On the computation of factorization invariants for affine semigroups

TL;DR

This paper introduces new algorithms for calculating key factorization invariants in affine semigroups, including delta sets, tame degrees, and catenary degrees, using advanced algebraic techniques.

Contribution

It presents the first algorithm for delta set computation, improves tame degree calculation, and develops a dynamic method for catenary degrees in affine semigroups.

Findings

First known algorithm for delta set of affine semigroups

Improved method for tame degree computation

Dynamic algorithm for catenary degrees

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.