MEGA 2007 Effective Methods in Algebraic Geometry Strobl, Austria, June 25th - 29th http://www.ricam.oeaw.ac.at/mega2007

Abstract

Title	Fast Computation of non-modular Invariant Rings of Finite Groups
Keywords	Invariant Ring, Secondary Invariant, irreducible Secondary Invariant, Gröbner basis
Abstract	A very classical subject in Commutative Algebra is the Invariant Theory of finite groups. In our work on 3-dimensional topology, we found certain examples of non-modular group actions on polynomial rings. When we tried to compute the invariant ring using Singular or Magma, it turned out that the existing algorithms did not suffice. Therefore we developed a new algorithm, using three new ideas. Our benchmarks show that the implementation of our algorithm in Singular release 3-0-2 marks a dramatic improvement in the manageable problem size. A particular benefit of our algorithm is that the computation of irreducible secondary invariants does not require the explicit computation of reducible secondary invariants, which may save resources.

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