numericalsgps, a GAP package for numerical semigroups

Abstract

Abstract. The package numericalsgps performs computations with and for numerical semigroups. Recently also affine semigroups are admitted as objects for calculations. This manuscript is a survey of what the package does, and at the same time of the trending topics on numerical semigroups.

Almost symmetric numerical semigroups with given Frobenius number and type

“…The algorithm ends because the sets B(F, t) and A(S ′ ), S ′ ∈ B(F, t), are empty or finite. We can verify this computation by using the NumericalSgps package (see [5]). It suffices to change the first line in the code provided in [15,Example 5] by almostnsfromirreducibleAlt := function(s,t) and set the variable pow as Combinations(msg,CeilingOfRational(t/2)-1).…”

“…A much more refined implementation of our algorithm can be found at the development version site of the NumericalSgps package ( [5]): https://github.com/gap-packages/num…”

“…AlmostSymmetricNumericalSemigroupsWithFrobeniusNumber is the one included in the version 1.1.8 of the NumericalSgps package ( [5]).…”

An algorithm to compute the primitive elements of an embedding dimension three numerical semigroup

“…For n = 3 there are at most two L-forms, but this is not the case for n > 3. For instance, for 5, 7, 11, 13 , we have We use the numericalsgps ( [5]) GAP package for the implementation. In the above representation, each L-form is given by a list containing a factorization for each of the elements in Ap(S, 13) with respect to the semigroup 5, 7, 11 .…”

The Catenary and Tame Degrees on a Numerical Monoid Are Eventually Periodic

“…We close this section by noting that computing done in connection with these results was run on the GAP numerical semigroups package [10]. Also, any undefined notation or definitions will be consistent with those used in the monograph [15].…”