#############################################################################
##
#W
display.
xml
#Y Copyright (C)
2011-
14 James D. Mitchell
##
## Licensing information can be found in the README file of this package.
##
#############################################################################
##
<#GAPDoc Label=
"TikzString">
<ManSection>
<Oper Name=
"TikzString" Arg=
"obj[, options]"/>
<Returns>A string.</Returns>
<Description>
This function produces a graphical representation of the object
<A>obj</A> using the <C>tikz</C> package for &LaTeX;.
More precisely, this operation outputs a string containing a minimal
&LaTeX; document which can be compiled using &LaTeX; to produce a picture
of <A>obj</A>.
<P/>
Currently the following types of objects are supported:
<List>
<Mark>blocks</Mark>
<Item>
If <A>obj</A> is the left or right blocks of a bipartition, then
<C>TikzString</C> returns a graphical representation of these blocks;
see Section <Ref Sect =
"section-blocks"/>.
</Item>
<Mark>bipartitions</Mark>
<Item>
If <A>obj</A> is a bipartition, then <C>TikzString</C> returns a
graphical representation of <A>obj</A>.
<P/>
If the optional second argument <A>options</A> is a record with the
component <C>colors</C> set to <K>true</K>, then the blocks of
<A>f</A> will be colored using the standard <C>tikz</C> colors. Due
to the limited number of colors available in <C>tikz</C> this option
only works when the degree of <A>obj</A> is less than
20.
See Chapter <Ref Chap =
"Bipartitions and blocks"/> for more details
about bipartitions.
</Item>
<Mark>pbrs</Mark>
<Item>
If <A>obj</A> is a <Ref Oper=
"PBR"/>, then <C>TikzString</C> returns a
graphical representation <A>obj</A>; see Chapter <Ref Sect =
"Partitioned binary relations (PBRs)"/>.
</Item>
<Mark>Cayley graphs</Mark>
<Item>
If <A>obj</A> is a <Ref Oper=
"Digraph" BookName=
"digraphs"/> in the
category <Ref Filt=
"IsCayleyDigraph" BookName=
"digraphs"/>, then
<C>TikzString</C> returns a picture of <A>obj</A>. No attempt is made
whatsoever to produce a sensible picture of the digraph <A>obj</A>,
in fact, the vertices are all given the same coordinates. Human
intervention is required to produce a meaningful picture from the
value returned by this method. It is intended to make the task of
drawing such a Cayley graph more straightforward by providing
everything except the final layout of the graph. Please use <Ref
Oper=
"DotString"/> if you want an automatically laid out diagram of
the digraph <A>obj</A>.
</Item>
</List>
<Log><![
CDATA[
gap> x := Bipartition([[
1,
4, -
2, -
3], [
2,
3,
5, -
5], [-
1, -
4]]);;
gap> TikzString(RightBlocks(x));
"%tikz\n\\documentclass{minimal}\n\\usepackage{tikz}\n\\begin{documen\
t}\n\\begin{tikzpicture}\n \\draw[ultra thick](
5,
2)circle(.
115);\n \
\\draw(
1.
8,
5) node [top] {{$
1$}};\n \\fill(
4,
2)circle(.
125);\n \\dr\
aw(
1.
8,
4) node [top] {{$
2$}};\n \\fill(
3,
2)circle(.
125);\n \\draw(
1\
.
8,
3) node [top] {{$
3$}};\n \\draw[ultra thick](
2,
2)circle(.
115);\n \
\\draw(
1.
8,
2) node [top] {{$
4$}};\n \\fill(
1,
2)circle(.
125);\n \\d\
raw(
1.
8,
1) node [top] {{$
5$}};\n\n \\draw (
5,
2.
125) .. controls (
5,
2\
.
8) and (
2,
2.
8) .. (
2,
2.
125);\n \\draw (
4,
2.
125) .. controls (
4,
2.
6)\
and (
3,
2.
6) .. (
3,
2.
125);\n\\end{tikzpicture}\n\n\\end{document}
"
gap> x := Bipartition([[
1,
5], [
2,
4, -
3, -
5], [
3, -
1, -
2], [-
4]]);;
gap> TikzString(x);
"%tikz\n\\documentclass{minimal}\n\\usepackage{tikz}\n\\begin{documen\
t}\n\\begin{tikzpicture}\n\n %block #
1\n %vertices and labels\n \\\
fill(
1,
2)circle(.
125);\n \\draw(
0.
95,
2.
2) node [above] {{ $
1$}};\n \
\\fill(
5,
2)circle(.
125);\n \\draw(
4.
95,
2.
2) node [above] {{ $
5$}};\
\n\n %lines\n \\draw(
1,
1.
875) .. controls (
1,
1.
1) and (
5,
1.
1) .. (
5\
,
1.
875);\n\n %block #
2\n %vertices and labels\n \\fill(
2,
2)circle(\
.
125);\n \\draw(
1.
95,
2.
2) node [above] {{ $
2$}};\n \\fill(
4,
2)circ\
le(.
125);\n \\draw(
3.
95,
2.
2) node [above] {{ $
4$}};\n \\fill(
3,
0)c\
ircle(.
125);\n \\draw(
3, -
0.
2) node [below] {{ $-
3$}};\n \\fill(
5,
0\
)circle(.
125);\n \\draw(
5, -
0.
2) node [below] {{ $-
5$}};\n\n %lines\
\n \\draw(
2,
1.
875) .. controls (
2,
1.
3) and (
4,
1.
3) .. (
4,
1.
875);\n \
\\draw(
3,
0.
125) .. controls (
3,
0.
7) and (
5,
0.
7) .. (
5,
0.
125);\n \\dr\
aw(
2,
2)--(
3,
0);\n\n %block #
3\n %vertices and labels\n \\fill(
3,
2)\
circle(.
125);\n \\draw(
2.
95,
2.
2) node [above] {{ $
3$}};\n \\fill(
1\
,
0)circle(.
125);\n \\draw(
1, -
0.
2) node [below] {{ $-
1$}};\n \\fill\
(
2,
0)circle(.
125);\n \\draw(
2, -
0.
2) node [below] {{ $-
2$}};\n\n %l\
ines\n \\draw(
1,
0.
125) .. controls (
1,
0.
6) and (
2,
0.
6) .. (
2,
0.
125);\
\n \\draw(
3,
2)--(
2,
0);\n\n %block #
4\n %vertices and labels\n \\f\
ill(
4,
0)circle(.
125);\n \\draw(
4, -
0.
2) node [below] {{ $-
4$}};\n\n \
%lines\n\\end{tikzpicture}\n\n\\end{document}
"
gap> TikzString(UniversalPBR(
2));
"%latex\n\\documentclass{minimal}\n\\usepackage{tikz}\n\\begin{docume\
nt}\n\\usetikzlibrary{arrows}\n\\usetikzlibrary{arrows.meta}\n\\newco\
mmand{\\arc}{\\draw[semithick, -{>[width =
1.
5mm, length =
2.
5mm]}]}\
\n\\begin{tikzpicture}[\n vertex/.style={circle, draw, fill=black, i\
nner sep =
0.
04cm},\n ghost/.style={circle, draw = none, inner sep = \
0.
14cm},\n botloop/.style={min distance =
8mm, out = -
70, in = -
110}\
,\n toploop/.style={min distance =
8mm, out =
70, in =
110}]\n\n % \
vertices and labels\n \\foreach \\i in {
1,...,
2} {\n \\node [vert\
ex] at (\\i/
1.
5,
3) {};\n \\node [ghost] (\\i) at (\\i/
1.
5,
3) {};\
\n }\n\n \\foreach \\i in {
1,...,
2} {\n \\node [vertex] at (\\i/\
1.
5,
0) {};\n \\node [ghost] (-\\i) at (\\i/
1.
5,
0) {};\n }\n\n \
% arcs from vertex
1\n \\arc (
1) to (-
2);\n \\arc (
1) to (-
1);\n \
\\arc (
1) edge [toploop] (
1);\n \\arc (
1) .. controls (
1.
06666666666\
66667,
2.
125) and (
0.
93333333333333324,
2.
125) .. (
2);\n\n % arcs fr\
om vertex -
1\n \\arc (-
1) .. controls (
1.
0666666666666667,
0.
875) an\
d (
0.
93333333333333324,
0.
875) .. (-
2);\n \\arc (-
1) edge [botloop] \
(-
1);\n \\arc (-
1) to (
1);\n \\arc (-
1) to (
2);\n\n % arcs from ve\
rtex
2\n \\arc (
2) to (-
2);\n \\arc (
2) to (-
1);\n \\arc (
2) .. co\
ntrols (
0.
93333333333333324,
2.
125) and (
1.
0666666666666667,
2.
125) .\
. (
1);\n \\arc (
2) edge [toploop] (
2);\n\n % arcs from vertex -
2\n \
\\arc (-
2) edge [botloop] (-
2);\n \\arc (-
2) .. controls (
0.
9333333\
3333333324,
0.
875) and (
1.
0666666666666667,
0.
875) .. (-
1);\n \\arc \
(-
2) to (
1);\n \\arc (-
2) to (
2);\n\n\\end{tikzpicture}\n\\end{docum\
ent}
"]]></Log>
</Description>
</ManSection>
<#/GAPDoc>
<#GAPDoc Label=
"DotString">
<ManSection>
<Oper Name=
"DotString" Arg=
"S[, options]"/>
<Returns>A string.</Returns>
<Description>
If the argument <A>S</A> is a semigroup, and the optional second argument
<A>options</A> is a record, then this operation produces a graphical
representation of the partial order of
the &D;-classes of the semigroup <A>S</A> together with the eggbox
diagram of each &D;-class. The output is in <C>dot</C> format (also known
as <C>GraphViz</C>) format. For details about this file format, and
information about how to
display or edit this format see
<
URL>
https://www.graphviz.org</
URL>.
<P/>
The string returned by <C>DotString</C> can be written to a file using
the command <Ref Func=
"FileString" BookName=
"GAPDoc"/>.
<P/>
The &D;-classes are shown as eggbox diagrams with &L;-classes as rows and
&R;-classes as columns; group &H;-classes are shaded gray and contain an
asterisk. The &L;-classes and &R;-classes within a &D;-class are arranged
to correspond to the normalization of the principal factor given by <Ref
Attr=
"NormalizedPrincipalFactor"/>.
The &D;-classes are numbered according to their index in
<C>GreensDClasses(<A>S</A>)</C>, so that an <C>i</C> appears next to the
eggbox diagram of <C>GreensDClasses(<A>S</A>)[i]</C>. A line from one
&D;-class to another indicates that the higher &D;-class is greater than
the lower one in the &D;-order on <A>S</A>.
<P/>
If the optional second argument <A>options</A> is present, it can be used
to specify some options for output.
<List>
<Mark>number</Mark>
<Item>
if <C><A>options</A>.number</C> is <K>false</K>, then the &D;-classes
in the diagram are not numbered according to their index in the list
of &D;-classes of <A>S</A>. The default value for this option is
<K>true</K>.
</Item>
<Mark>maximal</Mark>
<Item>
if <C><A>options</A>.maximal</C> is <K>true</K>, then the structure
description of the group &H;-classes is displayed; see
<Ref Attr=
"StructureDescription" BookName=
"ref"/>. Setting
this attribute to <K>true</K> can adversely affect the performance of
<C>DotString</C>. The default value for this option is
<K>false</K>.
</Item>
<Mark>normal</Mark>
<Item>
if <C><A>options</A>.normal</C> is <K>false</K>, then the &L;- and
&R;-classes within each &D;-class arranged to correspond to <Ref
Attr=
"PrincipalFactor"/>. If <C><A>options</A>.normal</C> is
<K>true</K>, they are instead arranged to correspond to <Ref
Attr=
"NormalizedPrincipalFactor"/>. Setting this attribute to
<K>false</K> may improve the performance of <C>DotString</C> as it
avoids the computation of <Ref
Attr=
"InjectionNormalizedPrincipalFactor"/>. The default value for
this option is <K>true</K>.
</Item>
</List>
<Log><![
CDATA[
gap> S := FullTransformationMonoid(
3);
<full transformation monoid of degree
3>
gap> DotString(S);
"//dot\ndigraph DClasses {\nnode [shape=plaintext]\nedge [color=blac\
k,arrowhead=none]\n1 [shape=box style=invisible label=<\n<TABLE BORDE\
R=\
"0\" CELLBORDER=\
"1\" CELLPADDING=\
"10\" CELLSPACING=\
"0\" PORT=\
"\
1\
">\n<TR BORDER=\"0\
"><TD COLSPAN=\"1\
" BORDER = \"0\
" > 1</TD></TR>\
<TR><TD BGCOLOR=\
"gray\">*</TD></TR>\n</TABLE>>];\n2 [shape=box style\
=invisible label=<\n<TABLE BORDER=\
"0\" CELLBORDER=\
"1\" CELLPADDING=\
\
"10\" CELLSPACING=\
"0\" PORT=\
"2\">\n<TR BORDER=\
"0\"><TD COLSPAN=\
"\
3\
" BORDER = \"0\
" > 2</TD></TR><TR><TD BGCOLOR=\"gray\
">*</TD><TD BG\
COLOR=\
"gray\">*</TD><TD BGCOLOR=\
"white\"></TD></TR>\n<TR><TD BGCOLO\
R=\
"gray\">*</TD><TD BGCOLOR=\
"white\"></TD><TD BGCOLOR=\
"gray\">*</T\
D></TR>\n<TR><TD BGCOLOR=\
"white\"></TD><TD BGCOLOR=\
"gray\">*</TD><T\
D BGCOLOR=\
"gray\">*</TD></TR>\n</TABLE>>];\n3 [shape=box style=invis\
ible label=<\n<TABLE BORDER=\
"0\" CELLBORDER=\
"1\" CELLPADDING=\
"10\"\
CELLSPACING=\
"0\" PORT=\
"3\">\n<TR BORDER=\
"0\"><TD COLSPAN=\
"1\" BO\
RDER = \
"0\" >
3</TD></TR><TR><TD BGCOLOR=\
"gray\">*</TD></TR>\n<TR><\
TD BGCOLOR=\
"gray\">*</TD></TR>\n<TR><TD BGCOLOR=\
"gray\">*</TD></TR>\
\n</TABLE>>];\n1 ->
2\n2 ->
3\n }
"
gap> FileString(
"t3.dot", DotString(S));
1040]]></Log>
</Description>
</ManSection>
<#/GAPDoc>
<#GAPDoc Label=
"DotStringDigraph">
<ManSection>
<Oper Name=
"DotString" Arg=
"digraph" Label=
"for a Cayley digraph"/>
<Returns>A string.</Returns>
<Description>
If <A>digraph</A> is a <Ref Oper=
"Digraph" BookName=
"digraphs"/> in the
category <Ref Filt=
"IsCayleyDigraph" BookName=
"digraphs"/>, then
<C>DotString</C> returns a graphical representation of <A>digraph</A>.
The output is in <C>dot</C> format (also known
as <C>GraphViz</C>) format. For details about this file format, and
information about how to
display or edit this format see
<
URL>
https://www.graphviz.org</
URL>.
<P/>
The string returned by <C>DotString</C> can be written to a file using
the command <Ref Func=
"FileString" BookName=
"GAPDoc"/>.<P/>
See also <Ref Oper=
"DotLeftCayleyDigraph"/> and <Ref
Oper=
"TikzLeftCayleyDigraph"/>.
</Description>
</ManSection>
<#/GAPDoc>
<#GAPDoc Label=
"DotSemilatticeOfIdempotents">
<ManSection>
<Attr Name=
"DotSemilatticeOfIdempotents" Arg=
"S"/>
<Returns>A string.</Returns>
<Description>
This function produces a graphical representation of the semilattice of
the idempotents of an inverse semigroup <A>S</A> where the elements of
<A>S</A> have a unique semigroup inverse accessible via <Ref
Attr=
"Inverse" BookName=
"ref"/>. The idempotents are grouped by the
&D;-class they belong to.
<P/>
The output is in <C>dot</C> format (also known as <C>GraphViz</C>) format.
For details about this file format, and information about how to
display
or edit this format see <
URL>
https://www.graphviz.org</
URL>. <P/>
<Example><![
CDATA[
gap> S := DualSymmetricInverseMonoid(
4);
<inverse block bijection monoid of degree
4 with
3 generators>
gap> DotSemilatticeOfIdempotents(S);
"//dot\ngraph graphname {\n node [shape=point]\nranksep=2;\nsubgraph \
cluster_1{\n15 \n}\nsubgraph cluster_2{\n5
11 14 12 13 8 \n}\nsubgraph\
cluster_3{\n2
10 6 3 4 9 7 \n}\nsubgraph cluster_4{\n1 \n}\n2 --
1\n3\
--
1\n4 --
1\n5 --
2\n5 --
3\n5 --
4\n6 --
1\n7 --
1\n8 --
2\n8 --
6\
\n8 --
7\n9 --
1\n10 --
1\n11 --
2\n11 --
9\n11 --
10\n12 --
3\n12 -- \
6\n12 --
9\n13 --
3\n13 --
7\n13 --
10\n14 --
4\n14 --
6\n14 --
10\n15\
--
5\n15 --
8\n15 --
11\n15 --
12\n15 --
13\n15 --
14\n }
"]]></Example>
</Description>
</ManSection>
<#/GAPDoc>
<#GAPDoc Label=
"TexString">
<ManSection>
<Oper Name=
"TexString" Arg=
"f[, n]"/>
<Returns>A string.</Returns>
<Description>
This function produces a string containing LaTeX code for the
transformation <A>f</A>. If the optional parameter <A>n</A> is used, then
this is taken to be the degree of the transformation <A>f</A>, if the
parameter <A>n</A> is not given, then <Ref Attr=
"DegreeOfTransformation"
BookName=
"ref"/> is used by default. If <A>n</A> is less than the
degree of <A>f</A>, then an error is given.
<P/>
<Example><![
CDATA[
gap> TexString(Transformation([
6,
2,
4,
3,
6,
4]));
"\\begin{pmatrix}\n 1 & 2 & 3 & 4 & 5 & 6 \\\\\n 6 & 2 & 4 & 3 & 6 &\
4\n\\end{pmatrix}
"
gap> TexString(Transformation([
1,
2,
1,
3]),
5);
"\\begin{pmatrix}\n 1 & 2 & 3 & 4 & 5 \\\\\n 1 & 2 & 1 & 3 & 5\n\\en\
d{pmatrix}
"]]></Example>
</Description>
</ManSection>
<#/GAPDoc>
<#GAPDoc Label=
"TikzLeftCayleyDigraph">
<ManSection>
<Oper Name=
"TikzLeftCayleyDigraph" Arg=
"S"/>
<Oper Name=
"TikzRightCayleyDigraph" Arg=
"S"/>
<Returns>A string.</Returns>
<Description>
If <A>S</A> is a semigroup satisfying
<Ref Prop=
"CanUseFroidurePin"/>, then <C>TikzLeftCayleyDigraph</C>
is simply short for <C>TikzString(LeftCayleyDigraph(<A>S</A>))</C>.<P/>
<C>TikzRightCayleyDigraph</C> can be used to produce a tikz string for
the right Cayley graph of <A>S</A>.<P/>
See <Ref Oper=
"TikzString"/> for more details, and see also
<Ref Oper=
"DotLeftCayleyDigraph"/>.
<Log><![
CDATA[
gap> TikzLeftCayleyDigraph(Semigroup(IdentityTransformation));
"\\begin{tikzpicture}[scale=1, auto, \n vertex/.style={c\
ircle, draw, thick, fill=white, minimum size=
0.
65cm},\n \
edge/.style={arrows={-angle
90}, thick},\n loop/.style={\
min distance=
5mm,looseness=
5,arrows={-angle
90},thick}]\n\
\n % Vertices . . .\n \\node [vertex] (a) at (
0,
0) {};\
\n \\node at (
0,
0) {$a$};\n\n % Edges . . .\n \\path[\
->] (a) edge [loop]\n node {$a$} (a);\n\\end{ti\
kzpicture}
"
gap> TikzRightCayleyDigraph(Semigroup(IdentityTransformation));
"\\begin{tikzpicture}[scale=1, auto, \n vertex/.style={c\
ircle, draw, thick, fill=white, minimum size=
0.
65cm},\n \
edge/.style={arrows={-angle
90}, thick},\n loop/.style={\
min distance=
5mm,looseness=
5,arrows={-angle
90},thick}]\n\
\n % Vertices . . .\n \\node [vertex] (a) at (
0,
0) {};\
\n \\node at (
0,
0) {$a$};\n\n % Edges . . .\n \\path[\
->] (a) edge [loop]\n node {$a$} (a);\n\\end{ti\
kzpicture}
"]]></Log>
</Description>
</ManSection>
<#/GAPDoc>
<#GAPDoc Label=
"DotLeftCayleyDigraph">
<ManSection>
<Oper Name=
"DotLeftCayleyDigraph" Arg=
"S"/>
<Oper Name=
"DotRightCayleyDigraph" Arg=
"S"/>
<Returns>A string.</Returns>
<Description>
If <A>S</A> is a semigroup satisfying <Ref
Prop=
"CanUseFroidurePin"/>, then <C>DotLeftCayleyDigraph</C> is
simply short for <C>DotString(LeftCayleyDigraph(<A>S</A>))</C>.<P/>
<C>DotRightCayleyDigraph</C> can be used to produce a dot string for
the right Cayley graph of <A>S</A>.<P/>
See <Ref Oper=
"DotString"/> for more details, and see also
<Ref Oper=
"TikzLeftCayleyDigraph"/>.
<Log><![
CDATA[
gap> DotLeftCayleyDigraph(Semigroup(IdentityTransformation));
"//dot\ndigraph hgn{\nnode [shape=circle]\n1 [label=\"a\
"]\n1 -> 1\n}\
\n
"
gap> DotRightCayleyDigraph(Semigroup(IdentityTransformation));
"//dot\ndigraph hgn{\nnode [shape=circle]\n1 [label=\"a\
"]\n1 -> 1\n}\
\n
"]]></Log>
</Description>
</ManSection>
<#/GAPDoc>
