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### C Contributions

Sebastian Gutsche helped in the implementation of inference of properties from already known properties. Max Horn adapted the definition of the objects numerical and affine semigroups; the behave like lists of integers or lists of lists of integers (affine case), and one can intersect numerical semigroups with lists of integers, or affine semigroup with cartesian products of lists of integers.

#### C.1 Functions implemented by A. Sammartano

A. Sammartano implemented the following functions.

IsAperySetGammaRectangular (6.2-10),

IsAperySetBetaRectangular (6.2-11),

IsAperySetAlphaRectangular (6.2-12),

TypeSequenceOfNumericalSemigroup (7.1-20),

IsGradedAssociatedRingNumericalSemigroupBuchsbaum (7.4-2),

IsGradedAssociatedRingNumericalSemigroupBuchsbaum (7.4-2),

TorsionOfAssociatedGradedRingNumericalSemigroup (7.4-3),

BuchsbaumNumberOfAssociatedGradedRingNumericalSemigroup (7.4-4),

IsMpureNumericalSemigroup (7.4-5),

IsPureNumericalSemigroup (7.4-6),

IsGradedAssociatedRingNumericalSemigroupGorenstein (7.4-7),

IsGradedAssociatedRingNumericalSemigroupCI (7.4-8).

#### C.2 Functions implemented by C. O'Neill

C. O'Neill implemented the following functions described in [BOP14]:

OmegaPrimalityOfElementListInNumericalSemigroup (9.4-2),

FactorizationsElementListWRTNumericalSemigroup (9.1-3),

DeltaSetPeriodicityBoundForNumericalSemigroup (9.2-7),

DeltaSetPeriodicityStartForNumericalSemigroup (9.2-8),

DeltaSetListUpToElementWRTNumericalSemigroup (9.2-9),

DeltaSetUnionUpToElementWRTNumericalSemigroup (9.2-10),

DeltaSetOfNumericalSemigroup (9.2-11).

And contributed to:

DeltaSetOfAffineSemigroup (11.4-3).

#### C.3 Functions implemented by K. Stokes

Klara Stokes helped with the implementation of functions related to patterns for ideals of numerical semigroups 7.3.

#### C.4 Functions implemented by I. Ojeda and C. J. Moreno Ávila

Ignacio and Carlos Jesús implemented the algorithms given in [Rou08] and [MCOT15] for the calculation of the Frobenius number and Apéry set of a numerical semigroup using Gröbner basis calculations. These methods will be used if 4ti2 is loaded (either 4ti2Interface or 4ti2gap). A faster algorithm is employed provided that singular is loaded.

#### C.5 Functions implemented by A. Sánchez-R. Navarro

Alfredo helped in the implementation of methods for 4ti2gap of the following functions.

FactorizationsVectorWRTList (11.4-1),

PrimitiveElementsOfAffineSemigroup (11.3-9),

MinimalPresentationOfAffineSemigroup (11.3-4).

He also helped in preliminary versions of the following functions.

CatenaryDegreeOfSetOfFactorizations (9.3-1),

TameDegreeOfSetOfFactorizations (9.3-6),

TameDegreeOfNumericalSemigroup (9.3-12),

TameDegreeOfAffineSemigroup (11.4-8),

OmegaPrimalityOfElementInAffineSemigroup (11.4-9),

CatenaryDegreeOfAffineSemigroup (11.4-4),

MonotoneCatenaryDegreeOfSetOfFactorizations (9.3-4).

EqualCatenaryDegreeOfSetOfFactorizations (9.3-3).

AdjacentCatenaryDegreeOfSetOfFactorizations (9.3-2).

HomogeneousCatenaryDegreeOfAffineSemigroup (11.4-6).

#### C.6 Functions implemented by G. Zito

Giuseppe gave the algorithms for the current version functions

ArfNumericalSemigroupsWithFrobeniusNumber (8.2-4),

ArfNumericalSemigroupsWithFrobeniusNumberUpTo (8.2-5),

ArfNumericalSemigroupsWithGenus (8.2-6),

ArfNumericalSemigroupsWithGenusUpTo (8.2-7),

ArfCharactersOfArfNumericalSemigroup (8.2-3).

#### C.7 Functions implemented by A. Herrera-Poyatos

Andrés Herrera-Poyatos gave new implementations of

IsSelfReciprocalUnivariatePolynomial (10.1-9) and

IsKroneckerPolynomial (10.1-7).

#### C.8 Functions implemented by Benjamin Heredia

Benjamin Heredia implemented a preliminary version of

FengRaoDistance (9.7-1).

#### C.9 Functions implemented by Juan Ignacio García-García

Juan Ignacio implemented a preliminary version of

NumericalSemigroupsWithFrobeniusNumber (5.4-1).

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