+ abstract =
+ "Computer algebra systems typically drop some degenerate cases when
evaluating expressions, e.g. $x/x$ becomes 1 dropping the case
$x=0$. We claim that it is feasible in practice to compute also the
degenerate cases yielding {\sl guarded expressions}. We work over real
@@ -7004,6 +7006,7 @@ England, Matthew; Wilson, David
described in this paper is implemented in the REDUCE package GUARDIAN,
which is freely available on the WWW.",
paper = "Dolz97.pdf"
+}
\end{chunk}
@@ -14508,6 +14511,42 @@ Proc ISSAC 97 pp172-175 (1997)
\subsection{A} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\index{Arnon, Dennis Soul\'e}
+\begin{chunk}{axiom.bib}
+@phdthesis{Arno81,
+ author = {Arnon, Dennis Soul\'e},
+ title = "Algorithms for the Geometry of Semi-algebraic Sets",
+ institution = "University of Wisconsin-Madison",
+ year = "1981",
+ abstract =
+ "Let A be a set of polynomials in r variables with integer
+ coefficients. An $A$-invariant cylindrical algebraic decomposition
+ (cad) of $r$-dimensional Euclidean space (G. Collins, Lect. Notes
+ Comp. Sci., 33, Springer-Verlag, 1975, pp 134-183) is a certain
+ cellular decomposition of $r$-space, such that each cell is a
+ semi-algebraic set, the polynomials of $A$ are sign-invariant on
+ each cell, and the cells are arranged into cylinders. The cad
+ algorithm given by Collins provides, among other applications,
+ the fastest known decision procedure for real closed fields, a
+ cellular decomposition algorithm for semi-algebraic sets, and a
+ method of solving nonlinear (polynomial) optimization problems
+ exactly. The time-consuming calculations with real algebraic
+ numbers required by the algorithm have been an obstacle to its
+ implementation and use. The major contribution of this thesis
+ is a new version of the cad algorithm for $r \le 3$, in which
+ one works with maximal connected $A$-invariant collections of
+ cells, in such a way as to often avoid the most time-consuming
+ algebraic number calculations. Essential to this new cad
+ algorithm is an algorithm we present for determination of
+ adjacenies among the cells of a cad. Computer programs for
+ the cad and adjacency algorithms have been written, providing
+ the first complete implementation of a cad algorithm. Empirical
+ data obtained from application of these programs are presented
+ and analyzed."
+}
+
+\end{chunk}
+
\index{Arnon, Dennis S.}
\index{Collins, George E.}
\index{McCallum, Scott}
@@ -14600,6 +14639,19 @@ Proc ISSAC 97 pp172-175 (1997)
\end{chunk}
+\index{Arnon, Dennis}
+\index{Buchberger, Bruno}
+@misc{Arno88a,
+\begin{chunk}{axiom.bib}
+ author = "Arnon, Dennis and Buchberger, Bruno",
+ title = "Algorithms in Real Algebraic Geometry",
+ publisher = "Academic Press",
+ year = "1988",
+ journal = "Journal of Symbolic Computation"
+}
+
+\end{chunk}
+
\subsection{B} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\index{Baker, Henry G.}
@@ -14647,6 +14699,21 @@ Proc ISSAC 97 pp172-175 (1997)
\end{chunk}
+\index{Basu, Saugata}
+\index{Pollack, Richard}
+\index{Roy, Marie-Francoise}
+\begin{chunk}{axiom.bib}
+@book{Basu06,
+ author = "Basu, Saugata and Pollack, Richard and
+ Roy, Marie-Francoise",
+ title = "Algorithms in Real Algebraic Geometry",
+ publisher = "Springer",
+ year = "2006",
+ isbn = "978-3-540-33098-1"
+}
+
+\end{chunk}
+
\index{Beaumont, James}
\index{Bradford, Russell}
\index{Davenport, James H.}
@@ -15081,6 +15148,30 @@ Proc ISSAC 97 pp172-175 (1997)
\end{chunk}
+\index{Dolzmann, Andreas}
+\index{Sturm, Thomas}
+\index{Weispfenning, Volker}
+\begin{chunk}{axiom.bib}
+@techreport{Dolz97a,
+ author = "Dolzmann, Andreas and Sturm, Thomas and
+ Weispfenning, Volker",
+ title = "Real Quantifier Elimination in Practice",
+ type = "technical report",
+ institution = "University of Passau",
+ number = "MIP-9720",
+ year = "1997",
+ abstract =
+ "We give a survey of three implemented real quantifier elimination
+ methods: partial cylindrical algebraic decomposition, virtual
+ substitution of test terms, and a combination of Groebner basis
+ computations with multivariate real root counting. We examine the
+ scope of these implementations for applications in various fields of
+ science, engineering, and economics",
+ paper = "Dolz97a.pdf"
+}
+
+\end{chunk}
+
\subsection{E} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\index{RealClosure}
@@ -15301,6 +15392,47 @@ Proc ISSAC 97 pp172-175 (1997)
\end{chunk}
+\index{McCallum, Scott}
+\begin{chunk}{axiom.bib}
+@phdthesis{Mcca84,
+ author = "McCallum, Scott",
+ title = "An Improved Projection Operator for Cylindrical
+ Algebraic Decomposition",
+ institution = "University of Wisconsin-Madison",
+ year = "1984",
+ comment = "Computer Sciences Technical Report \#578",
+ link = "\url{ftp://ftp.cs.wisc.edu/pub/techreports/1985/TR578.pdf}",
+ abstract =
+ "A fundamental algorithm pertaining to the solution of polynomial
+ equations in several variables is the {\sl cylindrical algebraic
+ decomposition (cad)} algorithm due to G.E. Collins. Given as input
+ a set $A$ of integral polynomials in $r$ variables, the cad
+ algorithm produces a decomposition of the euclidean space of $r$
+ dimensions into cells, such that each polynomial in $A$ is
+ invariant in sign throughout each of the cells in the decomposition.
+
+ A key component of the cad algorithm is the projection operation:
+ the {\sl projection} of a set $A$ of $r$-variate polynomials is
+ defined to be a certain set $P$ of $(r-1)$-variate polynomials.
+ The solution set, or variety, of the polynomials in $P$ comprises
+ a projection in the geometric sense of the variety of $A$. The cad
+ algorithm proceeds by forming successive projections of the input
+ set $A$, each projection resulting in the elimination of one
+ variable.
+
+ This thesis is concerned with a refinement to the cad algorithm,
+ and to its projection operation in particular. It is shown, using
+ a theorem from real algebraic geometry, that the original
+ projection set that Collins used can be substantially reduced in
+ size, without affecting its essential properties. The results of
+ theoretical analysis and empirical observations suggest that the
+ reduction in the projection set size leads to an overall decrease
+ in the computing time of the cad algorithm.",
+ paper = "Mcca84.pdf"
+}
+
+\end{chunk}
+
\subsection{R} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\index{Richardson, Daniel}
@@ -15410,6 +15542,17 @@ Proc ISSAC 97 pp172-175 (1997)
\end{chunk}
+\subsection{T} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\index{Tarski, Alfred}
+@misc{Tars48,
+ author = "Tarski, Alfred",
+ title = "A Decision Method for Elementary Algebra and Geometry",
+ year = "1948",
+ link = "\url{}",
+ paper = "Tars48.pdf"
+}
+
\subsection{W} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\index{Weispfenning, V.}
@@ -31103,6 +31246,7 @@ Springer-Verlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
The choice of topics is excellent, there are many exercises and
examples. It is a very useful book.",
+ paer = "Mish93.pdf",
keywords = "axiomref"
}
diff --git a/changelog b/changelog
index f8824b4..15680a6 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,5 @@
+20170528 tpd src/axiom-website/patches.html 20170528.01.tpd.patch
+20170528 tpd bookvolbib reference for Cylindrical Algebraic Decomposition
20170527 tpd src/axiom-website/patches.html 20170527.01.tpd.patch
20170527 tpd bookvolbib reference for Cylindrical Algebraic Decomposition
20170526 tpd src/axiom-website/patches.html 20170526.01.tpd.patch
diff --git a/patch b/patch
index 102ed30..a0370eb 100644
--- a/patch
+++ b/patch
@@ -2,13 +2,158 @@ bookvolbib reference for Cylindrical Algebraic Decomposition
Goal: Axiom Algebra
-\index{Hong, Hoon}
+\index{Arnon, Dennis}
+\index{Buchberger, Bruno}
\begin{chunk}{axiom.bib}
-@misc{Hong05,
- author = "Hong, Hoon",
- title = "Tutorial on CAD",
- year = "2005",
- paper = "Hong05.pdf"
+@misc{Arno88a,
+ author = "Arnon, Dennis and Buchberger, Bruno",
+ title = "Algorithms in Real Algebraic Geometry",
+ publisher = "Academic Press",
+ year = "1988",
+ journal = "Journal of Symbolic Computation"
+}
+
+\end{chunk}
+
+\index{Dolzmann, Andreas}
+\index{Sturm, Thomas}
+\index{Weispfenning, Volker}
+\begin{chunk}{axiom.bib}
+@techreport{Dolz97a,
+ author = "Dolzmann, Andreas and Sturm, Thomas and
+ Weispfenning, Volker",
+ title = "Real Quantifier Elimination in Practice",
+ type = "technical report",
+ institution = "University of Passau",
+ number = "MIP-9720",
+ year = "1997",
+ abstract =
+ "We give a survey of three implemented real quantifier elimination
+ methods: partial cylindrical algebraic decomposition, virtual
+ substituion of test terms, and a combination of Groebner basis
+ computations with multivariate real root counting. We examine the
+ scope of these implementations for applications in various fields of
+ science, engineering, and economics",
+ paper = "Dolz97a.pdf"
+}
+
+\end{chunk}
+
+\index{Dolzmann, Andreas}
+\index{Sturm, Thomas}
+\begin{chunk}{axiom.bib}
+@misc{Dolz97,
+ author = "Dolzmann, Andreas and Sturm, Thomas",
+ title = "Guarded Expressions in Practice",
+ link = "\url{http://redlog.dolzmann.de/papers/pdf/MIP-9702.pdf}",
+ year = "1997",
+ abstract =
+ "Computer algebra systems typically drop some degenerate cases when
+ evaluating expressions, e.g. $x/x$ becomes 1 dropping the case
+ $x=0$. We claim that it is feasible in practice to compute also the
+ degenerate cases yielding {\sl guarded expressions}. We work over real
+ closed fields but our ideas about handling guarded expressions can be
+ easily transferred to other situations. Using formulas as guards
+ provides a powerful tool for heuristically reducing the combinatorial
+ explosion of cases: equivalent, redundant, tautological, and
+ contradictive cases can be detected by simplification and quantifier
+ elimination. Our approach allows to simplify the expressions on the
+ basis of simplification knowledge on the logical side. The method
+ described in this paper is implemented in the REDUCE package GUARDIAN,
+ which is freely available on the WWW.",
+ paper = "Dolz97.pdf"
+}
+
+\end{chunk}
+
+\index{Basu, Saugata}
+\index{Pollack, Richard}
+\index{Roy, Marie-Francoise}
+\begin{chunk}{axiom.bib}
+@book{Basu06,
+ author = "Basu, Saugata and Pollack, Richard and
+ Roy, Marie-Francoise",
+ title = "Algorithms in Real Algebraic Geometry",
+ publisher = "Springer",
+ year = "2006",
+ isbn = "978-3-540-33098-1"
+}
+
+\end{chunk}
+
+\index{Arnon, Dennis Soul\'e}
+\begin{chunk}{axiom.bib}
+@phdthesis{Arno81,
+ author = {Arnon, Dennis Soul\'e},
+ title = "Algorithms for the Geometry of Semi-algebraic Sets",
+ institution = "University of Wisconsin-Madison",
+ year = "1981",
+ abstract =
+ "Let A be a set of polynomials in r variables with integer
+ coefficients. An $A$-invariant cylindrical algebraic decomposition
+ (cad) of $r$-dimensional Euclidean space (G. Collins, Lect. Notes
+ Comp. Sci., 33, Springer-Verlag, 1975, pp 134-183) is a certain
+ cellular decomposition of $r$-space, such that each cell is a
+ semi-algebraic set, the polynomials of $A$ are sign-invariant on
+ each cell, and the cells are arranged into cylinders. The cad
+ algorithm given by Collins provides, among other applications,
+ the fastest known decision procedure for real closed fields, a
+ cellular decomposition algorithm for semi-algebraic sets, and a
+ method of solving nonlinear (polynomial) optimization problems
+ exactly. The time-consuming calculations with real algebraic
+ numbers required by the algorithm have been an obstacle to its
+ implementation and use. The major contribution of this thesis
+ is a new version of the cad algorithm for $r \le 3$, in which
+ one works with maximal connected $A$-invariant collections of
+ cells, in such a way as to often avoid the most time-consuming
+ algebraic number calculations. Essential to this new cad
+ algorithm is an algorithm we present for determination of
+ adjacenies among the cells of a cad. Computer programs for
+ the cad and adjacency algorithms have been written, providing
+ the first complete implementation of a cad algorithm. Empirical
+ data obtained from application of these programs are presented
+ and analyzed."
+}
+
+\end{chunk}
+
+\index{McCallum, Scott}
+\begin{chunk}{axiom.bib}
+@phdthesis{Mcca84,
+ author = "McCallum, Scott",
+ title = "An Improved Projection Operator for Cylindrical
+ Algebraic Decomposition",
+ institution = "University of Wisconsin-Madison",
+ year = "1984",
+ comment = "Computer Sciences Technical Report \#578",
+ link = "\url{ftp://ftp.cs.wisc.edu/pub/techreports/1985/TR578.pdf}",
+ abstract =
+ "A fundamental algorithm pertaining to the solution of polynomial
+ equations in several variables is the {\sl cylindrical algebraic
+ decomposition (cad)} algorithm due to G.E. Collins. Given as input
+ a set $A$ of integral polynomials in $r$ variables, the cad
+ algorithm produces a decomposition of the euclidean space of $r$
+ dimensions into cells, such that each polynomial in $A$ is
+ invariant in sign throughout each of the cells in the decomposition.
+
+ A key component of the cad algorithm is the projection operation:
+ the {\sl projection} of a set $A$ of $r$-variate polynomials is
+ defined to be a certain set $P$ of $(r-1)$-variate polynomials.
+ The solution set, or variety, of the polynomials in $P$ comprises
+ a projection in the geometric sense of the variety of $A$. The cad
+ algorithm proceeds by forming successive projections of the input
+ set $A$, each projection resulting in the elimination of one
+ variable.
+
+ This thesis is concerned with a refinement to the cad algorithm,
+ and to its projection operation in particular. It is shown, using
+ a theorem from real algebraic geometry, that the original
+ projection set that Collins used can be substantially reduced in
+ size, without affecting its essential properties. The results of
+ theoretical analysis and empirical observations suggest that the
+ reduction in the projection set size leads to an overall decrease
+ in the computing time of the cad algorithm.",
+ paper = "Mcca84.pdf"
}
\end{chunk}
diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html
index c7b9326..3f867f9 100644
--- a/src/axiom-website/patches.html
+++ b/src/axiom-website/patches.html
@@ -5744,6 +5744,8 @@ bookvolbib reference to Axiom in publications

bookvolbib reference for proofs

20170527.01.tpd.patch
bookvolbib reference for Cylindrical Algebraic Decomposition

+20170528.01.tpd.patch
+bookvolbib reference for Cylindrical Algebraic Decomposition

--
1.7.5.4