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Iris: design of an user interface program for symbolic algebra
We present the design of a user interface program that can be used with Maple and other symbolic algebra packages. Through the use of a standard communications protocol to such a program, symbolic algebra packages can shed the bulk of code not directly ...
MathScribe: a user interface for computer algebra systems
This paper describes MathScribe, a powerful user interface for computer algebra systems. The interface makes use of a bitmapped display, windows, menus, and a mouse. Significant new features of MathScribe are its display of both input and output in two-...
PowerMath: a system for the Macintosh
PowerMath is a symbolic algebra system for the MacIntosh computer. This paper outlines the design decisions that were made during its development, and explains how the novel MacIntosh environment helped and hindered the development of the system. While ...
An object-oriented approach to algebra system design
This paper describes a new computer algebra system design based on the object-oriented style of programming and an implementation of this design, called Views, written in Smalltalk-80. The design is similar in goals to other 'new' generation computer ...
Construction of rational approximations by means of REDUCE
1. In recent years the rational approximations have been widely used to solve physical and computational problems /1,2/. When a real function f(x) is repeatedly calculated on a ≤ × ≤ b, it is reasonable to replace it by a polynomial or rational ...
Alkahest III: automatic analysis of periodic weakly nonlinear ODEs
In previous papers by the current authors various attempts that have been made in the automatic derivation of periodic solutions to weakly nonlinear differential equations have been reported. The equations in question are all perturbations of y′+y = 0, ...
Code generation for hybrid mixed mode formulation in finite element analysis
Recently developed techniques for the symbolic derivation of formulas and the automatic generation of code for numerical computation are applied to formulate the hybrid mixed model in finite element analysis. The hybrid mixed model is a promising ...
How to compute multivariate Pade approximants
We present here various ways of generalizing the Padé approximation to multivariate functions. To compute them, we use a computer algebra system: REDUCE.
Divide-and-conquer in computational group theory
The paradigm of divide-and-conquer appears in five guises in computational group theory: Subgroup Restriction, Subgroup Lifting, Extension, Normal Lifting, and Homomorphic Lifting. The building blocks for these strategies are algorithms for subgroup ...
Limitations to algorithm solvability: Galois methods and models of computation
We use simple arguments from Galois theory to prove the impossibility of exact algorithms for problems under various models of computation. In particular we show that there exist applied computational problems for which there are no closed from ...
Summation of binomial coefficients using hypergeometric functions
An algorithm which finds the definite sum of many series involving binomial coefficients is presented. The method examines the ratio of two consecutive terms of the series in an attempt to express the sum as an ordinary hypergeometric function. A closed ...
There is no “Uspensky's method.”
In this paper an attempt is made to correct the misconception of several authors [1] that there exists a method by Upensky (based on Vincent's theorem) for the isolation of the real roots of a polynomial equation with rational coefficients. Despite ...
A numerical code generation facility for REDUCE
Many scientific problems require mathematical modeling and symbolic derivation to produce formulas which are evaluated numerically. Computer algebra systems can be used effectively in the symbolic derivation phase and subsequently to generate numerical ...
Enlarging the REDUCE domain of computation
We describe the methods available in the current REDUCE system for introducing new mathematical domains, and illustrate these by discussing several new domains that significantly increase the power of the overall system.
A sparse distributed representation using prime numbers
The Fundamental Theorem of Arithmetic (uniqueness of the prime factorisation of positive integers) allows us to represent multivariate polynomials by LISP lists of ordered pairs of numbers. In this representation one can perform all the elementary ...
Simplification of algebraic expression by multiterm rewriting rules
In simplifying an algebraic expression, human often applies multiterm rewriting rules cleverly. This paper describes a simple multiterm rewriting algorithm which simulates human simplification naively. The algorithm is simple but seems to be quite ...
Constructive solid geometry: a symbolic computation approach
A method of parameterizing an object that is represented by constructive solid geometry (CSG) is provided. A method is developed for generating the constraint equations on the parameters which provides a sufficient condition so that the object remains ...
New results for random determination of equivalence of expressions
We devise several procedures based on signatures (or hashing functions) to determine equivalence of expressions in Random Polynomial Time (also called Probabilistic Polynomial Time) (RPT). We extend the previous results known to include various new ...
Computer algebra in the undergraduate mathematics classroom
Unrestricted usage of the computer algebra system Maple was made available to many sections of undergraduate mathematics classes in 1985 as part of an on-going investigation into the uses of computers in mathematics education. The paper discusses some ...
Computer understanding and generalization of symbolic mathematical calculations: a case study in physics problem solving
An artificial intelligence system that learns by observing its users perform symbolic mathematical problem solving is presented. This fully-implemented system is being evaluated as a problem solver in the domain of classical physics. Using its ...
Index Terms
- Proceedings of the fifth ACM symposium on Symbolic and algebraic computation