Master thesis in mathematics by Yunong Wang

Title: Computation of Invariant Rings of Finite Groups Using Canonical Bases

Abstract: This thesis investigates the computation of SAGBI-Gröbner bases for ideals in invariant polynomial rings under non-modular permutation group actions. We extend Buchberger’s Algorithm for ideals in polynomial rings to ideals in invariant polynomial rings. By introducing a suitable degree bound, we construct a partial invariant Gröbner basis for an ideal in an invariant ring, from which minimal generating sets of the invariant ring can be recovered as a by product. The algorithms are presented with examples, and future directions on
modular actions are discussed.

Advisor: Anna Torstensson

Examiner: Thomas Edlund