The Altran system for rational function manipulation — a survey
Communications of the ACM
ACM SIGSAM Bulletin
ALTRAN programs for SIGSAM problem #6
ACM SIGSAM Bulletin
On computing with factored rational expressions
ACM SIGSAM Bulletin
A rational function arithmetic and simplification system in common Lisp
ACM SIGSAM Bulletin
A new REDUCE model for algebraic simplification
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
On computing with factored rational expressions
ACM SIGSAM Bulletin
ACM SIGSAM Bulletin
Ten commandments for good default expression simplification
Journal of Symbolic Computation
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In this paper we present detailed algorithms for the basic arithmetic operations on symbolic rational expressions represented by formal quotients of factored polynomials. These algorithms are currently implemented in the ALTRAN system for symbolic algebra but the descriptions given in this paper are system independent.First we describe the representation and examine the need for options to permit control over the amount of effort expended in the search for factors or in canonicalizing results. We then present algorithms in the form of programs for equality-test, exponentiation, multiplication, and addition, and mention the modifications required for division and subtraction.We conclude by presenting the results of several benchmark tests comparing the performance of these algorithms with others previously used.