conglatt: improve congruence lattice code

Makefile.am

@@ -22,6 +22,7 @@ GAPINSTALLLIB = $(abs_top_srcdir)/$(BINARCHDIR)/semigroups.so
 lib_LTLIBRARIES = semigroups.la
 
 semigroups_la_SOURCES =  src/bipart.cpp
+semigroups_la_SOURCES += src/conglatt.cpp
 semigroups_la_SOURCES += src/cong.cpp
 semigroups_la_SOURCES += src/froidure-pin-base.cpp
 semigroups_la_SOURCES += src/froidure-pin-bipart.cpp

doc/cong.xml

@@ -333,8 +333,9 @@ gap> congs[pos];
 gap> S := Semigroup(Transformation([1, 3, 2]),
 >                   Transformation([3, 1, 3]));;
 gap> min := MinimalCongruencesOfSemigroup(S);
-[ <2-sided semigroup congruence over <transformation semigroup of 
-     degree 3 with 2 generators> with 1 generating pairs> ]
+[ <2-sided semigroup congruence over <transformation semigroup 
+     of size 13, degree 3 with 2 generators> with 1 generating pairs> 
+ ]
 gap> minl := MinimalLeftCongruencesOfSemigroup(S);
 [ <left semigroup congruence over <transformation semigroup 
      of size 13, degree 3 with 2 generators> with 1 generating pairs>,
@@ -391,16 +392,17 @@ gap> minl := MinimalLeftCongruencesOfSemigroup(S);
 gap> S := Semigroup(Transformation([1, 3, 2]),
 >                   Transformation([3, 1, 3]));;
 gap> congs := PrincipalCongruencesOfSemigroup(S);
-[ <2-sided semigroup congruence over <transformation semigroup of 
-     degree 3 with 2 generators> with 1 generating pairs>, 
-  <2-sided semigroup congruence over <transformation semigroup of 
-     degree 3 with 2 generators> with 1 generating pairs>, 
-  <2-sided semigroup congruence over <transformation semigroup of 
-     degree 3 with 2 generators> with 1 generating pairs>, 
-  <2-sided semigroup congruence over <transformation semigroup of 
-     degree 3 with 2 generators> with 1 generating pairs>, 
-  <2-sided semigroup congruence over <transformation semigroup of 
-     degree 3 with 2 generators> with 1 generating pairs> ]
+[ <universal semigroup congruence over <transformation semigroup 
+     of size 13, degree 3 with 2 generators>>, 
+  <2-sided semigroup congruence over <transformation semigroup 
+     of size 13, degree 3 with 2 generators> with 1 generating pairs>,
+  <2-sided semigroup congruence over <transformation semigroup 
+     of size 13, degree 3 with 2 generators> with 1 generating pairs>,
+  <2-sided semigroup congruence over <transformation semigroup 
+     of size 13, degree 3 with 2 generators> with 1 generating pairs>,
+  <2-sided semigroup congruence over <transformation semigroup 
+     of size 13, degree 3 with 2 generators> with 1 generating pairs> 
+ ]
 ]]></Example>
     </Description>
   </ManSection>

doc/congsemigraph.xml

@@ -116,10 +116,10 @@ gap> AsCongruenceByWangPair(cong);
 
 <#GAPDoc Label="GeneratingCongruencesOfLattice">
   <ManSection>
-    <Oper Name = "GeneratingCongruencesOfLattice" Arg = "S"/>
+    <Attr Name = "GeneratingCongruencesOfLattice" Arg = "S"/>
     <Returns>A semigroup.</Returns>
     <Description>
-      This operation takes a finite graph inverse semigroup <A>S</A> and returns a
+      This attribute takes a finite graph inverse semigroup <A>S</A> and returns a
       minimal generating set for the lattice of congruences of <A>S</A>, as described
       in <Cite Key="Anagnostopoulou-Merkouri2021aa"/>. This operation works only if
       the corresponding digraph of the graph inverse semigroup is simple. If there

doc/conguniv.xml

@@ -72,3 +72,26 @@ gap> UniversalSemigroupCongruence(S);
   </Description>
 </ManSection>
 <#/GAPDoc>
+
+<#GAPDoc Label="TrivialCongruence">
+<ManSection>
+  <Attr Name = "TrivialCongruence" Arg = "S"/>
+  <Returns>A trivial semigroup congruence.</Returns>
+  <Description>
+    This operation returns the trivial semigroup congruence for the
+    semigroup <A>S</A>.  It can be used in the same way as any other
+    semigroup congruence object.
+    <Example><![CDATA[
+gap> S := ReesZeroMatrixSemigroup(SymmetricGroup(3),
+> [[(), (1, 3, 2)], [(1, 2), 0]]);;
+gap> TrivialCongruence(S);
+<semigroup congruence over <Rees 0-matrix semigroup 2x2 over 
+  Sym( [ 1 .. 3 ] )> with linked triple (1,2,2)>
+gap> S := PartitionMonoid(2);
+<regular bipartition *-monoid of size 15, degree 2 with 3 generators>
+gap> TrivialCongruence(S);
+<2-sided semigroup congruence over <regular bipartition *-monoid 
+ of size 15, degree 2 with 3 generators> with 0 generating pairs>]]></Example>
+  </Description>
+</ManSection>
+<#/GAPDoc>

doc/z-chap13.xml

@@ -109,11 +109,13 @@
     <#Include Label = "PrincipalCongruencesOfSemigroup">
     <#Include Label = "IsCongruencePoset">
     <#Include Label = "LatticeOfCongruences">
+    <#Include Label = "CayleyDigraphOfCongruences">
     <#Include Label = "PosetOfPrincipalCongruences">
     <#Include Label = "CongruencesOfPoset">
     <#Include Label = "UnderlyingSemigroupOfCongruencePoset">
     <#Include Label = "PosetOfCongruences">
     <#Include Label = "JoinSemilatticeOfCongruences">
+    <#Include Label = "GeneratingCongruencesOfJoinSemilattice">
     <#Include Label = "MinimalCongruences">
     <#Include Label = "NumberOfRightCongruences">
     <#Include Label = "IteratorOfRightCongruences">
@@ -310,7 +312,7 @@
   </Section>
 
   <Section>
-    <Heading>Universal congruences</Heading>
+    <Heading>Universal and trivial congruences</Heading>
 
     The linked triples of a completely 0-simple Rees 0-matrix semigroup describe
     only its non-universal congruences.  In any one of these, the zero element
@@ -329,5 +331,6 @@
     <#Include Label = "IsUniversalSemigroupCongruence">
     <#Include Label = "IsUniversalSemigroupCongruenceClass">
     <#Include Label = "UniversalSemigroupCongruence">
+    <#Include Label = "TrivialCongruence">
   </Section>
 </Chapter>

gap/congruences/cong.gd

@@ -100,6 +100,8 @@ DeclareGlobalFunction("SemigroupCongruence");
 DeclareGlobalFunction("LeftSemigroupCongruence");
 DeclareGlobalFunction("RightSemigroupCongruence");
 
+DeclareAttribute("TrivialCongruence", IsSemigroup);
+
 # Properties of congruences
 DeclareProperty("IsRightSemigroupCongruence", IsLeftSemigroupCongruence);
 DeclareProperty("IsSemigroupCongruence", IsLeftSemigroupCongruence);

gap/congruences/cong.gi

@@ -187,6 +187,16 @@ function(arg)
   return _LeftOrRightCong(RightSemigroupCongruenceByGeneratingPairs, arg);
 end);
 
+########################################################################
+# Trivial congruence
+########################################################################
+
+InstallMethod(TrivialCongruence, "for a semigroup",
+[IsSemigroup],
+function(S)
+  return SemigroupCongruence(S, []);
+end);
+
 ########################################################################
 # Congruence operators
 ########################################################################

gap/congruences/conglatt.gd

@@ -20,15 +20,15 @@ DeclareCategory("IsCongruencePoset", IsDigraph);
 
 DeclareAttribute("UnderlyingSemigroupOfCongruencePoset", IsCongruencePoset);
 DeclareAttribute("PosetOfPrincipalCongruences", IsCongruencePoset);
-DeclareOperation("JoinSemilatticeOfCongruences",
-                 [IsCongruencePoset, IsFunction]);
+DeclareAttribute("JoinSemilatticeOfCongruences", IsCongruencePoset);
 DeclareAttribute("MinimalCongruences", IsCongruencePoset);
 
 DeclareAttribute("CongruencesOfPoset", IsCongruencePoset);
 
 # Constructs the poset object consisting of the congruences given in the
 # argument.
 DeclareOperation("PosetOfCongruences", [IsListOrCollection]);
+DeclareAttribute("JoinSemilatticeOfCongruences", IsListOrCollection);
 
 DeclareAttribute("GeneratingPairsOfPrincipalCongruences", IsSemigroup);
 DeclareAttribute("GeneratingPairsOfPrincipalLeftCongruences", IsSemigroup);
@@ -49,18 +49,25 @@ DeclareAttribute("LatticeOfCongruences", IsSemigroup);
 DeclareAttribute("LatticeOfLeftCongruences", IsSemigroup);
 DeclareAttribute("LatticeOfRightCongruences", IsSemigroup);
 
-DeclareOperation("LatticeOfCongruences",
+DeclareAttribute("CayleyDigraphOfCongruences", IsSemigroup);
+DeclareAttribute("CayleyDigraphOfLeftCongruences", IsSemigroup);
+DeclareAttribute("CayleyDigraphOfRightCongruences", IsSemigroup);
+
+DeclareOperation("CayleyDigraphOfCongruences",
                  [IsSemigroup, IsListOrCollection]);
-DeclareOperation("LatticeOfCongruencesNC",
+DeclareOperation("CayleyDigraphOfLeftCongruences",
                  [IsSemigroup, IsListOrCollection]);
-DeclareOperation("LatticeOfLeftCongruences",
+DeclareOperation("CayleyDigraphOfRightCongruences",
+                 [IsSemigroup, IsListOrCollection]);
+
+DeclareCategory("IsCayleyDigraphOfCongruences", IsCongruencePoset);
+
+DeclareOperation("LatticeOfCongruences",
                  [IsSemigroup, IsListOrCollection]);
-DeclareOperation("LatticeOfLeftCongruencesNC",
+DeclareOperation("LatticeOfLeftCongruences",
                  [IsSemigroup, IsListOrCollection]);
 DeclareOperation("LatticeOfRightCongruences",
                  [IsSemigroup, IsListOrCollection]);
-DeclareOperation("LatticeOfRightCongruencesNC",
-                 [IsSemigroup, IsListOrCollection]);
 
 DeclareAttribute("CongruencesOfSemigroup", IsSemigroup);
 DeclareAttribute("LeftCongruencesOfSemigroup", IsSemigroup);
@@ -90,3 +97,5 @@ DeclareOperation("PrincipalLeftCongruencesOfSemigroup",
                  [IsSemigroup, IsListOrCollection]);
 DeclareOperation("PrincipalRightCongruencesOfSemigroup",
                  [IsSemigroup, IsListOrCollection]);
+
+DeclareAttribute("GeneratingCongruencesOfJoinSemilattice", IsCongruencePoset);