bluuebunny/crossref_metadata_2025 huggingface dataset:
Automatic programming in LISP
Authors: Campbell J. A.
Published: January 2007

"Automatic programming" is presently a popular part of research in artificial intelligence. It has been defined ambitiously as "reducing the effort required to get a task running on a computer". That definition has some interest for symbolic computing, because the success of the best-known systems has led to their wide distribution in places where there are no experts to advise casual users, who may therefore have much trouble in understanding the systems well enough to get their computations working efficiently and without excessive numbers of debugging runs. Designers generally exploit their own knowledge of favourable peculiarities of their systems to code users' problems which are slightly out of the ordinary. If the number of
types
of peculiarity is small, it should be possible to mechanize this part of a designer's intuition and make life correspondingly easier for the inexperienced user. The question is worth more study: evidence provided by inspection of some designers' coding of exercises and by my own automatic production of parts of programs for two problems (one in fluid mechanics and one in thermodynamics) suggests that systematic programming in this direction is feasible. I hope to report some detailed results in a later note.
Course notes
Authors: Fitch John
Published: January 2007

Algebraic manipulation covers branches of software, particularly list processing, mathematics, notably logic and number theory, and applications largely in physics. The lectures will deal with all of these to a varying extent. The mathematical content will be kept to a minimum.
Problem #10
Authors: Loos Rudiger
Published: January 2007

"A problem which Archimedes found among (some) epigrams and sent, to be solved by those in Alexandria who occupy themselves with such matters, in his letter to Eratosthenes of Cyrene."
What programmers should know
Authors: Schwartz J. T.
Published: January 2007

In this short sermon, I will summarize some of the views concerning the programming process to which I have been led by my involvement with the design and use of very high level programming languages, formulating these views as recommendations concerning the intellectual equipment and cast of mind which a creative, high level programmer should attempt to acquire.
A note on abnormal polynomial remainder sequences
Authors: Johnson S. C.
Published: January 2007

Polynomial Remainder Sequences (PRS) have been used in the computation of greatest common divisors of polynomials for many years. We call a polynomial division
abnormal
if the degree of the remainder is strictly less than the degree of the divisor minus one; an abnormal PRS is one with at least one abnormal division. An abnormal polynomial division in general implies a nontrivial greatest common divisor among the coefficients of the remainder; this can lead to inefficiencies in the later computations in the PRS.These results suggest that the "classical" PRS methods may have not exploited all of the algebraic structure available in the problem.
An efficient quantifier elimination algorithm for algebraically closed fields of any characteristic
Authors: Heintz J. , Wüthrich R.
Published: January 2007

An Algorithm is given which, as input, accepts a formula φ in prenex normal form, with prime formulas P=o, P≠o, for P ε
Z
[x
1
,...,x
1
], and some r ε N. It produces a quantifierfree formula ψ in disjunctive normal form (DNF) such that, in any algebraically closed field, φ ψ is true. The time required for a formula of length l with q quantifiers and r-q free variables is bounded by (c
1
·l) c
r
2
r
q
, for some constants c
1
, c
2
. If no ∀-quantifiers occur and the matrix of φ is in DNF, then the time is bounded by (c
1
·l)rc
q
2
.
Solution to SIGSAM problem no. 5 using schoonschip
Authors: Rochon M. , Strubbe H.
Published: January 2007

The formulation of SIGSAM problem No. 5, "Construction of high-order Runge-Kutta-Nyström formulae" is given by Campbell). We consider his description as too concise and state the problem here in more detail. We used the work of Fehlberg) as a major guideline.
Computer symbolic math & education
Authors: Stoutemyer David R.
Published: January 2007

None of the commonly-taught programming languages is very relevant to the typical elementary-school through college math curriculum, but computer symbolic math is relevant to most of that curriculum. Consequently, a vast opportunity for beneficial mutual reinforcement and cross-motivation between math and computer education is being squandered. This paper substantiates these claims, explains their major causes, then proposes remedies.
The state of symbolic computation
Authors: Griesmer James H.
Published: January 2007

When I was first asked to give this banquet talk, I was somewhat hesitant to accept. I have not been very heavily involved in the field of symbolic and algebraic manipulation for the past three years. I have contented myself with such behind-the-scenes activities as serving as an associate editor for the
ACM Transactions on Mathematical Software
and as a member of the SIGSAM Nominating Committees two years ago and again this year.
Anatomy of an integral
Authors: Davenport J. H.
Published: January 2007

In the course of my research (Davenport, 1979) into algorithms for indefinite integration, I was asked to consider the following integral (Caviness, 1978):[EQUATION]where
a
and
b
are generic (e.g. independent transcendental) constants. In particular we assume that no two roots of the denominator coincide, and that
a
≠ ±
b
. This integral is in no integral table I have been able to find, and although it appears to be elliptic, there are many surprises in this area.
Problem #11 solved in REDUCE
Authors: Weber Lawrence A. , Rayna Gerhard
Published: January 2007

This report is an account of the hand translation of a program from the SCRATCHPAD/360 language into the REDUCE language [1]. The program is a solution of SIGSAM Problem #11 [2], as solved in SCRATCHPAD by R. D. Jenks in [3]. This report can be regarded as a tutorial in some of the aspects of REDUCE, or as a case study of what is involved in the translation of a program between languages which have similar but not identical constructs.
On the formulation and solution of shell problems by means of computerized algebraic manipulation
Authors: Jensen Jarl
Published: January 2007

The basic equations of shell theory are conveniently formulated as tensor equations. However, the compactness and elegance of tensor notation are counteracted by the fact that the writing out of tensor equations for a given coordinate system results in tedious and cumbersome work in all but the simplest cases.Use of the symbolic and algebraic manipulation language TENSOR FORMAC removes this limitation. It is shown that TENSOR FORMAC makes it possible to generate and handle, say, the equations of equilibrium expressed in the displacements, for a shell described by a non-trivial coordinate system with non-linear geometric effects taken into account.The solution of the system of equations generated manually or by TENSOR FORMAC can only be expressed in a few, exceptionally simple cases by elementary functions. But for axisymmetric deformations of shells of revolution is it possible to obtain the solution of the system of equations as a power series expansion utilizing a symbolic and algebraic manipulation language.
Titles and abstracts
Authors: Wang Paul S.
Published: January 2007

In 1973 G. E. Collins gave a new quantifier elimination algorithm for the first order theory of real closed fields. We utilize the main ideas of this algorithm to prove that any real algebraic variety (in fact, any semi-algebraic set) can be decomposed into a finite union of open cells.
On implementing arbitrary precision arithmetic in NIL
Authors: Purtilo Jim
Published: January 2007

NIL, currently under development at MIT's Laboratory for Computer Science, is the "New Implementation of Lisp" intended for the latest generation of large address space computers. This system is being developed in Lisp itself (following the successful pattern of the Lisp Machine Project at MIT), and among other goals, eliminates a few internal inconsistencies that still exist in Lisp constructions. More notably, NIL introduces a "typed data" method of representing information (doing away with older schemes which group together only data of one type on a given page, and then keep a table on what is on each page) and provides to the user primitives which may introduce to the environment novel data structures that are very efficiently handled by NIL.
Some remarks on a proposed taxonomy for algebraic computation
Authors: Neubüser J.
Published: January 2007

In vol. 12, no. 3, p. 25ff of this Bulletin J. H. Griesmer, R. D. Jenkins, and D. Y. Y. Yun proposed a taxonomy tree rooted at the node "Algebraic Computation" which was meant as part of a general taxonomy of Computer Science. In the accompanying text they asked for supplements and criticism. I apologize that my remarks on this proposal come so late, but I had first written directly to David Yun in November, 1978 and it was only by September, 1979 that he encouraged me to make them public in the Bulletin. I apologize further that all I can offer are in fact some remarks and not a counterproposal as carefully designed as the original one, but I think what is really needed before one can engage in a new proposal is an agreement about i) the scope of the concept "Algebraic Computation" and ii) some basic principles for its organisation into a taxonomy.
Tests for polynomials
Authors: Mignotte Maurice
Published: January 2007

This is an extended abstract of a talk given in Oberwolfach for the meeting of "Komplexität Theorie", october 1979.
Standard LISP report
Authors: Marti J. , Hearn A. C. , Griss M. L. , Griss C.
Published: January 2007

Although the programming language LISP was first formulated in 1960 [6], a widely accepted standard has never appeared. As a result, various dialects of LISP have been produced [4-12], in some cases several on the same machine! Consequently, a user often faces considerable difficulty in moving programs from one system to another. In addition, it is difficult to write and use programs which depend on the structure of the source code such as translators, editors and cross-reference programs.
Titles and abstracts
Authors: Wang Paul S.
Published: January 2007

This is a brief outline of recently developed algorithms capable of computing in matrix groups of very large order. Among others, we will discuss the computation of order, derived series, intersection of subgroups, centralizers, Sylow subgroups, and conjugacy classes of elements. The algorithms have been incorporated into CAYLEY, a group-theoretical system.
Change in applied mathematics is revolutionary
Authors: Frauenthal James C.
Published: January 2007

Shortly after the turn of the century, Niels Bohr and Albert Einstein presented theoretical results which revolutionized physics. This is not news; a quick look through the catalog of my university convinced me that not one of the fifty-five members of the Department of Physics lists classical mechanics as an area of interest. I doubt if a single Ph.D. will be awarded in 1980 by a physics department for the solution of a problem in Newtonian mechanics. Of course Bohr and Einstein and their friends did not instantly solve all the old problems; instead, they created a new set. What happened to all of the old problems which did not simply disappear? They moved into other disciplines called by names like applied mechanics and mechanical engineering.
A note about Laplace transform tables for computer use
Authors: Norton Lewis M.
Published: January 2007

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.)
PICOMATH-80™
Authors: Stoutemyer David R.
Published: January 2007

The last issue of the Bulletin contained an announcement titled "More about PICOMATH-80", referring to an earlier article that was mistakenly omitted. Here then is the full story about PICOMATH:MuMath
1
was intended to popularize computer algebra by making it available on the personal computers that are increasingly prevalent in homes, schools, and government or commercial research labs. It is too early to assess how much of the intended influence will occur, but the Radio Shack TRS-80
tm
version being distributed by Microsoft
2
will surely contribute more significantly toward that goal than does the original version for more expensive personal computers running the CP/M
tm
operating system. Unfortunately, even the TRS-80 version requires a floppy disk drive and at least 32 kilobytes of RAM storage, whereas most TRS-80 owners have only a cassette drive and 16 kilobytes or less of RAM storage. As a lower bound, the Level I TRS-80 provides only 4 kilobytes of RAM, which permits only 100 statements or so of BASIC. Moveover, Level I BASIC is quite spartan, lacking even primitive string operations or more than a single 1-dimensional array. The least expensive computers produced by Apple, Atari, Commodore, Heath and Texas Instruments similarly provide only a cassette drive, 16 kilobytes of RAM or less, and some built-in dialect of BASIC. These mass marketed minimal machines account for the vast majority of personal computers. Moreover, most people with these machines do not upgrade them to the point where they could run muMATH or something like it if were available for the microprocessor which is employed. Perhaps if they could experience a taste of computer algebra on their machines, their interest would be awakened. Who knows -- perhaps they might ultimately upgrade all the way to a LISP machine, or else encourage their schools or employers to do so.
State-space sets, state-space graphs and n-prefix expressions
Authors: Köfalusi Victor , Halmay Edit
Published: January 2007

In this paper we intend to discuss some methods for solving a crucial problem in formula manipulation. This problem arises when a tree is elected -- as the best-fitting data structure - for the representation of a formula.
A general investigation of integration in finite form of differential equations of the first order article 1
Authors: Mordukhai-Boltovskoi D. , Korenblum Boris , Prelle Myra
Published: January 2007

Numerous investigations on integration in finite form of Abelian integrals are based on theorems of Liouville [6,7,8] and Abel [1].
A novel symbolic ordinary differential equation solver
Authors: Chan Woon Cheung
Published: January 2007

This paper describes a symbolic ordinary differential equation solver written as a package for the muMATH computer algebra system. The novel features of this solver are:1. Whereas previous ODE solvers generally require the equation to be quasi-linear and generally yield only implicit results, this new solver is highly integrated with an algebraic equation solver before, during and after solution. In fact, the same function named SOLVE is used for both algebraic and differential equations.2. By not insisting upon quasi-linear input, it is also practical to incorporate in the same solver methods for quasi-linear equations and a generalized version of Clairaut's equation, including singular envelope solutions. To my knowledge, previous ODE solvers have not treated even the ordinary Clairaut's equation, even using a separate solver.3. Since integration constants introduced at intermediate stages can become deeply embedded in a final explicit solution, the new solver automatically replaces subexpressions containing only an integration constant and numerical constants with a new constant, in order to greatly simplify the appearance of results, with no loss of generality.4. Whereas previous ODE solvers are generally restricted to first or second order (or to linear equations with constant coefficients) the new solver attempts to solve equations of any order, even if they are nonlinear and/or have variable coefficients.5. When the new solver is unable to obtain a closed-form solution, Picard iteration or a Taylor-series method is automatically employed so as to obtain a symbolic truncated series solution.muMATH does not yet provide the algebraic operations necessary to support the recently-discovered ODE decision procedures. Consequently the methods used to solve quasi-linear first and second order equations are essentially the same as those employed by other solvers of the pre-decision-procedure era.
Efficient polynomial substitutions of a sparse argument
Authors: Rowan William H.
Published: January 2007

Methods are presented for taking powers of symbolic polynomials and substituting them into univariate polynomials with scalar coefficients. It is shown that the size of the result is a sharp lower bound on the number of coefficient multiplications required to raise a completely sparse polynomial to a power. Other theoretical results prove the optimality or near-optimality of the methods given, in terms of numbers of coefficient operations, under the condition of complete sparsity of the argument.
Computer calculus
Authors: Steen Lynn Arthur
Published: January 2007

"Awesome ... invaluable ... unbelievable...." These are the assessments by normally taciturn research scientists of symbolic computer algebra, a group of programs that allows computers to carry out theoretical (rather than merely numerical) calculations. These programs do in a few brief minutes virtually all mathematics that most engineers and scientists know; their ability to slog through theoretical solutions to large systems of equations has already led to advances in gravitation and high energy physics. "It is only a matter of time before these programs provide major breakthroughs," says physicist Richard Pavelle of Massachusetts Institute of Technology's Lincoln Labs in Lexington, Mass.
The application of algebraic optimisation techniques to algebraic mode programs for reduce
Authors: Pearce P. D. , Hicks R. J.
Published: January 2007

Two examples showing the use of optimisation techniques on algebraic mode programs for the REDUCE Algebraic Manipulator are discussed.
NETFORM and code optimizer manual
Authors: Smit J. , van Hulzen J. A. , Hulshof B. J. A
Published: January 2007

NETFORM is a very powerful and flexible tool for solving (sparse) systems of linear equations in algebraic form. The system includes convenient facilities to generate (and solve) linear equations for electrical networks.The accompanying Code Optimizer is a general purpose tool to automatically optimize sets of algebraic expressions, with emphasis on those generated by the NETFORM system.Thus the combination of both systems can be used to solve numerous problems of a symbolic and/or numeric nature, taking full advantage of the REDUCE 2 embedding in which it is supported.For instance NETFORM can automatically provide a user with descriptive (tableau) equations of an arbitrary linear electrical network and, as it solves such linear equations too, calculate any transferfunction of that linear electrical network. The NETFORM environment encourages users to think of electrical networks in terms of network elements, one port elements as well as subnetworks, which can be conveniently described and manipulated.Given a complete network description, NETFORM allows different approaches in analyzing it, i.e. a full symbolic analysis, a hybrid analysis, a state analysis or a mixed hybrid and state analysis.
Running REDUCE and lisp/360 interactively under a time sharing option
Authors: Kalina Zdenêk
Published: January 2007

The users of algebraic systems are acquainted with many advantages of using diaglog versions of these systems.
Fast reduce
Authors: Davenport James H.
Published: January 2007

This short note describes various changes the author has made to REDUCE, which, by reducing the power of the REDUCE system, increase its performance. Detailed measurements are made, both of CPU savings and of store savings. We conclude by asking what lessons these specific changes (which are not recommended for general applications, since they do decrease the scope of REDUCE) have for the designers of computer algebra systems, and we ask whether it would be possible to design a system with the power of a general-purpose system, but with the performance of the specifically tuned system.
Mathematics and symbol manipulation
Authors: Steinberg Stanly
Published: January 2007

I would like to present some ideas on what I believe symbol manipulation programs should look like. My comments are based on my experience using MACSYMA [6] for the past seven years. I am also somewhat familiar with REDUCE [3] and the new program, SMP [1]. Some of my comments come from difficulties I have encountered in using MACSYMA and teaching others to use MACSYMA. However, my basic interest is in making symbol manipulation programs know more mathematics than they now know.
Statistics on factoring polynomials mod p and p-adically
Authors: Trotter Hale F.
Published: January 2007

A well-known way to factor a polynomial f over the integers is to factor it modulo some prime p and then use Hensel's method to refine the mod p factorization to an approximate p-adic one, i.e., one correct modulo a suitably high power of p. Any integral factor of f is the product of some subset of the irreducible p-adic factors, so the computation reduces to testing a finite number of trial factors. The number of trial factors depends exponentially on the number of p-adic factors, so the latter is critical to the efficiency of the method.
Computer algebra symbolic and algebraic computation
Authors: Buchberger B. , Collins G. E. , Loos R. , Albrecht R.
Published: January 2007

Computer algebra is an alternative and complement to numerical mathematics. Its importance is steadily increasing. This volume is the first systematic and complete treatment of computer algebra. It presents the basic problems of computer algebra and the best algorithms now known for their solution with their mathematical foundations, and complete references to the original literature. The volume follows a top-down structure proceeding from very high-level problems which will be well-motivated for most readers to problems whose solution is needed for solving the problems at the higher level. The volume is written as a supplementary text for a traditional algebra course or for a general algorithms course. It also provides the basis for an independent computer algebra course.
What do we want from a high-level language?
Authors: Davenport James H.
Published: January 2007

In this paper, we discuss some of the issues involved in choosing a better language in which to write computer algebra systems. We conclude that no wide-spread existing language is superior to those we currently use, and mention some of the alternatives.
Some reduction strategies for algebraic term rewriting
Authors: Küchlin Wolfgang
Published: January 2007

A general algorithm for reduction with algebraic term rewriting systems is presented and several aspects of rewriting are discussed.It turns out that the well known strategies of innermost and outermost rewriting, which are special cases of the general algorithm, exhibit good performance under different aspects. The general rewriting algorithm suggests improvements for naive reduction algorithms with specific strategies, which in some cases give them better asymptotic behaviour. Empirical results with an algebraic axiomatization of natural numbers show considerably faster runtimes for the improved algorithms.The algorithms presented here do not impose any restrictions on the rewriting systems. They are currently used both within an implementation of the Knuth-Bendix completion algorithm and in a separate term reduction system, whenever sufficiently large terms are involved.
Global data flow analysis in Aldes
Authors: Bundschuh Florian
Published: January 2007

A technique of gathering information within a program which can be useful for both code improvement ("optimization") and detecting some programming errors is illustrated on the basis of ALDES, in which programming language SAC-2 is written. This technique is usually called global data-flow analysis. It is shown how to formalize some aspects of global data-flow analysis by an attribute grammar.
Some reduce facilities for pretty printing subscripts and formal derivatives
Authors: Hulshof B. J. A. , van Hulzen J. A.
Published: January 2007

Some REDUCE facilities are presented for pretty printing formal (partial) derivatives, for array-and matrix subcripts and for operators with arbitrary arguments. The package is completely written in Standard LISP and can be considered as an addition to the output repertoire of the algebraic mode of REDUCE.
About the realization of an extended, but really interactive reduce by integration of a small editing and executing system
Authors: Kruse Hans-Guenther , Ohlsen Karin
Published: January 2007

Working with REDUCE for algebraic and symbolic calculations on IBM-like machines and operating systems (OS) the user needs a lot of Job-Centrol-Language (JCL) tools in order-to build up files with algebraic statements-to link these files with the REDUCE-System-to start fast saving mechanism for the interactive session, if he feels that the OS gets a nervous breakdownwhich do not concern the way to solve the original algebraic problems.
Data structures and execution times of Algebraic mode programs for REDUCE
Authors: Pearce P. D. , Hicks R. J.
Published: January 2007

The effect of the "ordering of identifiers" on the data structures generated and on the execution time and space required by algebraic mode programs for the REDUCE Algebraic Manipulator is illustrated by examples. Possible explanations for these results are discussed.
A reduce package for series analysis by Hadamard's Theorem and QD schemes
Authors: Schwarz Fritz
Published: January 2007

A package of REDUCE programs is described which may be used to determine the positions of poles and branch points of analytic functions which are given in terms of a power series.
Synthesizing recurrence relations I
Authors: Calmet Jacques , Cohen Ian
Published: January 2007

Recurrence relations (RR) play an important role in many domains of Science. Mathematics, Physics or Computer Science are obvious examples. It is rather intriguing to remark that few attempts to handle them as generic objects have been made in the field of Computer Algebra [24]. The only genuine effort is due to Verbaeten [1] who studied recurrence relations of hypergeometric functions. The same type of functions was considered by Lafferty [2], who was interested in reducing them to elementary or special functions by doing pattern matching with RR.
Symbol manipulation and formula manipulation
Authors: Dongyue Chen
Published: January 2007

For years, Chinese research workers have noticed that there are systems for symbol manipulation and formula manipulation abroad. But use of computers in China is later. In early years, only assemblers, ALGOL, BASIC and FORTRAN languages were used, which were not suited to help manipulate formulas. Someone has considered extending FORTRAN by manipulation functions. Many people hope to use LISP language and some formula manipulation languages.
A note on leftmost innermost term reduction
Authors: Stickel Mark E.
Published: January 2007

Küchlin presents an indeterministic abstract term-reduction algorithm that allows one to select arbitrarily which node to reduce next---an algorithm that (by using explicit labeling of nodes) is optimal in the sense that it does not attempt to reduce nodes again that have already been fully reduced by it. He then analyzes two standard reduction algorithms (leftmost innermost and leftmost outermost reduction) that employ implicit labeling of nodes to preclude attempts to reduce anew already fully reduced nodes. In the case of leftmost innermost reduction, the implicit labeling designates all terms to the left of or below the term currently being reduced as being already fully reduced. His algorithm for leftmost innermost reduction is as follows:
A criterion for eliminating unnecessary reductions in the Knuth-Bendix algorithm
Authors: Winkler F. , Buchberger B.
Published: January 2007

Given a finite set
E
of multivariate polynomials, the second author's 1965 algorithm constructs a set
E'
of polynomials such that
E
and
E'
generate the same ideal congruence, but
E'
has the additional property that the congruence can be decided by "reduction to normal forms w.r.t.
E'."
The two essential ideas of this algorithm are: the consideration of certain "critical pairs" associated with elements in
E
and the successive "completion" of
E
by adjoining the difference of normal forms of critical pairs.
Clarifications to the symbolic mode in REDUCE
Authors: Abi-Ezzi Salim S.
Published: January 2007

I assume the reader's knowledge of REDUCE's syntax, see [1,2]. The symbolic mode in REDUCE is best thought of as LISP presented in PASCAL like form. This mode should be used for system building and major enhancements to the algebraic mode, while most application programs will be written in algebraic mode.
A discussion and implementation of Brown's REX simplification algorithm
Authors: McGeer Patrick C.
Published: January 2007

We discuss a simplification algorithm written by W. S. Brown [Bro69], which gives a normal form algorithm for a class of rational expressions merged with (perhaps complex) exponential expressions. Here we describe the algorithm as revised for implementation in the Maple Symbolic Computation System at the University of Waterloo [Cha83]. We provide some tests and comparisons with alternative systems.
Implementation of a package of tools for manipulation of sums
Authors: Smith C. J.
Published: January 2007

This paper describes the design and implementation of a prototype package of tools for manipulating formal mathematics in a graphics and symbolic computation system. Our particular example is the manipulation of formal sums. We define a 'sum' datatype in a more general way than in current algebra systems such as Macsyma. We use integer intervals or other sets as the domain of summation. At each step of an interactive computation, the names of possibly appropriate rules are presented for further transformations. Further study is necessary to determine if this kind of prompting is generally useful.
Taylor series solutions of explicit ODE's in a strongly typed algebra system
Authors: Williamson Clifton
Published: January 2007

This paper describes how Taylor series solutions of explicit ODE's were implemented in a strongly typed algebra system. The use of hierarchical typing allows one to write code which can be modified and expanded easily in a mathematically structured way. We also give a brief explanation of recent work at UC Berkeley in the context of algebraic system building.
A computer-aided vector algebra system for use in high schools
Authors: Lounesto Pertti
Published: January 2007

A computer program has been developed to be used in conjunction with college algebra and geometry courses when introducing complex numbers and vector algebra. The input and output form of complex numbers looks like this: a=1+3i. It is possible to define functions, for example, f(z) = a*z + z/(z-a), by just writing the definition, and evaluate their values: f(3+4i) = -7+14i. Similarly, the input-output form for vectors is the usual 5i-3j+7k or then a form applicable also in higher dimensions 5<1-3<2+7<3. The system can be used to evaluate numerically expressions containing vector formulas, like several cross-products, and so students can benefit from this program while doing their homework in vector algebra. The system can also be used to demonstrate subgroups, commutators, idempotents, zero factors, etc., in elementary courses on group theory and ring theory. This program is written in PASCAL and it is called CLICAL.
Complexity issues in algebraic algorithms
Authors: Miola Alfonso
Published: January 2007

The area of Symbolic Mathematics has received a wide attention in the last years, with significant results in algorithms design, systems implementation and development of applications. Many of these results have a direct relation to mathematical education, either as new topics to be covered in mathematical curricula or as powerful methods and effective tools for teaching and learning.
Classroom experience with interactive formula manipulation
Authors: Ollongren Alexander
Published: January 2007

Some experiences with the use of an interactive formula manipulator in classroom situations are reported. Although a kind of script must be prepared in advance, it is not necessary to program the sessions in detail.
The introduction of a computer-based tool for solving mathematical problems analytically to an undergraduate course
Authors: Pearce P. D.
Published: January 2007

This paper suggests why it is appropriate to now introduce the use of a computer-based tool for solving mathematical problems analytically into a BSc degree course in Information Systems Design. Students enter this course from different mathematical backgrounds and need to be able to use mathematics itself, as a tool, to solve other problems.
A radical proposal for computer algebra in education
Authors: Stoutemyer David R.
Published: January 2007

Unlike ordinary numeric computation, computer algebra systems can perform nonnumeric mathematical operations such as factoring and expanding or symbolically integrating and differentiating. These operations can entail complicated expressions containing thousands of terms. Moreover, the arithmetic that compliments these nonnumeric operations includes exact rational arithmetic, automatically using as many digits as necessary to accomplish this. These systems can even perform analytical operations on non-scalars such as vectors, matrices and tensors having nonnumeric components.None of the commonly-taught programming languages is very relevant to the typical primary through university math curriculum, but computer algebra is relevant to most of that curriculum. Consequently, a vast opportunity for beneficial mutual reinforcement and cross-motivation between math and computer education is being squandered. This paper substantiates these claims, then proposes remedies.
The future of computer algebra
Authors: Zippel Richard
Published: January 2007

Great strides have been made in computer algebra over the past dozen years. These include our progress on integrating elementary and higher functions, improved algorithms for greatest common divisor calculations and for factoring polynomials and the Gröbner basis algorithm and its application to problems in commutative algebra including solving systems of algebraic equations. All of these results have made possible calculations that were unthinkable a dozen years ago. In addition there has been significant progress developing portable versions of algebraic manipulation systems that run a wide variety of readily accessible computers. It should soon be the case that anyone who wants will have computer algebra facilities of some type at his or her disposal. This, the dream of the founders of algebraic manipulation, is nearly at hand.
Factorization of polynomials
Authors: Lenstra Arjen K.
Published: January 2007

The last few years there have been a lot of exciting new results in the area of factorization of polynomials. In this note we give an overview of the most important results, and we give some directions for future research.
Computing with geometric objects
Authors: Nievergelt J.
Published: January 2007

The types of computer applictions dominant at different times may be classified into three generations according to their influence on the development of computing.
Integration in finite terms
Authors: Davenport James
Published: January 2007

The first remark that must be made about integration in finite terms is that all the algorithms, and nearly all the implementations (Wang [1971] is the exception), deal with indefinite integration. Definite integration is largely restricted to a combination of table look-up and "guess the contour" heuristics. As has often been pointed out [Askey, 1984], definite integration is far more applicable than indefinite integration, since many special functions (β and Γ functions, for example) are defined by definite integrals, and whole tools, such as Laplace transforms, are built on definite integrals. We note that these problems are fundamentally algebraic, rather than numerical, since we are computing, not a number, but a function defined by
F
(
y
) = ∫
f
(
x
,
y
)d
x
. Very little is known about algorithmic definite integration, though recent work in transcendence theory (see, e.g., Chudnovsky [1982]) may at least provide some methods for showing negative results.
Algorithms in algebraic number theory
Authors: Zimmer Horst G.
Published: January 2007

Symbolic and algebraic computation has gained increasing importance and interest in algebra, algebraic number theory and algebraic geometry during the last years. For doing research in these fields the need for examples arises. The use of high speed computers makes it possible to provide large scale examples which in turn contribute to the progress of research. Such examples are obtained in a systematic manner by means of a comprehensive and connected system of algorithms. At the University of Saarbrücken we use the SAC-2-System of Collins and Loos on a Siemens computer since 1981.
Procedures for polynomial and rational function recognition
Authors: Smith Carolyn J.
Published: January 2007

Suppose we are given a class of expressions closed under the rational operations and a set of indeterminates with the property that a procedure (essentially an "oracle") exists to recognize any member of the class that simplifies to zero. Let us call such a class over which such an oracle exists, a ZE class.
Work with non-commutative variables in the reduce-2 system for analytical calculations
Authors: Rodionov A. Ya.
Published: January 2007

A brief description and examples of using a program package for handling non-commutative variables in the REDUCE-2 system are presented. The package facilitates work with arbitrary commutation rules. The user may declare operators, variables, and procedures to be non-commutative, and introduce the rules for their rearrangement. Tools are included for reducing delta functions and Kronecker symbols in expressions involving non-commutative variables. During calculation, expressions are rearranged according to the rules introduced by the user, and similar terms are grouped together with explicit singling out of the non-commutative part.
Completing the L-th power in Z[x]
Authors: Zwillinger Daniel
Published: January 2007

In this note we give an algorithm for solving the equation:[EQUATION]using MACSYMA. In equation (1) the polynomials with integer coefficients {p
i
(x)} and the numbers N, K, L and the degree of d(x) are assumed to be known (with K≠O). We look for the polynomial d(x), with integer coefficients, such that the left hand side of (1) is K times a perfect L-th power of some polynomial r(x). We do not know r(x), only that it must have integer coefficients.
The Church-Rosser property in computer algebra and special theorem proving
Authors: Winkler Franz
Published: January 2007

An important problem both in computer algebra and special theorem proving in connection with automatic program verification is the calculation of canonical forms with respect to some given side relations. If these side relations can be viewed as a rewrite system which has the Church-Rosser property then a normal form algorithm with respect to this system provides a canonical simplifier. For many computational domains there exists a "completion algorithm" for transforming an arbitrary rewrite system into an equivalent one which has the Church-Rosser property. Improvements to the existing completion algorithms are presented. A very general completion algorithm is described which contains all these various algorithms as special cases. A complexity bound for the Buchberger algorithm for trivariate polynomial equations is derived.
A forum for the synergy of ACM special interest groups
Authors: Ören Tuncer I.
Published: January 2007

Simulation which is experimentation with models is an important model-based activity and can have two-way interaction with almost all of the fields of knowledge represented by ACM Special Interest Groups which are listed herebelow:
Pattern matching algebraic identities
Authors: McIsaac Kevin
Published: January 2007

The problem of matching an identity to a function is explored. Two methods of improving the speed of the matching process are given. One involves detecting failure as early as possible in the matching process. The other is a notational extension that improves the scaling behaviour of the identity.
An improvement to the centralizer algorithm for permutation groups
Authors: Butler Gregory
Published: January 2007

This note presents an improvement to an algorithm due to Sims(1971) for computing the centralizer of an element in a permutation group. We assume the reader is familiar with the algorithm and the related concepts and notation.
Comments on SMP
Authors: Fateman Richard J.
Published: January 2007

Some time ago, a student here at UC Berkeley was interested in trying the pattern matching program in the computer algebra system, SMP. Before he could really get started, a letter from friends at another university, detailing a number of fairly astonishing bugs in SMP, arrived. After confirming that the bugs existed in the SMP (version 1.3.7, July 1984) system we were using at Lawrence Livermore National Lab, we felt that SMP had lost a fair amount of credibility, and we were hesitant to poke at it very much. Nevertheless it seemed important to bring to light some of the more striking observations so they could be fixed or explained.
Gentran
Authors: Gates Barbara L.
Published: January 2007

GENTRAN is a code generation and translation package implemented in RLISP to run under REDUCE. It generates complete numerical programs directly from REDUCE by transforming REDUCE prefix forms into formatted FORTRAN, RATFOR or C code. Assignment statements, control structures, type declarations, and subprogram headings can be generated from algorithmic specifications and symbolically derived formulas. An expression segmentation facility breaks large expressions into subexpressions of manageable size, and an interface to an existing code optimizer allows sequences of assignment statements to be replaced by their optimized equivalents. In addition, special file-handling facilities allow code generation to be guided by template files and output to be redirected to one or more files. GENTRAN provides the flexibility necessary to handle most code generation applications.
Instance Filtering for entity recognition
Authors: Gliozzo Alfio Massimiliano , Giuliano Claudio , Rinaldi Raffaella
Published: January 2007

In this paper we propose
Instance Filtering
as preprocessing step for supervised classification-based learning systems for entity recognition. The goal of Instance Filtering is to reduce both the skewed class distribution and the data set size by eliminating negative instances, while preserving positive ones as much as possible. This process is performed on both the training and test set, with the effect of reducing the learning and classification time, while maintaining or improving the prediction accuracy. We performed a comparative study on a class of Instance Filtering techniques, called
Stop Word Filters
, that simply remove all the tokens belonging to a list of stop words. We evaluated our approach on three different entity recognition tasks (i.e. Named Entity, Bio-Entity and Temporal Expression Recognition) in English and Dutch, showing that both the skewness and the data set size are drastically reduced. Consequently, we reported an impressive reduction of the computation time required for training and classification, while maintaining (and sometimes improving) the prediction accuracy.
Distributed higher order association rule mining using information extracted from textual data
Authors: Li Shenzhi , Wu Tianhao , Pottenger William M.
Published: January 2007

The burgconing amount of textual data in distributed sources combined with the obstacles involved in creating and maintaining central repositories motivates the need for effective distributed information extraction and mining techniques. Recently, as the need to mine patterns across distributed databases has grown, Distributed Association Rule Mining (D-ARM) algorithms have been developed. These algorithms, however, assume that the databases are either horizontally or vertically distributed. In the special case of databases populated from information extracted from textual data, existing D-ARM algorithms cannot discover rules based on higher-order associations between items in distributed textual documents that are neither vertically nor horizontally distributed, but rather a hybrid of the two. In this article we present D-HOTM, a framework for Distributed Higher Order Text Mining. D-HOTM is a hybrid approach that combines information extraction and distributed data mining. We employ a novel information extraction technique to extract meaningful entities from unstructured text in a distributed environment. The information extracted is stored in local databases and a mapping function is applied to identify globally unique keys. Based on the extracted information, a novel distributed association rule mining algorithm is applied to discover higher-order associations between items (i.e., entities) in records fragmented across the distributed databases using the keys. Unlike existing algorithms, D-HOTM requires neither knowledge of a global schema nor that the distribution of data be horizontal or vertical. Evaluation methods are proposed to incorporate the performance of the mapping function into the traditional support metric used in ARM evaluation. An example application of the algorithm on distributed law enforcement data demonstrates the relevance of D-HOTM in the fight against terrorism.
Remarks about the application of decision-methods of elementary Real Algebra
Authors: Böqe W.
Published: January 2007

Many problems in numerical mathematics can be described by formulas and sentences of elementary real algebra, i.e. by real variables, +, ., -, >, =, by logical operations [EQUATION] and by existential and universal quantifiers. In 1933 A. Tarski found a method which enables one to decide in a finite number of steps whether such a sentence is true or false.
Analysis of the subtractive algorithm for greatest common divisors
Authors: Yao C. C. , Knuth D. E.
Published: January 2007

The sum of all partial quotients in the regular continued fraction expansions of m/n, for 1 ≤m≤n, is shown to be 6Π
-2
n(ln n)
2
+ O(n log n(log log n)
2
). This result is applied to the analysis of what is perhaps the oldest nontrivial algorithm for number-theoretic computations.
Reference count overflow
Authors: Lauer M. , Saemann M.
Published: January 2007

There exists an implementation of the SAC-1 System [2] on computers with 32 bits per word (such as IBM 370, Siemens 7.730) in which each cell has the form:[EQUATION]Its easy to see, that there will be no reference count overflow in this version.
Symbolic solution of a system of first order linear differential equations
Authors: Clark S. James
Published: January 2007

PL/I FORMAC is used to find the symbolic solution to a system of first order simultaneous linear differential equations with alphanumeric coefficients by applying the Laplace transform. The program incorporates routines to solve systems of linear equations with alphanumeric coefficients, Nth order determinants with alphanumeric elements, and divisions of one polynomial by another.