An Algorithm to Calculate Optimal Homogeneous Systems of Parameters

When a homogeneous system of parametersf1,...,fnis chosen for a graded algebraA, it is important for subsequent computations that the degrees, deg(fi), are as small as possible. More precisely, one would like the product or the sum of the degrees to be minimal, depending on the application. This article investigates which degree vectors can occur as the degrees of a homogeneous system of parameters. From this, an algorithm is derived which constructs an optimal homogeneous system of parameters. Here the notion of what is considered asoptimalis part of the input. An important application is the case whereAis the invariant ring of a finite linear group. There is an implementation of the algorithm in Magma which applies to this case.