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Gis #1203

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Done I think?
joe-dw Jul 24, 2026
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Update semigraph.tst
joe-dw Jul 24, 2026
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Update README.md
joe-dw Jul 24, 2026
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Update semigraph.tst
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32 changes: 32 additions & 0 deletions doc/congsemigraph.xml
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Expand Up @@ -114,6 +114,38 @@ gap> AsCongruenceByWangPair(cong);
</ManSection>
<#/GAPDoc>

<#GAPDoc Label="TraceOfCongruenceByWangPair">
<ManSection>
<Oper Name = "TraceOfCongruenceByWangPair" Arg = "cong"/>
<Returns>The trace of congruence by Wang pair.</Returns>
<Description>
This operation takes <A>cong</A>, a finite graph inverse semigroup
congruence represented by a Wang pair <P/>, and returns an object
representing the trace of <A>cong</A>. <Ref Attr="IsCongruenceByWangPair"/>
<Example><![CDATA[
gap> D := Digraph([[2, 3], [3], [4], []]);
<immutable digraph with 4 vertices, 4 edges>
gap> S := GraphInverseSemigroup(D);
<finite graph inverse semigroup with 4 vertices, 4 edges>
gap> cong := CongruenceByWangPair(S, [4], [2]);
<graph inverse semigroup congruence with H = [ 4 ] and W = [ 2 ]>
gap> tr := TraceOfCongruenceByWangPair(cong);
<trace of graph inverse semigroup congruence with H = [ 4 ] and W = [ 2 ]>
gap> a := S.2 * S.4 * S.4 ^ -1 * S.2 ^ -1;
e_2e_4e_4^-1e_2^-1
gap> ImagesElm(tr, a);
[ 0, v_4, e_4e_4^-1, e_2e_4e_4^-1e_2^-1, e_3e_4e_4^-1e_3^-1, e_1e_3e_4e_4^-1e_3^-1e_1^-1 ]
gap> b := S.8;
v_4
gap> CongruenceTestMembershipNC(tr, a, b);
true
gap> EquivalenceRelationPartition(tr);
[ [ 0, v_4, e_4e_4^-1, e_2e_4e_4^-1e_2^-1, e_3e_4e_4^-1e_3^-1, e_1e_3e_4e_4^-1e_3^-1e_1^-1 ], [ v_2, e_3e_3^-1 ], [ e_1e_1^-1, e_1e_3e_3^-1e_1^-1 ] ]
]]></Example>
</Description>
</ManSection>
<#/GAPDoc>

<#GAPDoc Label="GeneratingCongruencesOfLattice">
<ManSection>
<Attr Name = "GeneratingCongruencesOfLattice" Arg = "S"/>
Expand Down
77 changes: 74 additions & 3 deletions doc/semigraph.xml
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Expand Up @@ -187,7 +187,7 @@ gap> GraphOfGraphInverseSemigroup(S);

<#GAPDoc Label="IsGraphInverseSemigroupElementCollection">
<ManSection>
<Filt Name="IsGraphInverseSemigroupElementCollection" Type="category"/>
<Filt Name="IsGraphInverseSemigroupElementCollection" Type="Category"/>
<Description>
Every collection of elements of a graph inverse semigroup belongs to the
category <C>IsGraphInverseSemigroupElementCollection</C>. For example,
Expand Down Expand Up @@ -258,8 +258,8 @@ gap> VerticesOfGraphInverseSemigroup(S);
<Returns>A positive integer.</Returns>
<Description>
If <A>v</A> is a vertex of a graph inverse semigroup (i.e. it satisfies
<Ref Filt="IsGraphInverseSemigroupElement"/>), then this attribute returns
the index of this vertex in its graph inverse semigroup.<P/>
<Ref Filt="IsGraphInverseSemigroupElement"/>), then this attribute returns the
index of this vertex in <A>S</A>.<P/>

<Example><![CDATA[
gap> D := Digraph([[3, 4], [3, 4], [4], []]);
Expand All @@ -273,3 +273,74 @@ gap> IndexOfVertexOfGraphInverseSemigroup(v_3);
</Description>
</ManSection>
<#/GAPDoc>

<#GAPDoc Label="EdgesWithRange">
<ManSection>
<Attr Name="EdgesWithRange" Arg="x"/>
<Returns>A list of graph inverse semigroup elements.</Returns>
<Description>
If <A>x</A> is a vertex of a graph inverse semigroup (i.e. it satisfies
<Ref Filt="IsGraphInverseSemigroupElement"/>), then this attribute returns a list
of all edges <A>e</A> such that <A>Range(e)=x</A>. If <A>x</A> is not a vertex
then it returns all edges with range <A>Source(x)</A>.
</Description>
</ManSection>
<#/GAPDoc>

<#GAPDoc Label="PathsWithRange">
<ManSection>
<Attr Name="PathsWithRange" Arg="x"/>
<Returns>A list of graph inverse semigroup elements.</Returns>
<Description>
If <A>x</A> is a vertex of a graph inverse semigroup (i.e. it satisfies
<Ref Filt="IsGraphInverseSemigroupElement"/>), then this attribute returns a list
of all paths (products of edges) <A>p</A> such that <A>Range(p)=x</A>, including
vertices as paths of length 0. If <A>x</A> is not a vertex then it returns all
paths with range <A>Source(x)</A>.
</Description>
</ManSection>
<#/GAPDoc>

<#GAPDoc Label="EdgesWithSource">
<ManSection>
<Attr Name="EdgesWithSource" Arg="x"/>
<Returns>A list of graph inverse semigroup elements.</Returns>
<Description>
If <A>x</A> is a vertex of a graph inverse semigroup (i.e. it satisfies
<Ref Filt="IsGraphInverseSemigroupElement"/>), then this attribute returns a list
of all edges <A>e</A> such that <A>Source(e)=x</A>. If <A>x</A> is not a vertex
then it returns all edges with source <A>Range(x)</A>.
</Description>
</ManSection>
<#/GAPDoc>

<#GAPDoc Label="PathsWithSource">
<ManSection>
<Attr Name="PathsWithSource" Arg="x"/>
<Returns>A list of graph inverse semigroup elements.</Returns>
<Description>
If <A>x</A> is a vertex of a graph inverse semigroup (i.e. it satisfies
<Ref Filt="IsGraphInverseSemigroupElement"/>), then this attribute returns a list
of all paths (products of edges) <A>p</A> such that <A>Source(p)=x</A>, including
vertices as paths of length 0. If <A>x</A> is not a vertex then it returns all
paths with source <A>Range(x)</A>.
<Example><![CDATA[
gap> D := Digraph([[2, 3], [3, 4], [4], []]);
<immutable digraph with 4 vertices, 5 edges>
gap> S := GraphInverseSemigroup(D);
<finite graph inverse semigroup with 4 vertices, 5 edges>
gap> EdgesWithRange(VerticesOfGraphInverseSemigroup(G)[4]);
Error, Variable: 'G' must have a value
not in any function at *stdin*:3
gap> EdgesWithRange(VerticesOfGraphInverseSemigroup(S)[4]);
[ e_4, e_5 ]
gap> PathsWithRange(VerticesOfGraphInverseSemigroup(S)[4]);
[ v_4, e_4, e_1e_4, e_5, e_2e_5, e_3e_5, e_1e_3e_5 ]
gap> EdgesWithSource(VerticesOfGraphInverseSemigroup(S)[2]);
[ e_3, e_4 ]
gap> PathsWithSource(VerticesOfGraphInverseSemigroup(S)[2]);
[ v_2, e_3, e_3e_5, e_4 ]
]]></Example>
</Description>
</ManSection>
<#/GAPDoc>
5 changes: 5 additions & 0 deletions doc/z-chap07.xml
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Expand Up @@ -248,6 +248,11 @@
<#Include Label = "IsGraphInverseSubsemigroup">
<#Include Label = "VerticesOfGraphInverseSemigroup">
<#Include Label = "IndexOfVertexOfGraphInverseSemigroup">
<#Include Label = "EdgesWithRange">
<#Include Label = "EdgesWithSource">
<#Include Label = "PathsWithRange">
<#Include Label = "PathsWithSource">


</Section>

Expand Down
16 changes: 15 additions & 1 deletion gap/congruences/congsemigraph.gd
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Expand Up @@ -23,6 +23,20 @@ DeclareOperation("CongruenceByWangPair",
DeclareOperation("AsCongruenceByWangPair", [IsSemigroupCongruence]);

DeclareOperation("MinimalHereditarySubsetsVertex",
[IsGraphInverseSemigroup, IsPosInt]);
[IsDigraph, IsPosInt]);

DeclareAttribute("GeneratingCongruencesOfLattice", IsGraphInverseSemigroup);

DeclareCategory("IsTraceOfCongruenceByWangPair",
IsSemigroupCongruence
and CanComputeEquivalenceRelationPartition
and IsMagmaCongruence
and IsAttributeStoringRep
and IsFinite);

DeclareAttribute("TraceOfCongruenceByWangPair", IsCongruenceByWangPair);

DeclareAttribute("EdgesWithRange", IsGraphInverseSemigroupElement);
DeclareAttribute("EdgesWithSource", IsGraphInverseSemigroupElement);
DeclareOperation("PathsWithRange", [IsGraphInverseSemigroupElement]);
DeclareOperation("PathsWithSource", [IsGraphInverseSemigroupElement]);
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