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Goal: Axiom references
\index{Stoutemyer, David R.}
\begin{chunk}{axiom.bib}
@article{Stou79,
author = "Stoutemyer, David R.",
title = "LISP Based Symbolic Math Systems",
journal = "Byte Magazine",
volume = "8",
pages = "176192",
year = "1979",
link = "\url{https://ia902603.us.archive.org/30/items/bytemagazine197908/1979_08_BYTE_0408_LISP.pdf}",
comment =
"SCRATCHPAD is a very large computeralgebra system implemented by the
IBM Thomas J. Watson Research Center. It is available there on an IBM
370, and it is available from other IBM corporate sites via
telephone. Regrettably, this fine system has not yet been released to
the public, but it is discussed here because of its novel features.
In its entirety, the system occupies about 1600K bytes on an IBM 370
with virtual storage, for which an additional minimum of 100 K bytes
is recommeded for workspace. The variety of builtin transformations
currently lies between that of REDUCE and MACSYMA. However, each of
the three systems has features that none of the others possess, and
one of these features may be a decisive advantage for a particular
application. Here are some highlights of the SCRATCHPAD system:
\begin{itemize}
\item The system provides singleprecision floatingpoint arithmetic
as well as indefiniteprecision rational arithmetic
\item The builtin unavoidable and optional algebraic transformations
are approximately similar to those of MACSYMA.
\item The builtin exponential, logarithmic, and trigonometric
transformations are approximately similar to those of REDUCE.
\item Besides builtin symbolic matrix algebra, APL like array
operations are included, and they are even further generalized to
permit symbolic operations of nonhomogeneous arrays and on arrays
of indefinite or infinite size.
\item Symbolic differentiation and integration are builtin, with
the latter employing the powerful RischNormal algorithm.
\item There is a particularly elegant builtin facility for
determining Taylor series expansions.
\item There is a builtin SOLVE function capable of determining the
exact solution to a system of linear equations.
\item There is a powerful patternmatching facility which serves as
the primary mechanism for user level extensions. The associated syntax
is at a very high level, being the closest of all computer algebra
systems to the declarative, nonprocedural notation of mathematics.
To implement the trigonometric multipleangle expansions, we can
merely enter the rewrite rules:
\[cos(n*x) == 2*cos(x)*cos((n1)*x)cos((n2)*x), n{\rm\ in\ }
(2,3,...), x{\rm\ arb}\]
\[sin(n*x) == 2*cos(x)*sin((n1)*x)sin((n2)*x), n{\rm\ in\ }
(2,3,...),x{\rm\ arb}\]
Then, whenever we subsequently enter an expression such as
$cos(4*b)$, the response will be a corresponding expanded
expression such as
\[8*cos(B)  8*cos^2(B)+1\]
Thus, programs resemble a collection of math formulae, much as they
would appear in a book or article.
\item SCRATCHPAD has a particularly powerful yet easily used mechanism
for controlling the output format of expressions.. For example, the user
can specify that an expression be displayed as a power series in x,
with coefficients which are factored rational functions in b and c,
etc. For large expressions, such fine control over the output may
mean the difference between an important new discovery and an
inconprehensible mess.
\end{itemize}
This generalized recursive format idea is so natural and effective
that SCRATCHPAD is now absorbing the idea into an internal
representation. A study of the polynomial additional algorithm in
the previous section reveals that it is written to be applicable
to any coefficient domain which has the algebraic properties of a
{\sl ring}. The coefficients could be matrices, powerseries, etc.
That coefficient domain could in turn have yet another coefficient
domain, and so on. With a careful modular design, packages to treat
each of these domains can be dynamically linked together so that
code can be shared and combined in new ways without extensive
rewriting and duplication. Then not only the output, but also the
internal computations can be selected most suitably for a particular
application.
For further information about SCRATCHPAD, contact Richard Jenks
at the IBM Thomas J. Watson Research Center, Yorktown Heights, NY
10598",
paper = "Stou79.pdf",
keywords = "axiomref"
}
\end{chunk}
\index{Shackell, John}
\begin{chunk}{axiom.bib}
@article{Shac90,
author = "Shackell, John",
title = "Growth Estimates for ExpLog Functions",
journal = "J. Symbolic Computation",
volume = "10",
pages = "611632",
abstract =
"Explog functions are those obtained from the constant 1 and the
variable X by means of arithmetic operations and the function symbols
exp() and log(). This paper gives an explicit algorithm for
determining eventual dominance of these functions modulo an oracle for
deciding zero equivalence of constant terms. This also provides
another proof that the dominance problem for explog functions is
Turingreducible to the identity problem for constant terms."
}
\end{chunk}
\index{Bronstein, Manuel}
\begin{chunk}{axiom.bib}
@article{Bron88,
author = "Bronstein, Manuel",
title = "The Transcendental Risch Differential Equation",
journal = "J. Symbolic Computation",
volume = "9",
year = "1988",
pages = "4960",
abstract =
"We present a new rational algorithm for solving Risch differential
equations in towers of transcendental elementary extensions. In
contrast to a recent algorithm of Davenport we do not require a
progressive reduction of the denominators involved, but use weak
normality to obtain a formula for the denominator of a possible
solution. Implementation timings show this approach to be faster than
a Hermitelike reduction.",
paper = "Bron88.pdf",
keywords = "axiomref"
}
\end{chunk}
\index{Erd\'elyi, A.}
\begin{chunk}{axiom.bib}
@book{Erde56,
author = {Erd\'elyi, A.},
title = "Asymptotic Expansions",
year = "1956",
isbn = "9780486155050",
publisher = "Dover Publications"
}
\end{chunk}
\index{Gradshteyn, I.S.}
\index{Ryzhik, I.M.}
\begin{chunk}{axiom.bib}
@incollection{Grad80,
author = "Gradshteyn, I.S. and Ryzhik, I.M.",
title = "Definite Integrals of Elementary Functions",
booktitle = "Table of Integrals, Series, and Products",
publisher = "Academic Press",
year = "1980",
comment = "Chapter 34"
}
\end{chunk}
\index{Piquette, J. C.}
\begin{chunk}{axiom.bib}
@article{Piqu89,
author = "Piquette, J. C.",
title = "Special Function Integration",
journal = "ACM SIGSAM Bulletin",
volume = "23",
number = "2",
year = "1989",
pages = "1121",
abstract =
"This article describes a method by which the integration capabilities
of symbolicmathematics computer programs can be extended to include
integrals that contain special functions. A summary of the theory that
forms the basis of the method is given in Appendix A. A few integrals
that have been evaluated using the method are presented in Appendix
B. A more thorough development and explanation of the method is given
in Piquette, in review (b)."
}
\end{chunk}
\index{Clarkson, M.}
\begin{chunk}{axiom.bib}
@article{Clar89,
author = "Clarkson, M.",
title = "MACSYMA's inverse Laplace transform",
journal = "ACM SIGSAM Bulletin",
volume = "23",
number = "1",
year = "1989"
pages = "3338",
abstract =
"The inverse Laplace transform capability of MACSYMA has been improved
and extended. It has been extended to evaluate certain limits, sums,
derivatives and integrals of Laplace transforms. It also takes
advantage of the inverse Laplace transform convolution theorem, and
can deal with a wider range of symbolic parameters.",
paper = "Clar89.pdf"
}
\end{chunk}
\index{Schou, Wayne C.}
\index{Broughan, Kevin A.}
\begin{chunk}{axiom.bib}
@article{Scho89,
author = "Schou, Wayne C. and Broughan, Kevin A.",
title = "The Risch Algorithms of MACSYMA and SENAC",
journal = "ACM SIGSAM",
volume = "23",
number = "3",
year = "1989",
abstract =
"The purpose of this paper is to report on a computer implementation
of the Risch algorithm for the symbolic integration of rational
functions containing nested exponential and logarithms. For the class
of transcendental functions, the Risch algorithm [4] represents a
practical method for symbolic integration. Because the Risch algorithm
describes a decision procedure for transcendental integration it is an
ideal final step in an integration package. Although the decision
characteristic cannot be fully realised in a computer system, because
of major algebraic problems such as factorisation, zeroequivalence
and simplification, the potential advantages are considerable.",
paper = "Scho89.pdf",
}
\end{chunk}
\index{Smith, Paul}
\index{Sterling, Leon}
\begin{chunk}{axiom.bib}
@article{Smit83,
author = "Smith, Paul and Sterling, Leon",
title = "Of Integration by Man and Machine",
journal = "ACM SIGSAM",
volume = "17",
number = "34",
year = "1983",
abstract =
"We describe a symbolic integration problem arising from an
application in engineering. A solution is given and compared with the
solution generated by the REDUCE integration package running at
Cambridge. Nontrivial symbol manipulation, particularly
simplification, is necessary to reconcile the answers.",
paper = "Smit83.pdf"
}
\end{chunk}
\index{Renbao, Zhong}
\begin{chunk}{axiom.bib}
@article{Renb82,
author = "Renbao, Zhong",
title = "An Algorithm for Avoiding Complex Numbers in Rational Function
Integration",
journal = "ACM SIGSAM",
volume = "16",
number = "3",
pages = "3032",
year = "1982",
abstract =
"Given a proper rational function $A(x)/B(x)$ where $A(x)$ and $B(x)$
both are in $R[x]$ with $gcd(A(x), B(x))= 1$, $B(x)$ monic and
$deg(A(x)) < deg(B(x))$, from the Hermite algorithm for rational
function integration in [3], we obtain
\[\int{frac{A(x)}{B(x)}~dx = S(x)+\int{\frac{T(x)}{B^*(x)}~dx\]
where $S(x)$ is a rational function
which is called the rational part of the integral of $A(x)/B(x)$ in
eq. (1), $B^*(x)$ is the greatest squarefree factor of $B(x)$, and
$T(x)$ is in $R[x]$ with $deg(T(x)) < deg(B^*(x))$. The integral of
$T(x)/B^*(x)$ is called the transcendental part of the integral of
$A(x)/B(x)$ in eq. (1).",
paper = "Renb82.pdf"
}
\end{chunk}
\index{Davenport, James H.}
\begin{chunk}{axiom.bib}
@article{Dave82a,
author = "Davenport, Jamess H.",
title = "The Parallel Risch Algorithm (I)",
journal = "Lecture Notes in Computer Science",
volume = "144",
year = "1982",
abstract =
"In this paper we review the socalled ``parallel Risch'' algorithm for
the integration of transcendental functions, and explain what the
problems with it are. We prove a positive result in the case of
logarithmic integrands.",
paper = "Dave82a.pdf"
}
\end{chunk}
\index{Davenport, James H.}
\begin{chunk}{axiom.bib}
@article{Dave85b
author = "Davenport, Jamess H.",
title = "The Parallel Risch Algorithm (II)",
journal = "ACM TOMS",
volume = "11",
number = "4",
pages = "356362",
year = "1985",
abstract =
"It is proved that, under the usual restrictions, the denominator of
the integral of a purely logarithmic function is the expected one,
that is, all factors of the denominator of the integrand have their
multiplicity decreased by one. Furthermore, it is determined which new
logarithms may appear in the integration.",
paper = "Dave85b.pdf"
}
\end{chunk}
\index{Davenport, James H.}
\begin{chunk}{axiom.bib}
@article{Dave82b,
author = "Davenport, Jamess H.",
title = "The Parallel Risch Algorithm (III): use of tangents",
journal = "ACM SIGSAM",
volume = "16",
number = "3",
pages = "36",
year = "1982",
abstract =
"In this note, we look at the extension to the parallel Risch
algorithm (see, e.g., the papers by Norman & Moore [1977], Norman &
Davenport [1979], ffitch [1981] or Davenport [1982] for a description
of the basic algorithm) which represents trigonometric functions in
terms of tangents, rather than instead of complex exponentials.",
paper = "Dave82b.pdf"
}
\end{chunk}
\index{Kempelmann, Helmut}
\begin{chunk}{axiom.bib}
@article{Kemp81,
author = "Kempelmann, Helmut",
title = "Recursive Algorithm for the Fast Calculation of the Limit of
Derivatives at Points of Indeterminateness",
journal = "ACM SIGSAM",
volume = "15",
number = "4",
year = "1981",
pages = "1011",
abstract =
"It is a common method in probability and queueing theory to gain the
$n$th moment $E[x^n]$ of a random variable X
with density function $f_x(x)$
by the $n$th derivative of the corresponding Laplace transform $L(s)$ at
the point $s = 0$
\[E[x^n] = (1)^n\cdot L^{n}(O)\]
Quite often we encounter indetermined
expressions of the form $0/0$ which normally are treated by the rule of
L'Hospital. This is a time and memory consuming task requiring
greatest common divisor cancellations. This paper presents an
algorithm that calculates only those derivatives of numerator and
denominator which do not equal zero when taking the limit /1/. The
algorithm has been implemented in REDUCE /2/. It is simpler and more
efficient than that one proposed by /3/.",
paper = "Kemp81.pdf"
}
\end{chunk}
\index{Norfolk, Timothy S.}
\begin{chunk}{axiom.bib}
@article{Norf82,
author = "Norfolk, Timothy S.",
title = "Symbolic Computation of Residues at Poles and Essential
Singularities",
journal = "ACM SIGSAM",
volume = "16",
number = "1",
year = "1982",
pages = "1723",
abstract =
"Although most books on the theory of complex variables include a
classification of the types of isolated singularities, and the
applications of residue theory, very few concern themselves with
methods of computing residues. In this paper we derive some results on
the calculation of residues at poles, and some special classes of
essential singularities, with a view to implementing an algorithm in
the VAXIMA computer algebra system.",
paper = "Norf82.pdf"
}
\end{chunk}
\index{Belovari, G.}
\begin{chunk}{axiom.bib}
@article{Belo83,
author = "Belovari, G.",
title = "Complex Analysis in Symbolic Computing of some Definite Integrals",
journal = "ACM SIGSAM",
volume = "17",
number = "2",
year = "1983",
pages = "611",
paper = "Belo83.pdf"
}
\end{chunk}
\index{Wang, Paul S.}
\begin{chunk}{axiom.bib}
@phdthesis{Wang71,
author = "Wang, Paul S.",
title = "Evaluation of Definite Integrals by Symbolic Manipulation",
school = "MIT",
year = "1971",
link = "\url{http://publications.csail.mit.edu/lcs/pubs/pdf/MITLCSTR092.pdf}",
comment = "MIT/LCS/TR92",
abstract =
"A heuristic computer program for the evaluation of real definite
integrals of elementary functions is described This program, called
WANDERER, (WANg's DEfinite integRal EvaluatoR), evaluates many proper
and improper integrals. The improper integrals may have a finite or
infinite range of integration. Evaluation by contour integration and
residue theory is among the methods used. A program called DELIMITER
(DEfinitive LIMIT EvaluatoR) is used for the limit computations needed
in evaluating some definite integrals. DELIMITER is a heuristic
program written for computing limits of real or complex analytic
functions. For real functions of a real variable, onesided as well
been implmented in the MACSYMA system, a symbolic and algebraic
manipulation system being developed at Project MAC, MIT. A typical
problem in applied mathematics, namely asymptotic analysis of a
definite integral, is solved using MACSYMA to demonstrate the
usefulness of such a system and the facilities provided by WANDERER."
paper = "Wang71.pdf"
}
\end{chunk}
\index{Harrington, Steven J.}
\begin{chunk}{axiom.bib}
@article{Harr79,
author = "Harrington, Steven J.",
title = "A Symbolic Limit Evaluation Program in REDUCE",
journal = "ACM SIGSAM",
volume = "13",
number = "1",
year = "1979",
pages = "2731",
abstract =
"A method for the automatic evaluation of algebraic limits is
described. It combines many of the techniques previously employed,
including topdown recursive evaluation, power series expansion, and
L'Hôpital's rule. It introduces the concept of a special algebraic
form for limits. The method has been implemented in MODEREDUCE.",
paper = "Harr79.pdf"
}
\end{chunk}
\index{Norton, Lewis M.}
\begin{chunk}{axiom.bib}
@article{Nort80,
author = "Norton, Lewis M.",
title = "A Note about Laplace Transform Tables for Computer use",
journal = "ACM SIGSAM",
volume = "14",
number = "2",
year = "1980",
pages = "3031",
abstract =
"The purpose of this note is to give another illustration of the fact
that the best way for a human being to represent or process
information is not necessarily the best way for a computer. The
example concerns the use of a table of inverse Laplace transforms
within a program, written in the REDUCE language [1] for symbolic
algebraic manipulation, which solves linear ordinary differential
equations with constant coefficients using Laplace transform
methods. (See [2] for discussion of an earlier program which solved
such equations.)",
paper = "Nort80.pdf"
}
\end{chunk}
\index{Stoutemyer, David R.}
\begin{chunk}{axiom.bib}
@article{Stou76,
author = "Stoutemyer, David R.",
title = "Automatic Simplification for the Absolutevalue Function and its
Relatives",
journal = "ACM SIGSAM",
volume = "10",
number = "4",
year = "1976",
pages = "4849",
abstract =
"Computer symbolic mathematics has made impressive progress for the
automatic simplification of rational expressions, algebraic
expressions, and elementary transcendental expressions. However,
existing computeralgebra systems tend to provide little or no
simplification for the absolutevalue function or for its relatives
such as the signum, unit ramp, unit step, max, min, modulo, and Dirac
delta functions. Although these functions lack certain desireable
properties that are helpful for canonical simplification, there are
opportunities for some ad hoc simplification. Moreover, a perusal of
most mathematics, engineering, and scientific journals or texts
reveals that these functions are too prevalent to be ignored.This
article describes specific simplification rules implemented in a
program that supplements the builtin rules for the MACSYMA ABS and
SIGNUM functions.",
paper = "Stou76.pdf"
}
\end{chunk}
\index{Kanoui, Henry}
\begin{chunk}{axiom.bib}
@article{Kano76,
author = "Kanoui, Henry",
title = "Some Aspects of Symbolic Integration via Predicate Logic
Programming",
journal = "ACM SIGSAM",
volume = "10",
number = "4",
year = "1976",
pages = "2942",
abstract =
"During the past years, various algebraic manipulations systems have
been described in the literature. Most of them are implemented via
``classic'' programming languages like Fortran, Lisp, PL1 ... We propose
an alternative approach: the use of Predicate Logic as a programming
language.",
paper = "Kano76.pdf"
}
\end{chunk}
\index{Gentleman, W. Morven}
\begin{chunk}{axiom.bib}
@article{Gent74,
author = "Gentleman, W. Morven",
title = "Experience with Truncated Power Series",
journal = "ACM SIGSAM",
volume = "8",
number = "3",
year = "1974",
pages = "6162",
abstract =
"The truncated power series package in ALTRAN has been available for
over a year now, and it has proved itself to be a useful and exciting
addition to the armoury of symbolic algebra. A wide variety of
problems have been attacked with this tool: moreover, through use in
the classroom, we have had the opportunity to observe how a large
number of people react to the availability of this tool.",
paper = "Gent74.pdf"
}
\end{chunk}
\index{Loos, Rudiger}
\begin{chunk}{Loos72a,
@article{Loos72a,
author = "Loos, Rudiger",
title = "Analytic Treatment of Three Similar Fredholm Integral Equations
of the second kind with REDUCE 2",
journal = "ACM SIGSAM",
volume = "21",
year = "1972",
pages = "3240"
}
\end{chunk}
\index{Collins, George E.}
\begin{chunk}{axiom.bib}
@article{Coll69,
author = "Collins, George E.",
title = "Algorithmic Approaches to Symbolic Integration and SImplification",
journal = "ACM SIGSAM",
volume = "12",
year = "1969",
pages = "5016",
abstract =
"This panel session followed the format announced by SIGSAM Chairman
Carl Engelman in the announcement published in SIGSAM Bulletin No. 10
(October 1968). Carl gave a brief (five or ten minutes) introduction
to the subject and introduced Professor Joel Moses (M. I. T.). Joel
presented an excellent exposition of the recent research
accomplishments of the other panel members, synthesizing their work
into a single large comprehensible picture. His presentation was
greatly enhanced by a series of 27 carefully prepared slides
containing critical examples and basic formulas, and was certainly the
feature of the show. A panel discussion followed, with some audience
participation. Panel members were Dr. W. S. Brown (Bell Telephone
Laboratories), Professor B. F. Caviness (Duke University), Dr. Daniel
Richardson and Dr. R. H. Risch (IBM).",
paper = "Coll69.pdf"
}
\end{chunk}
\index{Kasper, Toni}
\begin{chunk}{axiom.bib}
@article{Kasp80,
author = "Kasper, Toni",
title = "Integration in Finite Terms: The Liouville Theory",
journal = "ACM SIGSAM",
volume = "14",
number = "4",
year = "1980",
pages = "28",
abstract =
"The search for elementary antiderivatives leads from classical
analysis through modern algebra to contemporary research in computer
algorithms.",
paper = "Kasp80.pdf"
}
\end{chunk}
\index{Munroe, M.E.}
\begin{chunk}{axiom.bib}
@book{Munr53,
author = "Munroe, M.E.",
title = "Introduction to Measure and Integration",
publisher = "AddisonWesley",
year = "1953"
}
\end{chunk}
\index{Hardy, G.}
\index{Littlewood, J.E.}
\index{Polya, G.}
\begin{chunk}{axiom.bib}
@book{Hard64,
author = "Hardy, G. and Littlewood, J.E. and Polya, G.",
title = "Inequalities",
publisher = "Cambridge University Press",
year = "1964"
}
\end{chunk}
\index{Baddoura, Jamil}
\begin{chunk}{axiom.bib}
@article{Badd06,
author = "Baddoura, Jamil",
title = "Integration in Finite Terms with Elementary Functions and
Dilogarithms",
journal = "J. Symbolic Computation",
volume = "41",
number = "8",
year = "2006",
pages = "909942",
abstract =
"In this paper, we report on a new theorem that generalizes
Liouville’s theorem on integration in finite terms. The new theorem
allows dilogarithms to occur in the integral in addition to
transcendental elementary functions. The proof is based on two
identities for the dilogarithm, that characterize all the possible
algebraic relations among dilogarithms of functions that are built up
from the rational functions by taking transcendental exponentials,
dilogarithms, and logarithms. This means that we assume the integral
lies in a transcendental tower.",
paper = "Badd06.pdf"
}
\end{chunk}
\index{Kahan, William}
\begin{chunk}{axiom.bib}
@misc{Kaha90,
author = "Kahan, William",
title = "The Persistence of Irrationals in Some Integrals",
year = "1990",
abstract =
"Computer algebra systems are expected to simplify formulas they
obtain for symbolic integrals whenever they can, and often they
succeed. However, the formulas so obtained may then produce incorrect
results for symblic definite integrals"
}
\end{chunk}

books/bookvolbib.pamphlet  789 ++++++++++++++++++++++++++++++++
changelog  2 +
patch  946 +++++++++++++++++++++++++
src/axiomwebsite/patches.html  2 +
4 files changed, 1340 insertions(+), 399 deletions()
diff git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index 0f84aa9..aa5edc0 100644
 a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ 4708,6 +4708,21 @@ when shown in factored form.
\section{Algebraic Algorithms} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\index{Belovari, G.}
+\begin{chunk}{axiom.bib}
+@article{Belo83,
+ author = "Belovari, G.",
+ title = "Complex Analysis in Symbolic Computing of some Definite Integrals",
+ journal = "ACM SIGSAM",
+ volume = "17",
+ number = "2",
+ year = "1983",
+ pages = "611",
+ paper = "Belo83.pdf"
+}
+
+\end{chunk}
+
\index{Brown, W. S.}
\begin{chunk}{axiom.bib}
@article{Brow78,
@@ 5009,6 +5024,19 @@ when shown in factored form.
\end{chunk}
+\index{Hardy, G.}
+\index{Littlewood, J.E.}
+\index{Polya, G.}
+\begin{chunk}{axiom.bib}
+@book{Hard64,
+ author = "Hardy, G. and Littlewood, J.E. and Polya, G.",
+ title = "Inequalities",
+ publisher = "Cambridge University Press",
+ year = "1964"
+}
+
+\end{chunk}
+
\index{Kaltofen, Erich}
\begin{chunk}{axiom.bib}
@InCollection{Kalt87a,
@@ 5042,6 +5070,75 @@ when shown in factored form.
\end{chunk}
+\index{Kempelmann, Helmut}
+\begin{chunk}{axiom.bib}
+@article{Kemp81,
+ author = "Kempelmann, Helmut",
+ title = "Recursive Algorithm for the Fast Calculation of the Limit of
+ Derivatives at Points of Indeterminateness",
+ journal = "ACM SIGSAM",
+ volume = "15",
+ number = "4",
+ year = "1981",
+ pages = "1011",
+ abstract =
+ "It is a common method in probability and queueing theory to gain the
+ $n$th moment $E[x^n]$ of a random variable $X$
+ with density function $f_x(x)$
+ by the $n$th derivative of the corresponding Laplace transform $L(s)$ at
+ the point $s = 0$
+ \[E[x^n] = (1)^n\cdot L^{n}(O)\]
+ Quite often we encounter indetermined
+ expressions of the form $0/0$ which normally are treated by the rule of
+ L'Hospital. This is a time and memory consuming task requiring
+ greatest common divisor cancellations. This paper presents an
+ algorithm that calculates only those derivatives of numerator and
+ denominator which do not equal zero when taking the limit /1/. The
+ algorithm has been implemented in REDUCE /2/. It is simpler and more
+ efficient than that one proposed by /3/.",
+ paper = "Kemp81.pdf"
+}
+
+\end{chunk}
+
+\index{Loos, Rudiger}
+\begin{chunk}{axiom.bib}
+@article{Loos72a,
+ author = "Loos, Rudiger",
+ title = "Analytic Treatment of Three Similar Fredholm Integral Equations
+ of the second kind with REDUCE 2",
+ journal = "ACM SIGSAM",
+ volume = "21",
+ year = "1972",
+ pages = "3240"
+}
+
+\end{chunk}
+
+\index{Norfolk, Timothy S.}
+\begin{chunk}{axiom.bib}
+@article{Norf82,
+ author = "Norfolk, Timothy S.",
+ title = "Symbolic Computation of Residues at Poles and Essential
+ Singularities",
+ journal = "ACM SIGSAM",
+ volume = "16",
+ number = "1",
+ year = "1982",
+ pages = "1723",
+ abstract =
+ "Although most books on the theory of complex variables include a
+ classification of the types of isolated singularities, and the
+ applications of residue theory, very few concern themselves with
+ methods of computing residues. In this paper we derive some results on
+ the calculation of residues at poles, and some special classes of
+ essential singularities, with a view to implementing an algorithm in
+ the VAXIMA computer algebra system.",
+ paper = "Norf82.pdf"
+}
+
+\end{chunk}
+
\index{Platzer, Andre}
\index{Quesel, JanDavid}
\index{Rummer, Philipp}
@@ 8527,6 +8624,54 @@ when shown in factored form.
\end{chunk}
+\index{Baddoura, Jamil}
+\begin{chunk}{axiom.bib}
+@article{Badd06,
+ author = "Baddoura, Jamil",
+ title = "Integration in Finite Terms with Elementary Functions and
+ Dilogarithms",
+ journal = "J. Symbolic Computation",
+ volume = "41",
+ number = "8",
+ year = "2006",
+ pages = "909942",
+ abstract =
+ "In this paper, we report on a new theorem that generalizes
+ Liouville’s theorem on integration in finite terms. The new theorem
+ allows dilogarithms to occur in the integral in addition to
+ transcendental elementary functions. The proof is based on two
+ identities for the dilogarithm, that characterize all the possible
+ algebraic relations among dilogarithms of functions that are built up
+ from the rational functions by taking transcendental exponentials,
+ dilogarithms, and logarithms. This means that we assume the integral
+ lies in a transcendental tower.",
+ paper = "Badd06.pdf"
+}
+
+\end{chunk}
+
+\index{Barnett, Michael P.}
+\begin{chunk}{axiom.bib}
+@article{Barn89,
+ author = "Barnett, Michael P.",
+ title = "Using Partial Fraction Formulas to Sum some slowly convergent
+ series analytically for molecular integral calculations",
+ journal = "ACM SIGSAM",
+ volume = "23",
+ number = "3",
+ year = "1989",
+ abstract =
+ "Two sets of rational expressions, needed for quantum chemical
+ calculations, have been constructed by mechanical application of
+ partial fraction and polynomial operations on a CYBER 205. The
+ algorithms were coded in FORTRAN, using simple array manipulation. The
+ results suggest extensions that could be tackled with general
+ algebraic manipulation programs.",
+ paper = "Barn89.pdf"
+}
+
+\end{chunk}
+
\index{Bertrand, Laurent}
\begin{chunk}{axiom.bib}
@inproceedings{Bert94,
@@ 8548,6 +8693,27 @@ when shown in factored form.
\end{chunk}
+\index{Clarkson, M.}
+\begin{chunk}{axiom.bib}
+@article{Clar89,
+ author = "Clarkson, M.",
+ title = "MACSYMA's inverse Laplace transform",
+ journal = "ACM SIGSAM Bulletin",
+ volume = "23",
+ number = "1",
+ year = "1989",
+ pages = "3338",
+ abstract =
+ "The inverse Laplace transform capability of MACSYMA has been improved
+ and extended. It has been extended to evaluate certain limits, sums,
+ derivatives and integrals of Laplace transforms. It also takes
+ advantage of the inverse Laplace transform convolution theorem, and
+ can deal with a wider range of symbolic parameters.",
+ paper = "Clar89.pdf"
+}
+
+\end{chunk}
+
\index{Corless, Robert M.}
\index{Jeffrey, David J.}
\index{Watt, Stephen M.}
@@ 8574,6 +8740,18 @@ when shown in factored form.
\end{chunk}
+\index{Erd\'elyi, A.}
+\begin{chunk}{axiom.bib}
+@book{Erde56,
+ author = {Erd\'elyi, A.},
+ title = "Asymptotic Expansions",
+ year = "1956",
+ isbn = "9780486155050",
+ publisher = "Dover Publications"
+}
+
+\end{chunk}
+
\index{Ng, Edward W.}
\index{Geller, Murray}
\begin{chunk}{ignore}
@@ 8589,6 +8767,53 @@ when shown in factored form.
\end{chunk}
+\index{Norton, Lewis M.}
+\begin{chunk}{axiom.bib}
+@article{Nort80,
+ author = "Norton, Lewis M.",
+ title = "A Note about Laplace Transform Tables for Computer use",
+ journal = "ACM SIGSAM",
+ volume = "14",
+ number = "2",
+ year = "1980",
+ pages = "3031",
+ abstract =
+ "The purpose of this note is to give another illustration of the fact
+ that the best way for a human being to represent or process
+ information is not necessarily the best way for a computer. The
+ example concerns the use of a table of inverse Laplace transforms
+ within a program, written in the REDUCE language [1] for symbolic
+ algebraic manipulation, which solves linear ordinary differential
+ equations with constant coefficients using Laplace transform
+ methods. (See [2] for discussion of an earlier program which solved
+ such equations.)",
+ paper = "Nort80.pdf"
+}
+
+\end{chunk}
+
+\index{Piquette, J. C.}
+\begin{chunk}{axiom.bib}
+@article{Piqu89,
+ author = "Piquette, J. C.",
+ title = "Special Function Integration",
+ journal = "ACM SIGSAM Bulletin",
+ volume = "23",
+ number = "2",
+ year = "1989",
+ pages = "1121",
+ abstract =
+ "This article describes a method by which the integration capabilities
+ of symbolicmathematics computer programs can be extended to include
+ integrals that contain special functions. A summary of the theory that
+ forms the basis of the method is given in Appendix A. A few integrals
+ that have been evaluated using the method are presented in Appendix
+ B. A more thorough development and explanation of the method is given
+ in Piquette, in review (b)."
+}
+
+\end{chunk}
+
\section{Exponential Integral $E_1(x)$} %%%%%%%%%%%%%%%%%%%%%%%%%
\index{Geller, Murray}
@@ 13510,38 +13735,59 @@ J. Symbolic COmputations 36 pp 855889
\end{chunk}
\section{Integration} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\index{Bronstein, Manuel}
+\index{Shackell, John}
\begin{chunk}{axiom.bib}
@misc{Bronxxa,
 author = "Bronstein, Manuel",
 title = "Symbolic Integration: towards Practical Algorithms",
+@article{Shac90,
+ author = "Shackell, John",
+ title = "Growth Estimates for ExpLog Functions",
+ journal = "J. Symbolic Computation",
+ volume = "10",
+ pages = "611632",
abstract =
 "After reviewing the Risch algorithm for the integration of elementary
 functions and the underlying theory, we descrbe the successive
 improvements in the field, and the current ``rational'' approach to
 symbolic integration. We describe how a technique discovered by
 Hermite a century ago can be efficiently applied to rational,
 algebraic, elementary transcendental and mixed elementary functions."
+ "Explog functions are those obtained from the constant 1 and the
+ variable X by means of arithmetic operations and the function symbols
+ exp() and log(). This paper gives an explicit algorithm for
+ determining eventual dominance of these functions modulo an oracle for
+ deciding zero equivalence of constant terms. This also provides
+ another proof that the dominance problem for explog functions is
+ Turingreducible to the identity problem for constant terms."
}
\end{chunk}
\index{Kaltofen, Erich}
+\index{Stoutemyer, David R.}
\begin{chunk}{axiom.bib}
@TechReport{Kalt84b,
 author = "Kaltofen, E.",
 title = "The Algebraic Theory of Integration",
 institution = "RPI",
 address = "Dept. Comput. Sci., Troy, New York",
 year = "1984",
 link = "\url{http://www.math.ncsu.edu/~kaltofen/bibliography/84/Ka84_integration.pdf}",
 paper = "Kalt84b.pdf"
+@article{Stou76,
+ author = "Stoutemyer, David R.",
+ title = "Automatic Simplification for the Absolutevalue Function and its
+ Relatives",
+ journal = "ACM SIGSAM",
+ volume = "10",
+ number = "4",
+ year = "1976",
+ pages = "4849",
+ abstract =
+ "Computer symbolic mathematics has made impressive progress for the
+ automatic simplification of rational expressions, algebraic
+ expressions, and elementary transcendental expressions. However,
+ existing computeralgebra systems tend to provide little or no
+ simplification for the absolutevalue function or for its relatives
+ such as the signum, unit ramp, unit step, max, min, modulo, and Dirac
+ delta functions. Although these functions lack certain desireable
+ properties that are helpful for canonical simplification, there are
+ opportunities for some ad hoc simplification. Moreover, a perusal of
+ most mathematics, engineering, and scientific journals or texts
+ reveals that these functions are too prevalent to be ignored.This
+ article describes specific simplification rules implemented in a
+ program that supplements the builtin rules for the MACSYMA ABS and
+ SIGNUM functions.",
+ paper = "Stou76.pdf"
}
\end{chunk}
+\section{Integration} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
\index{Adamchik, Victor}
\begin{chunk}{ignore}
\bibitem[Adamchik xx]{Adamxx} Adamchik, Victor
@@ 13659,6 +13905,45 @@ J. Math Vol 8 pp229241 (2011)
\end{chunk}
\index{Bronstein, Manuel}
+\begin{chunk}{axiom.bib}
+@misc{Bronxxa,
+ author = "Bronstein, Manuel",
+ title = "Symbolic Integration: towards Practical Algorithms",
+ abstract =
+ "After reviewing the Risch algorithm for the integration of elementary
+ functions and the underlying theory, we descrbe the successive
+ improvements in the field, and the current ``rational'' approach to
+ symbolic integration. We describe how a technique discovered by
+ Hermite a century ago can be efficiently applied to rational,
+ algebraic, elementary transcendental and mixed elementary functions."
+}
+
+\end{chunk}
+
+\index{Bronstein, Manuel}
+\begin{chunk}{axiom.bib}
+@article{Bron88,
+ author = "Bronstein, Manuel",
+ title = "The Transcendental Risch Differential Equation",
+ journal = "J. Symbolic Computation",
+ volume = "9",
+ year = "1988",
+ pages = "4960",
+ abstract =
+ "We present a new rational algorithm for solving Risch differential
+ equations in towers of transcendental elementary extensions. In
+ contrast to a recent algorithm of Davenport we do not require a
+ progressive reduction of the denominators involved, but use weak
+ normality to obtain a formula for the denominator of a possible
+ solution. Implementation timings show this approach to be faster than
+ a Hermitelike reduction.",
+ paper = "Bron88.pdf",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Bronstein, Manuel}
\begin{chunk}{ignore}
\bibitem[Bronstein 89]{Bro89a} Bronstein, M.
title = "An Algorithm for the Integration of Elementary Functions",
@@ 14008,6 +14293,34 @@ SIAM J. Computing Vol 18 pp 893905 (1989)
\end{chunk}
+\index{Collins, George E.}
+\begin{chunk}{axiom.bib}
+@article{Coll69,
+ author = "Collins, George E.",
+ title = "Algorithmic Approaches to Symbolic Integration and SImplification",
+ journal = "ACM SIGSAM",
+ volume = "12",
+ year = "1969",
+ pages = "5016",
+ abstract =
+ "This panel session followed the format announced by SIGSAM Chairman
+ Carl Engelman in the announcement published in SIGSAM Bulletin No. 10
+ (October 1968). Carl gave a brief (five or ten minutes) introduction
+ to the subject and introduced Professor Joel Moses (M. I. T.). Joel
+ presented an excellent exposition of the recent research
+ accomplishments of the other panel members, synthesizing their work
+ into a single large comprehensible picture. His presentation was
+ greatly enhanced by a series of 27 carefully prepared slides
+ containing critical examples and basic formulas, and was certainly the
+ feature of the show. A panel discussion followed, with some audience
+ participation. Panel members were Dr. W. S. Brown (Bell Telephone
+ Laboratories), Professor B. F. Caviness (Duke University), Dr. Daniel
+ Richardson and Dr. R. H. Risch (IBM).",
+ paper = "Coll69.pdf"
+}
+
+\end{chunk}
+
\index{Davenport, James H.}
\begin{chunk}{axiom.bib}
@book{Dave81,
@@ 14042,23 +14355,64 @@ Lecture Notes in Computer Science V 72 pp415425 (1979)
\end{chunk}
\index{Davenport, James H.}
\begin{chunk}{ignore}
\bibitem[Davenport 82a]{Dav82a} Davenport, J.H.
 title = "The Parallel Risch Algorithm (I)"
 abstract = "
 In this paper we review the socalled ``parallel Risch'' algorithm for
+\begin{chunk}{axiom.bib}
+@article{Dave82a,
+ author = "Davenport, Jamess H.",
+ title = "The Parallel Risch Algorithm (I)",
+ journal = "Lecture Notes in Computer Science",
+ volume = "144",
+ pages = "144157",
+ year = "1982",
+ abstract =
+ "In this paper we review the socalled ``parallel Risch'' algorithm for
the integration of transcendental functions, and explain what the
problems with it are. We prove a positive result in the case of
logarithmic integrands.",
 paper = "Dav82a.pdf"
+ paper = "Dave82a.pdf"
+}
\end{chunk}
\index{Davenport, James H.}
\begin{chunk}{ignore}
\bibitem[Davenport 82]{Dav82} Davenport, J.H.
 title = "On the Parallel Risch Algorithm (III): Use of Tangents",
SIGSAM V16 no. 3 pp36 August 1982
+\index{Trager, Barry M.}
+\begin{chunk}{axiom.bib}
+@article{Dave85b,
+ author = "Davenport, Jamess H. and Trager, Barry M.",
+ title = "The Parallel Risch Algorithm (II)",
+ journal = "ACM TOMS",
+ volume = "11",
+ number = "4",
+ pages = "356362",
+ year = "1985",
+ abstract =
+ "It is proved that, under the usual restrictions, the denominator of
+ the integral of a purely logarithmic function is the expected one,
+ that is, all factors of the denominator of the integrand have their
+ multiplicity decreased by one. Furthermore, it is determined which new
+ logarithms may appear in the integration.",
+ paper = "Dave85b.pdf"
+}
+
+\end{chunk}
+
+\index{Davenport, James H.}
+\begin{chunk}{axiom.bib}
+@article{Dave82b,
+ author = "Davenport, Jamess H.",
+ title = "The Parallel Risch Algorithm (III): use of tangents",
+ journal = "ACM SIGSAM",
+ volume = "16",
+ number = "3",
+ pages = "36",
+ year = "1982",
+ abstract =
+ "In this note, we look at the extension to the parallel Risch
+ algorithm (see, e.g., the papers by Norman and Moore [1977], Norman and
+ Davenport [1979], ffitch [1981] or Davenport [1982] for a description
+ of the basic algorithm) which represents trigonometric functions in
+ terms of tangents, rather than instead of complex exponentials.",
+ paper = "Dave82b.pdf"
+}
\end{chunk}
@@ 14129,6 +14483,20 @@ Algorithms for Computer Algebra, Ch 12 pp511573 (1992)
\end{chunk}
+\index{Gradshteyn, I.S.}
+\index{Ryzhik, I.M.}
+\begin{chunk}{axiom.bib}
+@incollection{Grad80,
+ author = "Gradshteyn, I.S. and Ryzhik, I.M.",
+ title = "Definite Integrals of Elementary Functions",
+ booktitle = "Table of Integrals, Series, and Products",
+ publisher = "Academic Press",
+ year = "1980",
+ comment = "Chapter 34"
+}
+
+\end{chunk}
+
\index{Hardy, G.H.}
\begin{chunk}{ignore}
\bibitem[Hardy 1916]{Hard16} Hardy, G.H.
@@ 14273,11 +14641,82 @@ Rich, A.D.
\end{chunk}
+\index{Kahan, William}
+\begin{chunk}{axiom.bib}
+@misc{Kaha90,
+ author = "Kahan, William",
+ title = "The Persistence of Irrationals in Some Integrals",
+ year = "1990",
+ abstract =
+ "Computer algebra systems are expected to simplify formulas they
+ obtain for symbolic integrals whenever they can, and often they
+ succeed. However, the formulas so obtained may then produce incorrect
+ results for symblic definite integrals"
+}
+
+\end{chunk}
+
+\index{Kaltofen, Erich}
+\begin{chunk}{axiom.bib}
+@TechReport{Kalt84b,
+ author = "Kaltofen, E.",
+ title = "The Algebraic Theory of Integration",
+ institution = "RPI",
+ address = "Dept. Comput. Sci., Troy, New York",
+ year = "1984",
+ link = "\url{http://www.math.ncsu.edu/~kaltofen/bibliography/84/Ka84_integration.pdf}",
+ paper = "Kalt84b.pdf"
+}
+
+\end{chunk}
+
+\index{Kanoui, Henry}
+\begin{chunk}{axiom.bib}
+@article{Kano76,
+ author = "Kanoui, Henry",
+ title = "Some Aspects of Symbolic Integration via Predicate Logic
+ Programming",
+ journal = "ACM SIGSAM",
+ volume = "10",
+ number = "4",
+ year = "1976",
+ pages = "2942",
+ abstract =
+ "During the past years, various algebraic manipulations systems have
+ been described in the literature. Most of them are implemented via
+ ``classic'' programming languages like Fortran, Lisp, PL1 ... We propose
+ an alternative approach: the use of Predicate Logic as a programming
+ language.",
+ paper = "Kano76.pdf"
+}
+
+\end{chunk}
+
+\index{Kasper, Toni}
+\begin{chunk}{axiom.bib}
+@article{Kasp80,
+ author = "Kasper, Toni",
+ title = "Integration in Finite Terms: The Liouville Theory",
+ journal = "ACM SIGSAM",
+ volume = "14",
+ number = "4",
+ year = "1980",
+ pages = "28",
+ abstract =
+ "The search for elementary antiderivatives leads from classical
+ analysis through modern algebra to contemporary research in computer
+ algorithms.",
+ paper = "Kasp80.pdf"
+}
+
+\end{chunk}
+
\index{Kiymaz, Onur}
\index{Mirasyedioglu, Seref}
\begin{chunk}{ignore}
\bibitem[Kiymaz 04]{Kiym04} Kiymaz, Onur; Mirasyedioglu, Seref
 title = "A new symbolic computation for formal integration with exact power series",
+ title = "A new symbolic computation for formal integration with exact
+ power series",
abstract = "
This paper describes a new symbolic algorithm for formal integration
of a class of functions in the context of exact power series by using
@@ 14510,6 +14949,17 @@ College Mathematics Journal Vol 25 No 4 (1994) pp295308
\end{chunk}
+\index{Munroe, M.E.}
+\begin{chunk}{axiom.bib}
+@book{Munr53,
+ author = "Munroe, M.E.",
+ title = "Introduction to Measure and Integration",
+ publisher = "AddisonWesley",
+ year = "1953"
+}
+
+\end{chunk}
+
\index{Moses, Joel}
\begin{chunk}{ignore}
\bibitem[Moses 76]{Mos76} Moses, Joel
@@ 14552,6 +15002,41 @@ CACM Aug 1971 Vol 14 No 8 pp548560
\index{Ng, Edward W.}
\begin{chunk}{axiom.bib}
+@article{Ngxx74,
+ author = "Ng, Edward W.",
+ title = "Symbolic Integration of a Class of Algebraic Functions",
+ journal = "ACM SIGSAM",
+ volume = "8",
+ number = "3",
+ year = "1974",
+ pages = "99102",
+ abstract =
+ "In this presentation we describe the outline of an algorithmic
+ approach to handle a class of algebraic integrands. (It is important
+ to stress that for an extended abstract of the present form, we can at
+ best convey the flavor of the approach, with numerous details
+ missing.) We shall label this approach Carlson's algorithm because it
+ is based on a series of analyses rendered by Carlson and his
+ associates in the last ten years (Refs. 2, 3, 4, 8, and 12). The class
+ of integrands is of the form $r(x,y)$, where $y^2$ is a polynomial in $x$,
+ and $r$ a rational function in $x$ and $y$. This is the type of integrand
+ that classically led to the study of elliptic integrals. At first
+ glance this is a rather restricted class of algebraic functions. But
+ in fact many trigonometric and hyperbolic integrands reduce to this
+ form. The richness of this class of integrands is exemplified by a
+ recently published handbook of 3000 integral formulas (Ref. 1). Our
+ proposed approach will cover fifty to seventy percent of the items in
+ the handbook. Furthermore the nonclassical approach we shall describe
+ holds great promise of developing to the case where definite integrals
+ can be evaluated in terms of a host of other wellknown functions
+ (e.g., Bessel and Legendre).",
+ paper = "Ngxx74.pdf"
+}
+
+\end{chunk}
+
+\index{Ng, Edward W.}
+\begin{chunk}{axiom.bib}
@techreport{Ngxx77,
author = "Ng, Edward W.",
title = "Observations on Approximate Integrations",
@@ 14751,6 +15236,34 @@ Comm. Math. Helv., Vol 18 pp 283308, (1946)
\end{chunk}
+\index{Renbao, Zhong}
+\begin{chunk}{axiom.bib}
+@article{Renb82,
+ author = "Renbao, Zhong",
+ title = "An Algorithm for Avoiding Complex Numbers in Rational Function
+ Integration",
+ journal = "ACM SIGSAM",
+ volume = "16",
+ number = "3",
+ pages = "3032",
+ year = "1982",
+ abstract =
+ "Given a proper rational function $A(x)/B(x)$ where $A(x)$ and $B(x)$
+ both are in $R[x]$ with $gcd(A(x), B(x))= 1$, $B(x)$ monic and
+ $deg(A(x)) < deg(B(x))$, from the Hermite algorithm for rational
+ function integration in [3], we obtain
+ \[\int{frac{A(x)}{B(x)}~dx} = S(x)+\int{\frac{T(x)}{B^*(x)}~dx}\]
+ where $S(x)$ is a rational function
+ which is called the rational part of the integral of $A(x)/B(x)$ in
+ eq. (1), $B^*(x)$ is the greatest squarefree factor of $B(x)$, and
+ $T(x)$ is in $R[x]$ with $deg(T(x)) < deg(B^*(x))$. The integral of
+ $T(x)/B^*(x)$ is called the transcendental part of the integral of
+ $A(x)/B(x)$ in eq. (1).",
+ paper = "Renb82.pdf"
+}
+
+\end{chunk}
+
\index{Rich, Albert D.}
\index{Jeffrey, David J.}
\begin{chunk}{ignore}
@@ 14997,6 +15510,32 @@ SIAM J. Computing Vol 8 No 3 (1979)
\end{chunk}
+\index{Schou, Wayne C.}
+\index{Broughan, Kevin A.}
+\begin{chunk}{axiom.bib}
+@article{Scho89,
+ author = "Schou, Wayne C. and Broughan, Kevin A.",
+ title = "The Risch Algorithms of MACSYMA and SENAC",
+ journal = "ACM SIGSAM",
+ volume = "23",
+ number = "3",
+ year = "1989",
+ abstract =
+ "The purpose of this paper is to report on a computer implementation
+ of the Risch algorithm for the symbolic integration of rational
+ functions containing nested exponential and logarithms. For the class
+ of transcendental functions, the Risch algorithm [4] represents a
+ practical method for symbolic integration. Because the Risch algorithm
+ describes a decision procedure for transcendental integration it is an
+ ideal final step in an integration package. Although the decision
+ characteristic cannot be fully realised in a computer system, because
+ of major algebraic problems such as factorisation, zeroequivalence
+ and simplification, the potential advantages are considerable.",
+ paper = "Scho89.pdf",
+}
+
+\end{chunk}
+
\index{Seidenberg, Abraham}
\begin{chunk}{ignore}
\bibitem[Seidenberg 58]{Sei58} Seidenberg, Abraham
@@ 15053,6 +15592,27 @@ Ph.D Diss. MIT, May 1961; also Computers and Thought, Feigenbaum and Feldman.
\end{chunk}
+\index{Smith, Paul}
+\index{Sterling, Leon}
+\begin{chunk}{axiom.bib}
+@article{Smit83,
+ author = "Smith, Paul and Sterling, Leon",
+ title = "Of Integration by Man and Machine",
+ journal = "ACM SIGSAM",
+ volume = "17",
+ number = "34",
+ year = "1983",
+ abstract =
+ "We describe a symbolic integration problem arising from an
+ application in engineering. A solution is given and compared with the
+ solution generated by the REDUCE integration package running at
+ Cambridge. Nontrivial symbol manipulation, particularly
+ simplification, is necessary to reconcile the answers.",
+ paper = "Smit83.pdf"
+}
+
+\end{chunk}
+
\index{Temme, N.M.}
\begin{chunk}{axiom.bib}
@misc{Temmxx,
@@ 15205,6 +15765,37 @@ MIT Master's Thesis.
\end{chunk}
+\index{Wang, Paul S.}
+\begin{chunk}{axiom.bib}
+@phdthesis{Wang71,
+ author = "Wang, Paul S.",
+ title = "Evaluation of Definite Integrals by Symbolic Manipulation",
+ school = "MIT",
+ year = "1971",
+ link =
+ "\url{http://publications.csail.mit.edu/lcs/pubs/pdf/MITLCSTR092.pdf}",
+ comment = "MIT/LCS/TR92",
+ abstract =
+ "A heuristic computer program for the evaluation of real definite
+ integrals of elementary functions is described This program, called
+ WANDERER, (WANg's DEfinite integRal EvaluatoR), evaluates many proper
+ and improper integrals. The improper integrals may have a finite or
+ infinite range of integration. Evaluation by contour integration and
+ residue theory is among the methods used. A program called DELIMITER
+ (DEfinitive LIMIT EvaluatoR) is used for the limit computations needed
+ in evaluating some definite integrals. DELIMITER is a heuristic
+ program written for computing limits of real or complex analytic
+ functions. For real functions of a real variable, onesided as well
+ been implmented in the MACSYMA system, a symbolic and algebraic
+ manipulation system being developed at Project MAC, MIT. A typical
+ problem in applied mathematics, namely asymptotic analysis of a
+ definite integral, is solved using MACSYMA to demonstrate the
+ usefulness of such a system and the facilities provided by WANDERER.",
+ paper = "Wang71.pdf"
+}
+
+\end{chunk}
+
\index{W\"urfl, Andreas}
\begin{chunk}{ignore}
\bibitem[W\"urfl 07]{Wurf07} W\"urfl, Andreas
@@ 21594,6 +22185,49 @@ Proc ISSAC 97 pp172175 (1997)
\end{chunk}
+\index{Gentleman, W. Morven}
+\begin{chunk}{axiom.bib}
+@article{Gent74a,
+ author = "Gentleman, W. Morven",
+ title = "Experience with Truncated Power Series",
+ journal = "ACM SIGSAM",
+ volume = "8",
+ number = "3",
+ year = "1974",
+ pages = "6162",
+ abstract =
+ "The truncated power series package in ALTRAN has been available for
+ over a year now, and it has proved itself to be a useful and exciting
+ addition to the armoury of symbolic algebra. A wide variety of
+ problems have been attacked with this tool: moreover, through use in
+ the classroom, we have had the opportunity to observe how a large
+ number of people react to the availability of this tool.",
+ paper = "Gent74a.pdf"
+}
+
+\end{chunk}
+
+\index{Harrington, Steven J.}
+\begin{chunk}{axiom.bib}
+@article{Harr79,
+ author = "Harrington, Steven J.",
+ title = "A Symbolic Limit Evaluation Program in REDUCE",
+ journal = "ACM SIGSAM",
+ volume = "13",
+ number = "1",
+ year = "1979",
+ pages = "2731",
+ abstract =
+ "A method for the automatic evaluation of algebraic limits is
+ described. It combines many of the techniques previously employed,
+ including topdown recursive evaluation, power series expansion, and
+ L'Hôpital's rule. It introduces the concept of a special algebraic
+ form for limits. The method has been implemented in MODEREDUCE.",
+ paper = "Harr79.pdf"
+}
+
+\end{chunk}
+
\index{Heckmann, Reinhold}
\index{Wilhelm, Reinhard}
\begin{chunk}{axiom.bib}
@@ 21716,6 +22350,95 @@ Proc ISSAC 97 pp172175 (1997)
\end{chunk}
+\index{Stoutemyer, David R.}
+\begin{chunk}{axiom.bib}
+@article{Stou79,
+ author = "Stoutemyer, David R.",
+ title = "LISP Based Symbolic Math Systems",
+ journal = "Byte Magazine",
+ volume = "8",
+ pages = "176192",
+ year = "1979",
+ link = "\url{https://ia902603.us.archive.org/30/items/bytemagazine197908/1979_08_BYTE_0408_LISP.pdf}",
+ comment =
+ "SCRATCHPAD is a very large computeralgebra system implemented by the
+ IBM Thomas J. Watson Research Center. It is available there on an IBM
+ 370, and it is available from other IBM corporate sites via
+ telephone. Regrettably, this fine system has not yet been released to
+ the public, but it is discussed here because of its novel features.
+
+ In its entirety, the system occupies about 1600K bytes on an IBM 370
+ with virtual storage, for which an additional minimum of 100 K bytes
+ is recommeded for workspace. The variety of builtin transformations
+ currently lies between that of REDUCE and MACSYMA. However, each of
+ the three systems has features that none of the others possess, and
+ one of these features may be a decisive advantage for a particular
+ application. Here are some highlights of the SCRATCHPAD system:
+ \begin{itemize}
+ \item The system provides singleprecision floatingpoint arithmetic
+ as well as indefiniteprecision rational arithmetic
+ \item The builtin unavoidable and optional algebraic transformations
+ are approximately similar to those of MACSYMA.
+ \item The builtin exponential, logarithmic, and trigonometric
+ transformations are approximately similar to those of REDUCE.
+ \item Besides builtin symbolic matrix algebra, APL like array
+ operations are included, and they are even further generalized to
+ permit symbolic operations of nonhomogeneous arrays and on arrays
+ of indefinite or infinite size.
+ \item Symbolic differentiation and integration are builtin, with
+ the latter employing the powerful RischNormal algorithm.
+ \item There is a particularly elegant builtin facility for
+ determining Taylor series expansions.
+ \item There is a builtin SOLVE function capable of determining the
+ exact solution to a system of linear equations.
+ \item There is a powerful patternmatching facility which serves as
+ the primary mechanism for user level extensions. The associated syntax
+ is at a very high level, being the closest of all computer algebra
+ systems to the declarative, nonprocedural notation of mathematics.
+ To implement the trigonometric multipleangle expansions, we can
+ merely enter the rewrite rules:
+ \[cos(n*x) == 2*cos(x)*cos((n1)*x)cos((n2)*x), n{\rm\ in\ }
+ (2,3,...), x{\rm\ arb}\]
+ \[sin(n*x) == 2*cos(x)*sin((n1)*x)sin((n2)*x), n{\rm\ in\ }
+ (2,3,...),x{\rm\ arb}\]
+ Then, whenever we subsequently enter an expression such as
+ $cos(4*b)$, the response will be a corresponding expanded
+ expression such as
+ \[8*cos(B)  8*cos^2(B)+1\]
+ Thus, programs resemble a collection of math formulae, much as they
+ would appear in a book or article.
+ \item SCRATCHPAD has a particularly powerful yet easily used mechanism
+ for controlling the output format of expressions.. For example, the user
+ can specify that an expression be displayed as a power series in x,
+ with coefficients which are factored rational functions in b and c,
+ etc. For large expressions, such fine control over the output may
+ mean the difference between an important new discovery and an
+ inconprehensible mess.
+ \end{itemize}
+
+ This generalized recursive format idea is so natural and effective
+ that SCRATCHPAD is now absorbing the idea into an internal
+ representation. A study of the polynomial additional algorithm in
+ the previous section reveals that it is written to be applicable
+ to any coefficient domain which has the algebraic properties of a
+ {\sl ring}. The coefficients could be matrices, powerseries, etc.
+ That coefficient domain could in turn have yet another coefficient
+ domain, and so on. With a careful modular design, packages to treat
+ each of these domains can be dynamically linked together so that
+ code can be shared and combined in new ways without extensive
+ rewriting and duplication. Then not only the output, but also the
+ internal computations can be selected most suitably for a particular
+ application.
+
+ For further information about SCRATCHPAD, contact Richard Jenks
+ at the IBM Thomas J. Watson Research Center, Yorktown Heights, NY
+ 10598",
+ paper = "Stou79.pdf",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
\index{Vakil, Ravi}
\begin{chunk}{axiom.bib}
@misc{Vaki98,
@@ 24958,7 +25681,7 @@ in [Wit87], p18
real elementary functions. We also provide examples from its
implementation that illustrate the advantages over the use of complex
logarithms and exponentials.",
 paper = "Bron88.djvu",
+ paper = "Bron89.djvu",
keywords = "axiomref",
beebe = "Bronstein:1989:SRE"
}
diff git a/changelog b/changelog
index 079f2ec..e87c31d 100644
 a/changelog
+++ b/changelog
@@ 1,3 +1,5 @@
+20170819 tpd src/axiomwebsite/patches.html 20170819.01.tpd.patch
+20170819 tpd books/bookvolbib Add references
20170817 tpd src/axiomwebsite/patches.html 20170817.01.tpd.patch
20170617 tpd books/bookvolbib Add references
20170816 tpd src/axiomwebsite/patches.html 20170816.01.tpd.patch
diff git a/patch b/patch
index dbd24af..d5261aa 100644
 a/patch
+++ b/patch
@@ 2,471 +2,685 @@ books/bookvolbib Add references
Goal: Axiom references
\index{Richardson, Dan}
\index{Fitch, John P.}
+\index{Stoutemyer, David R.}
\begin{chunk}{axiom.bib}
@inproceedings{Rich94,
 author = "Richardson, Dan and Fitch, John P.",
 title = "The identity problem for elementary functions and constants",
 booktitle = "ACM Proc. of ISSAC 94",
 pages = "285290",
 isbn = "0897916387",
 year = "1994",
+@article{Stou79,
+ author = "Stoutemyer, David R.",
+ title = "LISP Based Symbolic Math Systems",
+ journal = "Byte Magazine",
+ volume = "8",
+ pages = "176192",
+ year = "1979",
+ link = "\url{https://ia902603.us.archive.org/30/items/bytemagazine197908/1979_08_BYTE_0408_LISP.pdf}",
+ comment =
+ "SCRATCHPAD is a very large computeralgebra system implemented by the
+ IBM Thomas J. Watson Research Center. It is available there on an IBM
+ 370, and it is available from other IBM corporate sites via
+ telephone. Regrettably, this fine system has not yet been released to
+ the public, but it is discussed here because of its novel features.
+
+ In its entirety, the system occupies about 1600K bytes on an IBM 370
+ with virtual storage, for which an additional minimum of 100 K bytes
+ is recommeded for workspace. The variety of builtin transformations
+ currently lies between that of REDUCE and MACSYMA. However, each of
+ the three systems has features that none of the others possess, and
+ one of these features may be a decisive advantage for a particular
+ application. Here are some highlights of the SCRATCHPAD system:
+ \begin{itemize}
+ \item The system provides singleprecision floatingpoint arithmetic
+ as well as indefiniteprecision rational arithmetic
+ \item The builtin unavoidable and optional algebraic transformations
+ are approximately similar to those of MACSYMA.
+ \item The builtin exponential, logarithmic, and trigonometric
+ transformations are approximately similar to those of REDUCE.
+ \item Besides builtin symbolic matrix algebra, APL like array
+ operations are included, and they are even further generalized to
+ permit symbolic operations of nonhomogeneous arrays and on arrays
+ of indefinite or infinite size.
+ \item Symbolic differentiation and integration are builtin, with
+ the latter employing the powerful RischNormal algorithm.
+ \item There is a particularly elegant builtin facility for
+ determining Taylor series expansions.
+ \item There is a builtin SOLVE function capable of determining the
+ exact solution to a system of linear equations.
+ \item There is a powerful patternmatching facility which serves as
+ the primary mechanism for user level extensions. The associated syntax
+ is at a very high level, being the closest of all computer algebra
+ systems to the declarative, nonprocedural notation of mathematics.
+ To implement the trigonometric multipleangle expansions, we can
+ merely enter the rewrite rules:
+ \[cos(n*x) == 2*cos(x)*cos((n1)*x)cos((n2)*x), n{\rm\ in\ }
+ (2,3,...), x{\rm\ arb}\]
+ \[sin(n*x) == 2*cos(x)*sin((n1)*x)sin((n2)*x), n{\rm\ in\ }
+ (2,3,...),x{\rm\ arb}\]
+ Then, whenever we subsequently enter an expression such as
+ $cos(4*b)$, the response will be a corresponding expanded
+ expression such as
+ \[8*cos(B)  8*cos^2(B)+1\]
+ Thus, programs resemble a collection of math formulae, much as they
+ would appear in a book or article.
+ \item SCRATCHPAD has a particularly powerful yet easily used mechanism
+ for controlling the output format of expressions.. For example, the user
+ can specify that an expression be displayed as a power series in x,
+ with coefficients which are factored rational functions in b and c,
+ etc. For large expressions, such fine control over the output may
+ mean the difference between an important new discovery and an
+ inconprehensible mess.
+ \end{itemize}
+
+ This generalized recursive format idea is so natural and effective
+ that SCRATCHPAD is now absorbing the idea into an internal
+ representation. A study of the polynomial additional algorithm in
+ the previous section reveals that it is written to be applicable
+ to any coefficient domain which has the algebraic properties of a
+ {\sl ring}. The coefficients could be matrices, powerseries, etc.
+ That coefficient domain could in turn have yet another coefficient
+ domain, and so on. With a careful modular design, packages to treat
+ each of these domains can be dynamically linked together so that
+ code can be shared and combined in new ways without extensive
+ rewriting and duplication. Then not only the output, but also the
+ internal computations can be selected most suitably for a particular
+ application.
+
+ For further information about SCRATCHPAD, contact Richard Jenks
+ at the IBM Thomas J. Watson Research Center, Yorktown Heights, NY
+ 10598",
+ paper = "Stou79.pdf",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Shackell, John}
+\begin{chunk}{axiom.bib}
+@article{Shac90,
+ author = "Shackell, John",
+ title = "Growth Estimates for ExpLog Functions",
+ journal = "J. Symbolic Computation",
+ volume = "10",
+ pages = "611632",
abstract =
 "A solution for a version of the identify problem is proposed for a
 class of functions including the elementary functions. Given f(x),
 g(x), defined at some point $\beta$ we decide whether or not
 $f(x) \equiv g(x)$
 in some neighbourhood of $\beta$. This problem is first reduced to a
 problem about zero equivalence of elementary constants. Then a semi
 algorithm is given to solve the elementary constant problem. This semi
 algorithm is guaranteed to give the correct answer whenever it
 terminates, and it terminates unless the problem being considered
 contains a counterexample to Schanuel's conjecture.",
 paper = "Rich94.pdf"
+ "Explog functions are those obtained from the constant 1 and the
+ variable X by means of arithmetic operations and the function symbols
+ exp() and log(). This paper gives an explicit algorithm for
+ determining eventual dominance of these functions modulo an oracle for
+ deciding zero equivalence of constant terms. This also provides
+ another proof that the dominance problem for explog functions is
+ Turingreducible to the identity problem for constant terms."
+}
+
+\end{chunk}
+
+\index{Bronstein, Manuel}
+\begin{chunk}{axiom.bib}
+@article{Bron88,
+ author = "Bronstein, Manuel",
+ title = "The Transcendental Risch Differential Equation",
+ journal = "J. Symbolic Computation",
+ volume = "9",
+ year = "1988",
+ pages = "4960",
+ abstract =
+ "We present a new rational algorithm for solving Risch differential
+ equations in towers of transcendental elementary extensions. In
+ contrast to a recent algorithm of Davenport we do not require a
+ progressive reduction of the denominators involved, but use weak
+ normality to obtain a formula for the denominator of a possible
+ solution. Implementation timings show this approach to be faster than
+ a Hermitelike reduction.",
+ paper = "Bron88.pdf",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Erd\'elyi, A.}
+\begin{chunk}{axiom.bib}
+@book{Erde56,
+ author = {Erd\'elyi, A.},
+ title = "Asymptotic Expansions",
+ year = "1956",
+ isbn = "9780486155050",
+ publisher = "Dover Publications"
+}
+
+\end{chunk}
+\index{Gradshteyn, I.S.}
+\index{Ryzhik, I.M.}
+\begin{chunk}{axiom.bib}
+@incollection{Grad80,
+ author = "Gradshteyn, I.S. and Ryzhik, I.M.",
+ title = "Definite Integrals of Elementary Functions",
+ booktitle = "Table of Integrals, Series, and Products",
+ publisher = "Academic Press",
+ year = "1980",
+ comment = "Chapter 34"
}
\end{chunk}
\index{Bertrand, Laurent}
+\index{Piquette, J. C.}
\begin{chunk}{axiom.bib}
@inproceedings{Bert94,
 author = "Bertrand, Laurent",
 title = "On the Implementation of a new Algorithm for the Computation
 of Hyperelliptic Integrals",
 booktitle = "ISSAC 94",
 isbn = "0897916387",
 pages = "211215",
 year = "1994",
+@article{Piqu89,
+ author = "Piquette, J. C.",
+ title = "Special Function Integration",
+ journal = "ACM SIGSAM Bulletin",
+ volume = "23",
+ number = "2",
+ year = "1989",
+ pages = "1121",
abstract =
 "In this paper, we present an implementation in Maple of a new
 aJgorithm for the algebraic function integration problem in the
 particular case of hyperelliptic integrals. This algo rithm is based
 on the general algorithm of Trager [9] and on the arithmetic in the
 Jacobian of hyperelliptic curves of Cantor [2].",
 paper = "Bert94.pdf"
}
+ "This article describes a method by which the integration capabilities
+ of symbolicmathematics computer programs can be extended to include
+ integrals that contain special functions. A summary of the theory that
+ forms the basis of the method is given in Appendix A. A few integrals
+ that have been evaluated using the method are presented in Appendix
+ B. A more thorough development and explanation of the method is given
+ in Piquette, in review (b)."
+}
\end{chunk}
\index{Baddoura, Jamil}
+\index{Clarkson, M.}
\begin{chunk}{axiom.bib}
@inproceedings{Badd94,
 author = "Baddoura, Jamil",
 title = "A Conjecture On Integration in Finite Terms with Elementary
 Functions and Polylogarithms",
 booktitle = "ISSAC 94",
 year = "1994",
 pages = "158162",
 isbn = "0897916387",
+@article{Clar89,
+ author = "Clarkson, M.",
+ title = "MACSYMA's inverse Laplace transform",
+ journal = "ACM SIGSAM Bulletin",
+ volume = "23",
+ number = "1",
+ year = "1989"
+ pages = "3338",
abstract =
 "In this abstract, we report on a conjecture that gives the form of an
 integral if it can be expressed using elementary functions and
 polylogarithms. The conjecture is proved by the author in the cases of
 the dilogarithm and the trilogarithm [3] and consists of a
 generalization of Liouville's theorem on integration in finite terms
 with elementary functions. Those last structure theorems, for the
 dilogarithm and the trilogarithm, are the first case of structure
 theorems where logarithms can appear with nonconstant
 coefficients. In order to prove the conjecture for higher
 polylogarithms we need to find the functional identities, for the
 polylogarithms that we are using, that characterize all the possible
 algebraic relations among the considered polylogarithms of functions
 that are built up from the rational functions by taking the considered
 polylogarithms, exponentials, logarithms and algebraics. The task of
 finding those functional identities seems to be a difficult one and is
 an unsolved problem for the most part to this date.",
 paper = "Badd94.pdf",
+ "The inverse Laplace transform capability of MACSYMA has been improved
+ and extended. It has been extended to evaluate certain limits, sums,
+ derivatives and integrals of Laplace transforms. It also takes
+ advantage of the inverse Laplace transform convolution theorem, and
+ can deal with a wider range of symbolic parameters.",
+ paper = "Clar89.pdf"
}
\end{chunk}
\index{Fateman, Richard}
+\index{Schou, Wayne C.}
+\index{Broughan, Kevin A.}
\begin{chunk}{axiom.bib}
@inproceedings{Fate92a,
 author = "Fateman, Richard",
 title = "Honest Plotting, Global Extrema, and Interval Arithmetic",
 booktitle = "ISSAC 92",
 year = "1992",
 pages = "216223",
 isbn = "0897914899",
+@article{Scho89,
+ author = "Schou, Wayne C. and Broughan, Kevin A.",
+ title = "The Risch Algorithms of MACSYMA and SENAC",
+ journal = "ACM SIGSAM",
+ volume = "23",
+ number = "3",
+ year = "1989",
abstract =
 "A computer program to honestly plot curves y = f(x) must locate
 maxima and minima in the domain of the graph. To do so it may have to
 solve a classic problem in computation – global optimization.
 Reducing an easy problem to a hard one is usually not an ad vantage,
 but in fact there is a route to solving both problems if the function
 can be evaluated using interval arithmetic. Since some computer
 algebra systems supply a version of interval arithmetic, it seems we
 have the ingredients for a solution.

 In this paper we address a particular problem how to compute and
 display ``honest'' graphs of 2D mathematical curves. By
 ``honest'' we mean that no significant features (such as the
 location of poles, the values at maxima or minima, or the behavior
 of a curve at asymptotes) are misrepresented, By “mathematical” we
 mean curves like those generally needed in scientific disciplines
 where functions are represented by composi tion of common
 mathematical operations: rational operations ($+, –, *, /$),
 exponential and log, trigonometric functions as well as continuous
 and differentiable functions from applied mathematics.",
 paper = "Fate92a.pdf"
+ "The purpose of this paper is to report on a computer implementation
+ of the Risch algorithm for the symbolic integration of rational
+ functions containing nested exponential and logarithms. For the class
+ of transcendental functions, the Risch algorithm [4] represents a
+ practical method for symbolic integration. Because the Risch algorithm
+ describes a decision procedure for transcendental integration it is an
+ ideal final step in an integration package. Although the decision
+ characteristic cannot be fully realised in a computer system, because
+ of major algebraic problems such as factorisation, zeroequivalence
+ and simplification, the potential advantages are considerable.",
+ paper = "Scho89.pdf",
}
\end{chunk}
\index{Einwohner, T.}
\index{Fateman, Richard J.}
+\index{Smith, Paul}
+\index{Sterling, Leon}
\begin{chunk}{axiom.bib}
@inproceedings{Einw95,
 author = "Einwohner, T. and Fateman, Richard J.",
 title = "Searching Techniques for Integral Tables",
 booktitle = "ISSAC 95",
 year = "1995",
 pages = "133139",
+@article{Smit83,
+ author = "Smith, Paul and Sterling, Leon",
+ title = "Of Integration by Man and Machine",
+ journal = "ACM SIGSAM",
+ volume = "17",
+ number = "34",
+ year = "1983",
abstract =
 "We describe the design of data structures and a computer program for
 storing a table of symbolic indefinite or definite integrals and
 retrieving userrequested integrals on demand. Typical times are so
 short that a preliminary lookup attempt prior to any algorithmic
 integration approach seems justified. In one such test for a table
 with around 700 entries, matches were found requiring an average of
 2.8 milliseconds per request, on a Hewlett Packard 9000/712
 workstation.",
 paper = "Eiwn95.pdf"
+ "We describe a symbolic integration problem arising from an
+ application in engineering. A solution is given and compared with the
+ solution generated by the REDUCE integration package running at
+ Cambridge. Nontrivial symbol manipulation, particularly
+ simplification, is necessary to reconcile the answers.",
+ paper = "Smit83.pdf"
}
\end{chunk}
\index{G{\'o}mezD{\'\i}az, Teresa}
+\index{Renbao, Zhong}
\begin{chunk}{axiom.bib}
@misc{Gome94,
 author = "GomezDiaz, Teresa",
 title = "The Possible Solutions to the Control Problem",
 year = "1994"
+@article{Renb82,
+ author = "Renbao, Zhong",
+ title = "An Algorithm for Avoiding Complex Numbers in Rational Function
+ Integration",
+ journal = "ACM SIGSAM",
+ volume = "16",
+ number = "3",
+ pages = "3032",
+ year = "1982",
+ abstract =
+ "Given a proper rational function $A(x)/B(x)$ where $A(x)$ and $B(x)$
+ both are in $R[x]$ with $gcd(A(x), B(x))= 1$, $B(x)$ monic and
+ $deg(A(x)) < deg(B(x))$, from the Hermite algorithm for rational
+ function integration in [3], we obtain
+ \[\int{frac{A(x)}{B(x)}~dx = S(x)+\int{\frac{T(x)}{B^*(x)}~dx\]
+ where $S(x)$ is a rational function
+ which is called the rational part of the integral of $A(x)/B(x)$ in
+ eq. (1), $B^*(x)$ is the greatest squarefree factor of $B(x)$, and
+ $T(x)$ is in $R[x]$ with $deg(T(x)) < deg(B^*(x))$. The integral of
+ $T(x)/B^*(x)$ is called the transcendental part of the integral of
+ $A(x)/B(x)$ in eq. (1).",
+ paper = "Renb82.pdf"
}
\end{chunk}
\index{Jeffrey, David}
+\index{Davenport, James H.}
\begin{chunk}{axiom.bib}
@misc{Jeffxx,
 author = "Jeffrey, David",
 title = "Real Integration on Domains of Maximum Extent",
+@article{Dave82a,
+ author = "Davenport, Jamess H.",
+ title = "The Parallel Risch Algorithm (I)",
+ journal = "Lecture Notes in Computer Science",
+ volume = "144",
+ year = "1982",
+ abstract =
+ "In this paper we review the socalled ``parallel Risch'' algorithm for
+ the integration of transcendental functions, and explain what the
+ problems with it are. We prove a positive result in the case of
+ logarithmic integrands.",
+ paper = "Dave82a.pdf"
+}
+
+\end{chunk}
+
+\index{Davenport, James H.}
+\begin{chunk}{axiom.bib}
+@article{Dave85b
+ author = "Davenport, Jamess H.",
+ title = "The Parallel Risch Algorithm (II)",
+ journal = "ACM TOMS",
+ volume = "11",
+ number = "4",
+ pages = "356362",
+ year = "1985",
+ abstract =
+ "It is proved that, under the usual restrictions, the denominator of
+ the integral of a purely logarithmic function is the expected one,
+ that is, all factors of the denominator of the integrand have their
+ multiplicity decreased by one. Furthermore, it is determined which new
+ logarithms may appear in the integration.",
+ paper = "Dave85b.pdf"
+}
+
+\end{chunk}
+
+\index{Davenport, James H.}
+\begin{chunk}{axiom.bib}
+@article{Dave82b,
+ author = "Davenport, Jamess H.",
+ title = "The Parallel Risch Algorithm (III): use of tangents",
+ journal = "ACM SIGSAM",
+ volume = "16",
+ number = "3",
+ pages = "36",
+ year = "1982",
+ abstract =
+ "In this note, we look at the extension to the parallel Risch
+ algorithm (see, e.g., the papers by Norman & Moore [1977], Norman &
+ Davenport [1979], ffitch [1981] or Davenport [1982] for a description
+ of the basic algorithm) which represents trigonometric functions in
+ terms of tangents, rather than instead of complex exponentials.",
+ paper = "Dave82b.pdf"
+}
+
+\end{chunk}
+
+\index{Kempelmann, Helmut}
+\begin{chunk}{axiom.bib}
+@article{Kemp81,
+ author = "Kempelmann, Helmut",
+ title = "Recursive Algorithm for the Fast Calculation of the Limit of
+ Derivatives at Points of Indeterminateness",
+ journal = "ACM SIGSAM",
+ volume = "15",
+ number = "4",
+ year = "1981",
+ pages = "1011",
abstract =
 "General purpose computer algebra systems are used by people with
 widely varying backgrounds. Amongst the many difficulties that face
 the developer because of this, one that is particularly relevant to
 the subject of this talk is the fact that different users attach
 different meanings, or definitions, to the same symbols. When a user
 asks a CAS to integrate a function, it is not clear which definition
 of integral should be used. Some of the disagreements over the
 ``correct'' value of an integral reduce to the fact that the different
 parties are using different defintions. This talk therefore starts by
 defining my version of integration. According to this definition,
 functions returned as integrals should not only differentiate to the
 function supplied by the user, they should also satisfy global
 continuity properties. In order to achieve these properties, the idea
 of a rectifying transform is intrduced. For the problem of integrating
 a rational trigonometric function, a new rectifying transform is
 described."
+ "It is a common method in probability and queueing theory to gain the
+ $n$th moment $E[x^n]$ of a random variable X
+ with density function $f_x(x)$
+ by the $n$th derivative of the corresponding Laplace transform $L(s)$ at
+ the point $s = 0$
+ \[E[x^n] = (1)^n\cdot L^{n}(O)\]
+ Quite often we encounter indetermined
+ expressions of the form $0/0$ which normally are treated by the rule of
+ L'Hospital. This is a time and memory consuming task requiring
+ greatest common divisor cancellations. This paper presents an
+ algorithm that calculates only those derivatives of numerator and
+ denominator which do not equal zero when taking the limit /1/. The
+ algorithm has been implemented in REDUCE /2/. It is simpler and more
+ efficient than that one proposed by /3/.",
+ paper = "Kemp81.pdf"
}
\end{chunk}
\index{Jeffrey, D. J.}
+\index{Norfolk, Timothy S.}
\begin{chunk}{axiom.bib}
@misc{Jeffxxa,
 author = "Jeffrey, D. J.",
 title = "The Integration of Functions Containing Fractional Powers",
+@article{Norf82,
+ author = "Norfolk, Timothy S.",
+ title = "Symbolic Computation of Residues at Poles and Essential
+ Singularities",
+ journal = "ACM SIGSAM",
+ volume = "16",
+ number = "1",
+ year = "1982",
+ pages = "1723",
abstract =
 "An algorithm is developed for integrating functions that contain
 fractional powers. The algorithm addresses the following points. The
 integral must be valid for all possible values of the variable,
 including those values of the variable that make the integrand, and
 hence the integral, take complex values. The algorithm must allow for
 the fact that there are two possible interpretations of the cube root
 as a real number (in fact of any odd root), and produce correct
 integrals for both interpretations (it is shown that it is possible
 for the functiona form of the integral to change with the
 interpretation). Finally, all simplifications, especially of complex
 quantities, must follow correct rules, what are here derived using the
 concept of the unwinding number."
+ "Although most books on the theory of complex variables include a
+ classification of the types of isolated singularities, and the
+ applications of residue theory, very few concern themselves with
+ methods of computing residues. In this paper we derive some results on
+ the calculation of residues at poles, and some special classes of
+ essential singularities, with a view to implementing an algorithm in
+ the VAXIMA computer algebra system.",
+ paper = "Norf82.pdf"
}
\end{chunk}
\index{Jeffrey, D.J.}
\index{Corless, R.M.}
+\index{Belovari, G.}
\begin{chunk}{axiom.bib}
@misc{Jeffxxb,
 author = "Jeffrey, D.J. and Corless, R.M.",
 title = {Explorations of uses of the unwinding number $\Kappa$},
+@article{Belo83,
+ author = "Belovari, G.",
+ title = "Complex Analysis in Symbolic Computing of some Definite Integrals",
+ journal = "ACM SIGSAM",
+ volume = "17",
+ number = "2",
+ year = "1983",
+ pages = "611",
+ paper = "Belo83.pdf"
}
\end{chunk}
\index{Ager, Tryg A.}
\index{Ravaglia, R.A.}
\index{Dooley, Sam}
+\index{Wang, Paul S.}
\begin{chunk}{axiom.bib}
@misc{Ager88,
 author = "Ager, Tryg A. and Ravaglia, R.A. and Dooley, Sam",
 title = "Representation of Inference in Computer Algebra Systems with
 Applications to Intelligent Tutoring",
 year = "1988",
+@phdthesis{Wang71,
+ author = "Wang, Paul S.",
+ title = "Evaluation of Definite Integrals by Symbolic Manipulation",
+ school = "MIT",
+ year = "1971",
+ link = "\url{http://publications.csail.mit.edu/lcs/pubs/pdf/MITLCSTR092.pdf}",
+ comment = "MIT/LCS/TR92",
abstract =
 "Presently computer algebra systems share with calculators the
 property that a sequence of computations is not a unified
 computational sequence, thereby allowing fallacies to occur. We argue
 that if computer algebra systems operate in a framework of strict
 mathematical proof, fallacies are eliminated. We show that this is
 possible in a working interactive system REQD. We explain why
 computational algebra, done under the strict constraints of proof, is
 relevant to uses of computer algebra systems in instruction."
+ "A heuristic computer program for the evaluation of real definite
+ integrals of elementary functions is described This program, called
+ WANDERER, (WANg's DEfinite integRal EvaluatoR), evaluates many proper
+ and improper integrals. The improper integrals may have a finite or
+ infinite range of integration. Evaluation by contour integration and
+ residue theory is among the methods used. A program called DELIMITER
+ (DEfinitive LIMIT EvaluatoR) is used for the limit computations needed
+ in evaluating some definite integrals. DELIMITER is a heuristic
+ program written for computing limits of real or complex analytic
+ functions. For real functions of a real variable, onesided as well
+ been implmented in the MACSYMA system, a symbolic and algebraic
+ manipulation system being developed at Project MAC, MIT. A typical
+ problem in applied mathematics, namely asymptotic analysis of a
+ definite integral, is solved using MACSYMA to demonstrate the
+ usefulness of such a system and the facilities provided by WANDERER."
+ paper = "Wang71.pdf"
}
\end{chunk}
\index{Davenport, James H.}
\index{Faure, Christ\'ele}
+\index{Harrington, Steven J.}
\begin{chunk}{axiom.bib}
@misc{Faurxx,
 author = {Davenport, James and Faure, Christ\'ele},
 title = "Parameters in Computer Algebra",
+@article{Harr79,
+ author = "Harrington, Steven J.",
+ title = "A Symbolic Limit Evaluation Program in REDUCE",
+ journal = "ACM SIGSAM",
+ volume = "13",
+ number = "1",
+ year = "1979",
+ pages = "2731",
abstract =
 "One of the main strengths of computer algebra is being able to solve
 a family of problems with one computation. In order to express not
 only one problem but a family of problems, one introduces some symbols
 which are in fact the parameters common to all the problems of the family.

 The user must be able to understand in which way these parameters
 affect the result when he looks at the answer. This is not the case in
 most current Computer Algebra Systems we know because the form of the
 answer is never explicitly conditioned by the values of the
 parameters. We have introduced multivalued expressions called
 {\sl conditional expressions}, in which each potential value is associated
 with a condition on some parameters. This is used, in particular, to
 capture the situation in integration, where the form of the answer can
 depend on whether certain quantities are positive, negative, or zero.",
 keywords = "axiomref, provisos"
+ "A method for the automatic evaluation of algebraic limits is
+ described. It combines many of the techniques previously employed,
+ including topdown recursive evaluation, power series expansion, and
+ L'Hôpital's rule. It introduces the concept of a special algebraic
+ form for limits. The method has been implemented in MODEREDUCE.",
+ paper = "Harr79.pdf"
}
\end{chunk}
\index{Norman, Arthur C.}
+\index{Norton, Lewis M.}
\begin{chunk}{axiom.bib}
@inproceedings{Norm90,
 author = "Norman, Arthur C.",
 title = "A CriticalPair/Completion based Integration ALgorithm",
 booktitle = "ISSAC 90",
 pages = "201205",
 isbn = "0201548925",
+@article{Nort80,
+ author = "Norton, Lewis M.",
+ title = "A Note about Laplace Transform Tables for Computer use",
+ journal = "ACM SIGSAM",
+ volume = "14",
+ number = "2",
+ year = "1980",
+ pages = "3031",
abstract =
 "In 1976 Risch [1] proposed a scheme for finding the integrals of
 forms built up out of transcendental functions that viewed general
 functions as rational forms in a suitable differential field and
 represented the polynomial parts of those forms in a distributed
 rather than recursive way. By using a data representation where all
 variables were (more or less) equally important this new method seemed
 to sidestep some of the complications that had appeared in his
 previous scheme [2] where various sideconstraints had to be
 propagated between the levels present in a tower of separate
 extensions of differential fields, otherwise seen as levels in
 recursive datastructures. An initial implementation of the method was
 prepared in the context of the SCRATCHPAD/1 algebra system and
 demonstrated at the 1976 SYMSAC meeting at Yorktown Heights, a
 subsequent version for Reduce [3][5] came after that, and made it
 possible to try the method on a large range of integrals. These
 practical studies showed up some problems with the method and its
 implementation. The presentation given here reexpresses the 1976
 Risch method in terms of rewrite rules, and thus exposes the major
 problem it suffers from as a manifestation of the fact that in certain
 circumstances the set of rewrites generated is not confluent. This
 difficulty is then attacked using a criticalpair/completion (CPC)
 approach. For very many integrands it is then easy to see that the
 initial set of rewrites used in the early implementations [1] and [3]
 do not need any extension, and this fact explains the high level of
 competence of the programs involved despite their shaky theoretical
 foundations. For a further large collection of problems even a simple
 CPC scheme converges rapidly; when the techniques presented here are
 applied to the REDUCE integration test suite in all applicable cases a
 short computation succeeds in completing the set of rewrites and hence
 gives a secure basis for testing for integrability. This paper
 describes the implementation of the CPC process and discusses current
 limitations to and possible future extended applications of it.",
 paper = "Norm90.pdf",
 keywords = "axiomref"
+ "The purpose of this note is to give another illustration of the fact
+ that the best way for a human being to represent or process
+ information is not necessarily the best way for a computer. The
+ example concerns the use of a table of inverse Laplace transforms
+ within a program, written in the REDUCE language [1] for symbolic
+ algebraic manipulation, which solves linear ordinary differential
+ equations with constant coefficients using Laplace transform
+ methods. (See [2] for discussion of an earlier program which solved
+ such equations.)",
+ paper = "Nort80.pdf"
}
\end{chunk}
\index{Davenport, J.H.}
+\index{Stoutemyer, David R.}
\begin{chunk}{axiom.bib}
@misc{Davexx,
 author = "Davenport, J.H.",
 title = "Computer algebra  past, present and future",
+@article{Stou76,
+ author = "Stoutemyer, David R.",
+ title = "Automatic Simplification for the Absolutevalue Function and its
+ Relatives",
+ journal = "ACM SIGSAM",
+ volume = "10",
+ number = "4",
+ year = "1976",
+ pages = "4849",
abstract =
 "Computer algebra started in 1953, and there were several systems in
 existence in the 1960's. Those inspired by physical applications
 largely implemented ``high school'' algebra and, from the point of
 view of today's much larger machines and more sophisticated
 programming languages, the miracle is that they worked at all, or as
 efficiently as they did.

 By the end of the 1960's it was clear that more sophisticated
 algorithms were necessary, either to solve problems for which the
 ``high school'' algorithms were inefficient on large data (e.g. gcd or
 factorization), or problems for which the ``high school'' techniques
 were not really algorithms at all (e.g. integration, solution of sets
 of equations).

 Hence the 1970's (and indeed much of the 1980's) were the ``age of
 algorithms''. It rapidly became obvious that these algorithms required
 more complex data structures and mathematical objects: finite fields,
 ideals, algebraic curves, divisor class groups to name but a few. This
 led to the growth of new systems, such as Axiom (formerly Scratchpad),
 Maple, Mathematica and Reduce 3. It is currently the case that many
 more algorithms are known than are implemented, and certainly that few
 systems implement even a reasonable crosssection of the known
 algorithms.

 At the present, there are two main trends. One is the rush to
 implement, which is causing a lot of duplication of work, but there is
 also a realisation that these systems need to be able to communicate,
 and that it is inherently impossible to have all the best algorithms
 in one system. To take an example, why implement from scratch enough
 group theory to analyse blocks of imprimitivity in a permutation
 group, when Cayley has all this and much more? However, parts of
 integration theory require this analysis.

 The other trend is the tendency to more ``structureoriented''
 algorithms, i.e. algorithms which take accound of the structure of the
 problem. To name two, there is Gatemann's work on polynomial equation
 systems with symmetry, and Richardson's work on roots of polynomials
 which can be written as $p(x,x^n)$ with $p$ of low degree.

 The paper concludes with some speculations on the future of computer
 algebra.",
 paper = "Davexx.pdf",
 keywords = "axiomref"
}
+ "Computer symbolic mathematics has made impressive progress for the
+ automatic simplification of rational expressions, algebraic
+ expressions, and elementary transcendental expressions. However,
+ existing computeralgebra systems tend to provide little or no
+ simplification for the absolutevalue function or for its relatives
+ such as the signum, unit ramp, unit step, max, min, modulo, and Dirac
+ delta functions. Although these functions lack certain desireable
+ properties that are helpful for canonical simplification, there are
+ opportunities for some ad hoc simplification. Moreover, a perusal of
+ most mathematics, engineering, and scientific journals or texts
+ reveals that these functions are too prevalent to be ignored.This
+ article describes specific simplification rules implemented in a
+ program that supplements the builtin rules for the MACSYMA ABS and
+ SIGNUM functions.",
+ paper = "Stou76.pdf"
+}
\end{chunk}
\index{Bronstein, Manuel}
+\index{Kanoui, Henry}
\begin{chunk}{axiom.bib}
@misc{Bronxxa,
 author = "Bronstein, Manuel",
 title = "Symbolic Integration: towards Practical Algorithms",
+@article{Kano76,
+ author = "Kanoui, Henry",
+ title = "Some Aspects of Symbolic Integration via Predicate Logic
+ Programming",
+ journal = "ACM SIGSAM",
+ volume = "10",
+ number = "4",
+ year = "1976",
+ pages = "2942",
abstract =
 "After reviewing the Risch algorithm for the integration of elementary
 functions and the underlying theory, we descrbe the successive
 improvements in the field, and the current ``rational'' approach to
 symbolic integration. We describe how a technique discovered by
 Hermite a century ago can be efficiently applied to rational,
 algebraic, elementary transcendental and mixed elementary functions."
+ "During the past years, various algebraic manipulations systems have
+ been described in the literature. Most of them are implemented via
+ ``classic'' programming languages like Fortran, Lisp, PL1 ... We propose
+ an alternative approach: the use of Predicate Logic as a programming
+ language.",
+ paper = "Kano76.pdf"
}
\end{chunk}
\index{Temme, N.M.}
+\index{Gentleman, W. Morven}
\begin{chunk}{axiom.bib}
@misc{Temmxx,
 author = "Temme, N.M.",
 title = "Uniform Asymptotic Expansions of Integrals",
+@article{Gent74,
+ author = "Gentleman, W. Morven",
+ title = "Experience with Truncated Power Series",
+ journal = "ACM SIGSAM",
+ volume = "8",
+ number = "3",
+ year = "1974",
+ pages = "6162",
abstract =
 "The purpose of the paper is to give an account of several aspects of
 uniform asymptotic expansions of integrals. We give examples of
 standard forms, the role of critical points and methods to construct
 the experiences."
+ "The truncated power series package in ALTRAN has been available for
+ over a year now, and it has proved itself to be a useful and exciting
+ addition to the armoury of symbolic algebra. A wide variety of
+ problems have been attacked with this tool: moreover, through use in
+ the classroom, we have had the opportunity to observe how a large
+ number of people react to the availability of this tool.",
+ paper = "Gent74.pdf"
+}
+
+\end{chunk}
+
+\index{Loos, Rudiger}
+\begin{chunk}{Loos72a,
+@article{Loos72a,
+ author = "Loos, Rudiger",
+ title = "Analytic Treatment of Three Similar Fredholm Integral Equations
+ of the second kind with REDUCE 2",
+ journal = "ACM SIGSAM",
+ volume = "21",
+ year = "1972",
+ pages = "3240"
}
\end{chunk}
\index{L\'opez, Jos\'e L.}
+\index{Collins, George E.}
\begin{chunk}{axiom.bib}
@article{Lope99,
 author = {L\'opez, Jos\'e L.},
 title = "Asymptotic expansions of integrals: The termbyterm integration
 method",
 year = "1999",
 journal = "Journal of Computational and Applied Mathematics",
 volume = "102",
 pages = "181194",
+@article{Coll69,
+ author = "Collins, George E.",
+ title = "Algorithmic Approaches to Symbolic Integration and SImplification",
+ journal = "ACM SIGSAM",
+ volume = "12",
+ year = "1969",
+ pages = "5016",
abstract =
 "The classical termbyterm integration technique used for obtaining
 asymptotic expansions of integrals requires the integrand to have an
 uniform asymptotic expansion in the integration variable. A
 modification of this method is presented in which the uniformity
 conditions provides the termbyterm integration technique a large
 range of applicability. As a consequence of this generality, Watson's
 lemma and the integration by parts technique applied to Laplace's and
 a special family of Fourier's transforms become corollaries of the
 termbyterm integration method."
 paper = "Lope99.pdf"
+ "This panel session followed the format announced by SIGSAM Chairman
+ Carl Engelman in the announcement published in SIGSAM Bulletin No. 10
+ (October 1968). Carl gave a brief (five or ten minutes) introduction
+ to the subject and introduced Professor Joel Moses (M. I. T.). Joel
+ presented an excellent exposition of the recent research
+ accomplishments of the other panel members, synthesizing their work
+ into a single large comprehensible picture. His presentation was
+ greatly enhanced by a series of 27 carefully prepared slides
+ containing critical examples and basic formulas, and was certainly the
+ feature of the show. A panel discussion followed, with some audience
+ participation. Panel members were Dr. W. S. Brown (Bell Telephone
+ Laboratories), Professor B. F. Caviness (Duke University), Dr. Daniel
+ Richardson and Dr. R. H. Risch (IBM).",
+ paper = "Coll69.pdf"
}
\end{chunk}
\index{Nordsieck, Arnold}
+\index{Kasper, Toni}
\begin{chunk}{axiom.bib}
@article{Nord62,
 author = "Nordsieck, Arnold",
 title = "On Numerical Integration of Ordinary Differential Equations",
 journal = "Mathematics of Computations",
 volume = "XVI",
 year = "1962",
 pages = "2249",
+@article{Kasp80,
+ author = "Kasper, Toni",
+ title = "Integration in Finite Terms: The Liouville Theory",
+ journal = "ACM SIGSAM",
+ volume = "14",
+ number = "4",
+ year = "1980",
+ pages = "28",
abstract =
 "A reliable efficient generalpurpose method for automatic digital
 computer integration of systems of ordinary differential equations is
 described. The method operates with the current values of the higher
 derivatives of a polynomial approximating the solution. It is
 thoroughly stable under all circumstances, incorporates automatic
 starting and automatic choice and revision of elementary interval
 size, approximately minimizes the amount of computation for a
 specified accuracy of solution, and applies to any system of
 differential equations with derivatives continuous or piecewise
 continuous with finite jumps. ILLIAC library subroutine F7, University
 of Illinois Digital Computer Laboratory, is a digital computer program
 applying this method."
+ "The search for elementary antiderivatives leads from classical
+ analysis through modern algebra to contemporary research in computer
+ algorithms.",
+ paper = "Kasp80.pdf"
}
\end{chunk}
\index{Faure, Christ\'ele}
\index{Davenport, James H.}
\index{Naciri, Hanane}
+\index{Munroe, M.E.}
\begin{chunk}{axiom.bib}
@techreport{Faur00,
 author = "Faure, Christele and Davenport, James H. and Naciri, Hanane",
 title = MultiValued Computer Algebra",
 year = "2000",
 type = "technical report",
 institution = "INRIA CAFE",
 number = "4001",
 abstract =
 "One of the main strengths of computer algebra is being able to solve
 a family of problems with one computation. In order to express not
 only one problem but a family of problems, one introduces some symbols
 which are in fact the parameters common to all the problems of the
 family. The user must be able to understand in which way these
 parameters affect the result when he looks at the answer. Otherwise it
 may lead to completely wrong calculations, which when used for
 numerical applications bring nonsensical answers. This is the case in
 most current Computer Algebra Systems we know because the form of the
 answer is never explicitly conditioned by the values of the
 parameters. The user is not even informed that the given answer may be
 wrong in some cases then computer algebra systems can not be entirely
 trustworthy. We have introduced multivalued expressions called
 conditional expressions, in which each potential value is associated
 with a condition on some parameters. This is used, in particular, to
 capture the situation in integration, where the form of the answer can
 depend on whether certain quantities are positive, negative or
 zero. We show that it is also necessary when solving modular linear
 equations or deducing congruence conditions from complex expressions."
 paper = "Faur00.pdf"
+@book{Munr53,
+ author = "Munroe, M.E.",
+ title = "Introduction to Measure and Integration",
+ publisher = "AddisonWesley",
+ year = "1953"
+}
+
+\end{chunk}
+
+\index{Hardy, G.}
+\index{Littlewood, J.E.}
+\index{Polya, G.}
+\begin{chunk}{axiom.bib}
+@book{Hard64,
+ author = "Hardy, G. and Littlewood, J.E. and Polya, G.",
+ title = "Inequalities",
+ publisher = "Cambridge University Press",
+ year = "1964"
+}
+
+\end{chunk}
+
+\index{Baddoura, Jamil}
+\begin{chunk}{axiom.bib}
+@article{Badd06,
+ author = "Baddoura, Jamil",
+ title = "Integration in Finite Terms with Elementary Functions and
+ Dilogarithms",
+ journal = "J. Symbolic Computation",
+ volume = "41",
+ number = "8",
+ year = "2006",
+ pages = "909942",
+ abstract =
+ "In this paper, we report on a new theorem that generalizes
+ Liouville’s theorem on integration in finite terms. The new theorem
+ allows dilogarithms to occur in the integral in addition to
+ transcendental elementary functions. The proof is based on two
+ identities for the dilogarithm, that characterize all the possible
+ algebraic relations among dilogarithms of functions that are built up
+ from the rational functions by taking transcendental exponentials,
+ dilogarithms, and logarithms. This means that we assume the integral
+ lies in a transcendental tower.",
+ paper = "Badd06.pdf"
+}
+
+\end{chunk}
+
+\index{Kahan, William}
+\begin{chunk}{axiom.bib}
+@misc{Kaha90,
+ author = "Kahan, William",
+ title = "The Persistence of Irrationals in Some Integrals",
+ year = "1990",
+ abstract =
+ "Computer algebra systems are expected to simplify formulas they
+ obtain for symbolic integrals whenever they can, and often they
+ succeed. However, the formulas so obtained may then produce incorrect
+ results for symblic definite integrals"
+}
\end{chunk}
diff git a/src/axiomwebsite/patches.html b/src/axiomwebsite/patches.html
index 7cac3a0..e054731 100644
 a/src/axiomwebsite/patches.html
+++ b/src/axiomwebsite/patches.html
@@ 5796,6 +5796,8 @@ books/bookvolbib Axiom References in External Literature
goals  a newly added file to explain current goals
20170817.01.tpd.patch
books/bookvolbib Add references
+20170819.01.tpd.patch
+books/bookvolbib Add references

1.9.1