From 1fc9f42acd6d656e3264e5172d7aab580f6939fc Mon Sep 17 00:00:00 2001
From: Tim Daly
Date: Tue, 23 May 2017 03:05:45 0400
Subject: [PATCH] bookvolbib reference to Axiom in publications
Goal: Proving Axiom Correct
\index{Wright, Francis J.}
\begin{chunk}{axiom.bib}
@misc{Wrig03,
author = "Wright, Francis J.",
title = "Mathematics and Algorithms for Computer Algebra: Part 1",
link = "\url{https://people.eecs.berkeley.edu/~fateman/282/F%20Wright%20notes/week1.pdf}",
year = "2003",
comment = "full course. week2=Wrig03a, wee3=Wrig03b,...week8=Wrig3g.pdf",
abstract =
"This course will be mainly mathematics, some computer science
and a little computing. Little or no essential use will be made of
actual computer languages, although I may occasionally use Pascal, C,
Lisp or REDUCE for concrete examples. The aim of the course is to
provide an entry into the current research literature, but not to present
the most recent research results.
The first half of the course (taught by me) will deal with basic math
ematics and algorithms for computer algebra, primarily at the level of
arithmetic and elementary abstract algebra, including an introduction
to GCDs and the solution of univariate polynomial equations. This
leads into the second half of the course (taught by Dr Jim Skea) on
the more advanced problems of polynomial factorization, indefinite in
tegration, multivariate polynomial equations, etc.
The first week provides an introduction to the computing aspects
of computer algebra, and contains almost no mathematics. It is in
tended to show how the later theory can be implemented for practical
computation. The second week provides a rapid but superficial survey
of the abstract algebra that is most important for computer algebra.
The next five weeks will build on this abstract basis to do some more
concrete mathematics in more details, referring back to the basis es
tablished in the first two weeks as necessary.
At the end of each set of notes will be exercises, one (or more) of
which will be assessed.",
paper = "Wrig03.pdf",
keywords = "axiomref"
}
\end{chunk}
\index{Brown, W. S.}
\begin{chunk}{axiom.bib}
@articla{Brow78,
author = "Brown, W. S.",
title = "The Subresultant PRS Algorithm",
journal = "ACM Transactions on Mathematical Software",
volume = "4",
number = "3",
year = "1978",
pages = "237249",
link =
"\url{https://people.eecs.berkeley.edu/~fateman/282/readings/brown.pdf}",
abstract =
"Two earlier papers described the generalizations of Euclid's
algorithm to deal with the problem of computing the greatest common
divisor (GCD) or the resultant of a pair of polynomials. A sequal to
those two papers is presented here.
In attempting such a generalization one easily arrives at the concept
of a polynomial remainder sequence (PRS) and then quickly discovers
the phenomenon of explosive coefficient growth. Fortunately, this
explosive growth is not inherent in the problem, but is only an
artifact of various naive solutions. If one removes the content (that
is, the GCD of the coefficients) from each polynomial in a PRS, the
coefficient growth in the resulting primitive PRS is relatively modest.
However, the cost of computing the content (by applying Euclid's
algorithm in the coefficient domain) may be unacceptably or even
prohibitively high, especially if the coefficients are themselves
polynomials in one or more addltional variables.
The key to controlling coefficient growth without the costly
computation of GCD's of coefficients is the fundamental theorem of
subresuitants, which shows that every polynomial in a PRS is
proportional to some subresultant of the first two. By arranging for
the constants of proportionahty to be unity, one obtains the
subresultant PRS algorithm, in which the coefficient growth is
essentially linear. A corollary of the fundamental theorem is given
here, which leads to a simple derivation and deeper understanding of
the subresultant PRS algorithm and converts a conjecture mentioned in
the earlier papers into an elementary remark.
A possible alternative method of constructing a subresultant PRS is to
evaluate all the subresultants directly from Sylvester's determinant
via expansion by minors. A complexity analysis is given in conclusion,
along lines pioneered by Gentleman and Johnson, showing that the
subresultant PRS algorithm is superior to the determinant method
whenever the given polynomials are sufficiently large and dense, but
is inferior in the sparse extreme.",
paper = "Brow78.pdf"
}
\end{chunk}
\index{Collins, George E.}
\begin{chunk}{axiom.bib}
@article{Coll87,
author = "Collins, George E.",
title = "Subresultants and Reduced Polynomial Remainder Sequences",
journal = "J. ACM",
volume = "14",
number = "1",
year = "1987",
pages = "128142",
link =
"\url{https://people.eecs.berkeley.edu/~fateman/282/readings/collins.pdf}",
paper = "Coll87.pdf"
}
\end{chunk}
\index{Gentleman, W. M.}
\index{Johnson, S. C.}
@article{Gent76,
author = "Gentleman, W. M. and Johnson, S. C.",
title = "Analysis of Algorithms, A Case Study: Determinants of Matrices
With Polynomial Entries",
journal = "ACM Transactions on Mathematical Software",
volume = "2",
number = "3",
year = "1976",
pages = "232241",
link =
"\url{https://people.eecs.berkeley.edu/~fateman/282/readings/gentleman.pdf}",
abstract =
"The problem of computing the deternunant of a matrix of polynomials
is considered; two algorithms (expansion by minors and expansion by
Gaussian elimination) are compared; and each is examined under two models
for polynomial computatmn (dense univariate and totally sparse). The
results, while interesting in themselves, also serve to display two
points: (1) Asymptotic results are sometimes misleading for noninfinite
(e.g. practical) problems. (2) Models of computation are by
definition simplifications of reality: algorithmic analysis should be
carried out under several distinct computatmnal models and should be
supported by empirical data.",
paper = "Gent76.pdf"
}
\end{chunk}
\index{Fateman, Richard}
\begin{chunk}{axiom.bib}
@misc{Fate00b,
author = "Fateman, Richard",
title = "The (finite field) Fast Fourier Transform",
year = "2000",
link =
"\url{https://people.eecs.berkeley.edu/~fateman/282/readings/fftnotes.pdf}",
abstract =
"There are numerous directions from which one can approach the subject
of the fast Fourier Transform (FFT). It can be explained via numerous
connections to convolution, signal processing, and various other
properties and applications of the algorithm. We (along with
Geddes/Czapor/Labahn) take a rather simple view from the algebraic
manipulation standpoint. As will be apparent shortly, we relate the
FFT to the evaluation of a polynomial. We also consider it of interest
primarily as an algorithm in a discrete (finite) computation structure
rather than over the complex numbers.",
paper = "Fate00b.pdf"
}
\end{chunk}
\index{Fateman, Richard}
\begin{chunk}{axiom.bib}
@misc{Fate00c,
author = "Fateman, Richard",
title = "Additional Notes on Polynomial GCDs, Hensel construction",
year = "2000",
link =
"\url{https://people.eecs.berkeley.edu/~fateman/282/readings/hensel.pdf}",
paper = "Fate00c.pdf"
}
\end{chunk}
\index{Liska, Richard}
\index{Drska, Ladislav}
\index{Limpouch, Jiri}
\index{Sinor, Milan}
\index{Wester, Michael J.}
\index{Winkler, Franz}
\begin{chunk}{axiom.bib}
@book{Lisk99,
author = "Liska, Richard and Drska, Ladislav and Limpouch, Jiri and
Sinor, Milan adn Wester, Michael and Winkler, Franz",
title = "Computer Algebra  Algorithms, Systems and Applications",
year = "1999",
publisher = "web",
link =
"\url{https://people.eecs.berkeley.edu/~fateman/282/readings/liska.pdf}",
paper = "Lisk99.pdf",
keywords = "axiomref"
}
\end{chunk}
\index{Mishra, Bhubaneswar}
\index{Yap, Chee}
\begin{chunk}{axiom.bib}
@misc{Mish87,
author = "Mishra, Bhubaneswar and Yap, Chee",
title = "Notes on Groebner Basis",
year = "1987",
link = "\url{https://people.eecs.berkeley.edu/~fateman/282/readings/mishra87note.pdf}",
abstract =
"We present a selfcontained exposition of the theory of Groebner
basis and its applications",
paper = "Mish87.pdf"
}
\end{chunk}
\index{Monagan, Michael}
\index{Wittkopf, Allan D.}
@inproceedings{Mona00,
author = "Monagan, Michael and Wittkopf, Allan D.",
title = "On the Design and Implementation of Brown's Algorithm over the
Integers and Number Fields",
booktitle = "ISSAC 2000",
pages = "225233",
year = "2000",
isbn = "1581132182",
abstract =
"We study the design and implementation of the dense modular GCD
algorithm of Brown applied to bivariate polynomial GCDs over the
integers and number fields. We present an improved design of Brown's
algorithm and compare it asymptotically with Brown's original
algorithm, with GCDHEU, the heuristic GCD algorithm, and with the
EEZGCD algorithm. We also make an empirical comparison based on Maple
implementations of the algorithms. Our findings show that a careful
implementation of our improved version of Brown's algorithm is much
better than the other algorithms in theory and in practice.",
paper = "Mona00.pdf"
}
\end{chunk}
\index{Yap, CheeKeng}
\begin{chunk}{axiom.bib}
@misc{Yap02a,
author = "Yap, CheeKeng",
title = "Lecture 0: Introduction",
year = "2002",
link =
"\url{https://people.eecs.berkeley.edu/~fateman/282/readings/yap0.pdf}",
paper = "Yap02a.pdf"
}
\end{chunk}
\index{Yap, CheeKeng}
\begin{chunk}{axiom.bib}
@misc{Yap02b,
author = "Yap, CheeKeng",
title = "Lecture II: The GCD",
year = "2002",
link =
"\url{https://people.eecs.berkeley.edu/~fateman/282/readings/yap2.pdf}",
paper = "Yap02b.pdf"
}
\end{chunk}

books/bookvolbib.pamphlet  293 ++++++++++++++++++++++++++++++++++++++
changelog  4 +
patch  288 +++++++++++++++++++++++++++++++++
src/axiomwebsite/patches.html  2 +
4 files changed, 530 insertions(+), 57 deletions()
diff git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index 51b2e55..65e830c 100644
 a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ 1637,6 +1637,59 @@ when shown in factored form.
\section{Algebraic Algorithms} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\index{Brown, W. S.}
+\begin{chunk}{axiom.bib}
+@articla{Brow78,
+ author = "Brown, W. S.",
+ title = "The Subresultant PRS Algorithm",
+ journal = "ACM Transactions on Mathematical Software",
+ volume = "4",
+ number = "3",
+ year = "1978",
+ pages = "237249",
+ link =
+ "\url{https://people.eecs.berkeley.edu/~fateman/282/readings/brown.pdf}",
+ abstract =
+ "Two earlier papers described the generalizations of Euclid's
+ algorithm to deal with the problem of computing the greatest common
+ divisor (GCD) or the resultant of a pair of polynomials. A sequal to
+ those two papers is presented here.
+
+ In attempting such a generalization one easily arrives at the concept
+ of a polynomial remainder sequence (PRS) and then quickly discovers
+ the phenomenon of explosive coefficient growth. Fortunately, this
+ explosive growth is not inherent in the problem, but is only an
+ artifact of various naive solutions. If one removes the content (that
+ is, the GCD of the coefficients) from each polynomial in a PRS, the
+ coefficient growth in the resulting primitive PRS is relatively modest.
+ However, the cost of computing the content (by applying Euclid's
+ algorithm in the coefficient domain) may be unacceptably or even
+ prohibitively high, especially if the coefficients are themselves
+ polynomials in one or more addltional variables.
+
+ The key to controlling coefficient growth without the costly
+ computation of GCD's of coefficients is the fundamental theorem of
+ subresuitants, which shows that every polynomial in a PRS is
+ proportional to some subresultant of the first two. By arranging for
+ the constants of proportionahty to be unity, one obtains the
+ subresultant PRS algorithm, in which the coefficient growth is
+ essentially linear. A corollary of the fundamental theorem is given
+ here, which leads to a simple derivation and deeper understanding of
+ the subresultant PRS algorithm and converts a conjecture mentioned in
+ the earlier papers into an elementary remark.
+
+ A possible alternative method of constructing a subresultant PRS is to
+ evaluate all the subresultants directly from Sylvester's determinant
+ via expansion by minors. A complexity analysis is given in conclusion,
+ along lines pioneered by Gentleman and Johnson, showing that the
+ subresultant PRS algorithm is superior to the determinant method
+ whenever the given polynomials are sufficiently large and dense, but
+ is inferior in the sparse extreme.",
+ paper = "Brow78.pdf"
+}
+
+\end{chunk}
+
\index{Cannon, John J.}
\index{Dimino, Lucien A.}
\index{Havas, George}
@@ 1663,6 +1716,23 @@ when shown in factored form.
\end{chunk}
+\index{Collins, George E.}
+\begin{chunk}{axiom.bib}
+@article{Coll87,
+ author = "Collins, George E.",
+ title = "Subresultants and Reduced Polynomial Remainder Sequences",
+ journal = "J. ACM",
+ volume = "14",
+ number = "1",
+ year = "1987",
+ pages = "128142",
+ link =
+ "\url{https://people.eecs.berkeley.edu/~fateman/282/readings/collins.pdf}",
+ paper = "Coll87.pdf"
+}
+
+\end{chunk}
+
\index{matrix computations}
\index{polynomial zero approximation}
\index{products of vectors}
@@ 1768,6 +1838,72 @@ when shown in factored form.
\end{chunk}
+\index{Fateman, Richard}
+\begin{chunk}{axiom.bib}
+@misc{Fate00b,
+ author = "Fateman, Richard",
+ title = "The (finite field) Fast Fourier Transform",
+ year = "2000",
+ link =
+ "\url{https://people.eecs.berkeley.edu/~fateman/282/readings/fftnotes.pdf}",
+ abstract =
+ "There are numerous directions from which one can approach the subject
+ of the fast Fourier Transform (FFT). It can be explained via numerous
+ connections to convolution, signal processing, and various other
+ properties and applications of the algorithm. We (along with
+ Geddes/Czapor/Labahn) take a rather simple view from the algebraic
+ manipulation standpoint. As will be apparent shortly, we relate the
+ FFT to the evaluation of a polynomial. We also consider it of interest
+ primarily as an algorithm in a discrete (finite) computation structure
+ rather than over the complex numbers.",
+ paper = "Fate00b.pdf"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard}
+\begin{chunk}{axiom.bib}
+@misc{Fate00c,
+ author = "Fateman, Richard",
+ title = "Additional Notes on Polynomial GCDs, Hensel construction",
+ year = "2000",
+ link =
+ "\url{https://people.eecs.berkeley.edu/~fateman/282/readings/hensel.pdf}",
+ paper = "Fate00c.pdf"
+}
+
+\end{chunk}
+
+\index{Gentleman, W. M.}
+\index{Johnson, S. C.}
+\begin{chunk}{axiom.bib}
+@article{Gent76,
+ author = "Gentleman, W. M. and Johnson, S. C.",
+ title = "Analysis of Algorithms, A Case Study: Determinants of Matrices
+ With Polynomial Entries",
+ journal = "ACM Transactions on Mathematical Software",
+ volume = "2",
+ number = "3",
+ year = "1976",
+ pages = "232241",
+ link =
+ "\url{https://people.eecs.berkeley.edu/~fateman/282/readings/gentleman.pdf}",
+ abstract =
+ "The problem of computing the deternunant of a matrix of polynomials
+ is considered; two algorithms (expansion by minors and expansion by
+ Gaussian elimination) are compared; and each is examined under two models
+ for polynomial computatmn (dense univariate and totally sparse). The
+ results, while interesting in themselves, also serve to display two
+ points: (1) Asymptotic results are sometimes misleading for noninfinite
+ (e.g. practical) problems. (2) Models of computation are by
+ definition simplifications of reality: algorithmic analysis should be
+ carried out under several distinct computatmnal models and should be
+ supported by empirical data.",
+ paper = "Gent76.pdf"
+}
+
+\end{chunk}
+
\index{Kaltofen, Erich}
\begin{chunk}{axiom.bib}
@InCollection{Kalt87a,
@@ 11957,7 +12093,31 @@ Proc ISSAC 97 pp172175 (1997)
volume = "35",
number = "1",
pages = "231264",
 link = "\url{http://www.math.ncsu.edu/~kaltofen/bibliography/88/Ka88_jacm.pdf}",
+ link =
+ "\url{http://www.math.ncsu.edu/~kaltofen/bibliography/88/Ka88_jacm.pdf}",
+ abstract =
+ "Algorithms on multivariate polynomials represented by straightline
+ programs are developed. First, it is shown that most algebraic
+ algorithms can be probabilistically applied to data that are given by
+ a straightline computation. Testing such rational numeric data for
+ zero, for instance, is facilitated by random evaluations modulo random
+ prime numbers. Then, auxiliary algorithms that determine the
+ coefficients of a multivariate polynomial in a single variable are
+ constructed. The first main result is an algorithm that produces the
+ greatest common divisor of the input polynomials, all in straightline
+ representation. The second result shows how to find a straightline
+ program for the reduced numerator and denominator from one for the
+ corresponding rational function. Both the algorithm for that
+ construction and the greatest common divisor algorithm are in random
+ polynomial time for the usual coefftcient fields and output a
+ straightline program, which with controllably high probability
+ correctly determines the requested answer. The running times are
+ polynomial functions in the binary input size, the input degrees as
+ unary numbers, and the logarithm of the inverse of the failure
+ probability. The algorithm for straightline programs for the
+ numerators and denominators of rational functions implies that every
+ degreebounded rational function can be computed fast in parallel,
+ that is, in polynomial size and polylogarithmic depth.",
paper = "Kalt88b.pdf"
}
@@ 16626,6 +16786,32 @@ Proc ISSAC 97 pp172175 (1997)
\end{chunk}
+\index{Yap, CheeKeng}
+\begin{chunk}{axiom.bib}
+@misc{Yap02a,
+ author = "Yap, CheeKeng",
+ title = "Problem of Algebra Lecture 0: Introduction",
+ year = "2002",
+ link =
+ "\url{https://people.eecs.berkeley.edu/~fateman/282/readings/yap0.pdf}",
+ paper = "Yap02a.pdf"
+}
+
+\end{chunk}
+
+\index{Yap, CheeKeng}
+\begin{chunk}{axiom.bib}
+@misc{Yap02b,
+ author = "Yap, CheeKeng",
+ title = "Lecture II: The GCD",
+ year = "2002",
+ link =
+ "\url{https://people.eecs.berkeley.edu/~fateman/282/readings/yap2.pdf}",
+ paper = "Yap02b.pdf"
+}
+
+\end{chunk}
+
\index{Burnikel, C.}
\index{Fleischer, R.}
\index{Mehlhom, K.}
@@ 29690,7 +29876,7 @@ ISBN 0897916999 LCCN QA76.95 I59 1995 ACM order number 505950
\index{Liao, HsinChao}
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@inproceedings{Laio95,
+@inproceedings{Liao95,
author = "Liao, HsinChao and Fateman, Richard J.",
title = "Evaluation of the heuristic polynomial GCD",
booktitle = "Proc. ISSAC 1995",
@@ 29724,9 +29910,8 @@ ISBN 0897916999 LCCN QA76.95 I59 1995 ACM order number 505950
sophisticated sparse algorithms are relatively slow on small problems
and only occasionally emerge as superior (on larger problems) it seems
the choice of a fast GCD algorithm is tricky.",
 paper = "phil8.pdf"
+ paper = "Liao95.pdf"
}

\end{chunk}
@@ 30055,13 +30240,18 @@ Math. and Computers in Simulation 42 pp 541549 (1996)
\index{Sinor, Milan}
\index{Wester, Michael J.}
\index{Winkler, Franz}
\begin{chunk}{ignore}
\bibitem[Liska 97]{LD97} Liska, Richard; Drska, Ladislav; Limpouch, Jiri;
Sinor, Milan; Wester, Michael; Winkler, Franz
 title = "Computer Algebra  algorithms, systems and applications",
June 2, 1997
 link = "\url{http://kfe.fjfi.cvut.cz/~liska/ca/all.html}",
+\begin{chunk}{axiom.bib}
+@book{Lisk99,
+ author = "Liska, Richard and Drska, Ladislav and Limpouch, Jiri and
+ Sinor, Milan adn Wester, Michael and Winkler, Franz",
+ title = "Computer Algebra  Algorithms, Systems and Applications",
+ year = "1999",
+ publisher = "web",
+ link =
+ "\url{https://people.eecs.berkeley.edu/~fateman/282/readings/liska.pdf}",
+ paper = "Lisk99.pdf",
keywords = "axiomref"
+}
\end{chunk}
@@ 30679,6 +30869,22 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
\end{chunk}
\index{Mishra, Bhubaneswar}
+\index{Yap, Chee}
+\begin{chunk}{axiom.bib}
+@misc{Mish87,
+ author = "Mishra, Bhubaneswar and Yap, Chee",
+ title = "Notes on Groebner Basis",
+ year = "1987",
+ link = "\url{https://people.eecs.berkeley.edu/~fateman/282/readings/mishra87note.pdf}",
+ abstract =
+ "We present a selfcontained exposition of the theory of Groebner
+ basis and its applications",
+ paper = "Mish87.pdf"
+}
+
+\end{chunk}
+
+\index{Mishra, Bhubaneswar}
\begin{chunk}{axiom.bib}
@book{Mish93,
author = "Mishra, Bhubaneswar",
@@ 30907,6 +31113,32 @@ in [Wit87], pp1718
\end{chunk}
+\index{Monagan, Michael}
+\index{Wittkopf, Allan D.}
+\begin{chunk}{axiom.bib}
+@inproceedings{Mona00,
+ author = "Monagan, Michael and Wittkopf, Allan D.",
+ title = "On the Design and Implementation of Brown's Algorithm over the
+ Integers and Number Fields",
+ booktitle = "ISSAC 2000",
+ pages = "225233",
+ year = "2000",
+ isbn = "1581132182",
+ abstract =
+ "We study the design and implementation of the dense modular GCD
+ algorithm of Brown applied to bivariate polynomial GCDs over the
+ integers and number fields. We present an improved design of Brown's
+ algorithm and compare it asymptotically with Brown's original
+ algorithm, with GCDHEU, the heuristic GCD algorithm, and with the
+ EEZGCD algorithm. We also make an empirical comparison based on Maple
+ implementations of the algorithms. Our findings show that a careful
+ implementation of our improved version of Brown's algorithm is much
+ better than the other algorithms in theory and in practice.",
+ paper = "Mona00.pdf"
+}
+
+\end{chunk}
+
\index{Montes, Antonio}
\begin{chunk}{axiom.bib}
@misc{Mont07,
@@ 35636,6 +35868,47 @@ LCCN QA76.7.S54 v22:7 SIGPLAN Notices, vol 22, no 7 (July 1987)
\end{chunk}
+\index{Wright, Francis J.}
+\begin{chunk}{axiom.bib}
+@misc{Wrig03,
+ author = "Wright, Francis J.",
+ title = "Mathematics and Algorithms for Computer Algebra: Part 1",
+ link = "\url{https://people.eecs.berkeley.edu/~fateman/282/F%20Wright%20notes/week1.pdf}",
+ year = "2003",
+ comment = "full course. week2=Wrig03a, wee3=Wrig03b,...week8=Wrig3g.pdf",
+ abstract =
+ "This course will be mainly mathematics, some computer science
+ and a little computing. Little or no essential use will be made of
+ actual computer languages, although I may occasionally use Pascal, C,
+ Lisp or REDUCE for concrete examples. The aim of the course is to
+ provide an entry into the current research literature, but not to present
+ the most recent research results.
+
+ The first half of the course (taught by me) will deal with basic math
+ ematics and algorithms for computer algebra, primarily at the level of
+ arithmetic and elementary abstract algebra, including an introduction
+ to GCDs and the solution of univariate polynomial equations. This
+ leads into the second half of the course (taught by Dr Jim Skea) on
+ the more advanced problems of polynomial factorization, indefinite in
+ tegration, multivariate polynomial equations, etc.
+
+ The first week provides an introduction to the computing aspects
+ of computer algebra, and contains almost no mathematics. It is in
+ tended to show how the later theory can be implemented for practical
+ computation. The second week provides a rapid but superficial survey
+ of the abstract algebra that is most important for computer algebra.
+ The next five weeks will build on this abstract basis to do some more
+ concrete mathematics in more details, referring back to the basis es
+ tablished in the first two weeks as necessary.
+
+ At the end of each set of notes will be exercises, one (or more) of
+ which will be assessed.",
+ paper = "Wrig03.pdf",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
\begin{chunk}{ignore}
\bibitem[WWW1]{WWW1}.
Software Preservation Group
diff git a/changelog b/changelog
index ca7b069..80065fa 100644
 a/changelog
+++ b/changelog
@@ 1,4 +1,6 @@
20170520 tpd src/axiomwebsite/patches.html 20170521.01.tpd.patch
+20170523 tpd src/axiomwebsite/patches.html 20170523.01.tpd.patch
+20170523 tpd bookvolbib reference to Axiom in publications
+20170521 tpd src/axiomwebsite/patches.html 20170521.01.tpd.patch
20170521 tpd bookvolbib type inferencing papers
20170520 tpd src/axiomwebsite/patches.html 20170520.02.tpd.patch
20170520 tpd bookvolbib type inferencing for Common Lisp
diff git a/patch b/patch
index 77dd5a9..77c0a9c 100644
 a/patch
+++ b/patch
@@ 1,71 +1,267 @@
bookvolbib type inferencing papers
+bookvolbib reference to Axiom in publications
Goal: Proving Axiom Correct
\index{Gentzen, Gerhard}
+\index{Wright, Francis J.}
\begin{chunk}{axiom.bib}
@misc{Gent35,
 author = "Gentzen, Gerhard",
 title = "Investigations into Logical Deduction",
 year = "1935",
 pages = "68131",
 paper = "Gent35.pdf"
+@misc{Wrig03,
+ author = "Wright, Francis J.",
+ title = "Mathematics and Algorithms for Computer Algebra: Part 1",
+ link = "\url{https://people.eecs.berkeley.edu/~fateman/282/F%20Wright%20notes/week1.pdf}",
+ year = "2003",
+ comment = "full course. week2=Wrig03a, wee3=Wrig03b,...week8=Wrig3g.pdf",
+ abstract =
+ "This course will be mainly mathematics, some computer science
+ and a little computing. Little or no essential use will be made of
+ actual computer languages, although I may occasionally use Pascal, C,
+ Lisp or REDUCE for concrete examples. The aim of the course is to
+ provide an entry into the current research literature, but not to present
+ the most recent research results.
+
+ The first half of the course (taught by me) will deal with basic math
+ ematics and algorithms for computer algebra, primarily at the level of
+ arithmetic and elementary abstract algebra, including an introduction
+ to GCDs and the solution of univariate polynomial equations. This
+ leads into the second half of the course (taught by Dr Jim Skea) on
+ the more advanced problems of polynomial factorization, indefinite in
+ tegration, multivariate polynomial equations, etc.
+
+ The first week provides an introduction to the computing aspects
+ of computer algebra, and contains almost no mathematics. It is in
+ tended to show how the later theory can be implemented for practical
+ computation. The second week provides a rapid but superficial survey
+ of the abstract algebra that is most important for computer algebra.
+ The next five weeks will build on this abstract basis to do some more
+ concrete mathematics in more details, referring back to the basis es
+ tablished in the first two weeks as necessary.
+
+ At the end of each set of notes will be exercises, one (or more) of
+ which will be assessed.",
+ paper = "Wrig03.pdf",
+ keywords = "axiomref"
}
\end{chunk}
\index{Gentzen, Gerhard}
+\index{Brown, W. S.}
\begin{chunk}{axiom.bib}
@article{Gent64,
 author = "Gentzen, Gerhard",
 title = "Investigations into Logical Deduction",
 journal = "American Philosophical Quarterly",
 volume = "1",
 number = "4",
 year = "1964",
 pages = "288306",
 paper = "Gent64.pdf"
+@articla{Brow78,
+ author = "Brown, W. S.",
+ title = "The Subresultant PRS Algorithm",
+ journal = "ACM Transactions on Mathematical Software",
+ volume = "4",
+ number = "3",
+ year = "1978",
+ pages = "237249",
+ link =
+ "\url{https://people.eecs.berkeley.edu/~fateman/282/readings/brown.pdf}",
+ abstract =
+ "Two earlier papers described the generalizations of Euclid's
+ algorithm to deal with the problem of computing the greatest common
+ divisor (GCD) or the resultant of a pair of polynomials. A sequal to
+ those two papers is presented here.
+
+ In attempting such a generalization one easily arrives at the concept
+ of a polynomial remainder sequence (PRS) and then quickly discovers
+ the phenomenon of explosive coefficient growth. Fortunately, this
+ explosive growth is not inherent in the problem, but is only an
+ artifact of various naive solutions. If one removes the content (that
+ is, the GCD of the coefficients) from each polynomial in a PRS, the
+ coefficient growth in the resulting primitive PRS is relatively modest.
+ However, the cost of computing the content (by applying Euclid's
+ algorithm in the coefficient domain) may be unacceptably or even
+ prohibitively high, especially if the coefficients are themselves
+ polynomials in one or more addltional variables.
+
+ The key to controlling coefficient growth without the costly
+ computation of GCD's of coefficients is the fundamental theorem of
+ subresuitants, which shows that every polynomial in a PRS is
+ proportional to some subresultant of the first two. By arranging for
+ the constants of proportionahty to be unity, one obtains the
+ subresultant PRS algorithm, in which the coefficient growth is
+ essentially linear. A corollary of the fundamental theorem is given
+ here, which leads to a simple derivation and deeper understanding of
+ the subresultant PRS algorithm and converts a conjecture mentioned in
+ the earlier papers into an elementary remark.
+
+ A possible alternative method of constructing a subresultant PRS is to
+ evaluate all the subresultants directly from Sylvester's determinant
+ via expansion by minors. A complexity analysis is given in conclusion,
+ along lines pioneered by Gentleman and Johnson, showing that the
+ subresultant PRS algorithm is superior to the determinant method
+ whenever the given polynomials are sufficiently large and dense, but
+ is inferior in the sparse extreme.",
+ paper = "Brow78.pdf"
}
\end{chunk}
\index{Gentzen, Gerhard}
+\index{Collins, George E.}
\begin{chunk}{axiom.bib}
@article{Gent65,
 author = "Gentzen, Gerhard",
 title = "Investigations into Logical Deduction: II",
 journal = "American Philosophical Quarterly",
+@article{Coll87,
+ author = "Collins, George E.",
+ title = "Subresultants and Reduced Polynomial Remainder Sequences",
+ journal = "J. ACM",
+ volume = "14",
+ number = "1",
+ year = "1987",
+ pages = "128142",
+ link =
+ "\url{https://people.eecs.berkeley.edu/~fateman/282/readings/collins.pdf}",
+ paper = "Coll87.pdf"
+}
+
+\end{chunk}
+
+\index{Gentleman, W. M.}
+\index{Johnson, S. C.}
+@article{Gent76,
+ author = "Gentleman, W. M. and Johnson, S. C.",
+ title = "Analysis of Algorithms, A Case Study: Determinants of Matrices
+ With Polynomial Entries",
+ journal = "ACM Transactions on Mathematical Software",
volume = "2",
number = "3",
 year = "1965",
 pages = "204218",
 paper = "Gent65.pdf"
+ year = "1976",
+ pages = "232241",
+ link =
+ "\url{https://people.eecs.berkeley.edu/~fateman/282/readings/gentleman.pdf}",
+ abstract =
+ "The problem of computing the deternunant of a matrix of polynomials
+ is considered; two algorithms (expansion by minors and expansion by
+ Gaussian elimination) are compared; and each is examined under two models
+ for polynomial computatmn (dense univariate and totally sparse). The
+ results, while interesting in themselves, also serve to display two
+ points: (1) Asymptotic results are sometimes misleading for noninfinite
+ (e.g. practical) problems. (2) Models of computation are by
+ definition simplifications of reality: algorithmic analysis should be
+ carried out under several distinct computatmnal models and should be
+ supported by empirical data.",
+ paper = "Gent76.pdf"
}
\end{chunk}
\index{Howard, W. A.}
+\index{Fateman, Richard}
\begin{chunk}{axiom.bib}
@misc{Howa80,
 author = "Howard, W. A.",
 title = "The FormulaeasTypes Notion of Construction",
 link = "\url{http://lecomte.al.free.fr/ressources/PARIS8_LSL/Howard80.pdf}",
 year = "1980",
+@misc{Fate00b,
+ author = "Fateman, Richard",
+ title = "The (finite field) Fast Fourier Transform",
+ year = "2000",
+ link =
+ "\url{https://people.eecs.berkeley.edu/~fateman/282/readings/fftnotes.pdf}",
abstract =
 "The following consists of notes which were privately circulated in
 1969. Since they have been referred to a few times in the literature,
 it seems worth while to publish them. They have been rearranged for
 easier reading, and some inessential corrections have been made.

 The ultimate goal was to develop a notion of construction suitable for
 the interpretation of intuitionistic mathematics. The notion of
 construction developed in the notes is certainly too crude for that,
 so the use of the word {\sl construction} is not very appropriate.
 However, the terminology has been kept in order to preserve the
 original title and also to preserve the character of the notes. The
 title has a second defect; namely, the {\sl type} should be regarded
 as a abstract object whereas a {\sl formula} is the name of a type.",
 paper = "Howa80.pdf"
+ "There are numerous directions from which one can approach the subject
+ of the fast Fourier Transform (FFT). It can be explained via numerous
+ connections to convolution, signal processing, and various other
+ properties and applications of the algorithm. We (along with
+ Geddes/Czapor/Labahn) take a rather simple view from the algebraic
+ manipulation standpoint. As will be apparent shortly, we relate the
+ FFT to the evaluation of a polynomial. We also consider it of interest
+ primarily as an algorithm in a discrete (finite) computation structure
+ rather than over the complex numbers.",
+ paper = "Fate00b.pdf"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard}
+\begin{chunk}{axiom.bib}
+@misc{Fate00c,
+ author = "Fateman, Richard",
+ title = "Additional Notes on Polynomial GCDs, Hensel construction",
+ year = "2000",
+ link =
+ "\url{https://people.eecs.berkeley.edu/~fateman/282/readings/hensel.pdf}",
+ paper = "Fate00c.pdf"
+}
+
+\end{chunk}
+
+\index{Liska, Richard}
+\index{Drska, Ladislav}
+\index{Limpouch, Jiri}
+\index{Sinor, Milan}
+\index{Wester, Michael J.}
+\index{Winkler, Franz}
+\begin{chunk}{axiom.bib}
+@book{Lisk99,
+ author = "Liska, Richard and Drska, Ladislav and Limpouch, Jiri and
+ Sinor, Milan adn Wester, Michael and Winkler, Franz",
+ title = "Computer Algebra  Algorithms, Systems and Applications",
+ year = "1999",
+ publisher = "web",
+ link =
+ "\url{https://people.eecs.berkeley.edu/~fateman/282/readings/liska.pdf}",
+ paper = "Lisk99.pdf",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Mishra, Bhubaneswar}
+\index{Yap, Chee}
+\begin{chunk}{axiom.bib}
+@misc{Mish87,
+ author = "Mishra, Bhubaneswar and Yap, Chee",
+ title = "Notes on Groebner Basis",
+ year = "1987",
+ link = "\url{https://people.eecs.berkeley.edu/~fateman/282/readings/mishra87note.pdf}",
+ abstract =
+ "We present a selfcontained exposition of the theory of Groebner
+ basis and its applications",
+ paper = "Mish87.pdf"
+}
+
+\end{chunk}
+
+\index{Monagan, Michael}
+\index{Wittkopf, Allan D.}
+@inproceedings{Mona00,
+ author = "Monagan, Michael and Wittkopf, Allan D.",
+ title = "On the Design and Implementation of Brown's Algorithm over the
+ Integers and Number Fields",
+ booktitle = "ISSAC 2000",
+ pages = "225233",
+ year = "2000",
+ isbn = "1581132182",
+ abstract =
+ "We study the design and implementation of the dense modular GCD
+ algorithm of Brown applied to bivariate polynomial GCDs over the
+ integers and number fields. We present an improved design of Brown's
+ algorithm and compare it asymptotically with Brown's original
+ algorithm, with GCDHEU, the heuristic GCD algorithm, and with the
+ EEZGCD algorithm. We also make an empirical comparison based on Maple
+ implementations of the algorithms. Our findings show that a careful
+ implementation of our improved version of Brown's algorithm is much
+ better than the other algorithms in theory and in practice.",
+ paper = "Mona00.pdf"
+}
+
+\end{chunk}
+
+\index{Yap, CheeKeng}
+\begin{chunk}{axiom.bib}
+@misc{Yap02a,
+ author = "Yap, CheeKeng",
+ title = "Lecture 0: Introduction",
+ year = "2002",
+ link =
+ "\url{https://people.eecs.berkeley.edu/~fateman/282/readings/yap0.pdf}",
+ paper = "Yap02a.pdf"
+}
+
+\end{chunk}
+
+\index{Yap, CheeKeng}
+\begin{chunk}{axiom.bib}
+@misc{Yap02b,
+ author = "Yap, CheeKeng",
+ title = "Lecture II: The GCD",
+ year = "2002",
+ link =
+ "\url{https://people.eecs.berkeley.edu/~fateman/282/readings/yap2.pdf}",
+ paper = "Yap02b.pdf"
}
\end{chunk}
diff git a/src/axiomwebsite/patches.html b/src/axiomwebsite/patches.html
index 97915aa..a6030f7 100644
 a/src/axiomwebsite/patches.html
+++ b/src/axiomwebsite/patches.html
@@ 5738,6 +5738,8 @@ bookvolbib cylindrical algorithmic decomposition references
bookvolbib type inferencing for Common Lisp
20170521.01.tpd.patch
bookvolbib type inferencing papers
+20170523.01.tpd.patch
+bookvolbib reference to Axiom in publications

1.7.5.4