GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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  6 Usage of IntPic in connection with the numericalsgps package
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  This  chapter  describes  functions  to  be  used  in  connection  with  the
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  numericalsgps  package.  We  found it particularly usefull to gain intuition
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  that led to the obtention of the results stated in [DGSRP16].
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  6.1 Tikz code for drawing numerical semigroups
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  6.1-1 Tikz code for drawing numerical semigroups
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  TikzCodeForNumericalSemigroup( arg )  function
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  The arguments (at most 4) are:
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  1   a numerical semigroup
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  2   (optional) a list whose elements are either
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            lists of integers or
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            one   of   the   strings  "pseudo_frobenius",  "small_elements",
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              "min_generators",        "frobenius_number",        "conductor",
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              "special_gaps",  "fundamental_gaps"  (the  default: used when no
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              list is present) or
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  3   a record whose fields are
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            func -- a function name
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            (optional)  argument -- an argument (that may be a function name
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              also)
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  4   (optional) a positive integer -- if it is bigger than the conductor or
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        biggest  minimal generator, it indicates the number of cells - 1 to be
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        drawn  and  these  are drawn in a single line; otherwise, it indicates
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        the maximum number of cells per line.
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    Example  
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    gap> ns1 := NumericalSemigroup(3,5);;
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    gap> TikzCodeForNumericalSemigroup(ns1,[[3,4],"pseudo_frobenius"],20);
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    "%tikz\n\\begin{tikzpicture}[every node/.style={draw,scale=1pt,\nminimum width\
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    =20pt,inner sep=3pt,\nline width=0pt,draw=black}]\n\\matrix[row sep=2pt,column\
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     sep=2pt]\n{\\node[]{0};&\n\\node[]{1};&\n\\node[]{2};&\n\\node[fill=red]{3};&\
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    \n\\node[fill=red]{4};&\n\\node[]{5};&\n\\node[]{6};&\n\\node[fill=green]{7};&\
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    \n\\node[]{8};&\n\\node[]{9};&\n\\node[]{10};&\n\\node[]{11};&\n\\node[]{12};&\
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    \n\\node[]{13};&\n\\node[]{14};&\n\\node[]{15};&\n\\node[]{16};&\n\\node[]{17}\
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    ;&\n\\node[]{18};&\n\\node[]{19};&\n\\node[]{20};\\\\\n};\n\\end{tikzpicture}\
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    \n"
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    Example  
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    gap> IP_Splash(TikzCodeForNumericalSemigroup(NumericalSemigroup(7,13,19,23),
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    > [[3,4],"small_elements","fundamental_gaps"],20),rec(viewer := "evince"));    
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  6.2 Drawing sets of numerical semigroups
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  6.2-1 Set of numerical semigroups
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  SetOfNumericalSemigroups( arg )  function
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  This  function is used to produce lists of numerical semigroups with a fixed
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  genus  or  Frobenius number. They are filtered and ordered according to some
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  criteria.
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  The argument is a record of options:
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  1   set -- a record whose possible fields are genus or frobenius
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  2   (optional)  filter  --  a record whose possible fields are genus, type
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        and/or multiplicity and/or frobenius and/or embedding_dimension
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  3   (optional)  order  --  ("genus",  "type", "multiplicity", "frobenius",
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        "embedding_dimension")
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    Example  
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    gap> SetOfNumericalSemigroups(rec(set:=rec(genus:=6),filter:=rec(type:= 2),
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    > order:="multiplicity"));
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    [ <Numerical semigroup with 3 generators>, 
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      <Numerical semigroup with 3 generators>, 
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      <Numerical semigroup with 4 generators>, 
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      <Numerical semigroup with 5 generators>, 
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      <Numerical semigroup with 5 generators>, 
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      <Numerical semigroup with 6 generators> ]
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    gap> SetOfNumericalSemigroups(rec(set:=rec(genus:=6),filter:=rec(type:= 2),
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    > order:="frobenius"));                                                 
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    [ <Numerical semigroup with 3 generators>, 
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      <Numerical semigroup with 5 generators>, 
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      <Numerical semigroup with 5 generators>, 
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      <Numerical semigroup with 3 generators>, 
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      <Numerical semigroup with 4 generators>, 
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      <Numerical semigroup with 6 generators> ]
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    gap> List(last,MinimalGeneratingSystem);
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    [ [ 3, 10, 11 ], [ 5, 6, 7 ], [ 5, 6, 8 ], [ 3, 8, 13 ], [ 4, 7, 9 ], 
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      [ 6, 7, 8, 9, 11 ] ]
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  6.2-2 Draw a set of numerical semigroups
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  DrawSetOfNumericalSemigroups( arg )  function
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  Produces a single image from the images of a set of numerical semigroups.
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  The arguments (at most 3) are:
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  1   a  list  of  numerical  semigroups  (given  as a list or each given as
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        argument)
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  2   (optional)  an  integer  that  (when present) determines the length of
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        each line
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  3   (optional) a record whose fields are
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            (optional)  splash  -- which (when present) consists of a record
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              of options for the Viz Splash function
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            (optional)  highlights: a list to be passed to the function that
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              produces  the tikz code for each individual semigroup (whose aim
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              is to say which elements are to be highlighted)
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    Example  
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    gap> ns1 := NumericalSemigroup(3,5);;
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    gap> ns2 := NumericalSemigroup(5,7,11);;
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    gap> DrawSetOfNumericalSemigroups(ns1,rec(splash:=                          
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    > rec(viewer := "evince"),highlights := 
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    > ["pseudo_frobenius","small_elements","min_generators"]));
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    gap> DrawSetOfNumericalSemigroups(ns1,ns2,rec(splash:= 
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    > rec(viewer := "evince"),highlights := 
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    > ["pseudo_frobenius","small_elements","min_generators"]));
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    gap> DrawSetOfNumericalSemigroups([ns1,ns2],rec(splash:=      
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    > rec(viewer := "evince"),highlights :=                    
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    > ["small_elements","min_generators"]));                   
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    Example  
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    gap> frob := 15;;
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    gap> tipo := 2;;
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    gap> set := SetOfNumericalSemigroups(rec(set := rec(frobenius := frob),
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    > filter := rec(type:= tipo),order := "embedding_dimension"));;
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    gap> DrawSetOfNumericalSemigroups(set,rec(splash:= rec(viewer := "evince"),
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    > highlights := ["small_elements","min_generators",
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    > rec(func:= "ForcedIntegersForPseudoFrobenius", 
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    > argument := "PseudoFrobeniusOfNumericalSemigroup")]));
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  The  following  example  helps in the understanding of the colors present in
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  the first line of previous figure.
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    Example  
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    gap> ns := NumericalSemigroup(4,9,19);;
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    gap> SmallElements(ns);
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    [ 0, 4, 8, 9, 12, 13, 16 ]
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    gap> MinimalGeneratingSystem(ns);
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    [ 4, 9, 19 ]
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    gap> ForcedIntegersForPseudoFrobenius(PseudoFrobeniusOfNumericalSemigroup(ns));
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    [ [ 1, 2, 3, 5, 6, 7, 14, 15 ], [ 0, 8, 9, 12, 13, 16 ] ]
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