Efficient Computation of Algebraic Local Cohomology Classes and Change of Ordering for Zero-Dimensional Standard Bases

Abstract

A new effective algorithm for computing a set of algebraic local cohomology classes is presented. The key ingredient of the proposed algorithm is to utilize a standard basis. As the application, an algorithm is given for the conversion of a standard basis of a zero-dimensional ideal with respect to any given local ordering into a standard basis with respect to any other local ordering, in the formal power series ring. The new algorithm always outputs a reduced standard basis.