Mora's holy graal : algorithms for computing in localizations at prime ideals

Abstract

This article discusses a computational treatment of the localization AL of an affine coordinate ring A at a prime ideal L and its associated graded ring Gra(AL) with the means of standard basis techniques. Building on Mora’s work, we present alternative proofs on two of the central statements and expand on the applications mentioned by Mora: resolutions of ideals, systems of parameters and Hilbert polynomials, as well as dimension and regularity of AL. All algorithms are implemented in the library graal.lib for the computer algebra system Singular.