When does ( T ) equal sat( T )?
François Lemaire, Marc Moreno Maza, Wei Pan, Yuzhen Xie · 2008
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 {T}=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.