From 24215a00089b59707dff6f944186ed1597c1263d Mon Sep 17 00:00:00 2001
From: Tim Daly
Date: Tue, 28 Jun 2016 00:51:57 0400
Subject: [PATCH] books/bookvolbib Axiom Citations in the Literature
Goal: Axiom Literate Programming
\index{Salem, Fatima Khaled Abu}
\begin{chunk}{axiom.bib}
@phdthesis{Sale04,
author = "Salem, Fatima Khaled Abu",
title = "Factorisation Algorithms for Univariate and Bivariate Polynomials
over Finite Fields",
school = "Meron College",
year = "2004",
paper = "Sale04",
url = "http://www.cs.aub.edu.lb/fa21/Dissertations/My\_thesis.pdf",
abstract =
"In this thesis we address algorithms for polynomial factorisation
over finite fields. In the univariate case, we study a recent
algorithm due to Niederreiter where the factorisation problem is
reduced to solving a linear system over the finite field in question,
and the solutions are used to produce the complete factorisation of
the polynomials into irreducibles. We develop a new algorithm for
solving the linear system using sparse Gaussian elimination with the
Markowitz ordering strategy, and conjecture that the Niederreiter
linear system is not only initially sparse, but also preserves its
sparsity throughout the Gaussian elimination phase. We develop a new
bulk synchronous parallel (BSP) algorithm base on the approach of
Gottfert for extracting the factors of a polynomial using a basis of
the Niederreiter solution set of $\mathbb{F}_2$. We improve upon the
complexity and performance of the original algorithm, and produce
binary univariate factorisations of trinomials up to degree 400000.
We present a new approach to multivariate polynomial factorisation
which incorporates ideas from polyhedral geometry, and generalises
Hensel lifting. The contribution is an algorithm for factoring
bivariate polynomials via polytopes which is able to exploit to some
extent the sparsity of polynomials. We further show that the polytope
method can be made sensitive to the number of nonzero terms of the
input polynomial. We describe a sparse adaptation of the polytope
method over finite fields of prime order which requires fewer bit
operations and memory references for polynomials which are known to be
the product of two sparse factors. Using this method, and to the best
of our knowledge, we achieve a world record in binary bivariate
factorisation of a sparse polynomial of degree 20000. We develop a BSP
variant of the absolute irreducibility testing via polytopes given in
[45], producing a more memory and run time efficient method that can
provide wider ranges of applicability. We achieve absolute
irreducibility testing of a bivariate and trivariate polynomial of
degree 30000, and of multivariate polynomials with up to 3000
variables."
}
\end{chunk}
\index{Gianni, P.}
\index{Trager, B.}
\begin{chunk}{axiom.bib}
@article{Gian96,
author = "Gianni, P. and Trager, B.",
title = "Squarefree algorithms in positive characteristic",
journal =
"J. of Applicable Algebra in Engineering, Communication and Computing",
volume = "7",
pages = "114",
year = "1996",
}
\end{chunk}
\index{Shoup, Victor}
\begin{chunk}{axiom.bib}
@InProceedings{Shou91,
author = "Shoup, Victor",
title = "A Fast Deterministic Algorithm for Factoring Polynomials over
Finite Fields of Small Characteristic",
booktitle = "Proc. ISSAC 1991",
series = "ISSAC 1991",
year = "1991",
pages = "1421",
paper = "Shou91.pdf",
url = "http://www.shoup.net/papers/quadfactor.pdf",
abstract =
"We present a new algorithm for factoring polynomials over finite
fields. Our algorithm is deterministic, and its running time is
``almost'' quadratic when the characteristic is a small fixed
prime. As such, our algorithm is asymptotically faster than previously
known deterministic algorithms for factoring polynomials over finite
fields of small characteristic."
}
\end{chunk}
\index{von zur Gathen, Joachim}
\index{Kaltofen, Erich}
\begin{chunk}{axiom.bib}
@Article{Gath85b,
author = "{von zur Gathen}, Joachim and Kaltofen, E.",
title = "PolynomialTime Factorization of Multivariate Polynomials over
Finite Fields",
journal = "Math. Comput.",
year = "1985",
volume = "45",
pages = "251261",
url =
"http://www.math.ncsu.edu/~kaltofen/bibliography/85/GaKa85_mathcomp.ps.gz",
paper = "Gath85.ps",
abstract =
"We present a probabilistic algorithm that finds the irreducible
factors of a bivariate polynomial with coefficients from a finite
field in time polynomial in the input size, i.e. in the degree of the
polynomial and $log$(cardinality of field). The algorithm generalizes
to multivariate polynomials and has polynomial running time for
densely encoded inputs. Also a deterministic version of the algorithm
is discussed whose running time is polynomial in the degree of the
input polynomial and the size of the field."
}
\end{chunk}
\index{von zur Gathen, Joachim}
\index{Panario, Daniel}
\begin{chunk}{axiom.bib}
@article{Gath01,
author = "von zur Gathen, Joachim and Panario, Daniel",
title = "Factoring Polynomials Over Finite Fields: A Survey",
journal = "J. Symbolic Computation",
year = "2001",
volume = "31",
pages = "317",
paper = "Gath01.pdf",
url =
"http://people.csail.mit.edu/dmoshdov/courses/codes/polyfactorization.pdf",
keywords = "survey",
abstract =
"This survey reviews several algorithms for the factorization of
univariate polynomials over finite fields. We emphasize the main ideas
of the methods and provide and uptodate bibliography of the problem.
This paper gives algorithms for {\sl squarefree factorization},
{\sl distinctdegree factorization}, and {\sl equaldegree factorization}.
The first and second algorithms are deterministic, the third is
probabilistic."
}
\end{chunk}
\index{Augot, Daniel}
\index{Camion, Paul}
\begin{chunk}{axiom.bib}
@article{Augo97,
author = "Augot, Daniel and Camion, Paul",
title = "On the computation of minimal polynomials, cyclic vectors,
and Frobenius forms",
journal = "Linear Algebra Appl.",
volume = "260",
pages = "6194",
year = "1997",
keywords = "axiomref",
paper = "Augo97.pdf",
abstract =
"Algorithms related to the computation of the minimal polynomial of an
$x\times n$ matrix over a field $K$ are introduced. The complexity of
the first algorithm, where the complete factorization of the
characteristic polynomial is needed, is $O(\sqrt{n}\cdot n^3)$. An
iterative algorithm for finding the minimal polynomial has complexity
$O(n^3+n^2m^2)$, where $m$ is a parameter of the shift Hessenberg
matrix used. The method does not require the knowlege of the
characteristic polynomial. The average value of $m$ is $O(log n)$.
Next methods are discussed for finding a cyclic vector for a matrix.
The authors first consider the case when its characteristic polynomial
is squarefree. Using the shift Hessenberg form leads to an algorithm
at cost $O(n^3 + n^2m^2)$. A more sophisticated recurrent procedure
gives the result in $O(n^3)$ steps. In particular, a normal basis for
an extended finite field of size $q^n$ will be obtained with complexity
$O(n^3+n^2 log q)$.
Finally, the Frobenius form is obtained with asymptotic average
complexity $O(n^3 log n)$."
}
\end{chunk}
\index{Bernardin, Laurent}
\index{Monagan, Michael B.}
\begin{chunk}{axiom.bib}
@InProceedings{Bern97a,
author = "Bernardin, Laurent and Monagan, Michael B.",
title = "Efficient multivariate factorization over finite fields",
booktitle = "Applied algebra, algebraic algorithms and errorcorrecting
codes",
series = "AAECC12",
year = "1997",
location = "Toulouse, France",
publisher = "Springer",
pages = "1528",
keywords = "axiomref",
paper = "Bern97a.pdf",
url = "http://www.cecm.sfu.ca/~monaganm/papers/AAECC.pdf",
abstract =
"We describe the Maple implementation of multivariate factorization
over general finite fields. Our first implementation is available in
Maple V Release 3. We give selected details of the algorithms and show
several ideas that were used to improve its efficiency. Most of the
improvements presented here are incorporated in Maple V Release 4. In
particular, we show that we needed a general tool for implementing
computations in GF$(p^k)[x_1,x_2,\cdots,x_v]$. We also needed an
efficient implementation of our algorithms $\mathbb{Z}_p[y][x]$ in
because any multivariate factorization may depend on several bivariate
factorizations. The efficiency of our implementation is illustrated by
the ability to factor bivariate polynomials with over a million
monomials over a small prime field."
}
\end{chunk}
\index{Bronstein, Manuel}
\index{Weil, JacquesArthur}
\begin{chunk}{axiom.bib}
@article{Bron97a,
author = "Bronstein, Manuel and Weil, JacquesArthur",
title = "On Symmetric Powers of Differential Operators",
series = "ISSAC'97",
year = "1997",
pages = "156163",
keywords = "axiomref",
url =
"http://wwwsop.inria.fr/cafe/Manuel.Bronstein/publications/mb_papers.html",
paper = "Bro97a.pdf",
publisher = "ACM, NY",
abstract = "
We present alternative algorithms for computing symmetric powers of
linear ordinary differential operators. Our algorithms are applicable
to operators with coefficients in arbitrary integral domains and
become faster than the traditional methods for symmetric powers of
sufficiently large order, or over sufficiently complicated coefficient
domains. The basic ideas are also applicable to other computations
involving cyclic vector techniques, such as exterior powers of
differential or difference operators."
}
\end{chunk}
\index{Calmet, J.}
\index{Campbell, J.A.}
\begin{chunk}{axiom.bib}
@article{Calm97,
author = "Calmet, J. and Campbell, J.A.",
title = "A perspective on symbolic mathematical computing and
artificial intelligence",
journal = "Ann. Math. Artif. Intell.",
volume = "19",
number = "34",
pages = "261277",
year = "1997",
keywords = "axiomref",
paper = "Calm97.pdf",
url =
"http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.52.5425&rep=rep1&type=pdf",
abstract =
"The nature and history of the research area common to artificial
intelligence and symbolic mathematical computation are examined, with
particular reference to the topics having the greatest current amount
of activity or potential for further development: mathematical
knowledgebased computing environments, autonomous agents and
multiagent systems, transformation of problem descriptions in logics
into algebraic forms, exploitation of machine learning, qualitative
reasoning, and constraintbased programming. Knowledge representation,
for mathematical knowledge, is identified as a central focus for much
of this work. Several promising topics for further research are stated."
}
\end{chunk}

books/bookvolbib.pamphlet  248 ++++++++++++++++
changelog  8 +
patch  583 +++++++++++++++
src/axiomwebsite/patches.html  2 +
4 files changed, 461 insertions(+), 380 deletions()
diff git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index fa94aaf..88a05d7 100644
 a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ 3621,22 +3621,27 @@ Proc. IMACS Symposium, Lille, France, (1993)
\index{von zur Gathen, Joachim}
\index{Panario, Daniel}
\begin{chunk}{ignore}
\bibitem[Gathen 01]{STPGCDGa01} von zur Gathen, Joachim; Panario, Daniel
+\begin{chunk}{axiom.bib}
+@article{Gath01,
+ author = "von zur Gathen, Joachim and Panario, Daniel",
title = "Factoring Polynomials Over Finite Fields: A Survey",
J. Symbolic Computation (2001) Vol 31, pp317\hfill{}
+ journal = "J. Symbolic Computation",
+ year = "2001",
+ volume = "31",
+ pages = "317",
+ paper = "Gath01.pdf",
url =
"http://people.csail.mit.edu/dmoshdov/courses/codes/polyfactorization.pdf",
 paper = "STPGCDGa01.pdf",
keywords = "survey",
 abstract = "
 This survey reviews several algorithms for the factorization of
+ abstract =
+ "This survey reviews several algorithms for the factorization of
univariate polynomials over finite fields. We emphasize the main ideas
of the methods and provide and uptodate bibliography of the problem.
This paper gives algorithms for {\sl squarefree factorization},
{\sl distinctdegree factorization}, and {\sl equaldegree factorization}.
The first and second algorithms are deterministic, the third is
probabilistic."
+}
\end{chunk}
@@ 7682,6 +7687,55 @@ Proc ISSAC 97 pp172175 (1997)
\section{Polynomial Factorization} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\index{Bernardin, Laurent}
+\index{Monagan, Michael B.}
+\begin{chunk}{axiom.bib}
+@InProceedings{Bern97a,
+ author = "Bernardin, Laurent and Monagan, Michael B.",
+ title = "Efficient multivariate factorization over finite fields",
+ booktitle = "Applied algebra, algebraic algorithms and errorcorrecting
+ codes",
+ series = "AAECC12",
+ year = "1997",
+ location = "Toulouse, France",
+ publisher = "Springer",
+ pages = "1528",
+ keywords = "axiomref",
+ paper = "Bern97a.pdf",
+ url = "http://www.cecm.sfu.ca/~monaganm/papers/AAECC.pdf",
+ abstract =
+ "We describe the Maple implementation of multivariate factorization
+ over general finite fields. Our first implementation is available in
+ Maple V Release 3. We give selected details of the algorithms and show
+ several ideas that were used to improve its efficiency. Most of the
+ improvements presented here are incorporated in Maple V Release 4. In
+ particular, we show that we needed a general tool for implementing
+ computations in GF$(p^k)[x_1,x_2,\cdots,x_v]$. We also needed an
+ efficient implementation of our algorithms $\mathbb{Z}_p[y][x]$ in
+ because any multivariate factorization may depend on several bivariate
+ factorizations. The efficiency of our implementation is illustrated by
+ the ability to factor bivariate polynomials with over a million
+ monomials over a small prime field."
+}
+
+\end{chunk}
+
+\index{Gianni, P.}
+\index{Trager, B.}
+\begin{chunk}{axiom.bib}
+@article{Gian96,
+ author = "Gianni, P. and Trager, B.",
+ title = "Squarefree algorithms in positive characteristic",
+ journal =
+ "J. of Applicable Algebra in Engineering, Communication and Computing",
+ volume = "7",
+ pages = "114",
+ year = "1996",
+
+}
+
+\end{chunk}
+
\index{Kaltofen, Erich}
\begin{chunk}{axiom.bib}
@PhdThesis{Kalt82,
@@ 7715,6 +7769,33 @@ Proc ISSAC 97 pp172175 (1997)
\end{chunk}
+\index{von zur Gathen, Joachim}
+\index{Kaltofen, Erich}
+\begin{chunk}{axiom.bib}
+@Article{Gath85b,
+ author = "{von zur Gathen}, Joachim and Kaltofen, E.",
+ title = "PolynomialTime Factorization of Multivariate Polynomials over
+ Finite Fields",
+ journal = "Math. Comput.",
+ year = "1985",
+ volume = "45",
+ pages = "251261",
+ url =
+ "http://www.math.ncsu.edu/~kaltofen/bibliography/85/GaKa85_mathcomp.ps.gz",
+ paper = "Gath85.ps",
+ abstract =
+ "We present a probabilistic algorithm that finds the irreducible
+ factors of a bivariate polynomial with coefficients from a finite
+ field in time polynomial in the input size, i.e. in the degree of the
+ polynomial and $log$(cardinality of field). The algorithm generalizes
+ to multivariate polynomials and has polynomial running time for
+ densely encoded inputs. Also a deterministic version of the algorithm
+ is discussed whose running time is polynomial in the degree of the
+ input polynomial and the size of the field."
+}
+
+\end{chunk}
+
\index{Kaltofen, Erich}
\index{Lecerf, Gr{\'e}goire}
\begin{chunk}{axiom.bib}
@@ 7834,6 +7915,13 @@ Proc ISSAC 97 pp172175 (1997)
\end{chunk}
+\index{von zur Gathen, J.}
+\index{Kaltofen, Erich}
+\begin{chunk}{axiom.bib}
+@article{
+
+\end{chunk}
+
\index{Kaltofen, Erich}
\index{Trager, Barry M.}
\begin{chunk}{axiom.bib}
@@ 8108,6 +8196,78 @@ Proc ISSAC 97 pp172175 (1997)
\end{chunk}
+\index{Salem, Fatima Khaled Abu}
+\begin{chunk}{axiom.bib}
+@phdthesis{Sale04,
+ author = "Salem, Fatima Khaled Abu",
+ title = "Factorisation Algorithms for Univariate and Bivariate Polynomials
+ over Finite Fields",
+ school = "Meron College",
+ year = "2004",
+ paper = "Sale04.pdf",
+ url = "http://www.cs.aub.edu.lb/fa21/Dissertations/My\_thesis.pdf",
+ abstract =
+ "In this thesis we address algorithms for polynomial factorisation
+ over finite fields. In the univariate case, we study a recent
+ algorithm due to Niederreiter where the factorisation problem is
+ reduced to solving a linear system over the finite field in question,
+ and the solutions are used to produce the complete factorisation of
+ the polynomials into irreducibles. We develop a new algorithm for
+ solving the linear system using sparse Gaussian elimination with the
+ Markowitz ordering strategy, and conjecture that the Niederreiter
+ linear system is not only initially sparse, but also preserves its
+ sparsity throughout the Gaussian elimination phase. We develop a new
+ bulk synchronous parallel (BSP) algorithm base on the approach of
+ Gottfert for extracting the factors of a polynomial using a basis of
+ the Niederreiter solution set of $\mathbb{F}_2$. We improve upon the
+ complexity and performance of the original algorithm, and produce
+ binary univariate factorisations of trinomials up to degree 400000.
+
+ We present a new approach to multivariate polynomial factorisation
+ which incorporates ideas from polyhedral geometry, and generalises
+ Hensel lifting. The contribution is an algorithm for factoring
+ bivariate polynomials via polytopes which is able to exploit to some
+ extent the sparsity of polynomials. We further show that the polytope
+ method can be made sensitive to the number of nonzero terms of the
+ input polynomial. We describe a sparse adaptation of the polytope
+ method over finite fields of prime order which requires fewer bit
+ operations and memory references for polynomials which are known to be
+ the product of two sparse factors. Using this method, and to the best
+ of our knowledge, we achieve a world record in binary bivariate
+ factorisation of a sparse polynomial of degree 20000. We develop a BSP
+ variant of the absolute irreducibility testing via polytopes given in
+ [45], producing a more memory and run time efficient method that can
+ provide wider ranges of applicability. We achieve absolute
+ irreducibility testing of a bivariate and trivariate polynomial of
+ degree 30000, and of multivariate polynomials with up to 3000
+ variables."
+}
+
+\end{chunk}
+
+\index{Shoup, Victor}
+\begin{chunk}{axiom.bib}
+@InProceedings{Shou91,
+ author = "Shoup, Victor",
+ title = "A Fast Deterministic Algorithm for Factoring Polynomials over
+ Finite Fields of Small Characteristic",
+ booktitle = "Proc. ISSAC 1991",
+ series = "ISSAC 1991",
+ year = "1991",
+ pages = "1421",
+ paper = "Shou91.pdf",
+ url = "http://www.shoup.net/papers/quadfactor.pdf",
+ abstract =
+ "We present a new algorithm for factoring polynomials over finite
+ fields. Our algorithm is deterministic, and its running time is
+ ``almost'' quadratic when the characteristic is a small fixed
+ prime. As such, our algorithm is asymptotically faster than previously
+ known deterministic algorithms for factoring polynomials over finite
+ fields of small characteristic."
+}
+
+\end{chunk}
+
\section{Branch Cuts} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\index{Beaumont, James}
@@ 10878,6 +11038,43 @@ American Mathematical Society (1994)
\end{chunk}
+\index{Augot, Daniel}
+\index{Camion, Paul}
+\begin{chunk}{axiom.bib}
+@article{Augo97,
+ author = "Augot, Daniel and Camion, Paul",
+ title = "On the computation of minimal polynomials, cyclic vectors,
+ and Frobenius forms",
+ journal = "Linear Algebra Appl.",
+ volume = "260",
+ pages = "6194",
+ year = "1997",
+ keywords = "axiomref",
+ paper = "Augo97.pdf",
+ abstract =
+ "Algorithms related to the computation of the minimal polynomial of an
+ $x\times n$ matrix over a field $K$ are introduced. The complexity of
+ the first algorithm, where the complete factorization of the
+ characteristic polynomial is needed, is $O(\sqrt{n}\cdot n^3)$. An
+ iterative algorithm for finding the minimal polynomial has complexity
+ $O(n^3+n^2m^2)$, where $m$ is a parameter of the shift Hessenberg
+ matrix used. The method does not require the knowlege of the
+ characteristic polynomial. The average value of $m$ is $O(log n)$.
+
+ Next methods are discussed for finding a cyclic vector for a matrix.
+ The authors first consider the case when its characteristic polynomial
+ is squarefree. Using the shift Hessenberg form leads to an algorithm
+ at cost $O(n^3 + n^2m^2)$. A more sophisticated recurrent procedure
+ gives the result in $O(n^3)$ steps. In particular, a normal basis for
+ an extended finite field of size $q^n$ will be obtained with complexity
+ $O(n^3+n^2 log q)$.
+
+ Finally, the Frobenius form is obtained with asymptotic average
+ complexity $O(n^3 log n)$."
+}
+
+\end{chunk}
+
\subsection{B} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\index{Baclawski, Krystian}
@@ 11526,8 +11723,8 @@ Elektronik, 43(15) CODEN EKRKAR ISSN 00135658
\index{Bronstein, Manuel}
\index{Weil, JacquesArthur}
\begin{chunk}{ignore}
\bibitem[Bronstein 97a]{Bro97a}
+\begin{chunk}{axiom.bib}
+@article{Bron97a,
author = "Bronstein, Manuel and Weil, JacquesArthur",
title = "On Symmetric Powers of Differential Operators",
series = "ISSAC'97",
@@ 11535,7 +11732,7 @@ Elektronik, 43(15) CODEN EKRKAR ISSN 00135658
pages = "156163",
keywords = "axiomref",
url =
 "http://wwwsop.inria.fr/cafe/Manuel.Bronstein/publications/mb_papers.html"
+ "http://wwwsop.inria.fr/cafe/Manuel.Bronstein/publications/mb_papers.html",
paper = "Bro97a.pdf",
publisher = "ACM, NY",
abstract = "
@@ 11547,6 +11744,7 @@ Elektronik, 43(15) CODEN EKRKAR ISSN 00135658
domains. The basic ideas are also applicable to other computations
involving cyclic vector techniques, such as exterior powers of
differential or difference operators."
+}
\end{chunk}
@@ 11560,6 +11758,7 @@ Elektronik, 43(15) CODEN EKRKAR ISSN 00135658
isbn = "3540424504",
publisher = "SpringerVerlag",
keywords = "axiomref"
+}
\end{chunk}
@@ 11733,6 +11932,37 @@ Universit{\"a}t Karsruhe, Karlsruhe, Germany 1994
\end{chunk}
+\index{Calmet, Jacques}
+\index{Campbell, John A.}
+\begin{chunk}{axiom.bib}
+@article{Calm97,
+ author = "Calmet, J. and Campbell, J.A.",
+ title = "A perspective on symbolic mathematical computing and
+ artificial intelligence",
+ journal = "Ann. Math. Artif. Intell.",
+ volume = "19",
+ number = "34",
+ pages = "261277",
+ year = "1997",
+ keywords = "axiomref",
+ paper = "Calm97.pdf",
+ url =
+"http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.52.5425&rep=rep1&type=pdf",
+ abstract =
+ "The nature and history of the research area common to artificial
+ intelligence and symbolic mathematical computation are examined, with
+ particular reference to the topics having the greatest current amount
+ of activity or potential for further development: mathematical
+ knowledgebased computing environments, autonomous agents and
+ multiagent systems, transformation of problem descriptions in logics
+ into algebraic forms, exploitation of machine learning, qualitative
+ reasoning, and constraintbased programming. Knowledge representation,
+ for mathematical knowledge, is identified as a central focus for much
+ of this work. Several promising topics for further research are stated."
+}
+
+\end{chunk}
+
\index{Camion, Paul}
\index{Courteau, Bernard}
\index{Montpetit, Andre}
diff git a/changelog b/changelog
index eddcd5a..534293e 100644
 a/changelog
+++ b/changelog
@@ 1,8 +1,10 @@
20160627 tpd src/axiomwebsite/patches.html 20160626.04.tpd.patch
+20160628 tpd src/axiomwebsite/patches.html 20160628.01.tpd.patch
+20160628 tpd books/bookvolbib Axiom Citations in the Literature
+20160627 tpd src/axiomwebsite/patches.html 20160627.04.tpd.patch
20160627 tpd books/bookvolbib Axiom Citations in the Literature
20160627 tpd src/axiomwebsite/patches.html 20160626.03.tpd.patch
+20160627 tpd src/axiomwebsite/patches.html 20160627.03.tpd.patch
20160627 tpd books/bookvolbib Axiom Citations in the Literature
20160627 tpd src/axiomwebsite/patches.html 20160626.02.tpd.patch
+20160627 tpd src/axiomwebsite/patches.html 20160627.02.tpd.patch
20160627 tpd books/bookvol10.4 additional citations
20160627 tpd books/bookvol10.2 additional citations
20160627 tpd books/bookvolbib Axiom Citations in the Literature
diff git a/patch b/patch
index 6ccb2f7..1fd0e7d 100644
 a/patch
+++ b/patch
@@ 2,424 +2,271 @@ books/bookvolbib Axiom Citations in the Literature
Goal: Axiom Literate Programming
\index{Rigal, Alain}
+\index{Salem, Fatima Khaled Abu}
\begin{chunk}{axiom.bib}
@article{Riga99,
 author = "Rigal, Alain",
 title = "Highorder compact schemes: Application to bidimensional unsteady
 diffusionconvection problems.",
 journal = "C. R. Acad. Sci.",
 volume = "328",
 number = "6",
 pages = "535538",
 year = "1999",
 keywords = "axiomref",
 abstract =
 "For unsteady 2D diffusionconvection problems, we present two classes
 of compact difference schemes of order 2 in time and 4 in space. These
 finite difference schemes are essentially derived from 1D schemes,
 extensively analyzed in our previous paper [J. Comput. Phys. 114,
 No. 1, 5976 (1994; Zbl 0807.65056)]. We propose two approaches:
 construction of 2D schemes as product of 1D schemes and global
 formulation of 2D schemes. Part II by M. Fournié [C. R. Acad. Sci.,
 Paris, Sér. I, Math. 328, No. 6, 539542 (1999; reviewed below)]
 focuses on the development and analysis of global schemes with the
 assistance of symbolic computation software (AXIOM)."
}

\end{chunk}

\index{Roesner, K. G.}
\begin{chunk}{axiom.bib}
@article{Roes99,
 author = "Roesner, K. G.",
 title = "Supersonic flow around accelerated and decelerated bodies,
 analysed by analytical methods",
 journal = "Z. Angew. Math. Mech.",
 volume = "79",
 number = "3",
 pages = "815816",
 year = "1999",
 keywords = "axiomref",
 abstract =
 "By an extensive use of the computer algebra system AXIOM, a power
 series expansion with respect to the radial variable $r$ is used to
 describe the accelerated or decelerated supersonic flow field around
 the tip of slender conical bodies. The set of coupled nonlinear
 differential equations for the coefficient functions, depending on
 $\theta$ and $t$, is derived in closed form, and the first and second
 approximation of the coefficient functions are determined
 numerically."
}

\end{chunk}

\index{Stroeker, Roelof J.}
\index{Kaashoek, Johan F.}
\begin{chunk}{axiom.bib}
@book{Stro99,
 author = "Stroeker, Roelof J. and Kaashoek, Johan F.",
 title = "Discovering mathematics with Maple. An interactive exploration for
 mathematicians, engineers and econometricians",
 year = "1999",
 publisher = "Birkhauser",
 keywords = "axiomref",
 abstract =
 "During the past decade, the mathematical computer software packages
 such as Mathematica, Maple, MATLAB (Axiom, Derive, Macsyma, MuPad are
 some further examples of such software) [see Macsyma 2.3. Lite – the
 student edition (1998; Zbl 0911.68089); B. W. Char, K. O. Geddes,
 G. H. Gonnet, B. L. Leong, M. B. Monagan, and S. M. Watt, Maple V
 Library reference manual (1991; Zbl 0763.68046); J. L. Zachary,
 Introduction to scientific programming. Computational problem solving
 using Mathematica and C (1997; Zbl 0891.68053); The student edition of
 MATLAB. Student user guide. The problemsolving tool for engineers,
 mathematicians, and scientists (1992; Zbl 0782.65001); H. Benker,
 Ingenieurmathematik mit ComputeralgebraSystemen. AXIOM, DERIVE,
 MACSYMA, MAPLE, MATHCAD, MATHEMATICA, MATLAB und MuPAD in der
 Anwendung (1998; Zbl 0909.68109); W. Koepf, Hohere Analysis mit DERIVE
 (1994; Zbl 0819.26003)] have greatly faciliated mathematical
 experiments and have thus become popular tools for the modern
 mathematician. It is a pity that most of these packages are quite
 expensive, and that the frequently upgraded versions are not free for
 the owners of the earlier versions (fortunately, there are inexpensive
 student versions of some of these packages). There is a constant
 demand of instructional textbooks by users of these packages. This
 demand is reflected in the growing number of such textbooks. Many of
 these books provide software support (diskette, CDROM, access by
 ftp). Such a textbook should meet, in my opinion, the following
 criteria: (1) The size should be small, not bulky like the complete
 technical descriptions of the software. (2) There should be a lot of
 examples of the use of the software covering a wide range of
 mathematical topics. Electronic versions of these examples should be
 made available for free to the users of the textbook
 (e.g. diskette/CDROM, access by ftp). (3) There should be a good
 supply of exercises covering the basic mathematical applications. (4)
 The book should be visually pleasing, easy to read, have good indexes
 and provide pointers to other books and electronic sources of
 information. The book under review provides, in addition to the actual
 text, an interactive exploratorium of its topics, based on the
 mechanism of Maple worksheets. These worksheets can be ``opened'' by
 the Maple program and they form a mixture of usual text, hypertext,
 and Maple commands and have a nice style appearance. They also can be
 ``exported'' in a file and included in a file for further treatment.
 The book meets all the aforementioned criteria (1)(4) with elegance.
 There are many exercises which cover all the usual mathematical topics
 from linear algebra to differential equations and statistics. A
 valuable feature is an appendix with hints and answers for all
 exercises. One of the highlights of the book is the examination of
 Riemann's nondifferentiable function
 \[x \mapsto \sum_{k=1}^\infty{k^{2}} sin(\pi kx)\]
 which is differentiable only at the rational points $p/q$ with $p$
 and $q$ odd and relatively prime, where its derivative is $1/2$.

 The book is intended for students of mathematics, engineering
 sciences, and econometry. This book is an ideal guide for this purpose
 and it could probably be used along, without the bulky technical
 documentation of the Maple language. Note that Maple has a
 comprehensive online help program, which contains large parts of the
 original documentation."
}

\end{chunk}

\index{Wester, Michael J.}
\begin{chunk}{axiom.bib}
@book{West99,
 author = "Wester, Michael J.",
 title = "Computer Algebra Systems. A practical guide",
 year = "1999",
 publisher = "Wiley",
 keywords = "axiomref",
 abstract =
 "In this book some of the most popular general purpose computer
 algebra systems (CAS), such as Mathematica, Maple, Derive, Axiom,
 MuPAD, and Macsyma, are examined. The strengths and weaknesses of
 these programs are compared and contrasted, and tutorial information
 for using these systems in various ways is given. The different
 packages are quantitatively compared using standard test suites,
 giving the possibility to asses the most appropriate for a particular
 user or application. The origins of these systems are revealed and
 many of their behaviors analyzed. This furnishes a feel for where the
 current computer algebra system state of the art stays and what can be
 expected for existing and future systems. The book is organized in
 several chapters written by different authors. Chapters 1,2, and 3 are
 organized as reviews, comparisons, and critiques of CAS
 capabilities. Then more technical issues are discussed considering
 different approaches taken by different CAS: simplifying square roots
 of square roots by denesting (chapter 4), complex number calculation
 (chapter 5), efficiently computing Chebyshev polynomials (chapter 6),
 solving single equations and systems of polynomial equations (chapters
 7, 8), computing limits (chapter 9), multiple integration (chapter
 10), solving ordinary differential equation (chapter 11), integration
 of nonlinear evolution equations (chapter 12), code generation
 (chapter 13), evaluation of expressions and programs in the embedded
 computer algebra programming language (chapter 14), and computer
 algebra in education (chapter 15). Chapter 16 covers the origin of CA,
 and, finally chapter 17 gives a list of most CAS available today."
+@phdthesis{Sale04,
+ author = "Salem, Fatima Khaled Abu",
+ title = "Factorisation Algorithms for Univariate and Bivariate Polynomials
+ over Finite Fields",
+ school = "Meron College",
+ year = "2004",
+ paper = "Sale04",
+ url = "http://www.cs.aub.edu.lb/fa21/Dissertations/My\_thesis.pdf",
+ abstract =
+ "In this thesis we address algorithms for polynomial factorisation
+ over finite fields. In the univariate case, we study a recent
+ algorithm due to Niederreiter where the factorisation problem is
+ reduced to solving a linear system over the finite field in question,
+ and the solutions are used to produce the complete factorisation of
+ the polynomials into irreducibles. We develop a new algorithm for
+ solving the linear system using sparse Gaussian elimination with the
+ Markowitz ordering strategy, and conjecture that the Niederreiter
+ linear system is not only initially sparse, but also preserves its
+ sparsity throughout the Gaussian elimination phase. We develop a new
+ bulk synchronous parallel (BSP) algorithm base on the approach of
+ Gottfert for extracting the factors of a polynomial using a basis of
+ the Niederreiter solution set of $\mathbb{F}_2$. We improve upon the
+ complexity and performance of the original algorithm, and produce
+ binary univariate factorisations of trinomials up to degree 400000.
+
+ We present a new approach to multivariate polynomial factorisation
+ which incorporates ideas from polyhedral geometry, and generalises
+ Hensel lifting. The contribution is an algorithm for factoring
+ bivariate polynomials via polytopes which is able to exploit to some
+ extent the sparsity of polynomials. We further show that the polytope
+ method can be made sensitive to the number of nonzero terms of the
+ input polynomial. We describe a sparse adaptation of the polytope
+ method over finite fields of prime order which requires fewer bit
+ operations and memory references for polynomials which are known to be
+ the product of two sparse factors. Using this method, and to the best
+ of our knowledge, we achieve a world record in binary bivariate
+ factorisation of a sparse polynomial of degree 20000. We develop a BSP
+ variant of the absolute irreducibility testing via polytopes given in
+ [45], producing a more memory and run time efficient method that can
+ provide wider ranges of applicability. We achieve absolute
+ irreducibility testing of a bivariate and trivariate polynomial of
+ degree 30000, and of multivariate polynomials with up to 3000
+ variables."
}
\end{chunk}
\index{Benker, Hans}
+\index{Gianni, P.}
+\index{Trager, B.}
\begin{chunk}{axiom.bib}
@book{Benk98,
 author = "Benker, Hans",
 title = "Engineering mathematics with computer algebra systems",
 year = "1998",
 keywords = "axiomref",
 comment = "german"
+@article{Gian96,
+ author = "Gianni, P. and Trager, B.",
+ title = "Squarefree algorithms in positive characteristic",
+ journal =
+ "J. of Applicable Algebra in Engineering, Communication and Computing",
+ volume = "7",
+ pages = "114",
+ year = "1996",
+
}
\end{chunk}
\index{Breuer, Thomas}
\index{Linton, Steve}
+\index{Shoup, Victor}
\begin{chunk}{axiom.bib}
@InProceedings{Breu98,
 author = "Breuer, Thomas and Linton, Steve",
 title = "The GAP 4 type system organising algebraic algorithms",
 booktitle = "Proc. ISSAC 98",
 series = "ISSAC 98",
 year = "1998",
 publisher = "ACM Press",
 location = "Rostock, Germany",
 pages = "1315",
 keywords = "axiomref",
 paper = "Breu98.pdf",
 url = "http://www.gapsystem.org/Doc/Talks/paper.ps",
+@InProceedings{Shou91,
+ author = "Shoup, Victor",
+ title = "A Fast Deterministic Algorithm for Factoring Polynomials over
+ Finite Fields of Small Characteristic",
+ booktitle = "Proc. ISSAC 1991",
+ series = "ISSAC 1991",
+ year = "1991",
+ pages = "1421",
+ paper = "Shou91.pdf",
+ url = "http://www.shoup.net/papers/quadfactor.pdf",
abstract =
 "Version 4 of the GAP (Groups, Algorithms, Programming) system for
 computational discrete mathematics has a number of novel features. In
 this paper, we describe the type system, and the way in which it is
 used for method selection. This system is central to the organization
 of the library which is the main part of the GAP system. Unlike
 simpler objectoriented systems, GAP allows method selection based on
 the types of all arguments and on certain aspects of the relationship
 between the arguments. In addition, the type of an object can change,
 in a controlled way, during its life. This reflects information about
 the object which has been computed and stored. Individual methods can
 be written and installed independently. Furthermore, most checking of
 the arguments is done in a uniform way by the method selection system,
 making individual methods simpler and less prone to error. The methods
 are combined automatically to produce a powerful and usable system for
 interactive use or programming."
}

\end{chunk}

\index{Linton, Stephen}
\begin{chunk}{axiom.bib}
@misc{Lint98,
 author = "Linton, Stephen",
 title = "The GAP 4 Type System Organising Algebraic Algorithms",
 paper = "Lint98.pdf",
 url = "http://www.gapsystem.org/Doc/Talks/kobe.ps",
 keywords = "axiomref"
+ "We present a new algorithm for factoring polynomials over finite
+ fields. Our algorithm is deterministic, and its running time is
+ ``almost'' quadratic when the characteristic is a small fixed
+ prime. As such, our algorithm is asymptotically faster than previously
+ known deterministic algorithms for factoring polynomials over finite
+ fields of small characteristic."
}
\end{chunk}
\index{Diaz, Angel}
+\index{von zur Gathen, Joachim}
\index{Kaltofen, Erich}
\begin{chunk}{axiom.bib}
@InProceedings{Diaz98,
 author = "Diaz, A. and Kaltofen, E.",
 title = "{FoxBox}, a System for Manipulating Symbolic Objects in Black Box
 Representation",
 booktitle = "Proc. 1998 Internat. Symp. Symbolic Algebraic Comput.",
 crossref = "ISSAC98",
 publisher = "ACM Press",
 year = "1998",
 pages = "3037",
 url = "http://www.math.ncsu.edu/~kaltofen/bibliography/98/DiKa98.pdf",
 paper = "Diaz98.pdf",
+@Article{Gath85b,
+ author = "{von zur Gathen}, Joachim and Kaltofen, E.",
+ title = "PolynomialTime Factorization of Multivariate Polynomials over
+ Finite Fields",
+ journal = "Math. Comput.",
+ year = "1985",
+ volume = "45",
+ pages = "251261",
+ url =
+ "http://www.math.ncsu.edu/~kaltofen/bibliography/85/GaKa85_mathcomp.ps.gz",
+ paper = "Gath85.ps",
abstract =
 "The FOXBOX system puts in practice the black box representation of
 symbolic objects and provides algorithms for performing the symbolic
 calculus with such representations. Black box objects are stored as
 functions. For instance: a black box polynomial is a procedure that
 takes values for the variables as input and evaluates the polynomial
 at that given point. FOXBOX can compute the greatest common divisor
 and factorize polynomials in black box representation, producing as
 output new black boxes. It also can compute the standard sparse
 distributed representation of a black box polynomial, for example, one
 which was computed for an irreducible factor. We establish that the
 black box representation of objects can push the size of symbolic
 expressions far beyond what standard data structures could handle
 before.

 Furthermore, FOXBOX demonstrates the generic program design
 methodology. The FOXBOX system is written in C++. C++ template
 arguments provide for abstract domain types. Currently, FOXBOX can be
 compiled with SACLIB 1.1, GnuMP 1.0, and NTL 2.0 as its underlying
 field and polynomial arithmetic. Multiple arithmetic plugins can be
 used in the same computation. FOXBOX provides an MPI compliant
 distribution mechanism that allows for parallel and distributed
 execution of FOXBOX programs. Finally, FOXBOX plugs into a
 server/clientstyle Maple application interface."
+ "We present a probabilistic algorithm that finds the irreducible
+ factors of a bivariate polynomial with coefficients from a finite
+ field in time polynomial in the input size, i.e. in the degree of the
+ polynomial and $log$(cardinality of field). The algorithm generalizes
+ to multivariate polynomials and has polynomial running time for
+ densely encoded inputs. Also a deterministic version of the algorithm
+ is discussed whose running time is polynomial in the degree of the
+ input polynomial and the size of the field."
}
\end{chunk}
\index{Dooley, Samuel S.}
+\index{von zur Gathen, Joachim}
+\index{Panario, Daniel}
\begin{chunk}{axiom.bib}
@InProceedings{Dool98,
 author = "Dooley, Samuel S.",
 title = "Coordinating mathematical content and presentation markup in
 interactive mathematical documents",
 booktitle = "Proc. ISSAC 1998",
 series = "ISSAC 98",
 year = "1998",
 publisher = "ACM Press",
 location = "Rostock, Germany",
 pages = "1315",
 keywords = "axiomref",
 abstract =
 "This paper presents a method for representing mathematical content
 and presentation markup in interactive mathematical documents that
 treats each view of the information on a separate and equal
 footing. By providing extensible, overridable, default mappings from
 content to presentation in a way that supports efficient mappings back
 from the presentation to the underlying content, a user interface for
 an interactive textbook has been implemented where the user interacts
 with highquality presentation markup that supports user operations
 defined in terms of the mathematical content. In addition, the user
 interface can be insulated from contentspecific information, while
 still being enabled to transfer that information to other programs for
 computation. This method has been employed to embed interactive
 mathematical content into the IBM techexplorer Interactive Textbook
 for Linear Algebra. The issues involved in the implementation of the
 interactive textbook also shed some light on the problems faced by the
 MathML working group in representing both presentation and content for
 mathematics for interactive web documents."
+@article{Gath01,
+ author = "von zur Gathen, Joachim and Panario, Daniel",
+ title = "Factoring Polynomials Over Finite Fields: A Survey",
+ journal = "J. Symbolic Computation",
+ year = "2001",
+ volume = "31",
+ pages = "317",
+ paper = "Gath01.pdf",
+ url =
+ "http://people.csail.mit.edu/dmoshdov/courses/codes/polyfactorization.pdf",
+ keywords = "survey",
+ abstract =
+ "This survey reviews several algorithms for the factorization of
+ univariate polynomials over finite fields. We emphasize the main ideas
+ of the methods and provide and uptodate bibliography of the problem.
+ This paper gives algorithms for {\sl squarefree factorization},
+ {\sl distinctdegree factorization}, and {\sl equaldegree factorization}.
+ The first and second algorithms are deterministic, the third is
+ probabilistic."
}
\end{chunk}
\index{Dunstan, Martin}
\index{Kelsey, Tom}
\index{Linton, Steve A.}
\index{Martin, Ursula}
+\index{Augot, Daniel}
+\index{Camion, Paul}
\begin{chunk}{axiom.bib}
@InProceedings{Duns98,
 author = "Dunstan, Martin and Kelsey, Tom and Linton, Steve and
 Martin, Ursula",
 title = "Lightweight Formal Methods For Computer Algebra Systems",
 publisher = "ACM Press",
 booktitle = "Proc. ISSAC 1998",
 year = "1998",
 location = "Rostock, Germany",
 pages = "8087",
 url = "http://www.cs.standrews.ac.uk/~tom/pub/issac98.pdf",
 paper = "Duns98.pdf",
+@article{Augo97,
+ author = "Augot, Daniel and Camion, Paul",
+ title = "On the computation of minimal polynomials, cyclic vectors,
+ and Frobenius forms",
+ journal = "Linear Algebra Appl.",
+ volume = "260",
+ pages = "6194",
+ year = "1997",
keywords = "axiomref",
+ paper = "Augo97.pdf",
abstract =
 "Demonstrates the use of formal methods tools to provide a semantics
 for the type hierarchy of the Axiom computer algebra system, and a
 methodology for Aldor program analysis and verification. There are
 examples of abstract specifications of Axiom primitives."
+ "Algorithms related to the computation of the minimal polynomial of an
+ $x\times n$ matrix over a field $K$ are introduced. The complexity of
+ the first algorithm, where the complete factorization of the
+ characteristic polynomial is needed, is $O(\sqrt{n}\cdot n^3)$. An
+ iterative algorithm for finding the minimal polynomial has complexity
+ $O(n^3+n^2m^2)$, where $m$ is a parameter of the shift Hessenberg
+ matrix used. The method does not require the knowlege of the
+ characteristic polynomial. The average value of $m$ is $O(log n)$.
+
+ Next methods are discussed for finding a cyclic vector for a matrix.
+ The authors first consider the case when its characteristic polynomial
+ is squarefree. Using the shift Hessenberg form leads to an algorithm
+ at cost $O(n^3 + n^2m^2)$. A more sophisticated recurrent procedure
+ gives the result in $O(n^3)$ steps. In particular, a normal basis for
+ an extended finite field of size $q^n$ will be obtained with complexity
+ $O(n^3+n^2 log q)$.
+
+ Finally, the Frobenius form is obtained with asymptotic average
+ complexity $O(n^3 log n)$."
}
\end{chunk}
\index{Harrison, J.}
\index{Thery, L.}
+\index{Bernardin, Laurent}
+\index{Monagan, Michael B.}
\begin{chunk}{axiom.bib}
@article{Harr98,
 author = "Harrison, J. and Thery, L.",
 title = "A Skeptic's approach to combining HOL and Maple",
 journal = "J. Autom. Reasoning",
 volume = "21",
 number = "3",
 pages = "279294",
 year = "1998",
+@InProceedings{Bern97a,
+ author = "Bernardin, Laurent and Monagan, Michael B.",
+ title = "Efficient multivariate factorization over finite fields",
+ booktitle = "Applied algebra, algebraic algorithms and errorcorrecting
+ codes",
+ series = "AAECC12",
+ year = "1997",
+ location = "Toulouse, France",
+ publisher = "Springer",
+ pages = "1528",
keywords = "axiomref",
 paper = "Harr98.pdf",
 url = "http://www.cl.cam.ac.uk/~jrh13/papers/cas.ps.gz",
+ paper = "Bern97a.pdf",
+ url = "http://www.cecm.sfu.ca/~monaganm/papers/AAECC.pdf",
abstract =
 "We contrast theorem provers and computer algebra systems, pointing
 out the advantages and disadvantages of each, and suggest a simple way
 to achieve a synthesis of some of the best features of both. Our
 method is based on the systematic separation of search for a solution
 and checking the solution, using a physical connection between
 systems. We describe the separation of proof search and checking in
 some detail, relating it to proof planning and to the complexity class
 NP, and discuss different ways of exploiting a physical link between
 systems. Finally, the method is illustrated by some concrete examples
 of computer algebra results proved formally in the HOL theorem prover
 with the aid of Maple."
+ "We describe the Maple implementation of multivariate factorization
+ over general finite fields. Our first implementation is available in
+ Maple V Release 3. We give selected details of the algorithms and show
+ several ideas that were used to improve its efficiency. Most of the
+ improvements presented here are incorporated in Maple V Release 4. In
+ particular, we show that we needed a general tool for implementing
+ computations in GF$(p^k)[x_1,x_2,\cdots,x_v]$. We also needed an
+ efficient implementation of our algorithms $\mathbb{Z}_p[y][x]$ in
+ because any multivariate factorization may depend on several bivariate
+ factorizations. The efficiency of our implementation is illustrated by
+ the ability to factor bivariate polynomials with over a million
+ monomials over a small prime field."
}
\end{chunk}
\index{Kerber, Manfred}
\index{Kohlhase, Michael}
\index{Volker, Sorge}
+\index{Bronstein, Manuel}
+\index{Weil, JacquesArthur}
\begin{chunk}{axiom.bib}
@article{Kerb98,
 author = "Kerber, Manfred and Kohlhase, Michael and Volker, Sorge",
 title = "Integrating computer algebra into proof planning",
 journal = "J. Autom. Reasoning",
 volume = "21",
 number = "3",
 pages = "327355",
+@article{Bron97a,
+ author = "Bronstein, Manuel and Weil, JacquesArthur",
+ title = "On Symmetric Powers of Differential Operators",
+ series = "ISSAC'97",
+ year = "1997",
+ pages = "156163",
keywords = "axiomref",
 paper = "Kerb98.pdf",
 url =
"http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.40.3914&rep=rep1&type=pdf",
 abstract =
 "Mechanized reasoning systems and computer algebra systems have
 different objectives. Their integration is highly desirable, since
 formal proofs often involve both of the two different tasks proving
 and calculating. Even more important, proof and computation are often
 interwoven and not easily separable.

 In this article, we advocate an integration of computer algebra into
 mechanized reasoning systems at the proof plan level. This approach
 allows us to view the computer algebra algorithms as methods, that is,
 declarative representations of the problemsolving knowledge specific
 to a certain mathematical domain. Automation can be achieved in many
 cases by searching for a hierarchic proof plan at the method level by
 using suitable domainspecific control knowledge about the
 mathematical algorithms. In other words, the uniform framework of
 proof planning allows us to solve a large class of problems that are
 not automatically solvable by separate systems.

 Our approach also gives an answer to the correctness problems inherent
 in such an integration. We advocate an approach where the computer
 algebra system produces highlevel protocol information that can be
 processed by an interface to derive proof plans. Such a proof plan in
 turn can be expanded to proofs at different levels of abstraction, so
 the approach is well suited for producing a highlevel verbalized
 explication as well as for a lowlevel, machinecheckable,
 calculuslevel proof. We present an implementation of our ideas and
 exemplify them using an automatically solved example."
+ url =
+ "http://wwwsop.inria.fr/cafe/Manuel.Bronstein/publications/mb_papers.html",
+ paper = "Bro97a.pdf",
+ publisher = "ACM, NY",
+ abstract = "
+ We present alternative algorithms for computing symmetric powers of
+ linear ordinary differential operators. Our algorithms are applicable
+ to operators with coefficients in arbitrary integral domains and
+ become faster than the traditional methods for symmetric powers of
+ sufficiently large order, or over sufficiently complicated coefficient
+ domains. The basic ideas are also applicable to other computations
+ involving cyclic vector techniques, such as exterior powers of
+ differential or difference operators."
}
\end{chunk}
\index{Naudin, Patrice}
\index{Quitte, Claude}
+\index{Calmet, J.}
+\index{Campbell, J.A.}
\begin{chunk}{axiom.bib}
@article{Naud98,
 author = "Naudin, Patrice and Quitte, Claude",
 title = "Univariate polynomial factorization over finite fields",
 journal = "Theor. Comput. Sci.",
 volume = "191",
 number = "12",
 pages = "136",
 year = "1998",
 paper = "Naud98.pdf",
+@article{Calm97,
+ author = "Calmet, J. and Campbell, J.A.",
+ title = "A perspective on symbolic mathematical computing and
+ artificial intelligence",
+ journal = "Ann. Math. Artif. Intell.",
+ volume = "19",
+ number = "34",
+ pages = "261277",
+ year = "1997",
+ keywords = "axiomref",
+ paper = "Calm97.pdf",
+ url =
+"http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.52.5425&rep=rep1&type=pdf",
abstract =
 "This paper is a tutorial introduction to univariate polynomial
 factorization over finite fields. The authors recall the classical
 methods that induced most factorization algorithms (Berlekamp’s and
 the CantorZassenhaus ones) and some refinements which can be applied
 to these methods. Explicit algorithms are presented in a form suitable
 for almost immediate implementation. They give a detailed description
 of an efficient implementation of the CantorZassenhaus algorithm used
 in the release 2 of the Axiom computer algebra system."
+ "The nature and history of the research area common to artificial
+ intelligence and symbolic mathematical computation are examined, with
+ particular reference to the topics having the greatest current amount
+ of activity or potential for further development: mathematical
+ knowledgebased computing environments, autonomous agents and
+ multiagent systems, transformation of problem descriptions in logics
+ into algebraic forms, exploitation of machine learning, qualitative
+ reasoning, and constraintbased programming. Knowledge representation,
+ for mathematical knowledge, is identified as a central focus for much
+ of this work. Several promising topics for further research are stated."
}
\end{chunk}
diff git a/src/axiomwebsite/patches.html b/src/axiomwebsite/patches.html
index 1006490..bdbc295 100644
 a/src/axiomwebsite/patches.html
+++ b/src/axiomwebsite/patches.html
@@ 5420,6 +5420,8 @@ books/bookvolbib Axiom Citations in the Literature
books/bookvolbib Axiom Citations in the Literature
20160627.04.tpd.patch
books/bookvolbib Axiom Citations in the Literature
+20160628.01.tpd.patch
+books/bookvolbib Axiom Citations in the Literature

1.7.5.4