Scratchpad's view of algebra I: Basic commutative algebra

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.KeywordsIntegral DomainCommutative AlgebraComputer Algebra SystemUnique FactorisationGreat Common DivisorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.