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