GAP (NumericalSgps) - Appendix C: Contributions

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C Contributions
C.1 Functions implemented by A. Sammartano
C.2 Functions implemented by C. O'Neill
C.3 Functions implemented by K. Stokes
C.4 Functions implemented by I. Ojeda and C. J. Moreno Ávila
C.5 Functions implemented by I. Ojeda
C.6 Functions implemented by A. Sánchez-R. Navarro
C.7 Functions implemented by G. Zito
C.8 Functions implemented by A. Herrera-Poyatos
C.9 Functions implemented by Benjamin Heredia
C.10 Functions implemented by Juan Ignacio García-García
C.11 Functions implemented by C. Cisto
C.12 Functions implemented by N. Matsuoka
C.13 Functions implemented by N. Maugeri
C.14 Functions implemented by H. Martín Cruz
C.15 Functions implemented by J. Angulo Rodríguez
C.16 Functions implemented by F. Strazzanti

### C Contributions

Sebastian Gutsche helped in the implementation of inference of properties from already known properties, and also with the integration of 4ti2Interface. 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` (6.2-11),

`IsAperySetBetaRectangular` (6.2-12),

`IsAperySetAlphaRectangular` (6.2-13),

`TypeSequenceOfNumericalSemigroup` (7.1-33),

`IsGradedAssociatedRingNumericalSemigroupBuchsbaum` (7.5-2),

`IsGradedAssociatedRingNumericalSemigroupBuchsbaum` (7.5-2),

`TorsionOfAssociatedGradedRingNumericalSemigroup` (7.5-3),

`BuchsbaumNumberOfAssociatedGradedRingNumericalSemigroup` (7.5-4),

`IsMpureNumericalSemigroup` (9.8-2),

`IsPureNumericalSemigroup` (9.8-1),

`IsGradedAssociatedRingNumericalSemigroupGorenstein` (7.5-5),

`IsGradedAssociatedRingNumericalSemigroupCI` (7.5-6).

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

Chris implemented the following functions described in [BOP17]:

`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` (11.4-5). Also he implemented the new version of

`AperyListOfNumericalSemigroupWRTElement` (3.1-16).

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

Klara Stokes helped with the implementation of functions related to patterns for ideals of numerical semigroups 7.4.

#### 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. Since the new implementation by Chris was included, these algorithms are no longer used.

#### C.5 Functions implemented by I. Ojeda

Ignacio also implemented the following functions.

`AlmostSymmetricNumericalSemigroupsFromIrreducibleAndGivenType` (6.3-2),

`AlmostSymmetricNumericalSemigroupsWithFrobeniusNumberAndType` (6.3-5),

`NumericalSemigroupsWithFrobeniusNumberAndMultiplicity` (5.4-2),

`IrreducibleNumericalSemigroupsWithFrobeniusNumberAndMultiplicity` (6.1-6).

Ignacio also implemented the new versions of

`AlmostSymmetricNumericalSemigroupsWithFrobeniusNumber` (6.3-4),

`NumericalSemigroupsWithFrobeniusNumber` (5.4-3),

#### C.6 Functions implemented by A. Sánchez-R. Navarro

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

`FactorizationsVectorWRTList` (11.4-1),

`DegreesOfPrimitiveElementsOfAffineSemigroup` (11.3-11),

`MinimalPresentationOfAffineSemigroup` (11.3-6).

He also helped in preliminary versions of the following functions.

`CatenaryDegreeOfSetOfFactorizations` (9.3-1),

`TameDegreeOfSetOfFactorizations` (9.3-6),

`TameDegreeOfNumericalSemigroup` (9.3-12),

`TameDegreeOfAffineSemigroup` (11.4-10),

`OmegaPrimalityOfElementInAffineSemigroup` (11.4-11),

`CatenaryDegreeOfAffineSemigroup` (11.4-6),

`MonotoneCatenaryDegreeOfSetOfFactorizations` (9.3-4).

`EqualCatenaryDegreeOfSetOfFactorizations` (9.3-3).

`AdjacentCatenaryDegreeOfSetOfFactorizations` (9.3-2).

`HomogeneousCatenaryDegreeOfAffineSemigroup` (11.4-8).

#### C.7 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.8 Functions implemented by A. Herrera-Poyatos

Andrés Herrera-Poyatos gave new implementations of

`IsSelfReciprocalUnivariatePolynomial` (10.1-11) and

`IsKroneckerPolynomial` (10.1-7). Andrés is also coauthor of the dot functions, see Chapter 14

#### C.9 Functions implemented by Benjamin Heredia

Benjamin Heredia implemented a preliminary version of

`FengRaoDistance` (9.7-1).

#### C.10 Functions implemented by Juan Ignacio García-García

Juan Ignacio implemented a preliminary version of

`NumericalSemigroupsWithFrobeniusNumber` (5.4-3).

#### C.11 Functions implemented by C. Cisto

Carmelo provided some functions to deal with affine semigroups given by gaps, and to compute gaps of affine semigroups with finite genus, see for instance

`AffineSemigroupByGaps` (11.1-5),

`RemoveMinimalGeneratorFromAffineSemigroup` (11.1-12),

`AddSpecialGapOfAffineSemigroup` (11.1-13).

#### C.12 Functions implemented by N. Matsuoka

Naoyuki implemented the function associated to the generalized Gorenstein property, see Section 6.4.

#### C.13 Functions implemented by N. Maugeri

Nicola fixed the implementation of `ArfGoodSemigroupClosure` (12.4-1). He also implemented

`ProjectionOfAGoodSemigroup` (12.2-12),

`GenusOfGoodSemigroup` (12.2-13),

`LengthOfGoodSemigroup` (12.2-14),

`AperySetOfGoodSemigroup` (12.2-15),

`StratifiedAperySetOfGoodSemigroup` (12.2-16),

`AbsoluteIrreduciblesOfGoodSemigroup` (12.5-8),

`TracksOfGoodSemigroup` (12.5-9),

`RandomGoodSemigroupWithFixedMultiplicity` (B.3-1). And the multiplicity and local property for good semigroups.

#### C.14 Functions implemented by H. Martín Cruz

Helena helped in the implementation of the code for ideals of affine semigroups 11.5

#### C.15 Functions implemented by J. Angulo Rodríguez

Jorge implemented the code corresponding to decompositions of ideals into irreducibles 7.2. He also implemented `NumericalSemigroupByNuSequence` (9.6-4) and `NumericalSemigroupByTauSequence` (9.6-5).

#### C.16 Functions implemented by F. Strazzanti

Francesco helped in the implementation of the following methods.

`IsAlmostCanonicalIdeal` (7.1-31),

`TraceIdealOfNumericalSemigroup` (7.1-32),

`IsNearlyGorenstein` (6.4-2),

`IsGeneralizedAlmostSymmetric` (6.4-4),

`IsHomogeneousNumericalSemigroup` (9.8-3),

`AsNumericalDuplication` (5.2-5),

`RFMatrices` (9.1-6),

`DilatationOfNumericalSemigroup` (5.2-7).

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