Scratchpad's view of algebra I: Basic commutative algebra

Reference:

Davenport, J. H. and Trager, B. M., 1990. Scratchpad's view of algebra I: Basic commutative algebra. In: Design and Implementation of Symbolic Computation Systems: International Symposium DISCO '90 Capri, Italy, April 10–12, 1990 Proceedings. Berlin: Springer, pp. 40-54. (Lecture Notes in Computer Science; 429/1990)

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Official URL:

http://dx.doi.org/10.1007/3-540-52531-9_122

Abstract

While computer algebra systems have dealt with polynomials and rational functions with integer coefficients for many years, dealing with more general constructs from commutative algebra is a more recent problem. In this paper we explain how one system solves this problem, what types and operators it is necessary to introduce and, in short, how one can construct a computational theory of commutative algebra. Of necessity, such a theory is rather different from the conventional, non-constructive, theory. It is also somewhat different from the theories of Seidenberg [1974] and his school, who are not particularly concerned with practical questions of efficiency.

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