Open 0f5ae6f6-e03a-45d9-b571-4ce01615e676 opened 14 years ago
Note that Sage (via Singular) can compute minimal generating sets for invariant rings of permutation groups. But the result is not implemented as a ring on its own (i.e., it is a method that returns a list of generators).
First implementation of the Algebra of multivariate polynomials invariant under the action of a permutation group.
From a permutation group and a ring, the goal is to implement an algebra on which one can ask the primary invariants, a minimal generating set and (irreducible)secondary invariants...
Using the category framework, we construct the abstract algebra of PermutationGroupInvariantRing and two representations of it : the graded algebra of multivariate polynomials view as combination of orbit sum of monomials (here #6812 is needed) and the polynomials view as vector evaluated in a collection of points.
This is a long run work but first implementation is comming in one or two months.
depends on #6812 and #5891
CC: @sagetrac-sage-combinat @tscrim
Component: combinatorics
Keywords: invariants, permutation, group, ring, orbit, evaluation
Issue created by migration from https://trac.sagemath.org/ticket/6889