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From: Tim Daly
Date: Fri, 5 Aug 2016 14:52:31 -0400
Subject: [PATCH] books/bookvolbib Axiom Citations in the Literature
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Goal: Axiom Literate Programming
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@misc{Fate13a,
author = "Fateman, Richard J.",
title = "Rational Function Computing with Poles and Residues",
url = "http://www.cs.berkeley.edu/~/fateman/papers/openmathcrit.pdf",
year = "2013",
abstract =
"Computer algebra systems (CAS) usually support computation with exact
or approximate rational functions as ratios of polynomials in
``expanded form'' with explicit coefficients. We examine the
consequences of introducing a partial-fraction type of form in which
some of the usual rational operations can be implemented in
substantially faster times. In this form an expression in one
variable, say $x$, is expressed as a polynomial in $x$ plus a sum of
terms each of which has a denominator $x-c$ perhaps to an integer
power, where $c$ is in general a complex constant. We show that some
common operations including rational function addition,
multiplication, and matrix determinant calculation can be performed
many times faster than in the conventional representation. Polynomial
GCD operations, the costliest part of rational additions, are entirely
eliminated. Applicaiton of Cauchy's integral theorem allow for trivial
integration of an expression around a closed contour. In some cases
the approximate evaluation of transcendental functions can be
accelerated, especially in parallel, by evaluation of a formula in
pole+residue form.",
paper = "Fate13a.pdf"
}
\end{chunk}
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@inproceedings{Fate03a,
author = "Fateman, Richard J.",
title = "High-level proofs of mathematical programs using automatic
differentiation, simplification, and some common sense",
booktitle = "Proc. ISSAC 2003",
pages = "88-94",
year = "2003",
isbn = "1-58113-641-2",
abstract =
"One problem in applying elementary methods to prove correctness of
interesting scientific programs is the large discrepancy in level of
discourse between low-level proof methods and the logic of scientific
calculation, especially that used in a complex numerical program. The
justification of an algorithm typically relies on algebra or analysis,
but the correctness of the program requires that the arithmetic
expressions are written correctly and that iterations converge to
correct values in spite of truncation of infinite processes or series
and the commission of numerical roundoff errors. We hope to help
bridge this gap by showing how we can, in some cases, state a
high-level requirement and by using a computer algebra system (CAS)
demonstrate that a program satisfies that requirement. A CAS can
contribute program manipulation, partial evaluation, simplification or
other algorithmic methods. A novelty here is that we add to the usual
list of techniques automatic differentiation, a method already widely
used in optimization contexts where algorithms are differentiated. We
sketch a proof of a numerical program to compute sine, and display a
related approach to a version of a Bessel function algorithm for J0(x)
based on a recurrence.",
paper = "Fate03a.pdf"
}
\end{chunk}
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@misc{Fate07,
author = "Fateman, Richard J.",
title = "Rational Function Computing with Poles and Residues",
url = "http://www.cs.berkeley.edu/~/fateman/papers/qd.pdf",
year = "2007",
abstract =
"In a numerical calculation sometimes we need higher-than
double-precision floating-point arithmetic to allow us to be confident
of a result. One alternative is to rewrite the program to use a
software package implementing arbitrary-precision extended
floating-point arithmetic such as ARPREC or MPFR, and try to choose a
suitable precision.
Such an arithmetic scheme, in spite of helpful tools, may be
inconvenient to write. There are also facilities in computer algebra
systems (CAS) for such software-implemented ``bigfloats.'' These
facilities are convenient if one is already using the CAS. In any of
these situations the bigfloats may be rather slow, a cost of its
generality.
There are possibilities intermediate between the largest hardware
floating-point format and the general arbitrary-precision software
which combine a considerable (but not arbitrary) amount of extra
precision with a (relatively speaking) modest factor loss in
speed. Sometimes merely doubling the number of bits in a
double-floating-point fraction is enough, in which case arithmetic on
double-double (DD) operands would suffice. Another possibility is to
go for yet another doubling to quad-double (QD) arithmetic: instead of
using the machine double-floats to give about 16 decimal digits of
precision, QD supplies about 64 digits. DD and QD as used here provide
the same exponent range as ordinary double.
Here we describe how we incorporated QD arithmetic implemented in a
library into a Common Lisp system, providing a smooth interface while
adding only modest overhead to the run-time costs (compared to
accessing the library from C or C++). One advantage is that we keep
the program text almost untouched while switching from double to
quad-double. Another is that the programs can be written, debugged,
and run in an interactive environment. Most of the lessons from QD can
be used for other versions of arithmetic which can be embedded in
Lisp, including MPFR, for indefinite (arbitrary) precision, should QD
provide inadequate precision or range.",
paper = "Fate07.pdf,
keywords = "axiomref"
}
\end{chunk}
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@misc{Fate99b,
author = "Fateman, Richard J.",
title = "Generation and Optimization of Numerical Programs by
Symbolic Mathematical Methods",
url = "http://www.cs.berkeley.edu/~/fateman/papers/RIMS.pdf",
year = "1999",
abstract =
"Symbolic mathematical methods and systems
\begin{itemize}
\item support scientific and engineering ``problem solving environments''
(PSEs),
\item The specific manipulation of mathematical models as a precursor
to the coding of algorithms
\item Expert system selection of modules from numerical libraries and
other facilities
\item The production of custom numerical software such as derivatives
or non-standard arithmetic code-generation packages,
\item The complete solution of certain classes of mathematical problems
that simply cannot be handled solely by conventional floating-point
computation.
\end{itemize}
Viewing computational objects and algorithms from a symbolic
perspective and then specializing them to numerical or graphical views
provides substantial additional flexibility over a more conventional view.
We also consider interactive symbolic computing as a tool to provide
an organizing principle or glue among otherwise dissimilar components.",
paper = "Fate99b.pdf",
keywords = "axiomref"
}
\end{chunk}
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@misc{Fate09,
author = "Fateman, Richard J.",
title = "Rational Integration, Simplified",
url = "http://www.cs.berkeley.edu/~/fateman/papers/root-integ.pdf",
year = "2009",
abstract =
"After all this computer algebra stuff, and several PhD theses in
the last few decades, what more could we say about symbolic
rational function integration?
How about a closed formula for the result, subject to a few algebraic
side-conditions, which works even with parameters in the denominator?",
paper = "Fate09.pdf"
}
\end{chunk}
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@misc{Fate09a,
author = "Fateman, Richard J.",
title = "Simplifying RootSum Expressions",
url = "http://www.cs.berkeley.edu/~/fateman/papers/rootsum.pdf",
year = "2009",
abstract =
"It's useful to sum an expression with a parameter varying over all
the roots of a given polynomial. Here's a defense of that statement
and a method to do the task.",
paper = "Fate09a.pdf"
}
\end{chunk}
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@misc{Fate02a,
author = "Fateman, Richard J.",
title = "Symbolic Execution Merges Construction, Debugging and Proving",
url = "http://www.cs.berkeley.edu/~/fateman/papers/symex.pdf",
year = "2002",
abstract =
"There is naturally an interest in any technology which promises to
assist us in producing correct programs. Some efforts attempt to
insure correct programs by making their construction simpler. Some
efforts are oriented toward increasing the effectiveness of testing to
make the programs appear to perform as required. Other efforts are
directed to prove the correctness of the resulting program. Symbolic
execution, in which symbols instead of numbers are used in what
appears to be a numerical program, is an old but to-date still not
widely-used technique. It has been available in various forms for
decades from the computer algebra community. Symbolic execution has
the potential to assist in all these phases: construction, debugging,
and proof. We describe how this might work specifically with regard to
our own recent experience in the construction of correct linear
algebra programs for structured matrices and LU factorization. We show
how developing these programs with a computer algebra system, and then
converting incrementally to use more efficient forms. Frequent symbolic
execution of the algorithms, equivalent to testing over infinite test
sets, aids in debugging, while strengthening beliefs that the correctness
of results is an algebraic truth rather than an accident.",
paper = "Fate02a.pdf"
}
\end{chunk}
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@misc{Fate03b,
author = "Fateman, Richard J.",
title = "Manipulation of Matrices Symbolically",
url = "http://www.cs.berkeley.edu/~/fateman/papers/symmat2.pdf",
year = "2003",
abstract =
"Traditionally, matrix algebra in computer algebra systems is
``implemented'' in three ways:
\begin{itemize}
\item numeric explicit computation in a special arithmetic domain:
exact rational or integer, high-precision software floating-point,
interval, or conventional hardware floating-point.
\item ‘symbolic’ explicit computation with polynomial or other
expression entries,
\item (implicit) matrix computation with symbols defined over a
(non-commuting) ring.
\end{itemize}
Manipulations which involve matrices of indefinite size (n × m) or
perhaps have components which are block submatrices of indefinite size
have little or no support in general-purpose computer algebra systems,
in spite of their importance in theorems, proofs, and generation of
programs. We describe some efforts to design and implement tools for
this mode of thinking about matrices in computer systems.",
paper = "Fate03b.pdf"
}
\end{chunk}
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@misc{Fate08b,
author = "Fateman, Richard J.",
title = "Applications and Methods for Recognition of (Anti)-Symmetric
Functions",
url = "http://www.cs.berkeley.edu/~/fateman/papers/symmetry.pdf",
year = "2008",
abstract =
"One of the important advantages held by computer algebra systems (CAS)
over purely-numerical computational frameworks is that the CAS can
provide a higher-level ``symbolic'' viewpoint for problem
solving. Sometimes this can convert apparently impossible problems to
trivial ones. Sometimes the symbolic perspective can provide
information about questions which cannot be directly answered, or
questions which might be hard to pose. For example, we might be able
to analyze the asymptotic behavior of a solution to a differential
equation even though we cannot solve the equation. One route to
implicitly solving problems is the use of symmetry arguments. In this
paper we suggest how, through symmetry, one can solve a large class of
definite integration problems, including some that we found could not
be solved by computer algebra systems. One case of symmetry provides
for recognition of periodicity, and this solves additional problems,
since removal of periodic components can be important in integration
and in asymptotic expansions.",
paper = "Fate08b.pdf"
}
\end{chunk}
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@phdthesis{Fate72,
author = "Fateman, Richard J.",
title = "Essays in Algebraic Simplification",
url = "http://www.cs.berkeley.edu/~/fateman/papers/tr-95.pdf",
institution = "MIT",
comment = "MAC TR-95 technical report",
year = "1972",
abstract =
"This thesis consists of essays on several aspects of the problem
of algebraic simplification by computer. We first discuss a pattern
matching system intended to recognize non-obvious occurrences of
patterns within Algebraic expression. A user of such a system can
``teach'' the computer new simplification rules. Then we report on
new applications of canonical simplification of rational functions.
These applications include techniques for picking out coefficients,
and for substituting for summs, products, quotients, etc. Our final
essay is on a new, practical, canonical simplification algorithms
for radical expressions (i.g. algebraic expressions including roots
of polynomials). The effectiveness of the procedure is assured
through proofs of appropriate properties of the simplified forms.
Two appendices describe MACSYM, a computer system for algebraic
manipulations, which served as the basis for this work.",
paper = "Fate72.pdf"
}
\end{chunk}
\index{Redfield, J.Howard}
\begin{chunk}{axiom.bib}
@article{Redf27,
author = "Redfield, J.Howard",
title = "The Theory of Group-Reduced Distributions",
journal = "American J. Math.",
volume = "49",
number = "3",
year = "1927",
pages = "433-455"
}
\end{chunk}
\index{Judson, Tom}
@book{Juds15,
author = "Judson, Tom",
title = "Abstract Algebra: Theory and Applications",
year = "2015",
publisher = "Tom Judson",
url = "http://abstract.ups.edu/download/aata-20150812.pdf",
paper = "Juds15.pdf"
}
\index{Judson, Tom}
\index{Beezer, Rob}
@book{Beez15,
author = "Judson, Tom and Beezer, Rob",
title = "Abstract Algebra: Theory and Applications",
year = "2015",
publisher = "Tom Judson",
url = "http://abstract.ups.edu/download/aata-20150812-sage-6.8.pdf",
paper = "Beez15.pdf"
}
\index{Axiom Authors}
\begin{chunk}{axiom.bib}
@book{Bookbug,
author = "Axiom Authors",
title = "Volume BugList: Axiom Bugs",
url = "http://axiom-developer.org/axiom-website/bookvolbug.pdf",
publisher = "Axiom Project",
year = "2016"
}
\end{chunk}
---
books/bookvolbib.pamphlet | 464 +++++++++++++++++++++++++++++++++++++++-
changelog | 2 +
patch | 357 ++++++++++++++++++++++++++++++-
src/axiom-website/patches.html | 2 +
4 files changed, 817 insertions(+), 8 deletions(-)
diff --git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index 4ceeadb..ba01518 100644
--- a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ -32,6 +32,7 @@ paragraph for those unfamiliar with the terms.
author = "Axiom Authors",
title = "Volume 0: Axiom Jenks and Sutor",
url = "http://axiom-developer.org/axiom-website/bookvol0.pdf",
+ publisher = "Axiom Project",
year = "2016",
keywords = "axiomref",
beebe = "Jenks:2003:AVS"
@@ -59,6 +60,7 @@ paragraph for those unfamiliar with the terms.
author = "Axiom Authors",
title = "Volume 1: Axiom Tutorial",
url = "http://axiom-developer.org/axiom-website/bookvol1.pdf",
+ publisher = "Axiom Project",
year = "2016"
}
@@ -70,6 +72,7 @@ paragraph for those unfamiliar with the terms.
author = "Axiom Authors",
title = "Volume 2: Axiom Users Guide",
url = "http://axiom-developer.org/axiom-website/bookvol2.pdf",
+ publisher = "Axiom Project",
year = "2016",
keywords = "axiomref",
beebe = "Daly:2005:AVAb"
@@ -97,6 +100,7 @@ paragraph for those unfamiliar with the terms.
author = "Axiom Authors",
title = "Volume 3: Axiom Programmers Guide",
url = "http://axiom-developer.org/axiom-website/bookvol3.pdf",
+ publisher = "Axiom Project",
year = "2016",
keywords = "axiomref",
beebe = "Daly:2005:AVAc"
@@ -124,6 +128,7 @@ paragraph for those unfamiliar with the terms.
author = "Axiom Authors",
title = "Volume 4: Axiom Developers Guide",
url = "http://axiom-developer.org/axiom-website/bookvol4.pdf",
+ publisher = "Axiom Project",
year = "2016",
keywords = "axiomref",
beebe = "Daly:2005:AVAd"
@@ -151,6 +156,7 @@ paragraph for those unfamiliar with the terms.
author = "Axiom Authors",
title = "Volume 5: Axiom Interpreter",
url = "http://axiom-developer.org/axiom-website/bookvol5.pdf",
+ publisher = "Axiom Project",
year = "2016",
keywords = "axiomref",
beebe = "Daly:2003:AVA",
@@ -178,6 +184,7 @@ paragraph for those unfamiliar with the terms.
author = "Axiom Authors",
title = "Volume 6: Axiom Command",
url = "http://axiom-developer.org/axiom-website/bookvol6.pdf",
+ publisher = "Axiom Project",
year = "2016",
keywords = "axiomref",
beebe = "Daly:2005:AVAe"
@@ -205,6 +212,7 @@ paragraph for those unfamiliar with the terms.
author = "Axiom Authors",
title = "Volume 7: Axiom Hyperdoc",
url = "http://axiom-developer.org/axiom-website/bookvol7.pdf",
+ publisher = "Axiom Project",
year = "2016",
keywords = "axiomref",
beebe = "Daly:2005:AVAj"
@@ -243,6 +251,7 @@ paragraph for those unfamiliar with the terms.
author = "Axiom Authors",
title = "Volume 8: Axiom Graphics",
url = "http://axiom-developer.org/axiom-website/bookvol8.pdf",
+ publisher = "Axiom Project",
year = "2016",
keywords = "axiomref",
beebe = "Daly:2005:AVAf"
@@ -281,6 +290,7 @@ paragraph for those unfamiliar with the terms.
author = "Axiom Authors",
title = "Volume 9: Axiom Compiler",
url = "http://axiom-developer.org/axiom-website/bookvol9.pdf",
+ publisher = "Axiom Project",
year = "2016",
keywords = "axiomref",
beebe = "Daly:2005:AVAg"
@@ -308,6 +318,7 @@ paragraph for those unfamiliar with the terms.
author = "Axiom Authors",
title = "Volume 9.1: Axiom Compiler Details",
url = "http://axiom-developer.org/axiom-website/bookvol9.1.pdf",
+ publisher = "Axiom Project",
year = "2016"
}
@@ -319,6 +330,7 @@ paragraph for those unfamiliar with the terms.
author = "Axiom Authors",
title = "Volume 10: Axiom Algebra: Implementation",
url = "http://axiom-developer.org/axiom-website/bookvol10.pdf",
+ publisher = "Axiom Project",
year = "2016",
keywords = "axiomref",
beebe = "Daly:2005:AVAh"
@@ -346,6 +358,7 @@ paragraph for those unfamiliar with the terms.
author = "Axiom Authors",
title = "Volume 10.1: Axiom Algebra: Theory",
url = "http://axiom-developer.org/axiom-website/bookvol10.1.pdf",
+ publisher = "Axiom Project",
year = "2016"
}
@@ -357,6 +370,7 @@ paragraph for those unfamiliar with the terms.
author = "Axiom Authors",
title = "Volume 10.2: Axiom Algebra: Categories",
url = "http://axiom-developer.org/axiom-website/bookvol10.2.pdf",
+ publisher = "Axiom Project",
year = "2016"
}
@@ -368,6 +382,7 @@ paragraph for those unfamiliar with the terms.
author = "Axiom Authors",
title = "Volume 10.3: Axiom Algebra: Domains",
url = "http://axiom-developer.org/axiom-website/bookvol10.3.pdf",
+ publisher = "Axiom Project",
year = "2016"
}
@@ -379,6 +394,7 @@ paragraph for those unfamiliar with the terms.
author = "Axiom Authors",
title = "Volume 10.4: Axiom Algebra: Packages",
url = "http://axiom-developer.org/axiom-website/bookvol10.4.pdf",
+ publisher = "Axiom Project",
year = "2016"
}
@@ -390,6 +406,7 @@ paragraph for those unfamiliar with the terms.
author = "Axiom Authors",
title = "Volume 10.5: Axiom Algebra: Numerics",
url = "http://axiom-developer.org/axiom-website/bookvol10.5.pdf",
+ publisher = "Axiom Project",
year = "2016"
}
@@ -401,6 +418,7 @@ paragraph for those unfamiliar with the terms.
author = "Axiom Authors",
title = "Volume 11: Axiom Browser",
url = "http://axiom-developer.org/axiom-website/bookvol11.pdf",
+ publisher = "Axiom Project",
year = "2016",
keywords = "axiomref",
beebe = "Portes:2007:AVA"
@@ -429,6 +447,7 @@ paragraph for those unfamiliar with the terms.
author = "Axiom Authors",
title = "Volume 12: Axiom Crystal",
url = "http://axiom-developer.org/axiom-website/bookvol12.pdf",
+ publisher = "Axiom Project",
year = "2016",
keywords = "axiomref",
beebe = "Daly:2005:AVAi"
@@ -456,6 +475,7 @@ paragraph for those unfamiliar with the terms.
author = "Axiom Authors",
title = "Volume 13: Proving Axiom Correct",
url = "http://axiom-developer.org/axiom-website/bookvol13.pdf",
+ publisher = "Axiom Project",
year = "2016"
}
@@ -467,6 +487,7 @@ paragraph for those unfamiliar with the terms.
author = "Axiom Authors",
title = "Volume 14: Algorithms",
url = "http://axiom-developer.org/axiom-website/bookvol14.pdf",
+ publisher = "Axiom Project",
year = "2016"
}
@@ -478,6 +499,19 @@ paragraph for those unfamiliar with the terms.
author = "Axiom Authors",
title = "Volume Bibliography: Axiom Literature Citations",
url = "http://axiom-developer.org/axiom-website/bookvolbib.pdf",
+ publisher = "Axiom Project",
+ year = "2016"
+}
+
+\end{chunk}
+
+\index{Axiom Authors}
+\begin{chunk}{axiom.bib}
+@book{Bookbug,
+ author = "Axiom Authors",
+ title = "Volume BugList: Axiom Bugs",
+ url = "http://axiom-developer.org/axiom-website/bookvolbug.pdf",
+ publisher = "Axiom Project",
year = "2016"
}
@@ -3866,6 +3900,9 @@ when shown in factored form.
@article{Sutt13,
author = "Sutton, Brian D.",
title = "Computing the Complete CS Decomposition",
+ journal = "Numerical Algorithms",
+ volume = "50",
+ pages = "33-65",
year = "2013",
month = "February",
url = "http://arxiv.org/pdf/0707.1838v3.pdf",
@@ -4516,6 +4553,73 @@ Martin, U.
\end{chunk}
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate02a,
+ author = "Fateman, Richard J.",
+ title = "Symbolic Execution Merges Construction, Debugging and Proving",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/symex.pdf",
+ year = "2002",
+ abstract =
+ "There is naturally an interest in any technology which promises to
+ assist us in producing correct programs. Some efforts attempt to
+ insure correct programs by making their construction simpler. Some
+ efforts are oriented toward increasing the effectiveness of testing to
+ make the programs appear to perform as required. Other efforts are
+ directed to prove the correctness of the resulting program. Symbolic
+ execution, in which symbols instead of numbers are used in what
+ appears to be a numerical program, is an old but to-date still not
+ widely-used technique. It has been available in various forms for
+ decades from the computer algebra community. Symbolic execution has
+ the potential to assist in all these phases: construction, debugging,
+ and proof. We describe how this might work specifically with regard to
+ our own recent experience in the construction of correct linear
+ algebra programs for structured matrices and LU factorization. We show
+ how developing these programs with a computer algebra system, and then
+ converting incrementally to use more efficient forms. Frequent symbolic
+ execution of the algorithms, equivalent to testing over infinite test
+ sets, aids in debugging, while strengthening beliefs that the correctness
+ of results is an algebraic truth rather than an accident.",
+ paper = "Fate02a.pdf"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@inproceedings{Fate03a,
+ author = "Fateman, Richard J.",
+ title = "High-level proofs of mathematical programs using automatic
+ differentiation, simplification, and some common sense",
+ booktitle = "Proc. ISSAC 2003",
+ pages = "88-94",
+ year = "2003",
+ isbn = "1-58113-641-2",
+ abstract =
+ "One problem in applying elementary methods to prove correctness of
+ interesting scientific programs is the large discrepancy in level of
+ discourse between low-level proof methods and the logic of scientific
+ calculation, especially that used in a complex numerical program. The
+ justification of an algorithm typically relies on algebra or analysis,
+ but the correctness of the program requires that the arithmetic
+ expressions are written correctly and that iterations converge to
+ correct values in spite of truncation of infinite processes or series
+ and the commission of numerical roundoff errors. We hope to help
+ bridge this gap by showing how we can, in some cases, state a
+ high-level requirement and by using a computer algebra system (CAS)
+ demonstrate that a program satisfies that requirement. A CAS can
+ contribute program manipulation, partial evaluation, simplification or
+ other algorithmic methods. A novelty here is that we add to the usual
+ list of techniques automatic differentiation, a method already widely
+ used in optimization contexts where algorithms are differentiated. We
+ sketch a proof of a numerical program to compute sine, and display a
+ related approach to a version of a Bessel function algorithm for J0(x)
+ based on a recurrence.",
+ paper = "Fate03a.pdf"
+}
+
+\end{chunk}
+
\index{Geuvers, Herman}
\index{Pollack, Randy}
\index{Wiedijk, Freek}
@@ -6542,6 +6646,28 @@ J. Symbolic COmputations 36 pp 855-889
\end{chunk}
+\index{Caviness, Bob F.}
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@inproceedings{Cavi76,
+ author = "Caviness, Bob F. and Fateman, Richard J.",
+ title = "Simplification of Radical Expressions",
+ booktitle = "Proc. 1976 SYMSAC",
+ pages = "329-338",
+ year = "1976",
+ abstract =
+ "In this paper we discuss the problem of simplifying unnested radical
+ expressions. We describe an algorithm implemented in MACSYMA that
+ simplifies radical expressions and then follow this description with
+ a formal treatment of the problem. Theoretical computing times for some
+ of the algorithms are briefly discussed as is related work of other
+ authors",
+ paper = "Cavi76.pdf",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
\index{Landau, Susan}
\begin{chunk}{axiom.bib}
@article{Land93,
@@ -11294,6 +11420,247 @@ J. Symbolic Computation 5, 237-259 (1988)
\section{To Be Classified} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@phdthesis{Fate72,
+ author = "Fateman, Richard J.",
+ title = "Essays in Algebraic Simplification",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/tr-95.pdf",
+ institution = "MIT",
+ comment = "MAC TR-95 technical report",
+ year = "1972",
+ abstract =
+ "This thesis consists of essays on several aspects of the problem
+ of algebraic simplification by computer. We first discuss a pattern
+ matching system intended to recognize non-obvious occurrences of
+ patterns within Algebraic expression. A user of such a system can
+ ``teach'' the computer new simplification rules. Then we report on
+ new applications of canonical simplification of rational functions.
+ These applications include techniques for picking out coefficients,
+ and for substituting for summs, products, quotients, etc. Our final
+ essay is on a new, practical, canonical simplification algorithms
+ for radical expressions (i.g. algebraic expressions including roots
+ of polynomials). The effectiveness of the procedure is assured
+ through proofs of appropriate properties of the simplified forms.
+ Two appendices describe MACSYM, a computer system for algebraic
+ manipulations, which served as the basis for this work.",
+ paper = "Fate72.pdf"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate08b,
+ author = "Fateman, Richard J.",
+ title = "Applications and Methods for Recognition of (Anti)-Symmetric
+ Functions",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/symmetry.pdf",
+ year = "2008",
+ abstract =
+ "One of the important advantages held by computer algebra systems (CAS)
+ over purely-numerical computational frameworks is that the CAS can
+ provide a higher-level ``symbolic'' viewpoint for problem
+ solving. Sometimes this can convert apparently impossible problems to
+ trivial ones. Sometimes the symbolic perspective can provide
+ information about questions which cannot be directly answered, or
+ questions which might be hard to pose. For example, we might be able
+ to analyze the asymptotic behavior of a solution to a differential
+ equation even though we cannot solve the equation. One route to
+ implicitly solving problems is the use of symmetry arguments. In this
+ paper we suggest how, through symmetry, one can solve a large class of
+ definite integration problems, including some that we found could not
+ be solved by computer algebra systems. One case of symmetry provides
+ for recognition of periodicity, and this solves additional problems,
+ since removal of periodic components can be important in integration
+ and in asymptotic expansions.",
+ paper = "Fate08b.pdf"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate03b,
+ author = "Fateman, Richard J.",
+ title = "Manipulation of Matrices Symbolically",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/symmat2.pdf",
+ year = "2003",
+ abstract =
+ "Traditionally, matrix algebra in computer algebra systems is
+ ``implemented'' in three ways:
+ \begin{itemize}
+ \item numeric explicit computation in a special arithmetic domain:
+ exact rational or integer, high-precision software floating-point,
+ interval, or conventional hardware floating-point.
+ \item ‘symbolic’ explicit computation with polynomial or other
+ expression entries,
+ \item (implicit) matrix computation with symbols defined over a
+ (non-commuting) ring.
+ \end{itemize}
+ Manipulations which involve matrices of indefinite size (n × m) or
+ perhaps have components which are block submatrices of indefinite size
+ have little or no support in general-purpose computer algebra systems,
+ in spite of their importance in theorems, proofs, and generation of
+ programs. We describe some efforts to design and implement tools for
+ this mode of thinking about matrices in computer systems.",
+ paper = "Fate03b.pdf"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate09a,
+ author = "Fateman, Richard J.",
+ title = "Simplifying RootSum Expressions",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/rootsum.pdf",
+ year = "2009",
+ abstract =
+ "It's useful to sum an expression with a parameter varying over all
+ the roots of a given polynomial. Here's a defense of that statement
+ and a method to do the task.",
+ paper = "Fate09a.pdf"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate09,
+ author = "Fateman, Richard J.",
+ title = "Rational Integration, Simplified",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/root-integ.pdf",
+ year = "2009",
+ abstract =
+ "After all this computer algebra stuff, and several PhD theses in
+ the last few decades, what more could we say about symbolic
+ rational function integration?
+
+ How about a closed formula for the result, subject to a few algebraic
+ side-conditions, which works even with parameters in the denominator?",
+ paper = "Fate09.pdf"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate99b,
+ author = "Fateman, Richard J.",
+ title = "Generation and Optimization of Numerical Programs by
+ Symbolic Mathematical Methods",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/RIMS.pdf",
+ year = "1999",
+ abstract =
+ "Symbolic mathematical methods and systems
+ \begin{itemize}
+ \item support scientific and engineering ``problem solving environments''
+ (PSEs),
+ \item The specific manipulation of mathematical models as a precursor
+ to the coding of algorithms
+ \item Expert system selection of modules from numerical libraries and
+ other facilities
+ \item The production of custom numerical software such as derivatives
+ or non-standard arithmetic code-generation packages,
+ \item The complete solution of certain classes of mathematical problems
+ that simply cannot be handled solely by conventional floating-point
+ computation.
+ \end{itemize}
+
+ Viewing computational objects and algorithms from a symbolic
+ perspective and then specializing them to numerical or graphical views
+ provides substantial additional flexibility over a more conventional view.
+
+ We also consider interactive symbolic computing as a tool to provide
+ an organizing principle or glue among otherwise dissimilar components.",
+ paper = "Fate99b.pdf",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate07,
+ author = "Fateman, Richard J.",
+ title = "Rational Function Computing with Poles and Residues",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/qd.pdf",
+ year = "2007",
+ abstract =
+ "In a numerical calculation sometimes we need higher-than
+ double-precision floating-point arithmetic to allow us to be confident
+ of a result. One alternative is to rewrite the program to use a
+ software package implementing arbitrary-precision extended
+ floating-point arithmetic such as ARPREC or MPFR, and try to choose a
+ suitable precision.
+
+ Such an arithmetic scheme, in spite of helpful tools, may be
+ inconvenient to write. There are also facilities in computer algebra
+ systems (CAS) for such software-implemented ``bigfloats.'' These
+ facilities are convenient if one is already using the CAS. In any of
+ these situations the bigfloats may be rather slow, a cost of its
+ generality.
+
+ There are possibilities intermediate between the largest hardware
+ floating-point format and the general arbitrary-precision software
+ which combine a considerable (but not arbitrary) amount of extra
+ precision with a (relatively speaking) modest factor loss in
+ speed. Sometimes merely doubling the number of bits in a
+ double-floating-point fraction is enough, in which case arithmetic on
+ double-double (DD) operands would suffice. Another possibility is to
+ go for yet another doubling to quad-double (QD) arithmetic: instead of
+ using the machine double-floats to give about 16 decimal digits of
+ precision, QD supplies about 64 digits. DD and QD as used here provide
+ the same exponent range as ordinary double.
+
+ Here we describe how we incorporated QD arithmetic implemented in a
+ library into a Common Lisp system, providing a smooth interface while
+ adding only modest overhead to the run-time costs (compared to
+ accessing the library from C or C++). One advantage is that we keep
+ the program text almost untouched while switching from double to
+ quad-double. Another is that the programs can be written, debugged,
+ and run in an interactive environment. Most of the lessons from QD can
+ be used for other versions of arithmetic which can be embedded in
+ Lisp, including MPFR, for indefinite (arbitrary) precision, should QD
+ provide inadequate precision or range.",
+ paper = "Fate07.pdf",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate13a,
+ author = "Fateman, Richard J.",
+ title = "Rational Function Computing with Poles and Residues",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/openmathcrit.pdf",
+ year = "2013",
+ abstract =
+ "Computer algebra systems (CAS) usually support computation with exact
+ or approximate rational functions as ratios of polynomials in
+ ``expanded form'' with explicit coefficients. We examine the
+ consequences of introducing a partial-fraction type of form in which
+ some of the usual rational operations can be implemented in
+ substantially faster times. In this form an expression in one
+ variable, say $x$, is expressed as a polynomial in $x$ plus a sum of
+ terms each of which has a denominator $x-c$ perhaps to an integer
+ power, where $c$ is in general a complex constant. We show that some
+ common operations including rational function addition,
+ multiplication, and matrix determinant calculation can be performed
+ many times faster than in the conventional representation. Polynomial
+ GCD operations, the costliest part of rational additions, are entirely
+ eliminated. Applicaiton of Cauchy's integral theorem allow for trivial
+ integration of an expression around a closed contour. In some cases
+ the approximate evaluation of transcendental functions can be
+ accelerated, especially in parallel, by evaluation of a formula in
+ pole+residue form.",
+ paper = "Fate13a.pdf"
+}
+
+\end{chunk}
+
\index{OpenMath}
\index{Complex}
\index{DoubleFloat}
@@ -17525,7 +17892,7 @@ December 1992.
\index{IntegerPrimesPackage}
\index{Davenport, James H.}
\begin{chunk}{axiom.bib}
-@article{Dave92,
+@inproceedings{Dave92,
author = "Davenport, James H.",
title = "Primality Testing Revisited",
url = "http://staff.bath.ac.uk/masjhd/ISSACs/ISSAC1992.pdf",
@@ -18966,6 +19333,64 @@ TPHOLS 2001, Edinburgh
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
+@inproceedings{Fate79,
+ author = "Fateman, Richard J.",
+ title = "MACSYMA's General Simplifier: Philosophy and Operation",
+ booktitle = "Proc. Macsyma Users' Conference 1979",
+ year = "1979",
+ url = "http://people.eecs.berkeley.edu/~fateman/papers/simplifier.txt",
+ abstract =
+ "Ideally the transformations performed by MACSYMA's simplification
+ program on algebraic expressions correspond to those simplifications
+ desired by each user and each program. Since it is impossible for a
+ program to intuit all users' requirements simultaneously, explicit
+ control of the simplifier is necessary to override default
+ transformations. A model of the simplification process is helpful in
+ controlling this large and complex program.
+
+ Having examined several algebraic simplification programs, it appears
+ that to date no program has been written which combines a conceptually
+ simple and useful view of simplification with a program nearly as
+ powerful as MACSYMA's. {note, 1979. not clear this would be different
+ in 2001. RJF} Rule-directed transformation schemes struggle to
+ approach the power of the varied control structures in more usual
+ program schemes [Fenichel, 68]. {note, Mathematica pushes rules
+ further. RJF}
+
+ It is our belief that a thorough grasp of the decision and data
+ structures of the MACSYMA simplifier program itself is the most direct
+ way of understanding its potential for algebraic expression
+ transformation. This is an unfortunate admission to have to make, but
+ it appears to reflect the state of the art in dealing with
+ formalizations of complex programs. Simplification is a perplexing
+ task. Because of this, we feel it behooves the ``guardians of the
+ simplifier'' to try to meet the concerned MACSYMA users part-way by
+ documenting the program as it has evolved. We hope this paper
+ continues to grow to reflect a reasonably accurate, complete, and
+ current description.
+
+ Of course Lisp program details are available to the curious, but even
+ for those without a working knowledge of the Lisp language (in which
+ the simplifier is written) we expect this paper to be of some help in
+ answering questions which arise perennially as to why MACSYMA deals
+ with some particular class of expressions in some unanticipated
+ fashion, or is inefficient in performing some set of transformations.
+ Most often difficulties such as these are accounted for by implicit
+ design decisions which are not evident from mere descriptions of what
+ is done in the anticipated and usual cases. We also hope that
+ improvements or revisions of the simplifier will benefit from the more
+ centralized treatment of issues given here. We also provide
+ additional commentary which reflects our current outlook on how
+ simplification programs should be written, and what capabilities they
+ should have.",
+ paper = "Fate79.txt",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
@inproceedings{Fate90,
author = "Fateman, Richard J.",
title = "Advances and trends in the design and construction of algebraic
@@ -31249,6 +31674,17 @@ J. Symbolic Computation (1993) 15, 393-413
\end{chunk}
+\index{Judson, Tom}
+\index{Beezer, Rob}
+@book{Beez15,
+ author = "Judson, Tom and Beezer, Rob",
+ title = "Abstract Algebra: Theory and Applications",
+ year = "2015",
+ publisher = "Tom Judson",
+ url = "http://abstract.ups.edu/download/aata-20150812-sage-6.8.pdf",
+ paper = "Beez15.pdf"
+}
+
\index{Bertrand, Laurent}
\begin{chunk}{axiom.bib}
@article{Bert95,
@@ -33316,6 +33752,16 @@ Comput. J. 9 281--285. (1966)
keywords = "axiomref"
}
+\index{Judson, Tom}
+@book{Juds15,
+ author = "Judson, Tom",
+ title = "Abstract Algebra: Theory and Applications",
+ year = "2015",
+ publisher = "Tom Judson",
+ url = "http://abstract.ups.edu/download/aata-20150812.pdf",
+ paper = "Juds15.pdf"
+}
+
\subsection{K} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\index{TriangularSetCategory}
@@ -33723,7 +34169,7 @@ Stanford University. (1977)
author = "Lidl, Rudolf and Niederreiter, Harald",
title = "Finite Field, Encyclopedia of Mathematics and Its Applications",
volume = "20",
- publishier = "Cambridge Univ. Press",
+ publisher = "Cambridge Univ. Press",
year = "1983",
isbn = "0-521-30240-4",
algebra =
@@ -34723,11 +35169,17 @@ ORSUM August 2003
\end{chunk}
-\index{Redfield, J.H.}
-\begin{chunk}{ignore}
-\bibitem[Redfield 27]{Red27} Redfield, J.H.
+\index{Redfield, J. Howard}
+\begin{chunk}{axiom.bib}
+@article{Redf27,
+ author = "Redfield, J. Howard",
title = "The Theory of Group-Reduced Distributions",
-American J. Math., 49 (1927) 433-455.
+ journal = "American J. Math.",
+ volume = "49",
+ number = "3",
+ year = "1927",
+ pages = "433-455"
+}
\end{chunk}
diff --git a/changelog b/changelog
index 0e8def6..e1de9d8 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,5 @@
+20160805 tpd src/axiom-website/patches.html 20160805.03.tpd.patch
+20160805 tpd books/bookvolbib Axiom Citations in the Literature
20160805 tpd src/axiom-website/patches.html 20160805.02.tpd.patch
20160805 tpd books/bookvolbug: add todo 341: merge endpapers with text
20160805 tpd src/axiom-website/patches.html 20160805.01.tpd.patch
diff --git a/patch b/patch
index 0dd1dcb..d8f31a1 100644
--- a/patch
+++ b/patch
@@ -1,6 +1,359 @@
-books/bookvolbug: add todo 341: merge endpapers with text
+books/bookvolbib Axiom Citations in the Literature
Goal: Axiom Literate Programming
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate13a,
+ author = "Fateman, Richard J.",
+ title = "Rational Function Computing with Poles and Residues",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/openmathcrit.pdf",
+ year = "2013",
+ abstract =
+ "Computer algebra systems (CAS) usually support computation with exact
+ or approximate rational functions as ratios of polynomials in
+ ``expanded form'' with explicit coefficients. We examine the
+ consequences of introducing a partial-fraction type of form in which
+ some of the usual rational operations can be implemented in
+ substantially faster times. In this form an expression in one
+ variable, say $x$, is expressed as a polynomial in $x$ plus a sum of
+ terms each of which has a denominator $x-c$ perhaps to an integer
+ power, where $c$ is in general a complex constant. We show that some
+ common operations including rational function addition,
+ multiplication, and matrix determinant calculation can be performed
+ many times faster than in the conventional representation. Polynomial
+ GCD operations, the costliest part of rational additions, are entirely
+ eliminated. Applicaiton of Cauchy's integral theorem allow for trivial
+ integration of an expression around a closed contour. In some cases
+ the approximate evaluation of transcendental functions can be
+ accelerated, especially in parallel, by evaluation of a formula in
+ pole+residue form.",
+ paper = "Fate13a.pdf"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@inproceedings{Fate03a,
+ author = "Fateman, Richard J.",
+ title = "High-level proofs of mathematical programs using automatic
+ differentiation, simplification, and some common sense",
+ booktitle = "Proc. ISSAC 2003",
+ pages = "88-94",
+ year = "2003",
+ isbn = "1-58113-641-2",
+ abstract =
+ "One problem in applying elementary methods to prove correctness of
+ interesting scientific programs is the large discrepancy in level of
+ discourse between low-level proof methods and the logic of scientific
+ calculation, especially that used in a complex numerical program. The
+ justification of an algorithm typically relies on algebra or analysis,
+ but the correctness of the program requires that the arithmetic
+ expressions are written correctly and that iterations converge to
+ correct values in spite of truncation of infinite processes or series
+ and the commission of numerical roundoff errors. We hope to help
+ bridge this gap by showing how we can, in some cases, state a
+ high-level requirement and by using a computer algebra system (CAS)
+ demonstrate that a program satisfies that requirement. A CAS can
+ contribute program manipulation, partial evaluation, simplification or
+ other algorithmic methods. A novelty here is that we add to the usual
+ list of techniques automatic differentiation, a method already widely
+ used in optimization contexts where algorithms are differentiated. We
+ sketch a proof of a numerical program to compute sine, and display a
+ related approach to a version of a Bessel function algorithm for J0(x)
+ based on a recurrence.",
+ paper = "Fate03a.pdf"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate07,
+ author = "Fateman, Richard J.",
+ title = "Rational Function Computing with Poles and Residues",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/qd.pdf",
+ year = "2007",
+ abstract =
+ "In a numerical calculation sometimes we need higher-than
+ double-precision floating-point arithmetic to allow us to be confident
+ of a result. One alternative is to rewrite the program to use a
+ software package implementing arbitrary-precision extended
+ floating-point arithmetic such as ARPREC or MPFR, and try to choose a
+ suitable precision.
+
+ Such an arithmetic scheme, in spite of helpful tools, may be
+ inconvenient to write. There are also facilities in computer algebra
+ systems (CAS) for such software-implemented ``bigfloats.'' These
+ facilities are convenient if one is already using the CAS. In any of
+ these situations the bigfloats may be rather slow, a cost of its
+ generality.
+
+ There are possibilities intermediate between the largest hardware
+ floating-point format and the general arbitrary-precision software
+ which combine a considerable (but not arbitrary) amount of extra
+ precision with a (relatively speaking) modest factor loss in
+ speed. Sometimes merely doubling the number of bits in a
+ double-floating-point fraction is enough, in which case arithmetic on
+ double-double (DD) operands would suffice. Another possibility is to
+ go for yet another doubling to quad-double (QD) arithmetic: instead of
+ using the machine double-floats to give about 16 decimal digits of
+ precision, QD supplies about 64 digits. DD and QD as used here provide
+ the same exponent range as ordinary double.
+
+ Here we describe how we incorporated QD arithmetic implemented in a
+ library into a Common Lisp system, providing a smooth interface while
+ adding only modest overhead to the run-time costs (compared to
+ accessing the library from C or C++). One advantage is that we keep
+ the program text almost untouched while switching from double to
+ quad-double. Another is that the programs can be written, debugged,
+ and run in an interactive environment. Most of the lessons from QD can
+ be used for other versions of arithmetic which can be embedded in
+ Lisp, including MPFR, for indefinite (arbitrary) precision, should QD
+ provide inadequate precision or range.",
+ paper = "Fate07.pdf,
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate99b,
+ author = "Fateman, Richard J.",
+ title = "Generation and Optimization of Numerical Programs by
+ Symbolic Mathematical Methods",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/RIMS.pdf",
+ year = "1999",
+ abstract =
+ "Symbolic mathematical methods and systems
+ \begin{itemize}
+ \item support scientific and engineering ``problem solving environments''
+ (PSEs),
+ \item The specific manipulation of mathematical models as a precursor
+ to the coding of algorithms
+ \item Expert system selection of modules from numerical libraries and
+ other facilities
+ \item The production of custom numerical software such as derivatives
+ or non-standard arithmetic code-generation packages,
+ \item The complete solution of certain classes of mathematical problems
+ that simply cannot be handled solely by conventional floating-point
+ computation.
+ \end{itemize}
+
+ Viewing computational objects and algorithms from a symbolic
+ perspective and then specializing them to numerical or graphical views
+ provides substantial additional flexibility over a more conventional view.
+
+ We also consider interactive symbolic computing as a tool to provide
+ an organizing principle or glue among otherwise dissimilar components.",
+ paper = "Fate99b.pdf",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate09,
+ author = "Fateman, Richard J.",
+ title = "Rational Integration, Simplified",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/root-integ.pdf",
+ year = "2009",
+ abstract =
+ "After all this computer algebra stuff, and several PhD theses in
+ the last few decades, what more could we say about symbolic
+ rational function integration?
+
+ How about a closed formula for the result, subject to a few algebraic
+ side-conditions, which works even with parameters in the denominator?",
+ paper = "Fate09.pdf"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate09a,
+ author = "Fateman, Richard J.",
+ title = "Simplifying RootSum Expressions",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/rootsum.pdf",
+ year = "2009",
+ abstract =
+ "It's useful to sum an expression with a parameter varying over all
+ the roots of a given polynomial. Here's a defense of that statement
+ and a method to do the task.",
+ paper = "Fate09a.pdf"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate02a,
+ author = "Fateman, Richard J.",
+ title = "Symbolic Execution Merges Construction, Debugging and Proving",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/symex.pdf",
+ year = "2002",
+ abstract =
+ "There is naturally an interest in any technology which promises to
+ assist us in producing correct programs. Some efforts attempt to
+ insure correct programs by making their construction simpler. Some
+ efforts are oriented toward increasing the effectiveness of testing to
+ make the programs appear to perform as required. Other efforts are
+ directed to prove the correctness of the resulting program. Symbolic
+ execution, in which symbols instead of numbers are used in what
+ appears to be a numerical program, is an old but to-date still not
+ widely-used technique. It has been available in various forms for
+ decades from the computer algebra community. Symbolic execution has
+ the potential to assist in all these phases: construction, debugging,
+ and proof. We describe how this might work specifically with regard to
+ our own recent experience in the construction of correct linear
+ algebra programs for structured matrices and LU factorization. We show
+ how developing these programs with a computer algebra system, and then
+ converting incrementally to use more efficient forms. Frequent symbolic
+ execution of the algorithms, equivalent to testing over infinite test
+ sets, aids in debugging, while strengthening beliefs that the correctness
+ of results is an algebraic truth rather than an accident.",
+ paper = "Fate02a.pdf"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate03b,
+ author = "Fateman, Richard J.",
+ title = "Manipulation of Matrices Symbolically",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/symmat2.pdf",
+ year = "2003",
+ abstract =
+ "Traditionally, matrix algebra in computer algebra systems is
+ ``implemented'' in three ways:
+ \begin{itemize}
+ \item numeric explicit computation in a special arithmetic domain:
+ exact rational or integer, high-precision software floating-point,
+ interval, or conventional hardware floating-point.
+ \item ‘symbolic’ explicit computation with polynomial or other
+ expression entries,
+ \item (implicit) matrix computation with symbols defined over a
+ (non-commuting) ring.
+ \end{itemize}
+ Manipulations which involve matrices of indefinite size (n × m) or
+ perhaps have components which are block submatrices of indefinite size
+ have little or no support in general-purpose computer algebra systems,
+ in spite of their importance in theorems, proofs, and generation of
+ programs. We describe some efforts to design and implement tools for
+ this mode of thinking about matrices in computer systems.",
+ paper = "Fate03b.pdf"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate08b,
+ author = "Fateman, Richard J.",
+ title = "Applications and Methods for Recognition of (Anti)-Symmetric
+ Functions",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/symmetry.pdf",
+ year = "2008",
+ abstract =
+ "One of the important advantages held by computer algebra systems (CAS)
+ over purely-numerical computational frameworks is that the CAS can
+ provide a higher-level ``symbolic'' viewpoint for problem
+ solving. Sometimes this can convert apparently impossible problems to
+ trivial ones. Sometimes the symbolic perspective can provide
+ information about questions which cannot be directly answered, or
+ questions which might be hard to pose. For example, we might be able
+ to analyze the asymptotic behavior of a solution to a differential
+ equation even though we cannot solve the equation. One route to
+ implicitly solving problems is the use of symmetry arguments. In this
+ paper we suggest how, through symmetry, one can solve a large class of
+ definite integration problems, including some that we found could not
+ be solved by computer algebra systems. One case of symmetry provides
+ for recognition of periodicity, and this solves additional problems,
+ since removal of periodic components can be important in integration
+ and in asymptotic expansions.",
+ paper = "Fate08b.pdf"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@phdthesis{Fate72,
+ author = "Fateman, Richard J.",
+ title = "Essays in Algebraic Simplification",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/tr-95.pdf",
+ institution = "MIT",
+ comment = "MAC TR-95 technical report",
+ year = "1972",
+ abstract =
+ "This thesis consists of essays on several aspects of the problem
+ of algebraic simplification by computer. We first discuss a pattern
+ matching system intended to recognize non-obvious occurrences of
+ patterns within Algebraic expression. A user of such a system can
+ ``teach'' the computer new simplification rules. Then we report on
+ new applications of canonical simplification of rational functions.
+ These applications include techniques for picking out coefficients,
+ and for substituting for summs, products, quotients, etc. Our final
+ essay is on a new, practical, canonical simplification algorithms
+ for radical expressions (i.g. algebraic expressions including roots
+ of polynomials). The effectiveness of the procedure is assured
+ through proofs of appropriate properties of the simplified forms.
+ Two appendices describe MACSYM, a computer system for algebraic
+ manipulations, which served as the basis for this work.",
+ paper = "Fate72.pdf"
+}
+
+\end{chunk}
+
+\index{Redfield, J.Howard}
+\begin{chunk}{axiom.bib}
+@article{Redf27,
+ author = "Redfield, J.Howard",
+ title = "The Theory of Group-Reduced Distributions",
+ journal = "American J. Math.",
+ volume = "49",
+ number = "3",
+ year = "1927",
+ pages = "433-455"
+}
+
+\end{chunk}
+
+\index{Judson, Tom}
+@book{Juds15,
+ author = "Judson, Tom",
+ title = "Abstract Algebra: Theory and Applications",
+ year = "2015",
+ publisher = "Tom Judson",
+ url = "http://abstract.ups.edu/download/aata-20150812.pdf",
+ paper = "Juds15.pdf"
+}
+
+\index{Judson, Tom}
+\index{Beezer, Rob}
+@book{Beez15,
+ author = "Judson, Tom and Beezer, Rob",
+ title = "Abstract Algebra: Theory and Applications",
+ year = "2015",
+ publisher = "Tom Judson",
+ url = "http://abstract.ups.edu/download/aata-20150812-sage-6.8.pdf",
+ paper = "Beez15.pdf"
+}
+
+\index{Axiom Authors}
+\begin{chunk}{axiom.bib}
+@book{Bookbug,
+ author = "Axiom Authors",
+ title = "Volume BugList: Axiom Bugs",
+ url = "http://axiom-developer.org/axiom-website/bookvolbug.pdf",
+ publisher = "Axiom Project",
+ year = "2016"
+}
+
+\end{chunk}
-The books/endpaper.pamphlet should be added to the Jenks book
diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html
index 2d2a5a7..8b0f371 100644
--- a/src/axiom-website/patches.html
+++ b/src/axiom-website/patches.html
@@ -5530,6 +5530,8 @@ books/Makefile.pamphlet automate build of bug report

books/bookvolbug: add bug 7319: ignoring return values

20160805.02.tpd.patch
books/bookvolbug: add todo 341: merge endpapers with text

+20160805.03.tpd.patch
+books/bookvolbib Axiom Citations in the Literature

--
1.7.5.4