bluuebunny/crossref_metadata_2025 huggingface dataset:
Analytic treatment of three similar Fredifolm integral equations of the second kind with reduce 2
Authors: Loos Rüdiger
Published: January 2007

This paper presents a solution to the following problem proposed by W. Morven Gentleman [1]:"For each of the following three integral equations, find the largest eigenvalue and the corresponding eigenfunction f(x). Note that in equations (a) and (b) these are functions of α; in equation (a) we are actually interested in the limit for large α, and in equation (b) as α approaches zero. In each case m is used as abbreviation for max (x,y).
ALTRAN
Authors: Brown W. S. , Hall A. D.
Published: January 2007

J. A. Campbell [1] has proposed the computation of his Y
2n
polynomials as a challenging problem for symbolic algebra systems. These polynomials are defined by a recurrence formula involving summations over two and four indices, and a special differentiation rule. Since the number of terms in Y
2n
grows almost exponentially, large amounts of time and memory are required for large values of n.
Problem #5
Authors: Campbell J. A.
Published: January 2007

I wish to express a few informal doubts about the effectiveness of a problem which I have previously proposed [1] here as a benchmark exercise for symbolic computing systems. In brief, that problem concerned the generation of functions Y
2n
to provide successive approximations to the solutions[EQUATION]of the equation[EQUATION]where[EQUATION]I suggested the use of a recurrence in Y
2n
obtained by direct substitution of (1) and (3) into (2). This recurrence contained rational-number coefficients, and one term was quadrilinear in the Y functions. However, Yngve Sundblad (KTH, Stockholm) has demonstrated to me that execution times in this computation can be reduced greatly (in SYMBAL on a CDC 6600) merely if the recurrence is rewritten to remove the numerical denominators, while there is at least one method of finding a recurrence for Y
2n
, known to the Uppsala group which has made the most extensive studies [2] of (2), that contains only bilinear terms. No doubt that method must require much less time (and space!) to compute. Thus we should agree on a common algorithm before we can compare benchmark runs directly.
On algorithms for solving systems of polynomial equations
Authors: Yun David Y. Y.
Published: January 2007

Methods for finding numerical solutions of nonlinear algebraic systems of equations have been given considerable attention since the birth of the field of numerical analysis. The fact that these methods find many applications to problems in physics, engineering, economics, and mathematical theory of optimization cannot be overstressed. However, a significant number of these problems contain indeterminants or parameters, which should only be given numerical values at the very end of the computational processes. Sometimes numerical results simply cannot provide enough insight for the analysis of the problem. Furthermore, symbolic solutions via elimination theory provide not only all solutions to a given system of equations but also a classification of solutions into solution surfaces or parametrized solutions. Thus, the symbolic method can provide an infinite number of solutions where this feat is clearly impossible for the numerical methods.
Problems #3 and #4 in REDUCE and MACSYMA
Authors: Fitch John
Published: January 2007

The algebra systems REDUCE and MACSYMA are used to solve SIGSAM Problem #3, the Reversion of a Double Series, and SIGSAM Problem #4, the Lie Transform Solution of the Harmonic Oscillator. All the algorithms used have been previously published, so the times may be used to compare both systems and algorithms independently.
Solution to problem #2
Authors: Tuttens W.
Published: January 2007

J. A. Campbell [1] has proposed the computation of his Y
2n
polynomials as a benchmark problem for algebraic manipulation systems. Eight solutions to problem #2 (SIGSAM Bulletin No. 22, March 1972) have been provided in SIGSAM Bulletin No. 24, October 1972. Here is a summary of a POLMAN [2,3] program which solves this problem. Using the POLMAN system installed on an IBM 370/155 at K.U.L., Computing Centre, these polynomials were computed through n = 8 in 16 sec., through n = 10 in 45 sec., through n = 12 in 2 min., 51 sec. The memory requirements for the POLMAN system together with the program (24,5 K bytes) and a workspace of approximately 34,5 K bytes occupied a total of 190 K bytes for the case of n = 10. The workspace has an overflow to a secondary store (disk) [2,3].
A case history in interactive problem-solving
Authors: Fateman Richard J.
Published: January 2007

MACSYMA [1], a computer program for algebraic manipulation, is used to solve, symbolically and exactly, a problem involving integration and the solution of an infinite set of linear equations. This is a tutorial in the use of MACSYMA, and illustrates some of the choices available to the interactive user which aid in solving a mathematical problem.
A solution to Kiang's problem #6
Authors: Starkey J. Denbigh
Published: January 2007

Three similar solutions for Problem #6 are offered. These solutions do not use any symbolic system, but are the results of simple mathematical analysis. The results are computationally elementary, and are intended to demonstrate that the power of symbolic systems is wasted on this problem, and there is no practical reason to use them. An Algol procedure for S
i
is given.
ALTRAN programs for SIGSAM problem #6
Authors: Hall A. D. , Johnson S. C.
Published: January 2007

In [1], it is suggested that an algebraic manipulation system be used to gain some insight into the following problem:[EQUATION]
Symbolic mathematical systems now and in the future
Authors: Sundblad Yngve
Published: January 2007

A survey of existing algebraic systems, from batch-oriented "formula-crunchers" to dialog systems with sophisticated mathematical knowledge is given. Results from a comparison of some systems from aspects such as availability, user-orientedness and runtime-efficiency are presented.Finally possible trends in hardware, firmware and software that would make algebraic systems svailable for the wide community of "small" users in science and technology are discussed.
Toward a formal implementation of computer algebra
Authors: Loos Ruediger G. K.
Published: January 2007

We consider in this paper the task of synthesizing an algebraic system. Today the task is significantly simpler than in the pioneer days of symbol manipulation, mainly because of the work done by the pioneers in our area, but also because of the progress in other areas of Computer Science. There is now a considerable collection of algebraic algorithms at hand and a much better understanding of data structures and programming constructs than only a few years ago.
ANALITIK
Authors: Husberg Nisse , Seppänen Jouko
Published: January 2007

A short discussion is given on the programming language ANALITIK available on the Soviet MIR-2 computer designed for description of numerical and analytical mathematical computations. Some properties and principles of the system are presented. Design objectives and their implementation are reviewed.The programming language ANALITIK available on the MIR-2 computer is a special purpose language designed for numerical and analytical computations. The language and the computer have been developed at the Institute of Cybernetics in Kiev under direction of the well known Soviet cybernetician, academician V. M. Glushkov. It represents a continuation of a product line of special purpose computers for mathematical problems. ANALITIK is a compatible extension of the programming language MIR, which was an Algol-like language but more specifically designed for the solution of numerical problems.
Computer recognition of divergences in Feynman diagrams
Authors: Calmet J.
Published: January 2007

Symbolic and Algebraic Manipulations techniques are applied to a problem of quantum electrodynamics: to find the divergences inclosed in a Feynman graph. These divergences are connected to the topology of the graph. No calculations are performed.
A non-numerical computation involving sums of many products of finite rotation matrices for spin 3/2
Authors: Frick I.
Published: January 2007

A LISP-program is described that computes the real part of the joint spin density matrix for N* and N* in the reaction p, p → N*, N*.
A perturbation calculation in general relativity
Authors: Cohen H. Ian
Published: January 2007

A perturbation method in general relativity, first developed by Levy was used to investigate a slowly pulsating axisymmetric system. The vacuum field equations were calculated to the second order of a small parameter. To be sure of the accuracy of the results obtained, one of the Bianchi identities was checked. The size of the calculations, especially that involved in the Bianchi identity, made it necessary to use an algebraic computer system, in this case LAM.
Formal representations for algebraic numbers
Authors: Weeks Dennis
Published: January 2007

Recent literature (e.g., [12]) shows a growing interest in the representation of algebraic numbers in terms of the polynomials they satisfy. The basis of this interest is the observation that for every algebraic number α there exists a unique polynomial p(x) having the following properties:
Symbolic integration of a class of algebraic functions
Authors: Ng Edward W.
Published: January 2007

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 non-classical 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 well-known functions (e.g., Bessel and Legendre).
MACSYMA - the fifth year
Authors: Moses Joel
Published: January 2007

MACSYMA is a large symbolic and algebraic manipulation system which has been under development at Project MAC, M.I.T. since 1969. We first discuss some of the design decisions, such as multiple representations, that led to the current system. We then give a brief description of the facilities of MACSYMA by dividing the system into seven packages: language and interactive facilities, general representation, rational function representation and related algorithms, the integration subsystem, the power series subsystem, the MACLISP system, and miscellaneous facilities.
Summary of the 1969 FJCC SIGSAM-SIGART technical session
Authors: Moses Joel
Published: January 2007

As noted in Stan Petrick's report on the meeting (SIGSAM Bulletin no. 13, p. 2), it was decided to hold a combined SIGSAM-SIGART session. The effect of this move was to swell the number of people present at the SIGSAM session from 16 to 45. The attendance at the conclusion of the SIGART half dropped to about 30.
Response from A. R. LeSchack
Authors: LeSchack A. R.
Published: January 2007

I refer to the paper by Joel Moses in the SIGSAM Bulletin Number 13 (December 1969), received today. In the example beginning near the bottom of page 25, the author refers to a "...potentially controversial disagreement between the program and the table.....," involving a term which is either 2ap
2
or 3ap
2
. Evidently neither the author nor W. D. Maurer, given as the source of the table in question, was able to resolve the disagreement.
Practical symbolic differentiation of large expressions using PL/I Formac
Authors: Eisenpress Harry , Bomberault Abel
Published: January 2007

The analytical differentiation of an arbitrary expression by means of PL/I Formac is modified in two ways: First, in order to economize on computer storage, the expression is partitioned into small segments that can be retained in memory throughout the processing, and can then be combined to form an expression that is equivalent to the original one. Secondly, extensive back substitution of lower-order derivatives into higher-order expressions is made in order to create more compact and efficient expressions. An extended example is printed out.
A structure theorem for exponential and primitive functions a preliminary report
Authors: Rothstein Michael , Caviness B. F.
Published: January 2007

In this paper a generalization of the Risch Structure Theorem is reported. The generalization applies to fields F (t
1
,...,t
n
) where F is a differential field (in our applications F will be a finitely generated extension of Q, the field of rational numbers) and each t
i
is either algebraic over F
i-1
= F(t
1
,...,t
i-1
), is an exponential of an element in F
i-1
, or is an integral of an element in F
i-1
If t
i
is an integral and can be expressed using logarithms, it must be so expressed for the generalized structure theorem to apply.
Amthor's solution of Archimedes' cattle problem
Authors: Loos Rüdiger
Published: January 2007

Archimedes' problem for his colleagues in Alexandria, as stated in this Bulletin [1], amounts to solving the system (1)-(9) for positive integers W, X, Y, Z and w, x, y, z.
An efficient squarefree decomposition algorithm
Authors: Wang Paul S.
Published: January 2007

The concept of polynomial squarefree decomposition is an important one in algebraic computation. The squarefree decomposition process has many uses in computer symbolic computation. A recent survey by D. Yun [3] describes many useful algorithms for this purpose. All of these methods depend on computing the greatest common divisior (gcd) of the polynomial to be decomposed and its first derivative (with respect to some variable). In the multivariate case, this gcd computation is non-trivial and dominates the cost for the squarefree decomposition.
A solution to Kahan's problem (SIGSAM problem no. 9)
Authors: Lauer Markus
Published: January 2007

The problem was ([Kah75]) :Let the variables a,b,c,d (which are supposed to take real values) be interpreted as the center (c,d) and the principal semiaxes a,b of an ellipse. Find necessary and sufficient conditions for a,b,c,d such that[EQUATION]holds. Furthermore the conditions should be given as polynomial inequalities.
Tim Hagen
Authors: Hagen G. Tim
Published: January 2007

A simple problem is described on the back of this sheet. I have been trying to solve it for more than a year as I have time to think about it, but my poor stubborn pea brain will not give. This irritates me so much that I am willing to pay for a solution.
Some problems connected with ambiguous expressions
Authors: Korpela Jukka
Published: January 2007

You are probably aware of the fact that careless application of commonly known algebraic rules can lead to absurdities:[EQUATION]The problem behind such jokes is that important functions like integer powers and trigonometric functions have no unique inverses.
How to find algebraic integers whose conjugates lie near the unit circle?
Authors: Mignotte Maurice
Published: January 2007

In 1933 D. H. Lehmer [3], in connexion with a method for discovering large prime numbers, posed the following question. Let α be an algebraic integer of degree D with conjugates α = α
1
, α
2
, ..., α
D
and put[EQUATION]where a is the leading (positive) coefficient of the minimal polynomial of α.
The use of formula manipulation systems to compute asymptotic expansions
Authors: de Queiroz F. Teixeira
Published: January 2007

The resolution of differential equations using assymptotic expansions may be a good method for testing formula manipulation systems.
Abstracts
Authors: Wang Paul S.
Published: January 2007

The Session on Symbolic and Algebraic Computation of the 1978 ACM Computer Science Conference, held in Detroit 21-23 February 1978, consists of five technical presentations. The abstracts of these talks reprinted here appeared in the 1978 ACM Computer Science Conference Proceedings.
Abstracts
Authors: Wang Paul S.
Published: January 2007

Some twenty eight contributed and invited papers are presented in the SIGSAM Sessions of the SIAM 1978 National Meeting held on May 24-26 at the University of Wisconsin at Madison. Reprinted here by permission are a majority of the abstracts of these presentations. A few were not provided to us in time by SlAM for inclusion. An author index can be found on page 17.
A taxonomy for algebraic computation
Authors: Griesmer J. H. , Jenks R. D. , Yun D. Y. Y.
Published: January 2007

Recently the authors responded to a request from Professor Anthony Ralston of the State University of New York at Buffalo to participate in the review of a proposed Taxonomy of Computer Science and Engineering which is being prepared under the auspices of AFIPS, with funding provided by a number of U.S. government agencies. To quote from Professor Ralston's letter:"The main purpose of this project is to provide a document which will enable those outside of CS&E to see what this discipline - or a part of it - is concerned with. Among the other uses to which such a taxonomy might be put are to influence the categories of Computing Reviews or job classifications in the federal government and elsewhere."
A MACSYMA solution to problem 8
Authors: Zippel Richard
Published: January 2007

Fitch's Random Walk problem [2], strikes the author as one of the first in the series of SIGSAM problems which may be used to demonstrate the ease of use of the various algebraic manipulation systems. In our case little effort was expended to speed up the computation, and yet we were able to generate all the terms one could desire in a few minutes. On the other hand, the solution of the problem is not so transparent as to obviate the calculation. It is a happy day for algebraic manipulation systems when it only takes a few minutes to go from the statement of a problem to its solution.
Utilizing the FORMAC novelties
Authors: Bahr Knut
Published: January 2007

FORMAC is a formula manipulation system and language, which was originally developed by IBM (ref. R. Tobey et al.: PL/1-FORMAC Symbolic Mathematics Interpreter, Contrib. Program Library 360D-03.3.004, Sept. 1969). Since IBM stopped support of FORMAC and released the source code in 1970, a number of extensions and improvements have been incorporated that make FORMAC more powerful and more modern.
An application of symbolic computation to crystal physics
Authors: Feldman Stuart I.
Published: January 2007

This paper describes a practical application of symbolic computation to a problem in chemical physics. We compute a series approximation to a fairly complicated integral using straightforward techniques, allowing the computer to take over when the problem becomes too messy. Even though Altran [1] has no direct way to handle non-rational functions, introducing a few auxiliary variables renders the problem tractable. We certainly hope that more users will attempt to solve standard problems of this sort using symbolic manipulation programs.
Course outline
Authors: Jenks Richard D.
Published: January 2007

The following is an outline of a course entitled "Introduction to Symbolic Mathematical Computation", offered by the Computer Science Department at Yale University in the Spring semester 1975. The course consisted of some 15 lectures, 1-1/2 to 2 hours in duration as outlined below. The three lectures entitled "Hensel's Lemma and Algorithm Applications" were given by David Yun. The course was taught principally as a seminar with most of the grade based on a rather tough final given below.
A SCRATCHPAD solution to problem #7
Authors: Griesmer J. H. , Jenks R. D. , Yun D. Y. Y.
Published: January 2007

The function F(x)= (1/2 - x)(1 - x
2
)
1/2
+ x(1 + (1 - (1/2 + x)
2
)
1/2
) has a maximum of y=0.674981 at x=0.3437715 (Figure 1). This y value was found [1] to be a root of an irreducible polynomial over the integers of degree 10. The object of problem #7 is to find this polynomial. In addition, we obtain these x and y values to high accuracy and verify that the above y is a global maximum over the domain of interest[2]: 0 < x < 1/2. The SCRATCHPAD conversation below involves the following 10 steps.
More on computing roots of integers
Authors: Caviness B. F.
Published: January 2007

Recently John Fitch [FITC 74] gave an algorithm for computing [A
1/n
] where A and n are positive integers. His algorithm, based on the classical Newton method, has the virtue of not only being an extremely simple algorithm but it is also fast - both in practice and in theory. One can hardly hope to improve upon an algorithm with such virtues. In this note I will present and analyze the computing time of a variation of the algorithm presented by Fitch. The variation is superior to Fitch's version in the sense that in some cases the theoretical computing time of the new version is dominated by the theoretical computing time of Fitch's version. I do not know which algorithm is faster in practice. I doubt that there is any significant difference for most problems of interest. Certainly Fitch's version is easier to program.
Factoring multivariate polynomials over algebraic number fields in MACSYMA
Authors: Wang Paul S.
Published: January 2007

The algorithm for factoring polynomials over the integers by Wang and Rothschild is generalized to an algorithm for the irreducible factorization of multivariate polynomials over any given algebraic number field. The extended method makes use of recent ideas in factoring univariate polynomials over large finite fields due to Berlekamp and Zassenhaus. The procedure has been implemented in the algebraic manipulation system MACSYMA. Some machine examples with timing are presented.
A brief description of Altran
Authors: Feldman Stuart I.
Published: January 2007

This paper contains a summary of the Altran (
Al
gebraic
Tran
slator) language and system for performing symbolic computations on algebraic data. We hope we have included enough details to make it easy to understand published Altran programs. To this end, we describe the syntax and semantics of the language and briefly define the available library procedures. We have not included all of the details of error conditions, special cases, and default that a user may need to know to program a complicated problem.
An enhanced SYMBAL system
Authors: Engeli Max
Published: January 2007

Earlier versions of the SYMBAL system have been operable on the CDC 1604 since 1965 and on the CDC 6000 computers since 1968. In confrontations of different systems (see footnote), SYMBAL has compared well with general purpose systems, including FORMAC, but has been slower than specialised polynomial systems. In judgements and measurements of the effort needed to obtain a working formula manipulation program for given problems, SYMBAL has repeatedly appeared in first rank. This conforms with the design goals which put heavy emphasis on the user aspects of the system.
With J
Authors: Reiter Cliff
Published: January 2007

Image processing includes techniques that are used to correct defects in images and to enhance the visibility of features of interest. In this note we will look at several different methods for smoothing images in order to remove specks of dust and artifacts from scanning. In future notes we plan to discuss other techniques for enhancing images in the spatial domain including the removal of orientation and lighting defects. Previous discussions [6,7] considered the removal of motion blur in frequency domain using Fast Fourier Transforms.
Efficient compilation of array expressions
Authors: Cockshott Paul
Published: January 2007

This article investigates some of the problems involved in generating efficient code for array expressions. It considers issues of cache pollution, effective register use, and vector instructions. It considers the impacts that such compilation efficiency issues can have of the definition of imperative array languages.
Typesetting APL dialects
Authors: de Almeida Pedro
Published: January 2007

Solutions to the problem of typesetting APL dialects were so far severely constrained, for they always relied on specific transliteration schemes or workspaces for automatic transliteration available for only a few interpreters. In this article I introduce an alternative solution to the problem of typesetting APL dialects which does not require transliteration of primitives. Instead, I implement a direct typesetting approach using a Type 1 (or outline) APL font, an encoding vector, and a LATEX package named listings. I finally present a series of examples in order to illustrate the typesetting of APL snippets, code segments, lists of standing files, and their straightforward integration into a document.
MACSYMA experiments with a modified Khachian-type algorithm in linear programming
Authors: Anderson Ned , Wang Paul S.
Published: January 2007

An algorithm of Khachian type for deciding the consistency of m ≥ 2 linear equalities with integer coefficients is described. New iteration formulas for updating the center and the matrix that define each localizing ellipsoid are given. A much sharper bound than that in [1] and [2] for the radius of the initial sphere is given. The new bound depends on the dimension of the solution space, but does not depend explicitly on m. The algorithm is much faster than Khachian's original algorithm. The volume reduction factor in the new algorithm is, in a sense, optimal. Results of computer experiments on the symbolic mathematical system MACSYMA are included.
A remark on the proposed syllabus for an AMS short course on computer algebra
Authors: Akritas Alkiviadis G.
Published: January 2007

It was a pleasure to see that our Special Interest Group initiated contacts with the AMS and that a short course on Computer Algebra has been proposed. The Syllabus [8] for this course seems very representative of our work and I am sure that it will be of great interest to the AMS members. However, as outlined in [8], the Syllabus contains a great historical inaccuracy when referring to "...Descartes' theorem and Uspensky's method;" (in 4: Factorization and Zeros of Polynomials), an inaccuracy which I would like to see corrected.
Computational problems in producing taylor coefficients for the rotating disk problem
Authors: van Hulzen J. A.
Published: January 2007

During the past few years I had the pleasure to cooperate with some of my colleagues, D. Dijkstra, P. Gragert and P. J. Zandbergen, in studying an intriguing problem in fluid mechanics. My intention is not to produce polished results explaining the phenomena we examined - we plan to publish them elsewhere - but merely to describe the process we went through. Is it prototypical?
Identifiability of compartmental models
Authors: Bossi A. , Colussi L. , Cobelli C. , Jacur G. Romanin
Published: January 2007

The problem considered in the present paper concerns a structural identifiability test for an appealing class of mathematical models, the so called compartmental models, which are widely employed in several fields of biology, medicine, ecology, etc.
On the Budan-Fourier controversy
Authors: Akritas Alkiviadis G.
Published: January 2007

In this short note we deal with the theorems by Budan and Fourier regarding the solution of polynomial equations with rational coefficients [1].
Symbolic and algebraic computer programming systems
Authors: Fateman Richard J.
Published: January 2007

To illustrate the difference between numeric and symbolic processing, consider a computer program (in FORTRAN, say) which given the quantities
a
,
b
, and
c
, can apply the quadratic formula to approximate the roots of the quadratic about 40 equation

ax
2
+bx+c=0.

The names
a, b
, and
c
must of course correspond to numerical values at run-time because the program has been written to provide numerical processing. If
a
had as its run-time value the expression
q
, b had value -
pq
- 1 and
c
had value
p
, the FORTRAN program would not be applicable. Nevertheless, by applying the quadratic formula symbolically, the two roots[EQUATION]can be represented. By further efforts, this expression can be reduced to the set of values
p
, 1/
q
. This substitution (in this case, into the quadratic formula) and subsequent simplification are but two of the necessary operations in an algebra system. Some of the more elaborate facilities that can be built up (and have been, in some systems), bring us to the edge of research areas in several fields of mathematics, and present us with problems in representation and communication of "knowledge" which border on the hardest problems in computer "artificial intelligence" -- natural language processing, representation of complex data, heuristic programming.
Abstracts
Authors: Saunders B. David
Published: January 2007

The following four abstracts of papers were given at ANTWERP81. These arrived too late to be included with the others which appeared in the November 1980 issue of the Bulletin. Ed.
LISP-based "big-float" system is not slow
Authors: Kanada Yasumasa , Sasaki Tateaki
Published: January 2007

The efficiency of evaluation is investigated on two "big-float" systems, our LISP-interpreter-based system and Brent's FORTRAN-compiler-based system. The test problems are computations of constants e and pi, and functions sqrt(x) and exp(x). We found that speeds of big-float addition, subtraction and multiplication on our LISP-based system are nearly the same as or rather faster than those on the FORTRAN-based system. This high efficiency of basic arithmetic operations in our system is essentially due to the efficient big-integer routines in a host LISP-system written in an assembly language. Evaluation speeds of the test problems themselves on the LISP-based system are, on an average, 1.5 times slower than those on the FORTRAN-based system. The ratio of the evaluation speeds depends, however, very much on how the routines of test problems are programmed. Therefore, we conclude that the speed of a LISP-based big-float system can be reduced to within two times of that of a FORTRAN-based system.
Algebra made mechanical
Authors: Saunders B. David
Published: January 2007

The notion that computers are mere number crunchers is fast being exorcised by one small group of people --- the computer algebraists. In the past twenty years, several classes of problems which require analytical and not numerical solutions have been tackled successfully. Now, for example, there are computer programs that can yield analytic expressions for indefinite integrals a good deal more reliably than the "random undergraduate", as one practitioner puts it.
Recursive algorithm for the fast calculation of the limit of derivatives at points of indeterminateness
Authors: Kempelmann Helmut
Published: January 2007

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[EQUATION]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/.
A proposal for extensions to reduce
Authors: Üçoluk G. , Hacinliyan A. , Karabudak E.
Published: January 2007

Three classes of extensions are proposed for REDUCE: A facility for evaluating arbitrary functions of matrices; a facility for grouping, modifying or restoring the status of various flags in REDUCE; further extensions and modifications for separating terms, coefficients of expressions, concatenation, and noncommuting algebra. These proposals have been implemented on the UNIVAC 1100 REDUCE system. Inclusion of these extensions on all version of REDUCE is suggested because of their usefulness.
The Jacobi symbol algorithm
Authors: Collins George E. , Loos Rüdiger G. K.
Published: January 2007

We describe a Jacobi symbol algorithm, verify its correctness and analyse its maximum computing time, which is codominant with the product of the length of the inputs.
Symbolic computation of residues at poles and essential singularities
Authors: Norfolk Timothy S.
Published: January 2007

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.
Polynomial reduction from multivariate to bivariate integral polynomial factorization
Authors: Kaltofen Erich
Published: January 2007

Given an arbitrary but fixed integer r ≥ 3. We show that testing r-variate polynomials with integer coefficients for irreducibility is m-reducible in polynomial time of the total degree and the largest coefficient length to testing bi variate polynomials for irreducibility. Factoring r-variate polynomials into irreducibles is polynomial time Turing-reducible to completely factoring bi variate polynomials.
An implementation of the exterior calculus in REDUCE
Authors: Schrüfer E.
Published: January 2007

A program package written in REDUCE for the basic operations of the exterior calculus - exterior multiplication, Hodge-*, exterior differentiation, inner product and Lie differentiation - is described. The syntax of the implementation is held as close as possible to standard textbook notation, i.e. the exterior product is a nary infix operator, the Hodge-* and the exterior differentiation are unary prefix operators and the inner product and Lie differentiation are binary infix operators. Remarks are made on an extended version currently under test, which includes the variational calculus. Aspects of future developments are discussed.
An expression analysis package for REDUCE
Authors: van Hulzen J. A. , Hulshof B. J. A.
Published: January 2007

An expression analysis package for REDUCE 2 is presented. This package, completely written in Standard LISP, can be considered as an extension of the algebraic mode. It allows to interactively dismantled and/or modify the last output expression as it is desplayed or printed. An interface with the Code Optimizer makes on line construction of optimized FORTRAN programs possible.
REDUCE 2 for CP/M
Authors: Marti Jed , Fitch John
Published: January 2007

Our experiences with the NLARGE system [1] convinced us that some computer algebra was possible on small machines. Since this previous report, improvements in the UOLISP compiler [2] have made it possible to implement a large portion of REDUCE 2 [3] on 64k byte Z80 CP/M microcomputer systems. This short report outlines the capabilities of the implementation and what further progress can be expected.
An extension to MACSYMA's concept of functional differentiation
Authors: Wester Michael , Steinberg Stanly
Published: January 2007

An important attribute that any symbolic mathematics program should have is that the user should be able to differentiate an arbitrary function of arbitrary arguments, and do so in a manner that is natural to him or her. Obtaining solutions to many types of problems does not require a complete implementation of this concept, but there will always be applications which will be difficult or even impossible to perform if some feature is missing. In this paper, we shall discuss some of the limitations of the implementation of symbolic differentiation in MACSYMA [2]. In particular, we shall consider some major weaknesses in the functional dependencies approach employed by the MACSYMA differentiator, and then present a method (in the form of a simple modification to the DIFF function) of how we attempted to eliminate these difficulties. Finally, we shall include a set of applications that can be done more naturally with our modifications than was possible in the current version of MACSYMA.
Experiments with muMATH in Austrian high schools
Authors: Aspetsberger K. , Funk G.
Published: January 2007

In Austrian high schools, some experiments for using computer algebra systems in secondary education have been made. The results of these experiments are discussed and some improvements for the systems are proposed. The experiments consisted of two parts: training of functional programming style in muSIMP, routine in the use of the muMATH/muSIMP arithmetic, equation, and solve package, application of muMATH to symbolic transformations in analytic geometry as it is used in school.
Introducing computer algebra to users and to students
Authors: Calmet Jacques
Published: January 2007

Many applications show the excellence of Computer Algebra (CA) as a computational tool in different field of science [1]. An unsolved problem is to evaluate it as a teaching aid in mathematics. The goal of this paper is to help to find an answer to this question.
Cayley
Authors: Cannon John J. , Richardson Jim
Published: January 2007

The Department of Pure Mathematics at the University of Sydney has developed a number of tutorial computer programs. Here we deal principally with Cayley, for the theory of groups [1,2], which has been used for teaching at the University of Sydney since 1975 and at the University of Melbourne since 1982. MATRIX, for linear algebra, is discussed in a variant [4] of the present paper. Both programs will be demonstrated at ICMES.
Position statement for EUROCAL 85
Authors: Zassenhaus H.
Published: January 2007

Nature has a way of producing mathematical models to beholders with an open mind for beauty. Those models provide a challenge to explore their constructive aspects, to investigate their properties by algorithmic methods implying a way to prove them, and to using them as a basis for further experimentation.
My view of the future of symbolic and algebraic computation
Authors: Fateman Richard J.
Published: January 2007

This note has been composed in response to Bruno Buchberger's invitation to the program committee of Eurocal '85 (and others), to provide a short paper on this topic.
Functional programming with combinators for symbolic computation
Authors: Krishnamurthy E. V.
Published: January 2007

The role of algebra in the design of machines, programming, and analysis of algorithms is now well understood. However, the use of machine as an aid for solving abstract algebraic, geometric and kinematic problems is still in its infancy due to the following difficulties: (i) Lack of an efficient representation for the discription of mathematical knowledge in the computer, (ii) complexity involved in the mechanical manipulation needed to carry out mathematical reasoning. Symbolic manipulation and algebraic computation have a leading role to play in the entire aspect of mathematical reasoning by machines and eventually in robotics.
The symbolic-numeric interface
Authors: van Hulzen J. A.
Published: January 2007

Since I believe the symbolic-numeric interface to be important for many potential application fields, I decided to limit my response to
Symbolic and algebraic computations in multidimensional systems theory
Authors: Bose N. K.
Published: January 2007

This article has been prepared as a response to Professor B. Buchberger's invitation to each member of the program committee of EUROCAL 85 to write a short paper on his or her view of the future of the symbolic and algebraic computation, especially within the context of the individual's special field of interest. In my case, this interest is centered around the topic of multidimensional systems theory, and my viewpoints on the present and potential impact of symbolic and algebraic computation on this subject are briefly summarized below.
Write a book!
Authors: Lüneburg Heinz
Published: January 2007

Five years ago, I discovered the computer for myself. This was certainly no accident, as some people thought not having read carefully enough the books I wrote. I always included one or the other algorithm in them for potential use as a calculation device. Most of these algorithms were very naive I must admit. Anyway, five years ago, I started using the computer. Since I had to learn the art right from the beginning, I began teaching the subject to my students. This seems absurd, but it is the way professors learn. I realized immediately several things. First of all, there existed no book presenting algebra in such a way that one could compute in the end the objects one is dealing with; I say "existed," since the book of Lipson [2] appeared in the meantime. Also, Buchberger, Collins and Loos [1] is a very valuable publication indeed in this context. Secondly, our students - I am speaking of Western Germany and of students of mathematics - do not got enough computing experience. The situation seems improving, but still a lot has to be done in my opinion. Thirdly, applied mathematics or rather applicable mathematics is still considered to be numerical mathematics by many collegues. Of course, one has to integrate numerically differential equations to get a probe near Saturn, but the quality of the pictures we get from there depends heavily on algebra and algebraic computing. Hence algebra has to be taught in a new way. All the beautiful achievements of the last two or three decades in computational algebra should become part of our teaching. For this purpose books must be written. Lipson [2] is a good example for what I mean, but it does not cover enough ground. I am actually writing one planned to have two or three volumes. It will be concerned with the basic algebraic structures including programs ready to use. A preliminary draft of some of them has been published [3]. Unfortunately, this preprint is out of print, but a friend of yours may happen to have got a copy as well as more material about the book to inform you.
Abstracts of computer algebra papers from 1984 national meeting of American Chemical Society
Authors: Abdali S. Kamal
Published: January 2007

The 188th National Meeting of American Chemical Society held in Philadelphia, Pennsylvania, during August 26-31, 1984, had a special symposium on symbolic algebraic manipulation. Following are the abstracts of computer algebra papers in that symposium (courtesy Dr. Richard Pavelle of Symbolics, Inc).
Eleven proofs of sin
2
x+cos
2
x = 1
Authors: Fateman Richard J.
Published: January 2007

Several papers in the algebraic manipulation literature have discussed the problem of recognizing, in various guises, the equivalence of sin
2
x+cos
2
x and 1. This is a simplified form of a general substitution problem, and it would seem that a neat, universally applicable technique would be of some interest. This paper does not provide one, but does attempt to show, in various ways, how a particular algebraic manipulation system "knows" this famous identity, in spite of its reluctance to apply it.
Improved simplification of odd and even functions in REDUCE
Authors: Mazzarella Giuseppe
Published: January 2007

Standard REDUCE doesn't perform those simplifications which are allowed by the even or odd simmetry of functions. To overcome this problem, a standard form for the argument of such functions is proposed and discussed. A very simple program performing the reduction to this form is also presented.
Dynamic-debugging system for the REDUCE programs
Authors: Kryukov A. P. , Rodionov A. Ya.
Published: January 2007

This paper describes a dynamic-debugging system for programs written in REDUCE. With the help of the debugger the user can trace the evaluation of the functions defined in the input language REDUCE and, moreover, interrupt the evaluation, if necessary. Operational experience has shown that the debugger is highly effective for training beginners and for debugging large programs in REDUCE and RLISP.
The relation of Lorenzen calculus to formal language theory
Authors: Prather Ronald E.
Published: January 2007

In a number of books and articles [1,2], Lorenzen has developed a general kind of calculus for deriving character strings inductively, using finite systems of
clauses
, reminiscent of those that appear in logic programming. At the same time, these clauses are remarkably similar to the productions that appear in the multiple antecedent canonical systems of Post [3], as used originally to derive a computational basis for the formal notion of an algorithm. However, the interpretation is quite different in the case of the
Lorenzen Calculus
, where each successively derived word is a member of the
theory
, rather than (as in the case of Post, Turing [4], or Chomsky [5] productions) simply a "way station" on the route to a single generated "terminal" word. We intend to make a clear distinction between these two approaches at an appropriate point in the development, but it is well that a tentative appreciation of this fundamental difference be understood at the outset.
An experiment in high-precision arithmetic on shared memory multiprocessors
Authors: Weber Ken
Published: January 2007

The task of verifying a result in computational number theory became a study in the parallel computation of high precision arithmetic, providing information that can be used to intelligently make decisions about the implementation of an arbitrary-precision integer arithmetic package for shared memory multiprocessors.
A baseline feature set for learning rhetorical zones using full articles in the biomedical domain
Authors: Mullen Tony , Mizuta Yoko , Collier Nigel
Published: January 2007

At a time when experimental throughput in the field of molecular biology is increasing, it is necessary for biologists and people working in related fields to have access to sophisticated tools to enable them to efficiently process large amounts of information in order to stay abreast of current research.Rhetorical zone analysis is an application of natural language processing in which areas of text in scientific papers are classified in terms of argumentation and intellectual contribution in order to pinpoint and distinguish certain types of information. Such analysis can be employed to assist in information extraction, helping to assess and integrate data generated by experiments into the scientific community's store of knowledge.We present results for several experiments in automatic zone identification on the ZAISA-1 dataset, a new dataset composed of full biomedical research papers hand-annotated for rhetorical zones. We concentrate on general purpose and linguistically motivated features, and report results for a variety of sets of features. It is our intention to provide a baseline feature set for modeling, which can be extended in future work using combinations of heuristics and more sophisticated and task-specific modeling techniques.
Problem #11
Authors: Jenks Richard D.
Published: January 2007

Generate a set of equations for an explicit k-th order, m stage, Runge-Kutta method for integrating an autonomous system of ordinary differential equations, k and m as large as possible. The number of conditions and variables for various k and m are given in Table 1. Tabulate the costs C(m,k).