  
  [1XC [33X[0;0YContributions[133X[101X
  
  [33X[0;0YSebastian  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.[133X
  
  
  [1XC.1 [33X[0;0YFunctions implemented by A. Sammartano[133X[101X
  
  [33X[0;0YA. Sammartano implemented the following functions.[133X
  
  [33X[0;0Y[2XIsAperySetGammaRectangular[102X ([14X6.2-10[114X),[133X
  
  [33X[0;0Y[2XIsAperySetBetaRectangular[102X ([14X6.2-11[114X),[133X
  
  [33X[0;0Y[2XIsAperySetAlphaRectangular[102X ([14X6.2-12[114X),[133X
  
  [33X[0;0Y[2XTypeSequenceOfNumericalSemigroup[102X ([14X7.1-20[114X),[133X
  
  [33X[0;0Y[2XIsGradedAssociatedRingNumericalSemigroupBuchsbaum[102X ([14X7.4-2[114X),[133X
  
  [33X[0;0Y[2XIsGradedAssociatedRingNumericalSemigroupBuchsbaum[102X ([14X7.4-2[114X),[133X
  
  [33X[0;0Y[2XTorsionOfAssociatedGradedRingNumericalSemigroup[102X ([14X7.4-3[114X),[133X
  
  [33X[0;0Y[2XBuchsbaumNumberOfAssociatedGradedRingNumericalSemigroup[102X ([14X7.4-4[114X),[133X
  
  [33X[0;0Y[2XIsMpureNumericalSemigroup[102X ([14X7.4-5[114X),[133X
  
  [33X[0;0Y[2XIsPureNumericalSemigroup[102X ([14X7.4-6[114X),[133X
  
  [33X[0;0Y[2XIsGradedAssociatedRingNumericalSemigroupGorenstein[102X ([14X7.4-7[114X),[133X
  
  [33X[0;0Y[2XIsGradedAssociatedRingNumericalSemigroupCI[102X ([14X7.4-8[114X).[133X
  
  
  [1XC.2 [33X[0;0YFunctions implemented by C. O'Neill[133X[101X
  
  [33X[0;0YC. O'Neill implemented the following functions described in [BOP14]:[133X
  
  [33X[0;0Y[2XOmegaPrimalityOfElementListInNumericalSemigroup[102X ([14X9.4-2[114X),[133X
  
  [33X[0;0Y[2XFactorizationsElementListWRTNumericalSemigroup[102X ([14X9.1-3[114X),[133X
  
  [33X[0;0Y[2XDeltaSetPeriodicityBoundForNumericalSemigroup[102X ([14X9.2-7[114X),[133X
  
  [33X[0;0Y[2XDeltaSetPeriodicityStartForNumericalSemigroup[102X ([14X9.2-8[114X),[133X
  
  [33X[0;0Y[2XDeltaSetListUpToElementWRTNumericalSemigroup[102X ([14X9.2-9[114X),[133X
  
  [33X[0;0Y[2XDeltaSetUnionUpToElementWRTNumericalSemigroup[102X ([14X9.2-10[114X),[133X
  
  [33X[0;0Y[2XDeltaSetOfNumericalSemigroup[102X ([14X9.2-11[114X).[133X
  
  [33X[0;0YAnd contributed to:[133X
  
  [33X[0;0Y[2XDeltaSetOfAffineSemigroup[102X ([14X11.4-3[114X).[133X
  
  
  [1XC.3 [33X[0;0YFunctions implemented by K. Stokes[133X[101X
  
  [33X[0;0YKlara Stokes helped with the implementation of functions related to patterns
  for ideals of numerical semigroups [14X7.3[114X.[133X
  
  
  [1XC.4 [33X[0;0YFunctions implemented by I. Ojeda and C. J. Moreno Ávila[133X[101X
  
  [33X[0;0YIgnacio  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.[133X
  
  
  [1XC.5 [33X[0;0YFunctions implemented by A. Sánchez-R. Navarro[133X[101X
  
  [33X[0;0YAlfredo helped in the implementation of methods for [3X4ti2gap[103X of the following
  functions.[133X
  
  [33X[0;0Y[2XFactorizationsVectorWRTList[102X ([14X11.4-1[114X),[133X
  
  [33X[0;0Y[2XPrimitiveElementsOfAffineSemigroup[102X ([14X11.3-9[114X),[133X
  
  [33X[0;0Y[2XMinimalPresentationOfAffineSemigroup[102X ([14X11.3-4[114X).[133X
  
  [33X[0;0YHe also helped in preliminary versions of the following functions.[133X
  
  [33X[0;0Y[2XCatenaryDegreeOfSetOfFactorizations[102X ([14X9.3-1[114X),[133X
  
  [33X[0;0Y[2XTameDegreeOfSetOfFactorizations[102X ([14X9.3-6[114X),[133X
  
  [33X[0;0Y[2XTameDegreeOfNumericalSemigroup[102X ([14X9.3-12[114X),[133X
  
  [33X[0;0Y[2XTameDegreeOfAffineSemigroup[102X ([14X11.4-8[114X),[133X
  
  [33X[0;0Y[2XOmegaPrimalityOfElementInAffineSemigroup[102X ([14X11.4-9[114X),[133X
  
  [33X[0;0Y[2XCatenaryDegreeOfAffineSemigroup[102X ([14X11.4-4[114X),[133X
  
  [33X[0;0Y[2XMonotoneCatenaryDegreeOfSetOfFactorizations[102X ([14X9.3-4[114X).[133X
  
  [33X[0;0Y[2XEqualCatenaryDegreeOfSetOfFactorizations[102X ([14X9.3-3[114X).[133X
  
  [33X[0;0Y[2XAdjacentCatenaryDegreeOfSetOfFactorizations[102X ([14X9.3-2[114X).[133X
  
  [33X[0;0Y[2XHomogeneousCatenaryDegreeOfAffineSemigroup[102X ([14X11.4-6[114X).[133X
  
  
  [1XC.6 [33X[0;0YFunctions implemented by G. Zito[133X[101X
  
  [33X[0;0YGiuseppe gave the algorithms for the current version functions[133X
  
  [33X[0;0Y[2XArfNumericalSemigroupsWithFrobeniusNumber[102X ([14X8.2-4[114X),[133X
  
  [33X[0;0Y[2XArfNumericalSemigroupsWithFrobeniusNumberUpTo[102X ([14X8.2-5[114X),[133X
  
  [33X[0;0Y[2XArfNumericalSemigroupsWithGenus[102X ([14X8.2-6[114X),[133X
  
  [33X[0;0Y[2XArfNumericalSemigroupsWithGenusUpTo[102X ([14X8.2-7[114X),[133X
  
  [33X[0;0Y[2XArfCharactersOfArfNumericalSemigroup[102X ([14X8.2-3[114X).[133X
  
  
  [1XC.7 [33X[0;0YFunctions implemented by A. Herrera-Poyatos[133X[101X
  
  [33X[0;0YAndrés Herrera-Poyatos gave new implementations of[133X
  
  [33X[0;0Y[2XIsSelfReciprocalUnivariatePolynomial[102X ([14X10.1-9[114X) and[133X
  
  [33X[0;0Y[2XIsKroneckerPolynomial[102X ([14X10.1-7[114X).[133X
  
  
  [1XC.8 [33X[0;0YFunctions implemented by Benjamin Heredia[133X[101X
  
  [33X[0;0YBenjamin Heredia implemented a preliminary version of[133X
  
  [33X[0;0Y[2XFengRaoDistance[102X ([14X9.7-1[114X).[133X
  
  
  [1XC.9 [33X[0;0YFunctions implemented by Juan Ignacio García-García[133X[101X
  
  [33X[0;0YJuan Ignacio implemented a preliminary version of[133X
  
  [33X[0;0Y[2XNumericalSemigroupsWithFrobeniusNumber[102X ([14X5.4-1[114X).[133X
  
