  
  [1XC [33X[0;0YContributions[133X[101X
  
  [33X[0;0YSebastian  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.[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 ([14X7.1-25[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;0YChris implemented the following functions described in [BOP17]:[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 ([14X11.4-5[114X). Also he implemented the new version of[133X
  
  [33X[0;0Y[2XAperyListOfNumericalSemigroupWRTElement[102X ([14X3.1-15[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.  Since  the  new
  implementation by Chris was included, these algorithms are no longer used.[133X
  
  
  [1XC.5 [33X[0;0YFunctions implemented by I. Ojeda[133X[101X
  
  [33X[0;0YIgnacio also implemented the following functions.[133X
  
  [33X[0;0Y[2XAlmostSymmetricNumericalSemigroupsFromIrreducibleAndGivenType[102X ([14X6.3-2[114X),[133X
  
  [33X[0;0Y[2XAlmostSymmetricNumericalSemigroupsWithFrobeniusNumberAndType[102X ([14X6.3-5[114X),[133X
  
  [33X[0;0Y[2XNumericalSemigroupsWithFrobeniusNumberAndMultiplicity[102X ([14X5.4-2[114X),[133X
  
  [33X[0;0Y[2XIrreducibleNumericalSemigroupsWithFrobeniusNumberAndMultiplicity[102X ([14X6.1-6[114X).[133X
  
  [33X[0;0YIgnacio also implemented the new versions of[133X
  
  [33X[0;0Y[2XAlmostSymmetricNumericalSemigroupsWithFrobeniusNumber[102X ([14X6.3-4[114X),[133X
  
  [33X[0;0Y[2XNumericalSemigroupsWithFrobeniusNumber[102X ([14X5.4-3[114X),[133X
  
  
  [1XC.6 [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[2XDegreesOfPrimitiveElementsOfAffineSemigroup[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 ([14X11.4-10[114X),[133X
  
  [33X[0;0Y[2XOmegaPrimalityOfElementInAffineSemigroup[102X ([14X11.4-11[114X),[133X
  
  [33X[0;0Y[2XCatenaryDegreeOfAffineSemigroup[102X ([14X11.4-6[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 ([14X11.4-8[114X).[133X
  
  
  [1XC.7 [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.8 [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 ([14X10.1-11[114X) and[133X
  
  [33X[0;0Y[2XIsKroneckerPolynomial[102X   ([14X10.1-7[114X).   Andrés  is  also  coauthor  of  the  dot
  functions, see Chapter [14X14[114X[133X
  
  
  [1XC.9 [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.10 [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 ([14X5.4-3[114X).[133X
  
  
  [1XC.11 [33X[0;0YFunctions implemented by C. Cisto[133X[101X
  
  [33X[0;0YCarmelo  provided  some  functions  to  deal with affine semigroups given by
  gaps,  and  to  compute gaps of affine semigroups with finite genus, see for
  instance[133X
  
  [33X[0;0Y[2XAffineSemigroupByGaps[102X ([14X11.1-5[114X),[133X
  
  [33X[0;0Y[2XRemoveMinimalGeneratorFromAffineSemigroup[102X ([14X11.1-12[114X),[133X
  
  [33X[0;0Y[2XAddSpecialGapOfAffineSemigroup[102X ([14X11.1-13[114X).[133X
  
  
  [1XC.12 [33X[0;0YFunctions implemented by N. Matsuoka[133X[101X
  
  [33X[0;0YNaoyuki  implemented  the  function associated to the generalized Gorenstein
  property, see Section [14X6.4[114X.[133X
  
  
  [1XC.13 [33X[0;0YFunctions implemented by N. Maugeri[133X[101X
  
  [33X[0;0YNicola fixed the implementation of [2XArfGoodSemigroupClosure[102X ([14X12.4-1[114X). He also
  implemented[133X
  
  [33X[0;0Y[2XProjectionOfAGoodSemigroup[102X ([14X12.2-12[114X),[133X
  
  [33X[0;0Y[2XGenusOfGoodSemigroup[102X ([14X12.2-13[114X),[133X
  
  [33X[0;0Y[2XLengthOfGoodSemigroup[102X ([14X12.2-14[114X),[133X
  
  [33X[0;0Y[2XAperySetOfGoodSemigroup[102X ([14X12.2-15[114X),[133X
  
  [33X[0;0Y[2XStratifiedAperySetOfGoodSemigroup[102X ([14X12.2-16[114X),[133X
  
  [33X[0;0Y[2XAbsoluteIrreduciblesOfGoodSemigroup[102X ([14X12.5-8[114X),[133X
  
  [33X[0;0Y[2XTracksOfGoodSemigroup[102X ([14X12.5-9[114X),[133X
  
  [33X[0;0Y[2XRandomGoodSemigroupWithFixedMultiplicity[102X  ([14XB.3-1[114X).  And the multiplicity and
  local property for good semigroups.[133X
  
