From 43feb9cb26ed01339c02015c8fa1e3e451a4006a Mon Sep 17 00:00:00 2001
From: Tim Daly
Date: Wed, 22 Jun 2016 17:31:58 0400
Subject: [PATCH] books/bookvolbib category RSETCAT
RegularTriangularSetCategory refs
Goal: Axiom Literate Programming
Collect algebra references in the bibliography

books/bookvol10.2.pamphlet  23 +
books/bookvolbib.pamphlet  66 +++++
changelog  3 +
patch  345 +
src/axiomwebsite/patches.html  2 +
5 files changed, 55 insertions(+), 384 deletions()
diff git a/books/bookvol10.2.pamphlet b/books/bookvol10.2.pamphlet
index b3cff2f..b48a9d6 100644
 a/books/bookvol10.2.pamphlet
+++ b/books/bookvol10.2.pamphlet
@@ 38198,12 +38198,6 @@ These exports come from \refto{FiniteLinearAggregate}(S:Type):
++ Author: Michael Monagan; revised by Manuel Bronstein and Richard Jenks
++ Date Created: August 87 through August 88
++ Date Last Updated: April 1991
++ Basic Operations:
++ Related Constructors:
++ Also See:
++ AMS Classifications:
++ Keywords:
++ References:
++ Description:
++ Onedimensionalarray aggregates serves as models for onedimensional
++ arrays. Categorically, these aggregates are finite linear aggregates
@@ 39327,20 +39321,21 @@ P:RecursivePolynomialCategory(R,E,V)):
?=? : (%,%) > Boolean
\end{verbatim}
+See: SALSA\cite{SALSA}, Kalkbrener\cite{Kalk91}\cite{Kalk98},
+Aubry\cite{Aubr99}, Moreno Maza\cite{Maza98}
+\label{category RSETCAT RegularTriangularSetCategory}
\begin{chunk}{category RSETCAT RegularTriangularSetCategory}
)abbrev category RSETCAT RegularTriangularSetCategory
++ Author: Marc Moreno Maza
++ Date Created: 09/03/1998
++ Date Last Updated: 12/15/1998
++ References :
++ [1] M. KALKBRENER "Three contributions to elimination theory"
++ Phd Thesis, University of Linz, Austria, 1991.
++ [2] M. KALKBRENER "Algorithmic properties of polynomial rings"
++ Journal of Symbol. Comp. 1998
++ [3] P. AUBRY, D. LAZARD and M. MORENO MAZA "On the Theories
++ of Triangular Sets" Journal of Symbol. Comp. (to appear)
++ [4] M. MORENO MAZA "A new algorithm for computing triangular
++ decomposition of algebraic varieties" NAG Tech. Rep. 4/98.
+++ SALSA Solvers for Algebraic Systems and Applications
+++ Kalk91 Three contributions to elimination theory
+++ Kalk98 Algorithmic properties of polynomial rings
+++ Aubr99 On the Theories of Triangular Sets
+++ Maza98 A new algorithm for computing triangular decomposition of
+++ algebraic varieties
++ Description:
++ The category of regular triangular sets, introduced under
++ the name regular chains in [1] (and other papers).
diff git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index 8a4fb21..df95e69 100644
 a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ 2086,7 +2086,7 @@ when shown in factored form.
institution = "Carnegie Mellon University",
paper = "Chel06.pdf",
url = "https://users.ece.cmu.edu/~franzf/papers/gttse07.pdf",
 comment = "\refto{package BLAS1 BlasLevelOne}",
+ comment = "\newline\refto{package BLAS1 BlasLevelOne}",
abstract =
"The complexity of modern computing platforms has made it extremely
difficult to write numerical code that achieves the best possible
@@ 4972,7 +4972,6 @@ O'Donnell, Michael J.
url = "http://www.johngustafson.net/presentations/Multicore2016JLG.pdf",
paper = "Gust16.pdf",
ppt = "Gust16.pptx",
 comment = "\refto{Gustafson}, \refto{Chellappa}",
abstract =
"If we are willing to give up compatibility with IEEE 754 floats and
design a number format with goals appropriate to 2016, we can achieve
@@ 5291,7 +5290,7 @@ Mathematics and Computers in Simulation 42 pp 387389 (1996)
url =
"http://wwwsop.inria.fr/cafe/Manuel.Bronstein/publications/mb_papers.html",
paper = "Bron96a.pdf",
 comment = "\refto{category LORER LeftOreRing}",
+ comment = "\newline\refto{category LORER LeftOreRing}",
abstract =
"Pseudolinear algebra is the study of common properties of linear
differential and difference operators. We introduce in this paper its
@@ 7133,7 +7132,7 @@ Proc ISSAC 97 pp172175 (1997)
title = "Noncommutative Symmetric functions and $W$polynomials",
url = "http://arxiv.org/pdf/math/0606614.pdf",
paper = "Dele06.pdf",
 comment = "\refto{category LORER LeftOreRing}",
+ comment = "\newline\refto{category LORER LeftOreRing}",
abstract = "
Let $K$, $S$, $D$ be a division ring an endomorphism and a
$S$derivation of $K$, respectively. In this setting we introduce
@@ 10348,7 +10347,7 @@ Soc. for Industrial and Applied Mathematics, Philadelphia (1990)
author = "Bremner, Murray R. and Murakami, Lucia I. and Shestakov, Ivan P.",
title = "Nonassociative Algebras",
year = "2008",
 comment = "\refto{category NARNG NonAssociativeRng}",
+ comment = "\newline\refto{category NARNG NonAssociativeRng}",
url =
"http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.146.2665\&rep=rep1\&type=pdf",
abstract =
@@ 12485,7 +12484,7 @@ Vol. 8 No. 3 pp195210 (2001)
volume = "I",
url = "http://www.win.tue.nl/~ruudp/paper/31.pdf",
paper = "Hold11.pdf",
 comment = "\refto{category PRSPCAT ProjectiveSpaceCategory}",
+ comment = "\newline\refto{category PRSPCAT ProjectiveSpaceCategory}",
isbn = "9780444814722"
}
@@ 13653,7 +13652,7 @@ Mathematik und Physik, 75 (suppl. 2):S435S438, 1995 ISSN 00442267
title = "Solvers for Algebraic Systems and Applications",
url =
"http://www.enslyon.fr/LIP/Arenaire/SYMB/teams/salsa/proposalsalsa.pdf",
 comment = "\refto{category RSETCAT RegularTriangularSetCategory}",
+ comment = "\newline\refto{category RSETCAT RegularTriangularSetCategory}",
paper = "SALSA.pdf"
}
@@ 14859,7 +14858,8 @@ J. Symbolic Computation 5, 237259 (1988)
volume = "28",
url = "http://www.csd.uwo.ca/~moreno/Publications/AubryLazardMorenoMaza1999JSC.pdf",
papers = "Aubr99.pdf",
 comment = "\refto{category TSETCAT TriangularSetCategory}",
+ comment = "\newline\refto{category TSETCAT TriangularSetCategory}
+ \newline\refto{category RSETCAT RegularTriangularSetCategory}",
abstract =
"Different notions of triangular sets are presented. The relationship
between these notions are studied. The main result is that four
@@ 16603,7 +16603,7 @@ IEEE Comput. Soc. Press, pp. 678687.
title = "A First Look at Differential Algebra",
url = "http://www.math.cornell.edu/~hubbard/diffalg1.pdf",
paper = "Hubb.pdf",
 comment = "\refto{category DVARCAT DifferentialVariableCategory}",
+ comment = "\newline\refto{category DVARCAT DifferentialVariableCategory}",
abstract =
"The object of the paper is to prove that the differential equation
\[u^{'}(t)=t[u(t)]^2\]
@@ 16676,7 +16676,7 @@ Inf. and Comp. 78, pp.171177, 1988
publisher = "Mathematical Society of Japan",
year = "1960",
isbn = "9780262090261",
 comment = "\refto{category GRALG GradedAlgebra}"
+ comment = "\newline\refto{category GRALG GradedAlgebra}"
}
\end{chunk}
@@ 16695,7 +16695,7 @@ Inf. and Comp. 78, pp.171177, 1988
pages = "509530",
url = "http://www.math.uci.edu/~brusso/jacobson1951.pdf",
paper = "Jaco51.pdf",
 comment = "\refto{category MONAD Monad}"
+ comment = "\newline\refto{category MONAD Monad}"
}
\end{chunk}
@@ 16711,8 +16711,8 @@ Inf. and Comp. 78, pp.171177, 1988
year = "1973",
pages = "509514",
url = "http://projecteuclid.org/euclid.bams/1183534656",
 comment = "\refto{category MONAD Monad},
 \refto{category MONADWU MonadWithUnit}"
+ comment = "\newline\refto{category MONAD Monad},
+ \newline\refto{category MONADWU MonadWithUnit}"
}
\end{chunk}
@@ 16761,16 +16761,25 @@ Comput. J. 9 281285. (1966)
title = "Three contributions to elimination theory",
school = "University of Linz, Austria",
year = "1991",
 comment = "\refto{category RSETCAT RegularTriangularSetCategory}"
+ comment = "\newline\refto{category RSETCAT RegularTriangularSetCategory}"
}
\end{chunk}
\index{Kalkbrener, M.}
\begin{chunk}{ignore}
\bibitem[Kalkbrener 98]{Kal98} Kalkbrener, M.
+\begin{chunk}{axiom.bib}
+@article{Kalk98,
+ author = "Kalkbrener, M.",
title = "Algorithmic properties of polynomial rings",
Journal of Symbolic Computation 1998
+ journal = "Journal of Symbolic Computation",
+ comment = "\newline\refto{category RSETCAT RegularTriangularSetCategory}",
+ year = "1998",
+ paper = "Kalk98.pdf",
+ abstract =
+ "In this paper we investigate how algorithms for computing heights,
+ radicals, unmixed and primary decompositions of ideals can be lifted
+ from a Noetherian commutative ring $R$ to polynomial rings over $R$."
+}
\end{chunk}
@@ 17235,10 +17244,15 @@ These, Universite P.etM. Curie, Paris, 1997.
\end{chunk}
\index{Maza, Marc Moreno}
\begin{chunk}{ignore}
\bibitem[Maza 98]{Maz98} Maza, M. Moreno
 title = "A new algorithm for computing triangular decomposition of algebraic varieties",
 NAG Tech. Rep. 4/98.
+\begin{chunk}{axiom.bib}
+@techreport{Maza98,
+ author = "Maza, M. Moreno",
+ title = "A new algorithm for computing triangular decomposition of
+ algebraic varieties",
+ institution = "Numerical Algorithms Group (NAG)",
+ comment = "\newline\refto{category RSETCAT RegularTriangularSetCategory}",
+ year = "1998"
+}
\end{chunk}
@@ 17991,7 +18005,7 @@ November 1996.
volume = "33",
isbn = "9780821846384",
paper = "Ritt50.pdf",
 comment = "\refto{category DVARCAT DifferentialVariableCategory}"
+ comment = "\newline\refto{category DVARCAT DifferentialVariableCategory}"
}
\end{chunk}
@@ 18040,7 +18054,7 @@ Num. Math. 16 205223. (1970)
title = "Algebra, Second Edition",
publisher = "MacMillan",
year = "1979",
 comment = "\refto{category GRMOD GradedModule}"
+ comment = "\newline\refto{category GRMOD GradedModule}"
}
\end{chunk}
@@ 18051,7 +18065,7 @@ Num. Math. 16 205223. (1970)
author = "Schafer, R.D.",
title = "An Introduction to Nonassociative Algebras",
year = "1961",
 comment = "\refto{category NARNG NonAssociativeRng}",
+ comment = "\newline\refto{category NARNG NonAssociativeRng}",
url = "http://www.gutenberg.org/ebooks/25156",
paper = "Scha61.pdf",
abstract =
@@ 18079,7 +18093,7 @@ Num. Math. 16 205223. (1970)
title = "An Introduction to Nonassociative Algebras",
year = "1966",
publisher = "Academic Press, New York",
 comment = "\refto{category NARNG NonAssociativeRng}",
+ comment = "\newline\refto{category NARNG NonAssociativeRng}",
comment = "documentation for AlgebraGivenByStructuralConstants"
}
@@ 18093,7 +18107,7 @@ Num. Math. 16 205223. (1970)
title = "An Introduction to Nonassociative Algebras",
year = "2010",
publisher = "Benediction Classics",
 comment = "\refto{category NARNG NonAssociativeRng}",
+ comment = "\newline\refto{category NARNG NonAssociativeRng}",
isbn = "9781849025904",
abstract =
"Concise study presents in a short space some of the important ideas
diff git a/changelog b/changelog
index 9dac499..65f36a6 100644
 a/changelog
+++ b/changelog
@@ 1,3 +1,6 @@
+20160622 tpd src/axiomwebsite/patches.html 20160622.02.tpd.patch
+20160622 tpd books/bookvol10.2 category RegularTriangularSetCategory refs
+20160622 tpd books/bookvolbib category RegularTriangularSetCategory refs
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
diff git a/patch b/patch
index a18c38a..cb4acfc 100644
 a/patch
+++ b/patch
@@ 1,349 +1,6 @@
books/bookvolbib add RISC references
+books/bookvolbib category RSETCAT RegularTriangularSetCategory refs
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}

diff git a/src/axiomwebsite/patches.html b/src/axiomwebsite/patches.html
index 739c7d3..5aa7787 100644
 a/src/axiomwebsite/patches.html
+++ b/src/axiomwebsite/patches.html
@@ 5360,6 +5360,8 @@ books/bookvolbib Aubr99 category TSETCAT TriangularSetCategory
books/bookvolbib Scha61,Scha66,Scha10,Brem08 NonAssociativeRng
20160622.01.tpd.patch
books/bookvolbib add RISC references
+20160622.02.tpd.patch
+books/bookvolbib category RegularTriangularSetCategory refs

1.7.5.4