An algorithm to calculate optimal homogeneous systems of parameters

When a homogeneous system of parameters f(1),...,f(n) is chosen for a grade d algebra A, it is important for subsequent computations that the degrees, deg(f(i)), are as small as possible. More precisely, one would like the pro duct 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 whic h constructs an optimal homogeneous system of parameters. Here the notion o f what is considered as optimal is part of the input. An important applicat ion is the case where A is the invariant ring of a finite linear group. The re is an implementation of the algorithm in Magma which applies to this cas e. (C) 1999 Academic Press.