The computation of factorization invariants for affine semigroups. (English) Zbl 1457.20045
Summary: 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 Gröbner bases, Hilbert bases, and other standard techniques. Implementation in the computer algebra system GAP is discussed.
MSC:
| 20M13 | Arithmetic theory of semigroups |
| 20M14 | Commutative semigroups |
| 05A17 | Combinatorial aspects of partitions of integers |
| 13F65 | Commutative rings defined by binomial ideals, toric rings, etc. |
| 13P10 | Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) |
Software:
SCIP; SageMath; SINGULAR; GAP; 4ti2; singular; Normaliz; NormalizInterface; 4ti2gap; GitHub; numericalsgpsReferences:
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