From 71dac9d86b639dcecebd6192ecf80ddef9e2d84b Mon Sep 17 00:00:00 2001
From: Tim Daly
Date: Wed, 22 Jun 2016 16:19:04 0400
Subject: [PATCH] books/bookvolbib add RISC references
Goal: Axiom Literate Programming
Collect algebra references in the bibliography
\index{Kalkbrener, M.}
\begin{chunk}{axiom.bib}
@phdthesis{Kalk91,
author = "Kalkbrener, M.",
title = "Three contributions to elimination theory",
school = "University of Linz, Austria",
year = "1991",
comment = "\refto{category RSETCAT RegularTriangularSetCategory}"
}
\end{chunk}
\begin{chunk}{axiom.bib}
@misc{SALSA,
title = "Solvers for Algebraic Systems and Applications",
url =
"http://www.enslyon.fr/LIP/Arenaire/SYMB/teams/salsa/proposalsalsa.pdf",
comment = "\refto{category RSETCAT RegularTriangularSetCategory}",
paper = "SALSA.pdf"
}
\end{chunk}
\index{Hemmecke, Ralf}
\begin{chunk}{axiom.bib}
@phdthesis{Hemm03,
author = "Hemmecke, Ralf",
title = "Involutive Bases for Polynomial Ideals",
school = "Johannes Kepler University, RISC",
year = "2003",
paper = "Hemm03.pdf",
abstract =
"This thesis contributes to the theory of polynomial involutive
bases. Firstly, we present the two existing theories of involutive
divisions, compare them, and come up with a generalised approach of
{\sl suitable partial divisions}. The thesis is built on this
generalized approach. Secondly, we treat the question of choosing a
``good'' suitable partial division in each iteration of the involutive
basis algorithm. We devise an efficient and flexible algorithm for
this purpose, the {\sl Sliced Division} algorithm. During the
involutive basis algorithm, the Sliced Division algorithm contributes
to an early detection of the involutive basis property and a
minimisation of the number of critical elements. Thirdly, we give new
criteria to avoid unnecessary reductions in an involutive basis
algorithm. We show that the termination property of an involutive
basis algorithm which applies our criteria is independent of the
prolongation selection strategy used during its run. Finally, we
present an implementation of the algorithm and results of this thesis
in our software package CALIX."
}
\end{chunk}
\index{Schorn, Markus}
\begin{chunk}{axiom.bib}
@phdthesis{Scho95,
author = "Schorn, Markus",
title = "Contributions to Symbolic Summation",
school = "Johannes Kepler University, RISC",
year = "1995",
paper = "Scho95.pdf",
url = "http://www.risc.jku.at/publications/download/risc_2246/diplom.pdf"
}
\end{chunk}
\index{Winkler, Franz}
\begin{chunk}{axiom.bib}
@book{Wink96,
author = "Winkler, Franz",
title = "Polynomial Algorithms in Computer Algebra",
year = "1996",
publisher = "SpringerVerlag",
isbn = "3.211827595"
}
\end{chunk}
\index{Buchberger, Bruno}
\begin{chunk}{axiom.bib}
@misc{Buch11,
author = "Buchberger, Bruno",
title = "Groebner Bases: A Short Introduction for System Theorists",
year = "2011",
abstract =
"In this paper, we give a brief overview on Groebner bases theory,
addressed to novices without prior knowledge in the field. After
explaining the general strategy for solving problems via the Groebner
approach, we develop the concept of Groebner bases by studying
uniqueness of polynomial division (``reduction''). For explicitly
constructing Groebner bases, the crucial notion of Spolynomials is
introduced, leading to the complete algorithmic solution of the
construction problem. The algorithm is applied to examples from
polynomial equation solving and algebraic relations. After a short
discussion of complexity issues, we conclude the paper with some
historical remarks and references."
}
\end{chunk}
\index{Winkler, Franz}
\begin{chunk}{axiom.bib}
@article{Wink89,
author = "Winkler, Franz",
title = "Equational Theorem Proving and Rewrite Rule Systems",
year = "1989",
publisher = "SpringerVerlag",
url = "http://www.risc.jku.at/publications/download/risc_3527/paper_47.pdf",
paper = "Wink89.pdf",
abstract =
"Equational theorem proving is interesting both from a mathematical
and a computational point of view. Many mathematical structures like
monoids, groups, etc. can be described by equational axioms. So the
theory of free monoids, free groups, etc. is the equational theory
defined by these axioms. A decision procedure for the equational
theory is a solution for the word problem over the associated
algebraic structure. From a computational point of view, abstract data
types are basically described by equations. Thus, proving properties
of an abstract data type amounts to proving theorems in the associated
equational theory.
One approach to equational theorem proving consists in associating a
direction with the equational axioms, thus transforming them into
rewrite rules. Now in order to prove an equation $a=b$, the rewrite
rules are applied to both sides, finally yielding reduced versions
$a^{'}$ and $b^{'}$ of the left and right hand sides, respectively. If
$a^{'}$ and $b^{'}$ agree syntactically, then the equation holds in
the equational theory. However, in general this argument cannot be
reversed; $a^{'}$ and $b^{'}$ might be different even if $a=b$ is a
theorem. The reason for this problem is that the rewrite system might
not have the ChurchRosser property. So the goal is to take the
original rewrite system and transform it into an equivalent one which
has the desired ChurchRosser property.
We show how rewrite systems can be used for proving theorems in
equational and inductive theories, and how an equational specification
of a problem can be turned into a rewrite program."
}
\end{chunk}
\index{Collins, G.E.}
\index{Mignotte, M.}
\index{Winkler, F.}
\begin{chunk}{axiom.bib}
@article{Coll82,
author = "Collins, G.E. and Mignotte, M. and Winkler, F.",
title = "Arithmetic in Basic Algebraic Domains",
publisher = "SpringerVerlag",
journal = "Computing, Supplement 4",
pages = "189220",
year = "1982",
abstract =
"This chapter is devoted to the arithmetic operations, essentially
addition, multiplication, exponentiation, division, gcd calculations
and evaluation, on the basic algebraic domains. The algorithms for
these basic domains are those most frequently used in any computer
algebra system. Therefore the best known algorithms, from a
computational point of view, are presented. The basic domains
considered here are the rational integers, the rational numbers,
integers modulo $m$, Gaussian integers, polynomials, rational
functions, power series, finite fields and $p$adic numbers. BOunds on
the maximum, minimum and average computing time ($t^{+},t^{},t^{*}$) for
the various algorithms are given."
}
\end{chunk}
\index{Paule, Peter}
\index{Kartashova, Lena}
\index{Kauers, Manuel}
\index{Schneider, Carsten}
\index{Winkler, Franz}
\begin{chunk}{axiom.bib}
@misc{Paulxx,
author = "Paule, Peter and Kartashova, Lena and Kauers, Manuel and
Schneider, Carsten and Winkler, Franz",
title = "Hot Topics in Symbolic Computation",
publisher = "Springer",
paper = "Paulxx.pdf",
url = "http://www.risc.jku.at/publications/download/risc_3845/chapter1.pdf"
}
\end{chunk}
\index{Johansson, Fredrik}
\begin{chunk}{axiom.bib}
@phdthesis{Joha14,
author = "Johansson, Fredrik",
title = "Fast and Rigorous Computation of Special Functions to High
Precision",
school = "Johannes Kepler University, Linz, Austria RISC",
year = "2014",
paper = "Joha14.pdf",
abstract =
"The problem of efficiently evaluating special functions to high
precision has been considered by numerous authors. Important tools
used for this purpose include algorithms for evaluation of linearly
recurrent sequences, and algorithms for power series arithmetic.
In this work, we give new babystep, giantstep algorithms for
evaluation of linearly recurrent sequences involving an expensive
parameter (such as a highprecision real number) and for computing
compositional inverses of power series. Our algorithms do not have the
best asymptotic complexity, but they are faster than previous
algorithms in practice over a large input range.
Using a combination of techniques, we also obtain efficient new
algorithms for numerically evaluating the gamma function $\Gamma(z)$
and the Hurwitz zeta function $\zeta(s,a)$, or Taylor series
expansions of those functions, with rigorous error bounds. Our methods
achieve softly optimal complexity when computing a large number of
derivatives to proportionally high precision.
Finally, we show that isolated values of the integer partition
function $p(n)$ can be computed rigorously with softly optimal
complexity by means of the HardyRamanuganRademacher formula and
careful numerical evaluation.
We provide open source implementations which run significantly faster
than previous published software. The implementations are used for
record computations of the partition function, including the
tabulation of several billion Ramanujantype congruences, and of
Taylor series associated with the Reimann zeta function."
}
\end{chunk}
\index{Hodorog, Madalina}
\begin{chunk}{axiom.bib}
@phdthesis{Hodo11,
author = "Hodorog, Madalina",
title = "SymbolicNumeric Algorithms for Plane Algebraic Curves",
year = "2011",
school = "RISC Research Institute for Symbolic Computation",
paper = "Hodo11.pdf",
abstract =
"In computer algebra, the problem of computing topological invariants
(i.e. deltainvariant, genus) of a plan complex algebraic curve is
wellunderstood if the coefficients of the defining polynomial of the
curve are exact data (i.e. integer numbers or rational numbers). The
challenge is to handle this problem if the coefficients are inexact
(i.e. numerical values).
In this thesis, we approach the algebraic problem of computing
invariants of a plane complex algebraic curve defined by a polynomial
with both exact and inexact data. For the inexact data, we associate a
positive real number called {\sl tolerance} or {\sl noise}, which
measures the error level in the coefficients. We deal with an {\sl
illposed} problem in the sense that, tiny changes in the input data
lead to dramatic modifications in the output solution.
For handling the illposedness of the problem we present a {\sl
regularization} method, which estimates the invariants of a plane
complex algebraic curve. Our regularization method consists of a set
of {\sl symbolicnumeric algorithms} that extract structural
information on the input curve, and of a {\sl parameter choice rule},
i.e. a function in the noise level. We first design the following
symbolicnumeric algorithms for computing the invariants of a plane
complex algebraic curve:
\begin{itemize}
\item we compute the link of each singularity of the curve by numerical
equation solving
\item we compute the Alexander polynomial of each link by using
algorithms from computational geometry (i.e. an adapted version of
the BentleyOttmann algorithm) and combinatorial objects from knot
theory.
\item we derive a formula for the deltainvariant and for the genus
\end{itemize}
We then prove that the symbolicnumeric algorithms together with the
parameter choice rule compute approximate solutions, which satisfy the
{\sl convergence for noisy data property}. Moreover, we perform
several numerical experiments, which support the validity for the
convergence statement.
We implement the designed symbolicnumeric algorithms in a new
software package called {\sl Genom3ck}, developed using the {\sl Axel}
free algebraic modeler and the {\sl Mathemagix} free computer algebra
system. For our purpose, both of these systems provide modern
graphical capabilities, and algebraic and geometric tools for
manipulating algebraic curves and surfaces defined by polynomials with
both exact and inexact data. Together with its main functionality to
compute the genus, the package {\sl Genom3ck} computes also other type
of information on a plane complex algebraic curve, such as the
singularities of the curve in the projective plane and the topological
type of each singularity."
}
\end{chunk}
\index{Er\"ocal, Bur\c{c}in}
\begin{chunk}{axiom.bib}
@phdthesis{Eroc11,
author = {Er\"ocal, Bur\c{c}in},
title = "Algebraic Extensions for Symbolic Summation",
school = "RISC Research Institute for Symbolic Computation",
year = "2011",
url =
"http://www.risc.jku.at/publications/download/risc_4320/erocal_thesis.pdf",
paper = "Eroc11.pdf",
abstract =
"The main result of this thesis is an effective method to extend Karr's
symbolic summation framework to algebraic extensions. These arise, for
example, when working with expressions involving $(1)^n$. An
implementation of this method, including a modernised version of
Karr's algorithm is presented.
Karr's algorithm is the summation analogue of the Risch algorithm for
indefinite integration. In the summation case, towers of specialized
difference fields called $\prod\sum$fields are used to model nested
sums and products. This is similar to the way elementary functions
involving nested logarithms and exponentials are represented in
differential fields in the integration case.
In contrast to the integration framework, only transcendental
extensions are allowed in Karr's construction. Algebraic extensions of
$\prod\sum$fields can even be rings with zero divisors. Karr's
methods rely heavily on the ability to solve firstorder linear
difference equations and they are no longer applicable over these
rings.
Based on Bronstein's formulation of a method used by Singer for the
solution of differential equations over algebraic extensions, we
transform a firstorder linear equation over an algebraic extension to
a system of firstorder equations over a purely transcendental
extension field. However, this domain is not necessarily a
$\prod\sum$field. Using a structure theorem by Singer and van der
Put, we reduce this system to a single firstorder equation over a
$\prod\sum$field, which can be solved by Karr's algorithm. We also
describe how to construct towers of difference ring extensions on an
algebraic extension, where the same reduction methods can be used.
A common bottleneck for symbolic summation algorithms is the
computation of nullspaces of matrices over rational function
fields. We present a fast algorithm for matrices over $\mathbb{Q}(x)$
which uses fast arithmetic at the hardware level with calls to BLAS
subroutines after modular reduction. This part is joint work with Arne
Storjohann."
}
\end{chunk}

books/bookvolbib.pamphlet  322 ++++++++++++++++++++++++++++++++
changelog  2 +
patch  394 ++++++++++++++++++++++++++++++++
src/axiomwebsite/patches.html  2 +
4 files changed, 640 insertions(+), 80 deletions()
diff git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index 3123e68..8a4fb21 100644
 a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ 3336,7 +3336,7 @@ when shown in factored form.
\end{chunk}
\index{Ward, Robert C.}
\begin{chunk}{axiom.sty}
+\begin{chunk}{axiom.bib}
@article{Ward81,
author = "Ward, Robert C.",
title = "Balancing the generalized eigenvalue problem",
@@ 8857,6 +8857,19 @@ rational righthand sides etc."
\end{chunk}
+\index{Schorn, Markus}
+\begin{chunk}{axiom.bib}
+@phdthesis{Scho95,
+ author = "Schorn, Markus",
+ title = "Contributions to Symbolic Summation",
+ school = "Johannes Kepler University, RISC",
+ year = "1995",
+ paper = "Scho95.pdf",
+ url = "http://www.risc.jku.at/publications/download/risc_2246/diplom.pdf"
+}
+
+\end{chunk}
+
\index{Gerhard, J.}
\index{Giesbrecht, M.}
\index{Storjohann, A.}
@@ 9059,9 +9072,8 @@ rational righthand sides etc."
url =
"http://www.risc.jku.at/publications/download/risc_4320/erocal_thesis.pdf",
paper = "Eroc11.pdf",
 abstract = "

 The main result of this thesis is an effective method to extend Karr's
+ abstract =
+ "The main result of this thesis is an effective method to extend Karr's
symbolic summation framework to algebraic extensions. These arise, for
example, when working with expressions involving $(1)^n$. An
implementation of this method, including a modernised version of
@@ 10329,9 +10341,11 @@ Soc. for Industrial and Applied Mathematics, Philadelphia (1990)
\end{chunk}
\index{Bremner, Murray R.}
+\index{Murakami, Lucia I.}
+\index{Shestakov, Ivan P.}
\begin{chunk}{axiom.bib}
@misc{Brem08,
 author = "Bremner, Murray R.",
+ author = "Bremner, Murray R. and Murakami, Lucia I. and Shestakov, Ivan P.",
title = "Nonassociative Algebras",
year = "2008",
comment = "\refto{category NARNG NonAssociativeRng}",
@@ 10799,6 +10813,28 @@ Elektronik, 43(15) CODEN EKRKAR ISSN 00135658
\end{chunk}
\index{Buchberger, Bruno}
+\begin{chunk}{axiom.bib}
+@misc{Buch11,
+ author = "Buchberger, Bruno",
+ title = "Groebner Bases: A Short Introduction for System Theorists",
+ year = "2011",
+ abstract =
+ "In this paper, we give a brief overview on Groebner bases theory,
+ addressed to novices without prior knowledge in the field. After
+ explaining the general strategy for solving problems via the Groebner
+ approach, we develop the concept of Groebner bases by studying
+ uniqueness of polynomial division (``reduction''). For explicitly
+ constructing Groebner bases, the crucial notion of Spolynomials is
+ introduced, leading to the complete algorithmic solution of the
+ construction problem. The algorithm is applied to examples from
+ polynomial equation solving and algebraic relations. After a short
+ discussion of complexity issues, we conclude the paper with some
+ historical remarks and references."
+}
+
+\end{chunk}
+
+\index{Buchberger, Bruno}
\index{Caviness, Bob F.}
\begin{chunk}{ignore}
\bibitem[Buchberger 85]{BC85} Buchberger, Bruno and Caviness, Bob F. (eds)
@@ 11025,6 +11061,33 @@ Proc. Natl. Acad. Sci. USA Vol 86
\end{chunk}
+\index{Collins, G.E.}
+\index{Mignotte, M.}
+\index{Winkler, F.}
+\begin{chunk}{axiom.bib}
+@article{Coll82,
+ author = "Collins, G.E. and Mignotte, M. and Winkler, F.",
+ title = "Arithmetic in Basic Algebraic Domains",
+ publisher = "SpringerVerlag",
+ journal = "Computing, Supplement 4",
+ pages = "189220",
+ year = "1982",
+ abstract =
+ "This chapter is devoted to the arithmetic operations, essentially
+ addition, multiplication, exponentiation, division, gcd calculations
+ and evaluation, on the basic algebraic domains. The algorithms for
+ these basic domains are those most frequently used in any computer
+ algebra system. Therefore the best known algorithms, from a
+ computational point of view, are presented. The basic domains
+ considered here are the rational integers, the rational numbers,
+ integers modulo $m$, Gaussian integers, polynomials, rational
+ functions, power series, finite fields and $p$adic numbers. BOunds on
+ the maximum, minimum and average computing time ($t^{+},t^{},t^{*}$) for
+ the various algorithms are given."
+}
+
+\end{chunk}
+
\index{Cohen, Arjeh M.}
\index{Cuypers, Hans}
\index{Barreiro, Hans}
@@ 12316,6 +12379,98 @@ Vol. 8 No. 3 pp195210 (2001)
\end{chunk}
+\index{Hemmecke, Ralf}
+\begin{chunk}{axiom.bib}
+@phdthesis{Hemm03,
+ author = "Hemmecke, Ralf",
+ title = "Involutive Bases for Polynomial Ideals",
+ school = "Johannes Kepler University, RISC",
+ year = "2003",
+ abstract =
+ "This thesis contributes to the theory of polynomial involutive
+ bases. Firstly, we present the two existing theories of involutive
+ divisions, compare them, and come up with a generalised approach of
+ {\sl suitable partial divisions}. The thesis is built on this
+ generalized approach. Secondly, we treat the question of choosing a
+ ``good'' suitable partial division in each iteration of the involutive
+ basis algorithm. We devise an efficient and flexible algorithm for
+ this purpose, the {\sl Sliced Division} algorithm. During the
+ involutive basis algorithm, the Sliced Division algorithm contributes
+ to an early detection of the involutive basis property and a
+ minimisation of the number of critical elements. Thirdly, we give new
+ criteria to avoid unnecessary reductions in an involutive basis
+ algorithm. We show that the termination property of an involutive
+ basis algorithm which applies our criteria is independent of the
+ prolongation selection strategy used during its run. Finally, we
+ present an implementation of the algorithm and results of this thesis
+ in our software package CALIX."
+}
+
+\end{chunk}
+
+\index{Hodorog, Madalina}
+\begin{chunk}{axiom.bib}
+@phdthesis{Hodo11,
+ author = "Hodorog, Madalina",
+ title = "SymbolicNumeric Algorithms for Plane Algebraic Curves",
+ year = "2011",
+ school = "RISC Research Institute for Symbolic Computation",
+ paper = "Hodo11.pdf",
+ abstract =
+ "In computer algebra, the problem of computing topological invariants
+ (i.e. deltainvariant, genus) of a plan complex algebraic curve is
+ wellunderstood if the coefficients of the defining polynomial of the
+ curve are exact data (i.e. integer numbers or rational numbers). The
+ challenge is to handle this problem if the coefficients are inexact
+ (i.e. numerical values).
+
+ In this thesis, we approach the algebraic problem of computing
+ invariants of a plane complex algebraic curve defined by a polynomial
+ with both exact and inexact data. For the inexact data, we associate a
+ positive real number called {\sl tolerance} or {\sl noise}, which
+ measures the error level in the coefficients. We deal with an {\sl
+ illposed} problem in the sense that, tiny changes in the input data
+ lead to dramatic modifications in the output solution.
+
+ For handling the illposedness of the problem we present a {\sl
+ regularization} method, which estimates the invariants of a plane
+ complex algebraic curve. Our regularization method consists of a set
+ of {\sl symbolicnumeric algorithms} that extract structural
+ information on the input curve, and of a {\sl parameter choice rule},
+ i.e. a function in the noise level. We first design the following
+ symbolicnumeric algorithms for computing the invariants of a plane
+ complex algebraic curve:
+ \begin{itemize}
+ \item we compute the link of each singularity of the curve by numerical
+ equation solving
+ \item we compute the Alexander polynomial of each link by using
+ algorithms from computational geometry (i.e. an adapted version of
+ the BentleyOttmann algorithm) and combinatorial objects from knot
+ theory.
+ \item we derive a formula for the deltainvariant and for the genus
+ \end{itemize}
+
+ We then prove that the symbolicnumeric algorithms together with the
+ parameter choice rule compute approximate solutions, which satisfy the
+ {\sl convergence for noisy data property}. Moreover, we perform
+ several numerical experiments, which support the validity for the
+ convergence statement.
+
+ We implement the designed symbolicnumeric algorithms in a new
+ software package called {\sl Genom3ck}, developed using the {\sl Axel}
+ free algebraic modeler and the {\sl Mathemagix} free computer algebra
+ system. For our purpose, both of these systems provide modern
+ graphical capabilities, and algebraic and geometric tools for
+ manipulating algebraic curves and surfaces defined by polynomials with
+ both exact and inexact data. Together with its main functionality to
+ compute the genus, the package {\sl Genom3ck} computes also other type
+ of information on a plane complex algebraic curve, such as the
+ singularities of the curve in the projective plane and the topological
+ type of each singularity."
+}
+
+\end{chunk}
+
\index{Hohold, Tom}
\index{van Lint, Jacobus H.}
\index{Pellikaan, Ruud}
@@ 12582,6 +12737,49 @@ In ACM [ACM94], pp3240 ISBN 0897916387 LCCN QA76.95.I59 1994
\end{chunk}
+\index{Johansson, Fredrik}
+\begin{chunk}{axiom.bib}
+@phdthesis{Joha14,
+ author = "Johansson, Fredrik",
+ title = "Fast and Rigorous Computation of Special Functions to High
+ Precision",
+ school = "Johannes Kepler University, Linz, Austria RISC",
+ year = "2014",
+ paper = "Joha14.pdf",
+ abstract =
+ "The problem of efficiently evaluating special functions to high
+ precision has been considered by numerous authors. Important tools
+ used for this purpose include algorithms for evaluation of linearly
+ recurrent sequences, and algorithms for power series arithmetic.
+
+ In this work, we give new babystep, giantstep algorithms for
+ evaluation of linearly recurrent sequences involving an expensive
+ parameter (such as a highprecision real number) and for computing
+ compositional inverses of power series. Our algorithms do not have the
+ best asymptotic complexity, but they are faster than previous
+ algorithms in practice over a large input range.
+
+ Using a combination of techniques, we also obtain efficient new
+ algorithms for numerically evaluating the gamma function $\Gamma(z)$
+ and the Hurwitz zeta function $\zeta(s,a)$, or Taylor series
+ expansions of those functions, with rigorous error bounds. Our methods
+ achieve softly optimal complexity when computing a large number of
+ derivatives to proportionally high precision.
+
+ Finally, we show that isolated values of the integer partition
+ function $p(n)$ can be computed rigorously with softly optimal
+ complexity by means of the HardyRamanuganRademacher formula and
+ careful numerical evaluation.
+
+ We provide open source implementations which run significantly faster
+ than previous published software. The implementations are used for
+ record computations of the partition function, including the
+ tabulation of several billion Ramanujantype congruences, and of
+ Taylor series associated with the Reimann zeta function."
+}
+
+\end{chunk}
+
\index{Joswig, Michael}
\index{Takayama, Nobuki}
\begin{chunk}{ignore}
@@ 13264,6 +13462,23 @@ Poster ISSAC 2007 Proceedings Vol 41 No 3 Sept 2007 p114
\end{chunk}
+\index{Paule, Peter}
+\index{Kartashova, Lena}
+\index{Kauers, Manuel}
+\index{Schneider, Carsten}
+\index{Winkler, Franz}
+\begin{chunk}{axiom.bib}
+@misc{Paulxx,
+ author = "Paule, Peter and Kartashova, Lena and Kauers, Manuel and
+ Schneider, Carsten and Winkler, Franz",
+ title = "Hot Topics in Symbolic Computation",
+ publisher = "Springer",
+ paper = "Paulxx.pdf",
+ url = "http://www.risc.jku.at/publications/download/risc_3845/chapter1.pdf"
+}
+
+\end{chunk}
+
\index{Petitot, Michel}
\begin{chunk}{ignore}
\bibitem[Petitot 90]{Pet90} Petitot, Michel
@@ 13433,6 +13648,17 @@ Mathematik und Physik, 75 (suppl. 2):S435S438, 1995 ISSN 00442267
\subsection{S} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{chunk}{axiom.bib}
+@misc{SALSA,
+ title = "Solvers for Algebraic Systems and Applications",
+ url =
+ "http://www.enslyon.fr/LIP/Arenaire/SYMB/teams/salsa/proposalsalsa.pdf",
+ comment = "\refto{category RSETCAT RegularTriangularSetCategory}",
+ paper = "SALSA.pdf"
+}
+
+\end{chunk}
+
\index{Stein, William}
\begin{chunk}{ignore}
\bibitem[Sage 14]{Sage14} Stein, William
@@ 14333,6 +14559,82 @@ LCCN QA76.7.S54 v22:7 SIGPLAN Notices, vol 22, no 7 (July 1987)
\end{chunk}
+\index{Winkler, Franz}
+\begin{chunk}{axiom.bib}
+@article{Wink89,
+ author = "Winkler, Franz",
+ title = "Equational Theorem Proving and Rewrite Rule Systems",
+ year = "1989",
+ publisher = "SpringerVerlag",
+ url = "http://www.risc.jku.at/publications/download/risc_3527/paper_47.pdf",
+ paper = "Wink89.pdf",
+ abstract =
+ "Equational theorem proving is interesting both from a mathematical
+ and a computational point of view. Many mathematical structures like
+ monoids, groups, etc. can be described by equational axioms. So the
+ theory of free monoids, free groups, etc. is the equational theory
+ defined by these axioms. A decision procedure for the equational
+ theory is a solution for the word problem over the associated
+ algebraic structure. From a computational point of view, abstract data
+ types are basically described by equations. Thus, proving properties
+ of an abstract data type amounts to proving theorems in the associated
+ equational theory.
+
+ One approach to equational theorem proving consists in associating a
+ direction with the equational axioms, thus transforming them into
+ rewrite rules. Now in order to prove an equation $a=b$, the rewrite
+ rules are applied to both sides, finally yielding reduced versions
+ $a^{'}$ and $b^{'}$ of the left and right hand sides, respectively. If
+ $a^{'}$ and $b^{'}$ agree syntactically, then the equation holds in
+ the equational theory. However, in general this argument cannot be
+ reversed; $a^{'}$ and $b^{'}$ might be different even if $a=b$ is a
+ theorem. The reason for this problem is that the rewrite system might
+ not have the ChurchRosser property. So the goal is to take the
+ original rewrite system and transform it into an equivalent one which
+ has the desired ChurchRosser property.
+
+ We show how rewrite systems can be used for proving theorems in
+ equational and inductive theories, and how an equational specification
+ of a problem can be turned into a rewrite program."
+}
+
+\end{chunk}
+
+\index{Winkler, Franz}
+\begin{chunk}{axiom.bib}
+@article{Wink93,
+ author = "Winkler, Franz",
+ title = "Algebraic Computation in Geometry",
+ year = "1993",
+ journal = "IMACS Symposium SC1993",
+ url = "http://www.risc.jku.at/publications/download/risc_3777/paper_35.pdf",
+ paper = "Wink93.pdf",
+ abstract =
+ "Computation with algebraic curves and surfaces are very well suited
+ for being treated with computer algebra. Many aspects of computer
+ algebra need to be combined for successfully solving problems in this
+ area, e.g. computations with algebraic coefficients, solution of
+ algebraic equations and elimination theory, and derivation of power
+ series approximations of branches. We will describe the application of
+ computer algebra to problems arising in algebraic geometry. The
+ program system CASA, which has been developed by the author and a
+ group of students will be introduced."
+}
+
+\end{chunk}
+
+\index{Winkler, Franz}
+\begin{chunk}{axiom.bib}
+@book{Wink96,
+ author = "Winkler, Franz",
+ title = "Polynomial Algorithms in Computer Algebra",
+ year = "1996",
+ publisher = "SpringerVerlag",
+ isbn = "3211827595"
+}
+
+\end{chunk}
+
\index{Wityak, Sandra}
\begin{chunk}{ignore}
\bibitem[Wityak 87]{Wit87} Wityak, Sandra
@@ 16453,10 +16755,14 @@ Comput. J. 9 281285. (1966)
\subsection{K} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\index{Kalkbrener, M.}
\begin{chunk}{ignore}
\bibitem[Kalkbrener 91]{Kal91} Kalkbrener, M.
+\begin{chunk}{axiom.bib}
+@phdthesis{Kalk91,
+ author = "Kalkbrener, M.",
title = "Three contributions to elimination theory",
Ph. D. Thesis, University of Linz, Austria, 1991
+ school = "University of Linz, Austria",
+ year = "1991",
+ comment = "\refto{category RSETCAT RegularTriangularSetCategory}"
+}
\end{chunk}
diff git a/changelog b/changelog
index 435003d..9dac499 100644
 a/changelog
+++ b/changelog
@@ 1,3 +1,5 @@
+20160622 tpd src/axiomwebsite/patches.html 20160622.01.tpd.patch
+20160622 tpd books/bookvolbib add RISC references
20160621 tpd src/axiomwebsite/patches.html 20160621.06.tpd.patch
20160621 tpd books/bookvol10.2 Scha61,Scha66,Scha10,Brem08 NonAssociativeRng
20160621 tpd books/bookvolbib Scha61,Scha66,Scha10,Brem08 NonAssociativeRng
diff git a/patch b/patch
index b1edb67..a18c38a 100644
 a/patch
+++ b/patch
@@ 1,99 +1,349 @@
books/bookvolbib Scha61,Scha66,Scha10,Brem08 category NonAssociativeRng
+books/bookvolbib add RISC references
Goal: Axiom Literate Programming
Collect algebra references in the bibliography
\index{Schafer, R.D.}
+\index{Kalkbrener, M.}
\begin{chunk}{axiom.bib}
@article{Scha61,
 author = "Schafer, R.D.",
 title = "An Introduction to Nonassociative Algebras",
 year = "1961",
 comment = "\refto{category NARNG NonAssociativeRng}",
 url = "http://www.gutenberg.org/ebooks/25156",
 paper = "Scha61.pdf",
+@phdthesis{Kalk91,
+ author = "Kalkbrener, M.",
+ title = "Three contributions to elimination theory",
+ school = "University of Linz, Austria",
+ year = "1991",
+ comment = "\refto{category RSETCAT RegularTriangularSetCategory}"
+}
+
+\end{chunk}
+
+\begin{chunk}{axiom.bib}
+@misc{SALSA,
+ title = "Solvers for Algebraic Systems and Applications",
+ url =
+ "http://www.enslyon.fr/LIP/Arenaire/SYMB/teams/salsa/proposalsalsa.pdf",
+ comment = "\refto{category RSETCAT RegularTriangularSetCategory}",
+ paper = "SALSA.pdf"
+}
+
+\end{chunk}
+
+\index{Hemmecke, Ralf}
+\begin{chunk}{axiom.bib}
+@phdthesis{Hemm03,
+ author = "Hemmecke, Ralf",
+ title = "Involutive Bases for Polynomial Ideals",
+ school = "Johannes Kepler University, RISC",
+ year = "2003",
+ paper = "Hemm03.pdf",
+ abstract =
+ "This thesis contributes to the theory of polynomial involutive
+ bases. Firstly, we present the two existing theories of involutive
+ divisions, compare them, and come up with a generalised approach of
+ {\sl suitable partial divisions}. The thesis is built on this
+ generalized approach. Secondly, we treat the question of choosing a
+ ``good'' suitable partial division in each iteration of the involutive
+ basis algorithm. We devise an efficient and flexible algorithm for
+ this purpose, the {\sl Sliced Division} algorithm. During the
+ involutive basis algorithm, the Sliced Division algorithm contributes
+ to an early detection of the involutive basis property and a
+ minimisation of the number of critical elements. Thirdly, we give new
+ criteria to avoid unnecessary reductions in an involutive basis
+ algorithm. We show that the termination property of an involutive
+ basis algorithm which applies our criteria is independent of the
+ prolongation selection strategy used during its run. Finally, we
+ present an implementation of the algorithm and results of this thesis
+ in our software package CALIX."
+}
+
+\end{chunk}
+
+\index{Schorn, Markus}
+\begin{chunk}{axiom.bib}
+@phdthesis{Scho95,
+ author = "Schorn, Markus",
+ title = "Contributions to Symbolic Summation",
+ school = "Johannes Kepler University, RISC",
+ year = "1995",
+ paper = "Scho95.pdf",
+ url = "http://www.risc.jku.at/publications/download/risc_2246/diplom.pdf"
+}
+
+\end{chunk}
+
+\index{Winkler, Franz}
+\begin{chunk}{axiom.bib}
+@book{Wink96,
+ author = "Winkler, Franz",
+ title = "Polynomial Algorithms in Computer Algebra",
+ year = "1996",
+ publisher = "SpringerVerlag",
+ isbn = "3.211827595"
+}
+
+\end{chunk}
+
+\index{Buchberger, Bruno}
+\begin{chunk}{axiom.bib}
+@misc{Buch11,
+ author = "Buchberger, Bruno",
+ title = "Groebner Bases: A Short Introduction for System Theorists",
+ year = "2011",
abstract =
 "These are notes for my lectures in July, 1961, at the Advanced
 Subject Matter Institute in Algebra which was held at Oklahoma State
 University in the summer of 1961.

 Students at the Institute were provided with reprints of my paper,
 {\sl Structure and representation of nonassociate algebras} (Bulletin
 of the American Mathematical Society, vol. 61 (1955), pp469484),
 together with copies of a selective bibliography of more recent papers
 on nonassociative algebras. These notes supplement the 1955 Bulletin
 article, bringing the statements there up to date and providing
 detailed proofs of a selected group of theorems. The proofs illustrate
 a number of important techniques used in the study of nonassociative
 algebras."
+ "In this paper, we give a brief overview on Groebner bases theory,
+ addressed to novices without prior knowledge in the field. After
+ explaining the general strategy for solving problems via the Groebner
+ approach, we develop the concept of Groebner bases by studying
+ uniqueness of polynomial division (``reduction''). For explicitly
+ constructing Groebner bases, the crucial notion of Spolynomials is
+ introduced, leading to the complete algorithmic solution of the
+ construction problem. The algorithm is applied to examples from
+ polynomial equation solving and algebraic relations. After a short
+ discussion of complexity issues, we conclude the paper with some
+ historical remarks and references."
}
\end{chunk}
\index{Schafer, R.D.}
+\index{Winkler, Franz}
\begin{chunk}{axiom.bib}
@book{Scha66,
 author = "Schafer, R.D.",
 title = "An Introduction to Nonassociative Algebras",
 year = "1966",
 publisher = "Academic Press, New York",
 comment = "\refto{category NARNG NonAssociativeRng}",
 comment = "documentation for AlgebraGivenByStructuralConstants"

+@article{Wink89,
+ author = "Winkler, Franz",
+ title = "Equational Theorem Proving and Rewrite Rule Systems",
+ year = "1989",
+ publisher = "SpringerVerlag",
+ url = "http://www.risc.jku.at/publications/download/risc_3527/paper_47.pdf",
+ paper = "Wink89.pdf",
+ abstract =
+ "Equational theorem proving is interesting both from a mathematical
+ and a computational point of view. Many mathematical structures like
+ monoids, groups, etc. can be described by equational axioms. So the
+ theory of free monoids, free groups, etc. is the equational theory
+ defined by these axioms. A decision procedure for the equational
+ theory is a solution for the word problem over the associated
+ algebraic structure. From a computational point of view, abstract data
+ types are basically described by equations. Thus, proving properties
+ of an abstract data type amounts to proving theorems in the associated
+ equational theory.
+
+ One approach to equational theorem proving consists in associating a
+ direction with the equational axioms, thus transforming them into
+ rewrite rules. Now in order to prove an equation $a=b$, the rewrite
+ rules are applied to both sides, finally yielding reduced versions
+ $a^{'}$ and $b^{'}$ of the left and right hand sides, respectively. If
+ $a^{'}$ and $b^{'}$ agree syntactically, then the equation holds in
+ the equational theory. However, in general this argument cannot be
+ reversed; $a^{'}$ and $b^{'}$ might be different even if $a=b$ is a
+ theorem. The reason for this problem is that the rewrite system might
+ not have the ChurchRosser property. So the goal is to take the
+ original rewrite system and transform it into an equivalent one which
+ has the desired ChurchRosser property.
+
+ We show how rewrite systems can be used for proving theorems in
+ equational and inductive theories, and how an equational specification
+ of a problem can be turned into a rewrite program."
}
\end{chunk}
\index{Schafer, R.D.}
+\index{Collins, G.E.}
+\index{Mignotte, M.}
+\index{Winkler, F.}
\begin{chunk}{axiom.bib}
@book{Scha10,
 author = "Schafer, R.D.",
 title = "An Introduction to Nonassociative Algebras",
 year = "2010",
 publisher = "Benediction Classics",
 comment = "\refto{category NARNG NonAssociativeRng}",
 isbn = "9781849025904",
+@article{Coll82,
+ author = "Collins, G.E. and Mignotte, M. and Winkler, F.",
+ title = "Arithmetic in Basic Algebraic Domains",
+ publisher = "SpringerVerlag",
+ journal = "Computing, Supplement 4",
+ pages = "189220",
+ year = "1982",
abstract =
 "Concise study presents in a short space some of the important ideas
 and results in the theory of nonassociative algebras, with particular
 emphasis on alternative and (commutative) Jordan algebras. Written as
 an introduction for graduate students and other mathematicians meeting
 the subject for the first time."
+ "This chapter is devoted to the arithmetic operations, essentially
+ addition, multiplication, exponentiation, division, gcd calculations
+ and evaluation, on the basic algebraic domains. The algorithms for
+ these basic domains are those most frequently used in any computer
+ algebra system. Therefore the best known algorithms, from a
+ computational point of view, are presented. The basic domains
+ considered here are the rational integers, the rational numbers,
+ integers modulo $m$, Gaussian integers, polynomials, rational
+ functions, power series, finite fields and $p$adic numbers. BOunds on
+ the maximum, minimum and average computing time ($t^{+},t^{},t^{*}$) for
+ the various algorithms are given."
}
\end{chunk}
\index{Bremner, Murray R.}
\begin{chunk}{axiom.sty}
@misc{Brem08,
 author = "Bremner, Murray R.",
 title = "Nonassociative Algebras",
 year = "2008",
 comment = "\refto{category NARNG NonAssociativeRng}",
+\index{Paule, Peter}
+\index{Kartashova, Lena}
+\index{Kauers, Manuel}
+\index{Schneider, Carsten}
+\index{Winkler, Franz}
+\begin{chunk}{axiom.bib}
+@misc{Paulxx,
+ author = "Paule, Peter and Kartashova, Lena and Kauers, Manuel and
+ Schneider, Carsten and Winkler, Franz",
+ title = "Hot Topics in Symbolic Computation",
+ publisher = "Springer",
+ paper = "Paulxx.pdf",
+ url = "http://www.risc.jku.at/publications/download/risc_3845/chapter1.pdf"
+}
+
+\end{chunk}
+
+\index{Johansson, Fredrik}
+\begin{chunk}{axiom.bib}
+@phdthesis{Joha14,
+ author = "Johansson, Fredrik",
+ title = "Fast and Rigorous Computation of Special Functions to High
+ Precision",
+ school = "Johannes Kepler University, Linz, Austria RISC",
+ year = "2014",
+ paper = "Joha14.pdf",
+ abstract =
+ "The problem of efficiently evaluating special functions to high
+ precision has been considered by numerous authors. Important tools
+ used for this purpose include algorithms for evaluation of linearly
+ recurrent sequences, and algorithms for power series arithmetic.
+
+ In this work, we give new babystep, giantstep algorithms for
+ evaluation of linearly recurrent sequences involving an expensive
+ parameter (such as a highprecision real number) and for computing
+ compositional inverses of power series. Our algorithms do not have the
+ best asymptotic complexity, but they are faster than previous
+ algorithms in practice over a large input range.
+
+ Using a combination of techniques, we also obtain efficient new
+ algorithms for numerically evaluating the gamma function $\Gamma(z)$
+ and the Hurwitz zeta function $\zeta(s,a)$, or Taylor series
+ expansions of those functions, with rigorous error bounds. Our methods
+ achieve softly optimal complexity when computing a large number of
+ derivatives to proportionally high precision.
+
+ Finally, we show that isolated values of the integer partition
+ function $p(n)$ can be computed rigorously with softly optimal
+ complexity by means of the HardyRamanuganRademacher formula and
+ careful numerical evaluation.
+
+ We provide open source implementations which run significantly faster
+ than previous published software. The implementations are used for
+ record computations of the partition function, including the
+ tabulation of several billion Ramanujantype congruences, and of
+ Taylor series associated with the Reimann zeta function."
+}
+
+\end{chunk}
+
+\index{Hodorog, Madalina}
+\begin{chunk}{axiom.bib}
+@phdthesis{Hodo11,
+ author = "Hodorog, Madalina",
+ title = "SymbolicNumeric Algorithms for Plane Algebraic Curves",
+ year = "2011",
+ school = "RISC Research Institute for Symbolic Computation",
+ paper = "Hodo11.pdf",
abstract =
+ "In computer algebra, the problem of computing topological invariants
+ (i.e. deltainvariant, genus) of a plan complex algebraic curve is
+ wellunderstood if the coefficients of the defining polynomial of the
+ curve are exact data (i.e. integer numbers or rational numbers). The
+ challenge is to handle this problem if the coefficients are inexact
+ (i.e. numerical values).
+
+ In this thesis, we approach the algebraic problem of computing
+ invariants of a plane complex algebraic curve defined by a polynomial
+ with both exact and inexact data. For the inexact data, we associate a
+ positive real number called {\sl tolerance} or {\sl noise}, which
+ measures the error level in the coefficients. We deal with an {\sl
+ illposed} problem in the sense that, tiny changes in the input data
+ lead to dramatic modifications in the output solution.
+
+ For handling the illposedness of the problem we present a {\sl
+ regularization} method, which estimates the invariants of a plane
+ complex algebraic curve. Our regularization method consists of a set
+ of {\sl symbolicnumeric algorithms} that extract structural
+ information on the input curve, and of a {\sl parameter choice rule},
+ i.e. a function in the noise level. We first design the following
+ symbolicnumeric algorithms for computing the invariants of a plane
+ complex algebraic curve:
+ \begin{itemize}
+ \item we compute the link of each singularity of the curve by numerical
+ equation solving
+ \item we compute the Alexander polynomial of each link by using
+ algorithms from computational geometry (i.e. an adapted version of
+ the BentleyOttmann algorithm) and combinatorial objects from knot
+ theory.
+ \item we derive a formula for the deltainvariant and for the genus
+ \end{itemize}
+
+ We then prove that the symbolicnumeric algorithms together with the
+ parameter choice rule compute approximate solutions, which satisfy the
+ {\sl convergence for noisy data property}. Moreover, we perform
+ several numerical experiments, which support the validity for the
+ convergence statement.
+
+ We implement the designed symbolicnumeric algorithms in a new
+ software package called {\sl Genom3ck}, developed using the {\sl Axel}
+ free algebraic modeler and the {\sl Mathemagix} free computer algebra
+ system. For our purpose, both of these systems provide modern
+ graphical capabilities, and algebraic and geometric tools for
+ manipulating algebraic curves and surfaces defined by polynomials with
+ both exact and inexact data. Together with its main functionality to
+ compute the genus, the package {\sl Genom3ck} computes also other type
+ of information on a plane complex algebraic curve, such as the
+ singularities of the curve in the projective plane and the topological
+ type of each singularity."
+}
+
+\end{chunk}
+
+\index{Er\"ocal, Bur\c{c}in}
+\begin{chunk}{axiom.bib}
+@phdthesis{Eroc11,
+ author = {Er\"ocal, Bur\c{c}in},
+ title = "Algebraic Extensions for Symbolic Summation",
+ school = "RISC Research Institute for Symbolic Computation",
+ year = "2011",
+ url =
+ "http://www.risc.jku.at/publications/download/risc_4320/erocal_thesis.pdf",
+ paper = "Eroc11.pdf",
+ abstract =
+ "The main result of this thesis is an effective method to extend Karr's
+ symbolic summation framework to algebraic extensions. These arise, for
+ example, when working with expressions involving $(1)^n$. An
+ implementation of this method, including a modernised version of
+ Karr's algorithm is presented.
+
+ Karr's algorithm is the summation analogue of the Risch algorithm for
+ indefinite integration. In the summation case, towers of specialized
+ difference fields called $\prod\sum$fields are used to model nested
+ sums and products. This is similar to the way elementary functions
+ involving nested logarithms and exponentials are represented in
+ differential fields in the integration case.
 "One of the earliest surveys on nonassociative algebras is the article
 by Shirshov which introduced the phrase ``rings that are nearly
 associative''. The first book in the English language devoted to a
 systematic study of nonassociative algebras is Schafer (Scha66). A
 comprehensive exposition of the work of the Russian School is
 Zhevlakov, Slinko, Shestakov and Shirshov. A collection of open
 research problems in algebra, including many problems on
 nonassociative algebra, is the {\sl Dniester Notebook}; the survey
 article by Kuzmin and Shetakov is from the same period. Three books on
 Jordan algebras which contain substantial material on general
 nonassociative algebras are Braun and Koecher, Jacobson, and
 McCrimmon. Recent research appears in the Proceedings of the
 International Conferences on Nonassociative Algebras and its
 Applications. The present section provides very limited information on
 Lie algebras, since they are the subject of Section 16.4. The last
 part (section 9) of the present section presents three applications of
 computational linear algebra to the study of polynomial identiies for
 nonassociative algebras: pseudorandom vectors in a nonassociative
 algebra, the expansion matrix for a nonassociative operation, and the
 representation theory of the symmetric group."
}
+ In contrast to the integration framework, only transcendental
+ extensions are allowed in Karr's construction. Algebraic extensions of
+ $\prod\sum$fields can even be rings with zero divisors. Karr's
+ methods rely heavily on the ability to solve firstorder linear
+ difference equations and they are no longer applicable over these
+ rings.
+
+ Based on Bronstein's formulation of a method used by Singer for the
+ solution of differential equations over algebraic extensions, we
+ transform a firstorder linear equation over an algebraic extension to
+ a system of firstorder equations over a purely transcendental
+ extension field. However, this domain is not necessarily a
+ $\prod\sum$field. Using a structure theorem by Singer and van der
+ Put, we reduce this system to a single firstorder equation over a
+ $\prod\sum$field, which can be solved by Karr's algorithm. We also
+ describe how to construct towers of difference ring extensions on an
+ algebraic extension, where the same reduction methods can be used.
+
+ A common bottleneck for symbolic summation algorithms is the
+ computation of nullspaces of matrices over rational function
+ fields. We present a fast algorithm for matrices over $\mathbb{Q}(x)$
+ which uses fast arithmetic at the hardware level with calls to BLAS
+ subroutines after modular reduction. This part is joint work with Arne
+ Storjohann."
+}
\end{chunk}
diff git a/src/axiomwebsite/patches.html b/src/axiomwebsite/patches.html
index cce1f82..739c7d3 100644
 a/src/axiomwebsite/patches.html
+++ b/src/axiomwebsite/patches.html
@@ 5358,6 +5358,8 @@ books/bookvolbib Hold11 category PRSPCAT ProjectiveSpaceCategory
books/bookvolbib Aubr99 category TSETCAT TriangularSetCategory
20160621.06.tpd.patch
books/bookvolbib Scha61,Scha66,Scha10,Brem08 NonAssociativeRng
+20160622.01.tpd.patch
+books/bookvolbib add RISC references

1.7.5.4