When does equal sat(T)?

Authors:
François Lemaire;Marc Moreno Maza;Wei Pan;Yuzhen Xie
Affiliations:
University Lille 1, France;University of Western Ontario, Department of Computer Science, London, Ontario, Canada N6A 5B7;University of Western Ontario, Department of Computer Science, London, Ontario, Canada N6A 5B7;University of Western Ontario, Department of Computer Science, London, Ontario, Canada N6A 5B7
Venue:
Journal of Symbolic Computation
Year:
2011

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Abstract

Given a regular chain T, we aim at finding an efficient way for computing a system of generators of sat(T), the saturated ideal of T. A natural idea is to test whether the equality =sat(T) holds, that is, whether T generates its saturated ideal. By generalizing the notion of primitivity from univariate polynomials to regular chains, we establish a necessary and sufficient condition, together with a Grobner basis free algorithm, for testing this equality. Our experimental results illustrate the efficiency of this approach in practice.