From 59a0c71f19aa902ba95af49888ac2564a5dab420 Mon Sep 17 00:00:00 2001
From: Tim Daly
Date: Tue, 12 Jul 2016 09:29:34 0400
Subject: [PATCH] buglist bug 7305: series should simplify
=========================================================================
bug 7305: series should simplify
> series(sin(x),x=0)
1 3 1 5 1 7 1 9 1 11 12
(1) x   x +  x   x +  x   x + O(x )
6 120 5040 362880 39916800
(2) > %/x
1 1 3 1 5 1 7 1 9 1 11 12
(2)  x   x +  x   x +  x   x + O(x )
x 6x 120x 5040x 362880x 39916800x
(3) > %1
1 1 3 1 5 1 7 1 9 11
(3)  1 +  x   x +  x   x +  x + O(x )
x 6x 120x 5040x 362880x

buglist  35 ++
changelog  2 +
patch  805 ++++++++++++++++++++++++++++++
src/axiomwebsite/patches.html  2 +
4 files changed, 637 insertions(+), 207 deletions()
diff git a/buglist b/buglist
index 83841cd..32f03db 100644
 a/buglist
+++ b/buglist
@@ 1,7 +1,7 @@
=========================================================================
bug 7305:
todo 340:
+bug 7306:
+todo 341:
wish 1012:
meh 5:
errors 10016:
@@ 12,6 +12,37 @@ dup 50006:
nonextend 60077:
=========================================================================
+bug 7305: series should simplify
+
+> series(sin(x),x=0)
+
+ 1 3 1 5 1 7 1 9 1 11 12
+ (1) x   x +  x   x +  x   x + O(x )
+ 6 120 5040 362880 39916800
+
+(2) > %/x
+
+ 1 1 3 1 5 1 7 1 9 1 11 12
+ (2)  x   x +  x   x +  x   x + O(x )
+ x 6x 120x 5040x 362880x 39916800x
+
+(3) > %1
+
+ 1 1 3 1 5 1 7 1 9 11
+ (3)  1 +  x   x +  x   x +  x + O(x )
+ x 6x 120x 5040x 362880x
+
+=========================================================================
+todo 340: exponentiallinear
+
+t1:=(1.6)^x + 122.35*x  5054.4
+ Type: Expression(Float)
+solve(t1,x) fails
+
+see: Corl93.pdf On the Lambert W Function
+see: Kalm01.pdf A Generalized Logarithm for ExponentialLinear Equations
+
+=========================================================================
todo 339: missing side conditions
integrate((xb)^(1),x)
diff git a/changelog b/changelog
index e4179ec..8e55e4a 100644
 a/changelog
+++ b/changelog
@@ 1,3 +1,5 @@
+20160712 tpd src/axiomwebsite/patches.html 20160712.01.tpd.patch
+20160712 tpd buglist bug 7305: series should simplify
20160710 tpd src/axiomwebsite/patches.html 20160710.01.tpd.patch
20160710 tpd books/bookvol10.4 reference Dupe99
20160710 tpd books/bookvol10.3 reference Hawk95 and Kead93
diff git a/patch b/patch
index fa8281d..99a8107 100644
 a/patch
+++ b/patch
@@ 2,239 +2,634 @@ books/bookvolbib Axiom Citations in the Literature
Goal: Axiom Literate Programming
\index{Hawkes, Evatt}
\index{Keady, Grant}
\begin{chunk}{axiom.bib}
@inproceedings{Hawk95,
 author = "Hawkes, Evatt and Keady, Grant",
 title = "Two more links to NAG numerics involving CA systems",
 booktitle = "IMACS Applied Computer Algebra Conference",
 location = "University of New Mexico",
 year = "1995",
+\index{Bradford, Russell}
+\begin{chunk}{axiom.bib}
+@inproceedings{Brad92,
+ author = "Bradford, Russell",
+ title = "Algebraic Simplification of MultipleValued Functions",
+ booktitle = "Proc. DISCO 92",
+ series = "Lecture Notes in Computer Science 721",
+ year = "1992",
+ paper = "Brad92.pdf",
+ abstract =
+ "Many current algebra systems have a lax attitude to the
+ simplification of expressions involving functions like log and
+ $\sqrt{}$, leading the the ability to ``prove'' equalities like $1=1$
+ in such systems. In fact, only a little elementary arithmetic is
+ needed to devise what the correct simplification should be. We detail
+ some of these simplification rules, and outline a method for their
+ incorporation into an algebra system."
+}
+
+\end{chunk}
+
+\index{Schwarz, Fritz}
+\begin{chunk}{axiom.bib}
+@article{Schw91,
+ author = "Schwarz, Fritz",
+ title = "Monomial orderings and Groebner bases",
+ journal = "SIGSAM Bulletin",
+ volume = "25",
+ number = "1",
+ pages = "1023",
keywords = "axiomref",
 paper = "Hawk95.pdf",
 algebra =
 "\newline\refto{domain ASP1 Asp1}
 \newline\refto{domain ASP10 Asp10}
 \newline\refto{domain ASP12 Asp12}
 \newline\refto{domain ASP19 Asp19}
 \newline\refto{domain ASP20 Asp20}
 \newline\refto{domain ASP24 Asp24}
 \newline\refto{domain ASP27 Asp27}
 \newline\refto{domain ASP28 Asp28}
 \newline\refto{domain ASP29 Asp29}
 \newline\refto{domain ASP30 Asp30}
 \newline\refto{domain ASP31 Asp31}
 \newline\refto{domain ASP33 Asp33}
 \newline\refto{domain ASP34 Asp34}
 \newline\refto{domain ASP35 Asp35}
 \newline\refto{domain ASP4 Asp4}
 \newline\refto{domain ASP41 Asp41}
 \newline\refto{domain ASP42 Asp42}
 \newline\refto{domain ASP49 Asp49}
 \newline\refto{domain ASP50 Asp50}
 \newline\refto{domain ASP55 Asp55}
 \newline\refto{domain ASP6 Asp6}
 \newline\refto{domain ASP7 Asp7}
 \newline\refto{domain ASP73 Asp73}
 \newline\refto{domain ASP74 Asp74}
 \newline\refto{domain ASP77 Asp77}
 \newline\refto{domain ASP78 Asp78}
 \newline\refto{domain ASP8 Asp8}
 \newline\refto{domain ASP80 Asp80}
 \newline\refto{domain ASP9 Asp9}",
 abstract =
 "The 'more' in the title is because this paper is a sequel to papers
 by Keving Broughan, [BKRRD,BK]. For some years GK has had interests in
 (i) interactive frontends to numeric computation, such as the
 NAG/IMSL library computation, and (ii) Fortran code generation for
 Argument SubPrograms (ASPs), such as those neede by some NAG/IMSL
 routines. Demonstrations of three links to the NAG library are
 described in [BKRRD]. A description of a link to NAG from Macsyma
 which was mentioned, but not in a sufficiently advanced state to
 demonstrate in early 1991, is given in [BK]. The situation at the end
 of 1991 was that there were links to NAG involving each of Macsyma,
 REDUCE and Mathematica. The links are called Naglink, IRENA and
 InterCall, respectively. The principal authors of IRENA are Mike Dewar
 and Mike Richardson. InterCall is not specific to the NAG library;
 indeed InterCall is used with calls to IMSL and to elsewhere at the
 conference venue, the University of New Mexico.

 The two futher links to NAG library treated in this paper are AXIOM2.0
 and genmex/ESC, genmex allows calls to NAG from Matlab. genmex can be
 regarded as similar to InterCall: genmes uses Matlab's mex files in a
 similar way to InterCall's use of Mathematica's MathLink. Again genmex
 is not specific to the NAG library. Mike Dewar is an author both of
 IRENA and the AXIOM2.0 link to the NAG library: see [D] foe discussion
 of the differences between the IRENA project and the AXIOMNAG link
 project."
}
+ abstract =
+ "Let there be given a set of monomials in n variables and some order
+ relations between them. The following {\sl fundamental problem of
+ monomial ordering} is considered. Is it possible to decide whether
+ these ordering relations are consistent and if so to extend them to an
+ {\sl admissible} ordering for all monomials? The answer is given in
+ terms of the algorithm {\sl MACOT} which constructs a matrix of so
+ called {\sl cotes} which establishes the desired ordering
+ relations. The main area of application of this algorithm, i.e. the
+ construction of Groebner bases for different orderings and of
+ universal Groebner bases is treated in the last section."
+}
+
+\end{chunk}
+
+\index{Bradford, Russell}
+\begin{chunk}{axiom.bib}
+@inproceedings{Brad92,
+ author = "Bradford, Russell",
+ title = "Algebraic Simplification of MultipleValued Functions",
+ booktitle = "Proc. DISCO 92",
+ series = "Lecture Notes in Computer Science 721",
+ year = "1992",
+ paper = "Brad92.djvu",
+ abstract =
+ "Many current algebra systems have a lax attitude to the
+ simplification of expressions involving functions like log and
+ $\sqrt{}$, leading the the ability to ``prove'' equalities like $1=1$
+ in such systems. In fact, only a little elementary arithmetic is
+ needed to devise what the correct simplification should be. We detail
+ some of these simplification rules, and outline a method for their
+ incorporation into an algebra system."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@article{Wang90,
+ author = "Wang, Dongming",
+ title = "A Class of Cubic Differential Systems with 6tuple Focus",
+ journal = "J. Differential Equations",
+ publisher = "Academic Press, Inc.",
+ volume = "87",
+ pages = "305315",
+ year = "1990",
+ keywords = "axiomref",
+ paper = "Wang90.pdf",
+ abstract =
+ "This paper presents a class of cubic differential systems with the
+ origin as a 6tuple focus from which 6 limit cycles may be
+ constructed. For this class of differential systems the stability of
+ the origin is given."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@article{Wang91,
+ author = "Wang, Dongming",
+ title = "Mechanical manipulation for a class of differential systems",
+ journal = "Journal of Symbolic Computation",
+ volume = "12",
+ number = "2",
+ pages = "233254",
+ year = "1991",
+ keywords = "axiomref",
+ abstract =
+ "The author describes a mechanical procedure for computing the
+ Liapunov functions and Liapunov constants for a class of differential
+ systems. These functions and constants are used for establishing the
+ stability criteria, the conditions for the existence of a center and
+ for the investigation of limit cycles. Some problems for handling the
+ computer constants, which are usually large polynomials in terms of
+ the coefficients of the differential system, and an approach towards
+ their solution by using computer algebraic methods are proposed. This
+ approach has been successfully applied to check some known results
+ mechanically. The author has implemented a system DEMS on an HP1000
+ and in Scratchpad II on an IBM4341 for computing and manipulating the
+ Liapunov functions and Liapunov constants. As examples, two particular
+ cubic systems are discussed in detail. The explicit algebraic
+ relations between the computed Liapunov constants and the conditions
+ given by Saharnikov are established, which leads to a rediscovery of
+ the incompleteness of his conditions. A class of cubic systems with
+ 6tuple focus is presented to demonstrate the feasibility of the
+ approach for finding systems with higher multiple focus."
+}
\end{chunk}
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@misc{Wang95,
+ author = "Wang, Dongming",
+ title = "Characteristic Sets and Zero Structure of Polynomial Sets",
+ institution = "Johannes Kepler University",
+ comment = "Lecture Notes",
+ paper = "Wang95.pdf",
+ url = "http://wwwpolsys.lip6.fr/~wang/papers/CharSet.ps.gz",
+ keywords = "axiomref",
+ abtract =
+ "This paper provides a tutorial on the theory and method of
+ characteristic sets and some relevant topics. The basic algorithms as
+ well as their generalization for computing the characteristic set and
+ characteristic series of a set of multivariate polynomials are
+ presented. The characeristic set, which is of certain triangular form,
+ reflects in general the major part of zeros, and the characteristic
+ series, which is a sequence of polynomial sets of triangular form,
+ furnishes a complete zero decomposition of the given polynomial
+ set. Using this decomposition, a complete solution to the algebraic
+ decision problem and a method for decomposing any algebraic variety
+ into irreducible components are described. Some applications of the
+ method are indicated."
+}
+
+\end{chunk}
+
+
\index{Keady, G.}
\index{Nolan, G.}
\begin{chunk}{axiom.bib}
@inproceedings{Kead93,
 author = "Keady, G. and Nolan, G.",
 title = "Production of Argument SubPrograms in the AXIOM  NAG link:
 examples involving nonlinear systems",
 booktitle = "Proc. Workshop on Symbolic and Numeric Computation",
 location = "Helsinki",
+\index{Richardson, M.G.}
+\begin{chunk}{axiom.bib}
+@inproceedings{Kead93a,
+ author = "Keady, G. and Richardson, M.G.",
+ title = "An application of IRENA to systems of nonlinear equations arising
+ in equilibrium flows in networks",
+ booktitle = "Proc. ISSAC 1993",
+ series = "ISSAC '93",
year = "1993",
 pages = "1332",
 comment = "NAG Technical Report TR1/94",
 url = "school.maths.uwa.edu.au/%7Ekeady/KeadyPapers/93Helsinki.ps",
 paper = "Kead93.pdf",
+ paper = "Kead93a.pdf",
keywords = "axiomref",
 algebra =
 "\newline\refto{domain ASP1 Asp1}
 \newline\refto{domain ASP10 Asp10}
 \newline\refto{domain ASP12 Asp12}
 \newline\refto{domain ASP19 Asp19}
 \newline\refto{domain ASP20 Asp20}
 \newline\refto{domain ASP24 Asp24}
 \newline\refto{domain ASP27 Asp27}
 \newline\refto{domain ASP28 Asp28}
 \newline\refto{domain ASP29 Asp29}
 \newline\refto{domain ASP30 Asp30}
 \newline\refto{domain ASP31 Asp31}
 \newline\refto{domain ASP33 Asp33}
 \newline\refto{domain ASP34 Asp34}
 \newline\refto{domain ASP35 Asp35}
 \newline\refto{domain ASP4 Asp4}
 \newline\refto{domain ASP41 Asp41}
 \newline\refto{domain ASP42 Asp42}
 \newline\refto{domain ASP49 Asp49}
 \newline\refto{domain ASP50 Asp50}
 \newline\refto{domain ASP55 Asp55}
 \newline\refto{domain ASP6 Asp6}
 \newline\refto{domain ASP7 Asp7}
 \newline\refto{domain ASP73 Asp73}
 \newline\refto{domain ASP74 Asp74}
 \newline\refto{domain ASP77 Asp77}
 \newline\refto{domain ASP78 Asp78}
 \newline\refto{domain ASP8 Asp8}
 \newline\refto{domain ASP80 Asp80}
 \newline\refto{domain ASP9 Asp9}",
 abstract =
 "Dewar's paper [6] earlier in this Proceedings 'sketches out the
 design of the AXIOMNAG link' and gives a general account of new tools
 for generating Fortran. This paper is a sequel to [6]. Here we present
 'examples' of some of the items discussed in [6]. We have attempted to
 achieve some coherence by selecting our 'examples' from just the one
 application area  solving nonlinear systems."
}

\end{chunk}

\index{Fateman, Richard J.}
\index{Einwohner, Theodore H.}
\begin{chunk}{axiom.bib}
@misc{Fate92,
 author = "Fateman, Richard J. and Einwohner, Theodore H.",
 title = "A Proposal for Automated Integral Tables (Work in Progress)",
 year = "1992",
 url = "http://people.eecs.berkeley.edu/~fateman/papers/intable.pdf",
 paper = "Fate92.pdf",
abstract =
"One of the longterm general goals of algebraic manipulation systems
has been the automation of difficult or tedious, yet common, symbolic
mathematical operations. Prominent amount these has been symbolic
integration. Although some effective algorithms have been devised for
integration expecially for those problems solvable in terms of
elementary functions and a few additional special functions, the vast
majority of entires in large tables of indefinite and definite
integrals remain out of reach of current machine algorithms. We
propose techniques for introducing the information in such tables to
computers, extending such tables, and measuring the success of such
automation.

Similar tabular data concerning simplifications, summation identities,
and similar formulas could also be treated by some of the same
techniques."
+ "IRENA  an $I$nterface from $RE$DUCE to $NA$G  runs under the REDUCE
+ Computer Algebra (CA) system and provides an interactive front end to
+ the NAG Fortran Library.
+
+ Here IRENA is tested on a problem closer to an engineering problem
+ than previously publised examples. We also illustrate the use of the
+ {\tt codeonly} switch, which is relevant to larger scale problems. We
+ describe progress on an issue raised in the 'Future Developments'
+ section in our {\sl SIGSAM Bulletin} article [2]: the progress improves
+ the practical effectiveness of IRENA."
}
\end{chunk}
\index{Dewar, Michael C.}
+\index{LeBlanc, S.E.}
\begin{chunk}{axiom.bib}
@phdthesis{Dewa91,
 author = "Dewar, Michael C.",
 title = "Interfacing algebraic and numeric computation",
+@inproceedings{LeBl91,
+ author = "LeBlanc, S.E.",
+ title = "The use of MathCAD and Theorist in the ChE classroom",
+ booktitle = "Proc. ASEE Annual Meeting",
year = "1991",
 institution = "University of Bath, UK, England"
+ pages = "287299",
+ keywords = "axiomref"
+ abstract =
+ "MathCAD and Theorist are two powerful mathematical packages available
+ for instruction in the ChE classroom. MathCAD is advertised as an
+ `electronic scratchpad' and it certainly lives up to its billing. It
+ is an extremely userfriendly collection of numerical routines that
+ eliminates the drudgery of solving many of the types of problems
+ encountered by undergraduate ChE's (and engineers in general). MathCAD
+ is available for both the Macintosh and IBM PC compatibles. The PC
+ version is available as a fullfunctioned student version for around
+ US\$40 (less than many textbooks). Theorist is a symbolic mathematical
+ package for the Macintosh. Many interesting and instructive things can
+ be done with it in the ChE curriculum. One of its many attractive
+ features includes the ability to generate high quality three
+ dimensional plots that can be very instructive in examining the
+ behavior of an engineering system. The author discusses the
+ application and use of these packages in chemical engineering and give
+ example problems and their solutions for a number of courses including
+ stoichiometry, unit operations, thermodynamics and design."
}
\end{chunk}
\index{Dupee, Brian J.}
\index{Davenport, James H.}
+\index{Wang, Dongming}
\begin{chunk}{axiom.bib}
@misc{Dupe99,
 author = "Dupee, Brian J. and Davenport, James H.",
 title = "An Automatic SymbolicNumeric Taylor Series ODE Solver",
 year = "1999",
 paper = "Dupe99.pdf",
 url = "http://people.eecs.berkeley.edu/~fateman/papers/casc9934.pdf",
+@book{Wang01,
+ author = "Wang, Dongming",
+ title = "Elimination Methods",
+ publisher = "SpringerVerlag",
+ isbn = "9783709162026",
keywords = "axiomref",
 algebra = "\newline\refto{package EXPRODE ExpressionSpaceODESolver}",
+ year = "2001",
+ abstract =
+ "The development of polynomialelimination techniques from classical
+ theory to modern algorithms has undergone a tortuous and rugged
+ path. This can be observed L. van der Waerden's elimination of the
+ ``elimination theory'' chapter from from B. his classic Modern Algebra
+ in later editions, A. Weil's hope to eliminate ``from algebraic
+ geometry the last traces of elimination theory,'' and S. Abhyankar's
+ suggestion to ``eliminate the eliminators of elimination theory.''
+ The renaissance and recognition of polynomial elimination owe much to
+ the advent and advance of modern computing technology, based on
+ which effective algorithms are implemented and applied to diverse
+ problems in science and engineering. In the last decade, both
+ theorists and practitioners have more and more realized the
+ significance and power of elimination methods and their underlying
+ theories. Active and extensive research has contributed a great deal
+ of new developments on algorithms and softÂ ware tools to the subject,
+ that have been widely acknowledged. Their applications have taken
+ place from pure and applied mathematics to geometric modeling and
+ robotics, and to artificial neural networks. This book provides a
+ systematic and uniform treatment of elimination algorithms that
+ compute various zero decompositions for systems of multivariate
+ polynomials. The central concepts are triangular sets and systems of
+ different kinds, in terms of which the decompositions are
+ represented. The prerequisites for the concepts and algorithms are
+ results from basic algebra and some knowledge of algorithmic
+ mathematics."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@inproceedings{Wang92,
+ author = "Wang, Dongming",
+ title = "A Method for Factorizing Multivariate Polynomials over Successive
+ Algebraic Extension Fields",
+ booktitle = "Mathematics and MathematicsMechanization (2001)",
+ pages = "138172",
+ institution = "Johannes Kepler University",
+ url = "http://wwwpolsys.lip6.fr/~wang/papers/Factor.ps.gz",
+ paper = "Wang92.pdf",
+ year = "1992",
+ abstract =
+ "We present a method for factorizing multivariate polynomials over
+ algebraic fields obtained from successive extensions of the rational
+ number field. The basic idea underlying this method is the reduction
+ of polynomial factorization over algebraic extension fields to the
+ factorization over the rational number vield via linear transformation
+ and the computation of characteristic sets with respect to a proper
+ variable ordering. The factors over the algebraic extension fields are
+ finally determined via GCD (greatest common divisor) computations. We
+ have implemented this method in the Maple system. Preliminary
+ experiments show that it is rather efficient. We give timing
+ statistics in Maple 4.3 on 40 test examples which were partly taken
+ from the literature and partly randomly generated. For all those
+ examples to which Maple builtin algorithm is applicable, our
+ algorithm is always faster."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@misc{Wang90a,
+ author = "Wang, Dongming",
+ title = "Some NOtes on Algebraic Methods for Geometry Theorem Proving",
+ url = "http://wwwpolsys.lip6.fr/~wang/papers/GTPnote.ps.gz",
+ year = "1990",
+ paper = "Wang90a.pdf",
abstract =
 "One of the basic techniques in every mathematician's toolkit is the
 Taylor series representation of functions. It is of such fundamental
 importance and it is so well understood that its use is often a first
 choice in numerical analysis. This faith has not, unfortunately, been
 transferred to the design of computer algorithms.

 Approximation by use of Taylor series methods is inherently partly a
 symbolic process and partly numeric> This aspect has often, with
 reason, been regared as a major hindrance in algorithm design. Whilst
 attempts have been made in the past to build a consistent set of
 programs for the symbolic and numeric paradigms, these have been
 necessarily multistage processes.

 Using current technology it has at last become possible to integrate
 these two concepts and build an automatic adaptive symbolicnumeric
 algorithm within a uniform framework which can hide the internal
 workings behind a modern interface."
+ "A new geometry theorem prover which provides the first complete
+ implementation of Wu's method and includes several Groebner bases
+ based methods is reported. This prover has been used to prove a number
+ of nontrivial geometry theorems including several {\sl large} ones
+ with less space and time cost than using the existing provers. The
+ author presents a new technique by introducing the notion of {\sl
+ normal ascending set}. This technique yields in some sense {\sl
+ simpler} nondegenerate conditions for Wu's method and allows one to
+ prove geometry theorems using characteristic sets but Groeber bases
+ type reduction. Parallel variants of Wu's method are discussed; an
+ implementation of the parallelized version of his algorithm utilizing
+ workstation networks has also been included in our prover. Timing
+ statistics for a set of typical examples is given."
+}
+
+\end{chunk}
+
+\index{Zhao, Ting}
+\index{Wang, Dongming}
+\index{Hong, Hoon}
+\begin{chunk}{axiom.bib}
+@article{Zhao11,
+ author = "Zhao, Ting and Wang, Dongming and Hong, Hoon",
+ title = "Solution formulats for cubic equations without or with constraints",
+ journal = "J. Symbolic Computation",
+ volume = "46",
+ pages = "904918",
+ year = "2011",
+ paper = "Zhao11.pdf",
+ abstract =
+ "We present a convention (for square/cubic roots) which provides
+ correct interpretations of the Lagrange formula for all cubic
+ polynomial equations with real coefficients. Using this convention, we
+ also present a real solution formula for the general cubic equation
+ with real coefficients under equality and inequality constraints."
+}
+
+\end{chunk}
+
+\index{Li, Xiaoliang}
+\index{Mou, Chenqi}
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@article{Lixx10,
+ author = "Li, Xiaoliang and Mou, Chenqi and Wang, Dongming",
+ title = "Decomposing polynomial sets into simple sets over finite fields:
+ The zerodimensional case",
+ comment = "Provides clear polynomial algorithms",
+ journal = "Computers and Mathematics with Applications",
+ volume = "60",
+ pages = "29832997",
+ year = "2010",
+ paper = "Lixx10.pdf",
+ abstract =
+ "This paper presents algorithms for decomposing any zerodimensional
+ polynomial set into simple sets over an arbitrary finite field, with
+ an associated ideal or zero decomposition. As a key ingredient of
+ these algorithms, we generalize the squarefree decomposition approach
+ for univariate polynomials over a finite field to that over the field
+ product determined by a simple set. As a subprocedure of the
+ generalized squarefree decomposition approach, a method is proposed to
+ extract the $p$th root of any element in the field
+ product. Experiments with a preliminary implementation show the
+ effectiveness of our algorithms."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@article{Wang98,
+ author = "Wang, Dongming",
+ title = "Decomposing Polynomial Systems into Simple Systems",
+ volume = "25",
+ number = "3",
+ pages = "295314",
+ year = "1998",
+ paper = "Wang98.pdf",
+ abstract =
+ "A simple system is a pair of multivariate polynomial sets (one set
+ for equations and the other for inequations) ordered in triangular
+ form, in which every polynomial is squarefree and has nonvanishing
+ leading coefficient with respect to its leading variable. This paper
+ presents a method that decomposes any pair of polynomial sets into
+ finitely many simple systems with an associated zero decomposition.
+ The method employs topdown elimination with splitting and the
+ formation of subresultant regular subchains as basic operation."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@article{Wang94,
+ author = "Wang, Dongming",
+ title = "Differentiation and Integration of Indefinite Summations with
+ Respect to Indexed Variables  Some Rules and Applications",
+ journal = "J. Symbolic Computation",
+ volume = "18",
+ number = "3",
+ pages = "249263",
+ year = "1994",
+ paper = "Wang94.pdf",
+ abstract =
+ "In this paper we present some rules for the differentiation and
+ integration of expressions involving indefinite summations with
+ respect to indexed variables which have not yet been taken into
+ account of current computer algebra systems. These rules, together
+ with several others, have been implemented in MACSYMA and MAPLE as a
+ toolkit for manipulating indefinite summations. We discuss some
+ implementation issues and report our experiments with a set of typical
+ examples. The present work is motivated by our investigation in the
+ computeraided analysis and derivation of artificial neural systems.
+ The application of our rules to this subject is briefly explained."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@article{Wang95a,
+ author = "Wang, Dongming",
+ title = "A Method for Proving Theorems in Differential Geometry and
+ Mechanics",
+ journal = "J. Universal Computer Science",
+ volume = "1",
+ number = "9",
+ pages = "658673",
+ year = "1995",
+ url = "http://www.jucs.org/jucs\_1\_9/a\_method\_for\_proving",
+ paper = "Wang95a.pdf",
+ abstract =
+ "A zero decomposition algorithm is presented and used to devise a
+ method for proving theorems automatically in differential geometry and
+ mechanics. The method has been implemented and its practical
+ efficiency is demonstrated by several nontrivial examples including
+ Bertrand s theorem, Schell s theorem and KeplerNewton s laws."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@article{Wang93,
+ author = "Wang, Dongming",
+ title = "An Elimination Method for Polynomial Systems",
+ journal = "J. Symbolic Computation",
+ volume = "16",
+ number = "2",
+ pages = "83114",
+ year = "1993",
+ paper = "Wang93.pdf",
+ abstract =
+ "We present an elimination method for polynomial systems, in the form
+ of three main algorithms. For any given system [$\mathbb{P}$,$\mathbb{Q}$]
+ of two sets of multivariate polynomials, one of the algorithms computes a
+ sequence of triangular forms $\mathbb{T}_1,\ldots,\mathbb{T}_e$ and
+ polynomial sets $\mathbb{U}_1,\ldots,\mathbb{U}_e$ such that
+ Zero($\mathbb{P}$/$\mathbb{Q}$)
+ $= \cup_{i=1}^e {\rm\ Zero}(\mathbb{T}_i/\mathbb{U}_i)$,
+ where Zero($\mathbb{P}$/$\mathbb{Q}$) denotes the set of common zeros of
+ the polynomials in $\mathbb{P}$ which are not zeros of any polynomial in
+ $\mathbb{Q}$, and similarly for Zero($\mathbb{T}_i$/$\mathbb{U}_i$).
+ The two other algorithms compute the same zero decomposition but with nicer
+ properties such as Zero$(\mathbb{T}_i/\mathbb{U}_i) \ne 0$ for each $i$.
+ One of them, for which the computed triangular systems
+ [$\mathbb{T}_i$, $\mathbb{U}_i$] possess the projection property, provides
+ a quantifier elimination procedure for algebraically closed fields.
+ For the other, the computed triangular forms $\mathbb{T}_i$ are
+ irreducible. The relationship between our method and some existing
+ elimination methods is explained. Experimental data for a set of test
+ examples by a draft implementation of the method are provided, and show
+ that the efficiency of our method is comparable with that of some
+ wellknown methods. A few encouraging examples are given in detail for
+ illustration."
}
\end{chunk}
\index{ExpressionSpaceODESolver}
\index{Lambe, Larry A.}
\index{Luczak, Richard}
\index{Nehrbass, John W.}
+\index{Houstis, E.N.}
+\index{Gaffney, P.W.}
\begin{chunk}{axiom.bib}
@article{Lamb03,
 author = "Lambe, Larry A. and Luczak, Richard and Nehrbass, John W.",
 title = "A New Finite Difference Method for the Helmholtz Equation
 Using Symbolic Computation",
 journal = "Int. J. Comp. Eng. Sci.",
 volume = "4",
 year = "2003",
 url = "http://pages.bangor.ac.uk.~mas019/papers/lln.pdf",
 paper = "Lamb03.pdf"
+@book{Hous92,
+ author = "Houstis, E.N. and Gaffney, P.W.",
+ title = "Programming environments for highlevel scientific problem solving",
+ year = "1992",
keywords = "axiomref",
+ publisher = "Elsevier",
+ isbn = "9780444891761",
+ abstract =
+ "Programming environments, as the name suggests, are intended to
+ provide a unified, extensive range of capabilities for a person
+ wishing to solve a problem using a computer. In this particular
+ proceedings volume, the problem considered is a highlevel scientific
+ computation. In other words, a scientific problem whose solution
+ usually requires sophisticated computing techniques and a large
+ allocation of computing resources."
+}
+
+\end{chunk}
+
+\index{Camion, Paul}
+\index{Courteau, Bernard}
+\index{Montpetit, Andre}
+\begin{chunk}{axiom.bib}
+@techreport{Cami92,
+ author = "Camion, Paul and Courteau, Bernard and Montpetit, Andre",
+ title = "A combinatorial problem in Hamming Graphs and its solution
+ in Scratchpad",
+ comment = {Un probl\`eme combinatoire dans les graphies de Hamming et sa
+ solution en Scratchpad},
+ year = "1992",
+ month = "January",
+ keywords = "axiomref",
+ paper = "Cami92.pdf",
+ url = "https://hal.inria.fr/inria00074974/document",
+ type = "Research report",
+ number = "1586",
+ institution = "Institut National de Recherche en Informatique et en
+ Automatique, Le Chesnay, France",
+ abstract =
+ "We present a combinatorial problem which arises in the determination
+ of the complete weight coset enumerators of errorcorrecting codes
+ [1]. In solving this problem by exponential power series with
+ coefficients in a ring of multivariate polynomials, we fall on a
+ system of differential equations with coefficients in a field of
+ rational functions. Thanks to the abstraction capabilities of
+ Scratchpad this differential equation may be solved simply and
+ naturally, which seems not to be the case for the other computer
+ algebra systems now available."
+}
+
+\end{chunk}
+
+\index{Dalmas, St\'ephane}
+\begin{chunk}{axiom.bib}
+ author = "Dalmas, Stephane",
+ title = "A polymorphic functional language applied to symbolic computation",
+ year = "1992",
+ booktitle = "Proc. ISSAC 1992",
+ series = "ISSAC 1992",
+ pages = "369375",
+ isbn = "0897914899 (soft cover) 0897914902 (hard cover)",
+ keywords = "axiomref",
+ "The programming language in which to describe mathematical objects
+ and algorithms is a fundamental issue in the design of a symbolic
+ computation system. XFun is a strongly typed functional programming
+ language. Although it was not designed as a specialized language, its
+ sophisticated type system can be successfully applied to describe
+ mathematical objects and structures. After illustrating its main
+ features, the author sketches how it could be applied to symbolic
+ computation. A comparison with Scratchpad II is attempted. XFun seems
+ to exhibit more flexibility simplicity and uniformity."
+}
+
+\end{chunk}
+
+\index{OpenMath}
+\index{Complex}
+\index{DoubleFloat}
+\index{Float}
+\index{Fraction}
+\index{Integer}
+\index{List}
+\index{SingleInteger}
+\index{String}
+\index{Symbol}
+\index{ExpressionToOpenMath}
+\index{OpenMathServerPackage}
+\index{Corless, Robert M.}
+\index{Jeffrey, David J.}
+\index{Watt, Stephen M.}
+\index{Davenport, James H.}
+\begin{chunk}{axiom.bib}
+@article{Corl00,
+ author = "Corless, Robert M. and Jeffrey, David J. and Watt, Stephen M. and
+ Davenport, James H.",
+ title = "``According to Abramowitz and Stegun'' or
+ arccoth needn't be Uncouth",
+ journal = "SIGSAM Bulletin  Special Issue on OpenMath",
+ volume = "34",
+ number = "2",
+ pages = "5865",
+ year = "2000",
+ paper = "Corl00.pdf",
+ algebra =
+ "\newline\refto{category OM OpenMath}
+ \newline\refto{domain COMPLEX Complex}
+ \newline\refto{domain DFLOAT DoubleFloat}
+ \newline\refto{domain FLOAT Float}
+ \newline\refto{domain FRAC Fraction}
+ \newline\refto{domain INT Integer}
+ \newline\refto{domain LIST List}
+ \newline\refto{domain SINT SingleInteger}
+ \newline\refto{domain STRING String}
+ \newline\refto{domain SYMBOL Symbol}
+ \newline\refto{package OMEXPR ExpressionToOpenMath}
+ \newline\refto{package OMSERVER OpenMathServerPackage}",
+ abstract =
+ "This paper addresses the definitions in OpenMath of the elementary
+ functions. The original OpenMath definitions, like most other sources,
+ simply cite [2] as the definition. We show that this is not adequate,
+ and propose precise definitions, and explore the relationships between
+ these definitions.In particular, we introduce the concept of a couth
+ pair of definitions, e.g. of arcsin and arcsinh, and show that the
+ pair arccot and {\sl arccoth} can be couth."
+}
+
+\end{chunk}
+
+\index{Bronstein, Manuel}
+\begin{chunk}{axiom.bib}
+@article{Bron90a,
+ author = "Bronstein, Manuel",
+ title = "Integration of Elementary Functions",
+ journal = "J. Symbolic Computation",
+ volume = "9"
+ pages = "117173",
+ year = "1990",
+ paper = "Bro90a.pdf",
abstract =
 "A new finite difference method for the Helmholtz equation is
 presented. The method involves replacing the standard ``weights'' in the
 central difference quotients (Secs. 2.1, 2.2, and 2.3) by weights that
 are optimal in a sense that will be explained in the sections just
 mentioned. The calculation of the optimal weights involves some
 complicated and errorprone manipulations of integral formulas that is
 best done using computeraided symbolic computation (SC). In addition,
 we discuss the important problem of interpolation involving meshes
 that have been refined in certain subregions. Analytic formulae are
 derived using SC for these interpolation schemes. Our results are
 discussed in Sec. 5. Some hints about the computer methods we used to
 accomplish these results are given in the Appendix. More information
 is available and access to that information is referenced.

 While we do not want to make SC the focus of this work, we also do not
 want to underestimate its value. Armed with robust and efficient SC
 libraries, a researcher can {\sl comfortably} and {\sl conveniently}
 experiment with ideas that he or she might not examine otherwise."
+ "We extend a recent algorithm of Trager to a decision procedure for the
+ indefinite integration of elementary functions. We can express the
+ integral as an elementary function or prove that it is not
+ elementary. We show that if the problem of integration in finite terms
+ is solvable on a given elementary function field $k$, then it is
+ solvable in any algebraic extension of $k(\theta)$, where $\theta$ is
+ a logarithm or exponential of an element of $k$. Our proof considers
+ an element of such an extension field to be an algebraic function of
+ one variable over $k$.
+
+ In his algorithm for the integration of algebraic functions, Trager
+ describes a Hermitetype reduction to reduce the problem to an
+ integrand with only simple finite poles on the associated Riemann
+ surface. We generalize that technique to curves over liouvillian
+ ground fields, and use it to simplify our integrands. Once the
+ multipe finite poles have been removed, we use the Puiseux expansions
+ of the integrand at infinity and a generalization of the residues to
+ compute the integral. We also generalize a result of Rothstein that
+ gives us a necessary condition for elementary integrability, and
+ provide examples of its use."
}
\end{chunk}
diff git a/src/axiomwebsite/patches.html b/src/axiomwebsite/patches.html
index 358d4df..4ae06c8 100644
 a/src/axiomwebsite/patches.html
+++ b/src/axiomwebsite/patches.html
@@ 5466,6 +5466,8 @@ books/bookvolbib Axiom Citations in the Literature
books/bookvolbib Axiom Citations in the Literature
20160710.01.tpd.patch
books/bookvolbib Axiom Citations in the Literature
+20160712.01.tpd.patch
+buglist bug 7305: series should simplify

1.7.5.4