On the computation of factorization invariants for affine semigroups

Abstract

We present several new algorithms for computing factorization invariant values over affine semigroups. In particular, we give (i) the first known algorithm to compute the delta set of any affine semigroup, (ii) an improved method of computing the tame degree of an affine semigroup, and (iii) a dynamic algorithm to compute catenary degrees of affine semigroup elements. Our algorithms rely on theoretical results from combinatorial commutative algebra involving Gr\"obner bases, Hilbert bases, and other standard techniques. Implementation in the computer algebra system GAP is discussed.