1############################################################################# 2# This file contains obsolet functions which are to be kept during a while for 3# compatibility 4# WARNING: the manual must be updated before removing the functions 5############################################################################# 6## 7#F GeneratorsOfNumericalSemigroupNC(S) 8## 9## Returns a set of generators of the numerical 10## semigroup S. 11## 12#####From version 0.980 is just a synonym of the check version of the function 13############################################################################# 14DeclareSynonym( "GeneratorsOfNumericalSemigroupNC",GeneratorsOfNumericalSemigroup); 15 16############################################################################# 17## 18#F ReducedSetOfGeneratorsOfNumericalSemigroup(arg) 19####From version 0.980 is a synonym of MinimalGenerating... 20## 21## Returns a set with possibly fewer generators than those recorded in <C>S!.generators</C>. It changes <C>S!.generators</C> to the set returned. 22##The function has 1 to 3 arguments. One of them a numerical semigroup. Then an argument is a boolean (<E>true</E> means that all the elements not belonging to the Apery set with respect to the multiplicity are removed; the default is "false") and another argument is a positive integer <M>n</M> (meaning that generators that can be written as the sum of <n> or less generators are removed; the default is "2"). The boolean or the integer may not be present. If a minimal generating set for <M>S</M> is known or no generating set is known, then the minimal generating system is returned. 23## 24#DeclareGlobalFunction("ReducedSetOfGeneratorsOfNumericalSemigroup"); 25DeclareSynonym("ReducedSetOfGeneratorsOfNumericalSemigroup",MinimalGeneratingSystemOfNumericalSemigroup); 26############################################################################# 27## the name "RandomNumericalSemigroupWithPseudoFrobeniusNumbers" should be removed in a further version... (it is not documented) 28DeclareSynonym("RandomNumericalSemigroupWithPseudoFrobeniusNumbers",ANumericalSemigroupWithPseudoFrobeniusNumbers); 29############################################################################# 30## 31#F NumericalSemigroupByMinimalGenerators(arg) 32## 33## Returns the numerical semigroup minimally generated by arg. 34## If the generators given are not minimal, the minimal ones 35## are computed and used. 36## 37############################################################################# 38DeclareGlobalFunction( "NumericalSemigroupByMinimalGenerators" ); 39#A 40#DeclareAttribute( "MinimalGeneratorsNS", IsNumericalSemigroup); 41#DeclareAttribute( "MinimalGenerators", IsNumericalSemigroup); 42DeclareSynonymAttr( "IsNumericalSemigroupByMinimalGenerators", HasMinimalGenerators); 43 44 45 46############################################################################# 47## 48#F NumericalSemigroupByMinimalGeneratorsNC(arg) 49## 50## Returns the numerical semigroup minimally generated by arg. 51## No test is made about args' minimality. 52## 53############################################################################# 54DeclareGlobalFunction( "NumericalSemigroupByMinimalGeneratorsNC" ); 55 56 57 58 59############################################################################# 60## 61#F FortenTruncatedNCForNumericalSemigroups(l) 62## 63## l contains the list of coefficients of a 64## single linear equation. FortenTruncatedNCForNumericalSemigroups 65## gives a minimal generator 66## of the affine semigroup of nonnegative solutions of this equation 67## with the first coordinate equal to one. 68## 69## Used for computing minimal presentations. 70## 71############################################################################# 72DeclareGlobalFunction("FortenTruncatedNCForNumericalSemigroups"); 73 74 75## The NC version of CatenaryDegreeOfElementNS works well for numbers 76## bigger than the Frobenius number 77DeclareGlobalFunction( "CatenaryDegreeOfElementInNumericalSemigroup_NC" ); 78############################################################################# 79## 80#F IsConnectedGraphNCForNumericalSemigroups(l) 81## 82## This function returns true if the graph is connected an false otherwise 83## 84## It is part of the NumericalSGPS package just to avoid the need of using 85## other graph packages only to this effect. It is used in 86## CatenaryDegreeOfElementNS 87## 88############################################################################# 89DeclareGlobalFunction("IsConnectedGraphNCForNumericalSemigroups"); 90