conglatt: perf improvements

semigroups · Apr 20, 2022 · 584bc0c · 584bc0c
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diff --git a/doc/cong.xml b/doc/cong.xml
@@ -204,47 +204,49 @@ gap> RightSemigroupCongruence(S, pair1, pair2);
   </ManSection>
 <#/GAPDoc>
 
-<#GAPDoc Label="GeneratingPairsOfSemigroupCongruence">
-  <ManSection>
+  <!--
+    <#GAPDoc Label="GeneratingPairsOfSemigroupCongruence">
+    <ManSection>
     <Attr Name = "GeneratingPairsOfSemigroupCongruence" Arg = "cong"/>
     <Attr Name = "GeneratingPairsOfLeftSemigroupCongruence" Arg = "cong"/>
     <Attr Name = "GeneratingPairsOfRightSemigroupCongruence" Arg = "cong"/>
     <Returns>A list of lists.</Returns>
     <Description>
-      If <A>cong</A> is a semigroup congruence, then
-      <C>GeneratingPairsOfSemigroupCongruence</C> returns a list of pairs of
-      elements from <C>Range(<A>cong</A>)</C> that <E>generates</E> the
-      congruence; i.e. <A>cong</A> is the least congruence on the semigroup
-      which contains all the pairs in the list. <P/>
-
-      If <A>cong</A> is a left or right semigroup congruence, then
-      <C>GeneratingPairsOfLeft/RightSemigroupCongruence</C> will instead give a
-      list of pairs which generate it as a left or right congruence.  Note that,
-      although a congruence is also a left and right congruence, its generating
-      pairs as a left or right congruence may differ from its generating pairs
-      as a two-sided congruence. <P/>
-
-      A congruence can be defined using a set of generating pairs: see
-      <Ref Func = "SemigroupCongruence"/>,
-      <Ref Func = "LeftSemigroupCongruence"/>, and
-      <Ref Func = "RightSemigroupCongruence"/>. <P/>
+    If <A>cong</A> is a semigroup congruence, then
+    <C>GeneratingPairsOfSemigroupCongruence</C> returns a list of pairs of
+    elements from <C>Range(<A>cong</A>)</C> that <E>generates</E> the
+    congruence; i.e. <A>cong</A> is the least congruence on the semigroup
+    which contains all the pairs in the list. <P/>
+
+    If <A>cong</A> is a left or right semigroup congruence, then
+    <C>GeneratingPairsOfLeft/RightSemigroupCongruence</C> will instead give a
+    list of pairs which generate it as a left or right congruence.  Note that,
+    although a congruence is also a left and right congruence, its generating
+    pairs as a left or right congruence may differ from its generating pairs
+    as a two-sided congruence. <P/>
+
+    A congruence can be defined using a set of generating pairs: see
+    <Ref Func = "SemigroupCongruence"/>,
+    <Ref Func = "LeftSemigroupCongruence"/>, and
+    <Ref Func = "RightSemigroupCongruence"/>. <P/>
 
-      <Example><![CDATA[
-gap> S := Semigroup([Transformation([3, 3, 2, 3]),
->                    Transformation([3, 4, 4, 1])]);;
-gap> pairs :=
->     [[Transformation([1, 1, 1, 1]), Transformation([2, 2, 2, 3])], 
->      [Transformation([2, 2, 3, 2]), Transformation([3, 3, 2, 3])]];;
-gap> cong := SemigroupCongruence(S, pairs);;
-gap> GeneratingPairsOfSemigroupCongruence(cong);
-[ [ Transformation( [ 1, 1, 1, 1 ] ), 
-      Transformation( [ 2, 2, 2, 3 ] ) ], 
-  [ Transformation( [ 2, 2, 3, 2 ] ), 
-      Transformation( [ 3, 3, 2, 3 ] ) ] ]
-]]></Example>
+    <Example><![CDATA[
+    gap> S := Semigroup([Transformation([3, 3, 2, 3]),
+    >                    Transformation([3, 4, 4, 1])]);;
+    gap> pairs :=
+    >     [[Transformation([1, 1, 1, 1]), Transformation([2, 2, 2, 3])], 
+    >      [Transformation([2, 2, 3, 2]), Transformation([3, 3, 2, 3])]];;
+    gap> cong := SemigroupCongruence(S, pairs);;
+    gap> GeneratingPairsOfSemigroupCongruence(cong);
+    [ [ Transformation( [ 1, 1, 1, 1 ] ), 
+    Transformation( [ 2, 2, 2, 3 ] ) ], 
+    [ Transformation( [ 2, 2, 3, 2 ] ), 
+    Transformation( [ 3, 3, 2, 3 ] ) ] ]
+    ]]></Example>
     </Description>
-  </ManSection>
-<#/GAPDoc>
+    </ManSection>
+    <#/GAPDoc>
+-->
 
 <#GAPDoc Label="CongruencesOfSemigroup">
   <ManSection>
@@ -331,7 +333,7 @@ gap> congs[pos];
 gap> S := Semigroup(Transformation([1, 3, 2]),
 >                   Transformation([3, 1, 3]));;
 gap> min := MinimalCongruencesOfSemigroup(S);
-[ <semigroup congruence over <transformation semigroup of size 13, 
+[ <2-sided semigroup congruence over <transformation semigroup of 
      degree 3 with 2 generators> with 1 generating pairs> ]
 gap> minl := MinimalLeftCongruencesOfSemigroup(S);
 [ <left semigroup congruence over <transformation semigroup 
@@ -389,15 +391,15 @@ gap> minl := MinimalLeftCongruencesOfSemigroup(S);
 gap> S := Semigroup(Transformation([1, 3, 2]),
 >                   Transformation([3, 1, 3]));;
 gap> congs := PrincipalCongruencesOfSemigroup(S);
-[ <semigroup congruence over <transformation semigroup of size 13, 
+[ <2-sided semigroup congruence over <transformation semigroup of 
      degree 3 with 2 generators> with 1 generating pairs>, 
-  <semigroup congruence over <transformation semigroup of size 13, 
+  <2-sided semigroup congruence over <transformation semigroup of 
      degree 3 with 2 generators> with 1 generating pairs>, 
-  <semigroup congruence over <transformation semigroup of size 13, 
+  <2-sided semigroup congruence over <transformation semigroup of 
      degree 3 with 2 generators> with 1 generating pairs>, 
-  <semigroup congruence over <transformation semigroup of size 13, 
+  <2-sided semigroup congruence over <transformation semigroup of 
      degree 3 with 2 generators> with 1 generating pairs>, 
-  <semigroup congruence over <transformation semigroup of size 13, 
+  <2-sided semigroup congruence over <transformation semigroup of 
      degree 3 with 2 generators> with 1 generating pairs> ]
 ]]></Example>
     </Description>
@@ -552,11 +554,11 @@ gap> cong := SemigroupCongruence(S, [Transformation([1, 2, 1]),
 >                                    Transformation([2, 1, 2])]);;
 gap> classes := NonTrivialEquivalenceClasses(cong);;
 gap> Set(classes);
-[ <congruence class of Transformation( [ 1, 2, 2 ] )>, 
-  <congruence class of Transformation( [ 3, 1, 3 ] )>, 
-  <congruence class of Transformation( [ 3, 1, 1 ] )>, 
-  <congruence class of Transformation( [ 2, 1, 2 ] )>, 
-  <congruence class of Transformation( [ 3, 3, 3 ] )> ]
+[ <2-sided congruence class of Transformation( [ 1, 2, 2 ] )>, 
+  <2-sided congruence class of Transformation( [ 3, 1, 3 ] )>, 
+  <2-sided congruence class of Transformation( [ 3, 1, 1 ] )>, 
+  <2-sided congruence class of Transformation( [ 2, 1, 2 ] )>, 
+  <2-sided congruence class of Transformation( [ 3, 3, 3 ] )> ]
 gap> cong := RightSemigroupCongruence(S, [Transformation([1, 2, 1]),
 >                                         Transformation([2, 1, 2])]);;
 gap> classes := NonTrivialEquivalenceClasses(cong);;
@@ -583,7 +585,7 @@ gap> cong := SemigroupCongruence(S, [Transformation([1, 2, 1]),
 >                                    Transformation([2, 1, 2])]);;
 gap> class := EquivalenceClassOfElement(cong,
 >                                       Transformation([3, 1, 1]));
-<congruence class of Transformation( [ 3, 1, 1 ] )>
+<2-sided congruence class of Transformation( [ 3, 1, 1 ] )>
 gap> IsCongruenceClass(class);
 true]]></Example>
     </Description>

diff --git a/doc/conginv.xml b/doc/conginv.xml
@@ -25,7 +25,7 @@ gap> I := InverseSemigroup([
 gap> cong := SemigroupCongruence(I,
 > [[PartialPerm([0, 1, 3]), PartialPerm([0, 1])],
 >  [PartialPerm([]), PartialPerm([1, 2])]]);
-<semigroup congruence over <inverse partial perm semigroup 
+<2-sided semigroup congruence over <inverse partial perm semigroup 
  of size 19, rank 3 with 2 generators> with 2 generating pairs>
 gap> TraceOfSemigroupCongruence(cong);
 [ [ <empty partial perm>, <identity partial perm on [ 1 ]>, 
@@ -55,7 +55,7 @@ gap> I := InverseSemigroup([
 gap> cong := SemigroupCongruence(I,
 > [[PartialPerm([0, 1, 3]), PartialPerm([0, 1])],
 >  [PartialPerm([]), PartialPerm([1, 2])]]);
-<semigroup congruence over <inverse partial perm semigroup 
+<2-sided semigroup congruence over <inverse partial perm semigroup 
  of size 19, rank 3 with 2 generators> with 2 generating pairs>
 gap> KernelOfSemigroupCongruence(cong);
 <inverse partial perm semigroup of size 19, rank 3 with 5 generators>
@@ -84,8 +84,8 @@ gap> I := InverseSemigroup([
 gap> cong := SemigroupCongruenceByGeneratingPairs(I,
 > [[PartialPerm([0, 1, 3]), PartialPerm([0, 1])],
 >  [PartialPerm([]), PartialPerm([1, 2])]]);
-<semigroup congruence over <inverse partial perm semigroup of rank 3 
- with 2 generators> with 2 generating pairs>
+<2-sided semigroup congruence over <inverse partial perm semigroup of 
+ rank 3 with 2 generators> with 2 generating pairs>
 gap> cong2 := AsInverseSemigroupCongruenceByKernelTrace(cong);
 <semigroup congruence over <inverse partial perm semigroup 
  of size 19, rank 3 with 2 generators> with congruence pair (19,1)>]]></Example>

diff --git a/doc/conglatt.xml b/doc/conglatt.xml
@@ -36,21 +36,23 @@
       <Example><![CDATA[
 gap> S := SymmetricInverseMonoid(2);;
 gap> poset := LatticeOfCongruences(S);
-<poset of 4 congruences over <symmetric inverse monoid of degree 2>>
+<lattice of 4 two-sided congruences over 
+ <symmetric inverse monoid of degree 2>>
 gap> IsCongruencePoset(poset);
 true
 gap> IsDigraph(poset);
 true
 gap> OutNeighbours(poset);
-[ [ 1 .. 4 ], [ 2, 3, 4 ], [ 3 ], [ 3, 4 ] ]
+[ [ 1, 2, 3, 4 ], [ 2 ], [ 2, 3 ], [ 2, 3, 4 ] ]
 gap> T := FullTransformationMonoid(3);;
 gap> congs := PrincipalCongruencesOfSemigroup(T);;
-gap> poset := JoinSemilatticeOfCongruences(congs,
->                                          JoinSemigroupCongruences);
-<poset of 6 congruences over <full transformation monoid of degree 3>>
+gap> poset := JoinSemilatticeOfCongruences(PosetOfCongruences(congs),
+>                                          WrappedTwoSidedCongruence);
+<lattice of 6 two-sided congruences over 
+ <full transformation monoid of degree 3>>
 gap> IsCongruencePoset(poset);
 true
-gap> Size(poset);
+gap> DigraphNrVertices(poset);
 6
 ]]></Example>
     </Description>
@@ -91,22 +93,23 @@ gap> Size(poset);
       <Example><![CDATA[
 gap> S := OrderEndomorphisms(2);;
 gap> LatticeOfCongruences(S);
-<poset of 3 congruences over <regular transformation monoid 
- of size 3, degree 2 with 2 generators>>
+<lattice of 3 two-sided congruences over <regular transformation 
+ monoid of size 3, degree 2 with 2 generators>>
 gap> LatticeOfLeftCongruences(S);
-<poset of 3 congruences over <regular transformation monoid 
+<lattice of 3 left congruences over <regular transformation monoid 
  of size 3, degree 2 with 2 generators>>
 gap> LatticeOfRightCongruences(S);
-<poset of 5 congruences over <regular transformation monoid 
+<lattice of 5 right congruences over <regular transformation monoid 
  of size 3, degree 2 with 2 generators>>
 gap> OutNeighbours(LatticeOfRightCongruences(S));
-[ [ 1 .. 5 ], [ 2, 5 ], [ 3, 5 ], [ 4, 5 ], [ 5 ] ]
+[ [ 1, 2, 3, 4, 5 ], [ 2 ], [ 2, 3 ], [ 2, 4 ], [ 2, 5 ] ]
 gap> S := FullTransformationMonoid(4);;
 gap> restriction := [Transformation([1, 1, 1, 1]),
 >                    Transformation([1, 1, 1, 2]),
 >                    Transformation([1, 1, 1, 3])];;
-gap> latt := LatticeOfCongruences(S, restriction);
-<poset of 2 congruences over <full transformation monoid of degree 4>>
+gap> latt := LatticeOfCongruences(S, Combinations(restriction, 2));
+<lattice of 2 two-sided congruences over 
+ <full transformation monoid of degree 4>>
 ]]></Example>
     </Description>
   </ManSection>
@@ -148,20 +151,21 @@ gap> latt := LatticeOfCongruences(S, restriction);
                Label = "for a semigroup"/>. <P/>
 
       <Example><![CDATA[
-gap> S := Semigroup([Transformation([1, 3, 1]),
->                    Transformation([2, 3, 3])]);;
+gap> S := Semigroup(Transformation([1, 3, 1]),
+>                   Transformation([2, 3, 3]));;
 gap> PosetOfPrincipalLeftCongruences(S);
-<poset of 12 congruences over <transformation semigroup of size 11, 
- degree 3 with 2 generators>>
+<poset of 12 left congruences over <transformation semigroup 
+ of size 11, degree 3 with 2 generators>>
 gap> PosetOfPrincipalCongruences(S);
-<poset of 3 congruences over <transformation semigroup of size 11, 
- degree 3 with 2 generators>>
+<lattice of 3 two-sided congruences over <transformation semigroup 
+ of size 11, degree 3 with 2 generators>>
 gap> restriction := [Transformation([3, 2, 3]),
 >                    Transformation([3, 1, 3]),
 >                    Transformation([2, 2, 2])];;
-gap> poset := PosetOfPrincipalRightCongruences(S, restriction);
-<poset of 3 congruences over <transformation semigroup of size 11, 
- degree 3 with 2 generators>>
+gap> poset := PosetOfPrincipalRightCongruences(S, 
+> Combinations(restriction, 2));
+<poset of 3 right congruences over <transformation semigroup 
+ of size 11, degree 3 with 2 generators>>
 ]]></Example>
     </Description>
   </ManSection>
@@ -183,7 +187,7 @@ gap> poset := PosetOfPrincipalRightCongruences(S, restriction);
       <Example><![CDATA[
 gap> S := OrderEndomorphisms(2);;
 gap> latt := LatticeOfRightCongruences(S);
-<poset of 5 congruences over <regular transformation monoid 
+<lattice of 5 right congruences over <regular transformation monoid 
  of size 3, degree 2 with 2 generators>>
 gap> CongruencesOfPoset(latt);
 [ <right semigroup congruence over <regular transformation monoid 
@@ -213,7 +217,7 @@ gap> CongruencesOfPoset(latt);
 gap> S := OrderEndomorphisms(2);
 <regular transformation monoid of degree 2 with 2 generators>
 gap> latt := LatticeOfRightCongruences(S);
-<poset of 5 congruences over <regular transformation monoid 
+<lattice of 5 right congruences over <regular transformation monoid 
  of size 3, degree 2 with 2 generators>>
 gap> UnderlyingSemigroupOfCongruencePoset(latt) = S;
 true
@@ -246,8 +250,8 @@ gap> coll := [RightSemigroupCongruence(S, pair1),
 >             RightSemigroupCongruence(S, pair2),
 >             RightSemigroupCongruence(S, [])];;
 gap> poset := PosetOfCongruences(coll);
-<poset of 3 congruences over <regular transformation monoid of 
- degree 2 with 2 generators>>
+<poset of 3 right congruences over <regular transformation monoid 
+ of size 3, degree 2 with 2 generators>>
 gap> OutNeighbours(poset);
 [ [ 1 ], [ 2 ], [ 1, 2, 3 ] ]
 ]]></Example>
@@ -282,13 +286,15 @@ gap> OutNeighbours(poset);
 gap> S := SymmetricInverseMonoid(2);;
 gap> pair1 := [PartialPerm([1], [1]), PartialPerm([2], [1])];;
 gap> pair2 := [PartialPerm([1], [1]), PartialPerm([1, 2], [1, 2])];;
-gap> pair3 := [PartialPerm([1, 2], [1, 2]), 
+gap> pair3 := [PartialPerm([1, 2], [1, 2]),
 >              PartialPerm([1, 2], [2, 1])];;
 gap> coll := [RightSemigroupCongruence(S, pair1),
 >             RightSemigroupCongruence(S, pair2),
 >             RightSemigroupCongruence(S, pair3)];;
-gap> JoinSemilatticeOfCongruences(coll, JoinRightSemigroupCongruences);
-<poset of 4 congruences over <symmetric inverse monoid of degree 2>>
+gap> JoinSemilatticeOfCongruences(PosetOfCongruences(coll),
+> WrappedRightCongruence);
+<poset of 4 right congruences over 
+ <symmetric inverse monoid of degree 2>>
 ]]></Example>
     </Description>
   </ManSection>
@@ -326,16 +332,17 @@ gap> pair3 := [PartialPerm([1, 2], [1, 2]),
 gap> coll := [RightSemigroupCongruence(S, pair1),
 >             RightSemigroupCongruence(S, pair2),
 >             RightSemigroupCongruence(S, pair3)];;
-gap> MinimalCongruences(coll);
+gap> MinimalCongruences(PosetOfCongruences(coll));
 [ <right semigroup congruence over <symmetric inverse monoid of degree\
  2> with 1 generating pairs>, 
   <right semigroup congruence over <symmetric inverse monoid of degree\
  2> with 1 generating pairs> ]
 gap> poset := LatticeOfCongruences(S);
-<poset of 4 congruences over <symmetric inverse monoid of degree 2>>
+<lattice of 4 two-sided congruences over 
+ <symmetric inverse monoid of degree 2>>
 gap> MinimalCongruences(poset);
-[ <semigroup congruence over <symmetric inverse monoid of degree 2> wi\
-th 0 generating pairs> ]
+[ <2-sided semigroup congruence over <symmetric inverse monoid of degr\
+ee 2> with 0 generating pairs> ]
 ]]></Example>
     </Description>
   </ManSection>

diff --git a/doc/congrms.xml b/doc/congrms.xml
@@ -156,7 +156,7 @@ gap> rowBlocks := [[1], [2], [3]];;
 gap> cong := RZMSCongruenceByLinkedTriple(S, N, colBlocks, rowBlocks);;
 gap> class := RZMSCongruenceClassByLinkedTriple(cong,
 > RightCoset(N, (1, 5)), 2, 3);
-<congruence class of (2,(3,4),3)>]]></Example>
+<2-sided congruence class of (2,(3,4),3)>]]></Example>
     </Description>
   </ManSection>
 <#/GAPDoc>

diff --git a/doc/congsemigraph.xml b/doc/congsemigraph.xml
@@ -38,8 +38,8 @@ e_1
 gap> e_3 := S.3;
 e_3
 gap> cong := SemigroupCongruence(S, [[e_1, e_3]]);
-<semigroup congruence over <finite graph inverse semigroup with 4 vert\
-ices, 5 edges> with 1 generating pairs>
+<2-sided semigroup congruence over <finite graph inverse semigroup wit\
+h 4 vertices, 5 edges> with 1 generating pairs>
 gap> IsCongruenceByWangPair(cong);
 false
 ]]></Example>
@@ -98,15 +98,15 @@ gap> S := GraphInverseSemigroup(D);
 gap> CongruenceByWangPair(S, [4], [2]);
 <graph inverse semigroup congruence with H = [ 4 ] and W = [ 2 ]>
 gap> cong := AsSemigroupCongruenceByGeneratingPairs(last);
-<semigroup congruence over <finite graph inverse semigroup with 4 vert\
-ices, 4 edges> with 2 generating pairs>
+<2-sided semigroup congruence over <finite graph inverse semigroup wit\
+h 4 vertices, 4 edges> with 2 generating pairs>
 gap> AsCongruenceByWangPair(cong);
 <graph inverse semigroup congruence with H = [ 4 ] and W = [ 2 ]>
 gap> CongruenceByWangPair(S, [3, 4], [1]);
 <graph inverse semigroup congruence with H = [ 3, 4 ] and W = [ 1 ]>
 gap> cong := AsSemigroupCongruenceByGeneratingPairs(last);
-<semigroup congruence over <finite graph inverse semigroup with 4 vert\
-ices, 4 edges> with 3 generating pairs>
+<2-sided semigroup congruence over <finite graph inverse semigroup wit\
+h 4 vertices, 4 edges> with 3 generating pairs>
 gap> AsCongruenceByWangPair(cong);
 <graph inverse semigroup congruence with H = [ 3, 4 ] and W = [ 1 ]>
 ]]></Example>
@@ -133,15 +133,15 @@ gap> S := GraphInverseSemigroup(D);
 gap> CongruenceByWangPair(S, [4], [2]);
 <graph inverse semigroup congruence with H = [ 4 ] and W = [ 2 ]>
 gap> cong := AsSemigroupCongruenceByGeneratingPairs(last);
-<semigroup congruence over <finite graph inverse semigroup with 4 vert\
-ices, 4 edges> with 2 generating pairs>
+<2-sided semigroup congruence over <finite graph inverse semigroup wit\
+h 4 vertices, 4 edges> with 2 generating pairs>
 gap> AsCongruenceByWangPair(cong);
 <graph inverse semigroup congruence with H = [ 4 ] and W = [ 2 ]>
 gap> CongruenceByWangPair(S, [3, 4], [1]);
 <graph inverse semigroup congruence with H = [ 3, 4 ] and W = [ 1 ]>
 gap> cong := AsSemigroupCongruenceByGeneratingPairs(last);
-<semigroup congruence over <finite graph inverse semigroup with 4 vert\
-ices, 4 edges> with 3 generating pairs>
+<2-sided semigroup congruence over <finite graph inverse semigroup wit\
+h 4 vertices, 4 edges> with 3 generating pairs>
 gap> AsCongruenceByWangPair(cong);
 <graph inverse semigroup congruence with H = [ 3, 4 ] and W = [ 1 ]>
 ]]></Example>

diff --git a/doc/z-chap13.xml b/doc/z-chap13.xml
@@ -58,7 +58,6 @@
     <#Include Label = "SemigroupCongruence">
     <#Include Label = "LeftSemigroupCongruence">
     <#Include Label = "RightSemigroupCongruence">
-    <#Include Label = "GeneratingPairsOfSemigroupCongruence">
 
   </Section>