Add missing tests and doc for IsSelfDualSemigroup and friends

doc/properties.xml

@@ -1194,3 +1194,36 @@ false]]></Example>
     </Description>
   </ManSection>
 <#/GAPDoc>
+
+<#GAPDoc Label="IsSelfDualSemigroup">
+  <ManSection>
+    <Prop Name="IsSelfDualSemigroup" Arg="S"/>
+    <Returns><K>true</K> or <K>false</K>.</Returns>
+    <Description>
+      Returns <K>true</K> if the semigroup <A>S</A> is self dual and
+      <K>false</K> otherwise.
+      <P/>
+
+      A semigroup is <E>self dual</E> if it is isomorphic to its dual,
+      that is, the semigroup <C>T</C> with multiplication <C>*</C> defined
+      by <C>x*y=yx</C> where <C>yx</C> denotes the product in <A>S</A>.
+
+      <Example><![CDATA[
+gap> F := FreeSemigroup("a", "b");
+<free semigroup on the generators [ a, b ]>
+gap> AssignGeneratorVariables(F);
+gap> R := [[a ^ 3, a], [b ^ 2, b], [(a * b) ^ 2, a]];
+[ [ a^3, a ], [ b^2, b ], [ (a*b)^2, a ] ]
+gap> S := F / R;
+<fp semigroup with 2 generators and 3 relations of length 14>
+gap> IsSelfDualSemigroup(S);
+false
+gap> IsSelfDualSemigroup(FreeBand(3));
+true
+gap> S := DualSymmetricInverseMonoid(3);
+<inverse block bijection monoid of degree 3 with 3 generators>
+gap> IsSelfDualSemigroup(S);
+true]]></Example>
+  </Description>
+</ManSection>
+<#/GAPDoc>

doc/semifp.xml

@@ -122,4 +122,40 @@ true]]></Example>
 </ManSection>
 <#/GAPDoc>
 
+<#GAPDoc Label="AntiIsomorphismDualFpSemigroup">
+<ManSection>
+  <Attr Name="AntiIsomorphismDualFpSemigroup" Arg="S"/>
+  <Attr Name="AntiIsomorphismDualFpMonoid" Arg="S"/>
+  <Returns>A finitely presented semigroup or monoid.</Returns>
+  <Description>
+    <C>AntiIsomorphismDualFpSemigroup</C> returns an anti-isomorphism (<Ref
+    Func="MappingByFunction" BookName="ref"/>) from the
+    finitely presented semigroup <A>S</A> to another finitely presented
+    semigroup. The range finitely presented semigroup is obtained from <A>S</A>
+    by reversing the relations of <A>S</A>.<P/>
+
+    <C>AntiIsomorphismDualFpMonoid</C> works analogously when <A>S</A> is a
+    finitely presented monoid, and the range of the returned anti-isomorphism
+    is a finitely presented monoid. 
+
+    <Example><![CDATA[
+gap> F := FreeSemigroup("a", "b");
+<free semigroup on the generators [ a, b ]>
+gap> AssignGeneratorVariables(F);
+gap> R := [[a ^ 3, a], [b ^ 2, b], [(a * b) ^ 2, a]];
+[ [ a^3, a ], [ b^2, b ], [ (a*b)^2, a ] ]
+gap> S := F / R;
+<fp semigroup with 2 generators and 3 relations of length 14>
+gap> map := AntiIsomorphismDualFpSemigroup(S);
+MappingByFunction( <fp semigroup with 2 generators and 
+  3 relations of length 14>, <fp semigroup with 2 generators and 
+  3 relations of length 14>
+ , function( x ) ... end, function( x ) ... end )
+gap> RelationsOfFpSemigroup(Range(map));
+[ [ a^3, a ], [ b^2, b ], [ (b*a)^2, a ] ]
+]]></Example>
+  </Description>
+</ManSection>
+<#/GAPDoc>
+
 

doc/z-chap06.xml

@@ -428,6 +428,7 @@ gap> AsSemigroup(IsPBRSemigroup, M);
      <#Include Label = "RZMSNormalization">
      <#Include Label = "RMSNormalization">
      <#Include Label = "IsomorphismReesZeroMatrixSemigroup">
+     <#Include Label = "AntiIsomorphismDualFpSemigroup">
 
    </Section>
 

doc/z-chap12.xml

@@ -46,7 +46,7 @@
     <#Include Label = "IsZeroRectangularBand">
     <#Include Label = "IsZeroSemigroup">
     <#Include Label = "IsZeroSimpleSemigroup">
-
+    <#Include Label = "IsSelfDualSemigroup">
   </Section>
 
   <Section>

gap/attributes/properties.gd

@@ -44,7 +44,7 @@ DeclareOperation("IsNormalInverseSubsemigroup",
                  [IsInverseSemigroup, IsInverseSemigroup]);
 
 if not IsBoundGlobal("IsSelfDualSemigroup") then
-  DeclareProperty("IsSelfDualSemigroup", IsSemigroup);
+  DeclareProperty("IsSelfDualSemigroup", IsSemigroup and CanUseFroidurePin);
 fi;
 
 DeclareSynonymAttr("IsRectangularGroup",

gap/attributes/properties.gi

@@ -1651,6 +1651,12 @@ InstallMethod(IsSelfDualSemigroup,
 [IsSemigroup and CanUseFroidurePin],
 function(S)
   local T, map;
+  if IsCommutativeSemigroup(S) then  # TODO(later) any more?
+    return true;
+  elif NrRClasses(S) <> NrLClasses(S) then
+    return false;
+  fi;
+
   T := AsSemigroup(IsFpSemigroup, S);
   map := AntiIsomorphismDualFpSemigroup(T);
   return SemigroupIsomorphismByImages(T,

tst/standard/attributes/properties.tst

@@ -2004,6 +2004,25 @@ gap> IsNormalInverseSubsemigroup(G,
 >                                InverseSemigroup(G.1, rec(acting := true)));
 false
 
+# IsSelfDualSemigroup
+gap> F := FreeSemigroup("a", "b");
+<free semigroup on the generators [ a, b ]>
+gap> AssignGeneratorVariables(F);
+gap> R := [[a ^ 3, a], [b ^ 2, b], [(a * b) ^ 2, a]];
+[ [ a^3, a ], [ b^2, b ], [ (a*b)^2, a ] ]
+gap> S := F / R;
+<fp semigroup with 2 generators and 3 relations of length 14>
+gap> IsSelfDualSemigroup(S);
+false
+gap> IsSelfDualSemigroup(FreeBand(3));
+true
+gap> S := DualSymmetricInverseMonoid(3);
+<inverse block bijection monoid of degree 3 with 3 generators>
+gap> IsSelfDualSemigroup(S);
+true
+gap> IsSelfDualSemigroup(MonogenicSemigroup(7, 8));
+true
+
 # SEMIGROUPS_UnbindVariables
 gap> Unbind(D);
 gap> Unbind(I);

tst/standard/semigroups/semifp.tst

@@ -2538,6 +2538,70 @@ gap> w := Factorization(F, One(F));
 gap> EvaluateWord(GeneratorsOfSemigroup(F), w) = One(F);
 true
 
+# Reversed for elements of a fp semigroup/monoid
+gap> F := FreeSemigroup("a", "b");
+<free semigroup on the generators [ a, b ]>
+gap> AssignGeneratorVariables(F);
+gap> R := [[a ^ 3, a], [b ^ 2, b], [(a * b) ^ 2, a]];
+[ [ a^3, a ], [ b^2, b ], [ (a*b)^2, a ] ]
+gap> S := F / R;
+<fp semigroup with 2 generators and 3 relations of length 14>
+gap> Reversed(a * b * b);
+b^2*a
+gap> Reversed(a * b * b * a);
+a*b^2*a
+gap> Reversed(a * b * b) = b * b * a;
+true
+gap> Reversed(a * b * b * a) = a * b * b * a;
+true
+gap> F := FreeMonoid("a", "b");
+<free monoid on the generators [ a, b ]>
+gap> AssignGeneratorVariables(F);
+gap> R := ParseRelations([a, b], "a ^ 3=a, b ^ 2= b, (ab) ^ 2= 1");
+[ [ a^3, a ], [ b^2, b ], [ (a*b)^2, <identity ...> ] ]
+gap> S := F / R;
+<fp monoid with 2 generators and 3 relations of length 13>
+gap> Reversed(a * b * b) = b * b * a;
+true
+gap> Reversed(a * b * b * a) = a * b * b * a;
+true
+gap> Reversed(a * b * b);
+b^2*a
+gap> Reversed(a * b * b * a);
+a*b^2*a
+gap> Reversed(One(S));
+<identity ...>
+
+# AntiIsomorphismDualFpMonoid/Semigroup
+gap> F := FreeSemigroup("a", "b");
+<free semigroup on the generators [ a, b ]>
+gap> AssignGeneratorVariables(F);
+gap> R := [[a ^ 3, a], [b ^ 2, b], [(a * b) ^ 2, a]];
+[ [ a^3, a ], [ b^2, b ], [ (a*b)^2, a ] ]
+gap> S := F / R;
+<fp semigroup with 2 generators and 3 relations of length 14>
+gap> map := AntiIsomorphismDualFpSemigroup(S);
+MappingByFunction( <fp semigroup with 2 generators and 
+  3 relations of length 14>, <fp semigroup with 2 generators and 
+  3 relations of length 14>, function( x ) ... end, function( x ) ... end )
+gap> RelationsOfFpSemigroup(Range(map));
+[ [ a^3, a ], [ b^2, b ], [ (b*a)^2, a ] ]
+gap> F := FreeMonoid("a", "b");
+<free monoid on the generators [ a, b ]>
+gap> AssignGeneratorVariables(F);
+gap> R := [[a ^ 3, One(F)], [b ^ 2, One(F)], [(a * b) ^ 2, One(F)]];
+[ [ a^3, <identity ...> ], [ b^2, <identity ...> ], 
+  [ (a*b)^2, <identity ...> ] ]
+gap> S := F / R;
+<fp monoid with 2 generators and 3 relations of length 11>
+gap> map := AntiIsomorphismDualFpMonoid(S);
+MappingByFunction( <fp monoid with 2 generators and 3 relations of length 11>
+ , <fp monoid with 2 generators and 3 relations of length 11>
+ , function( x ) ... end, function( x ) ... end )
+gap> RelationsOfFpMonoid(Range(map));
+[ [ a^3, <identity ...> ], [ b^2, <identity ...> ], 
+  [ (b*a)^2, <identity ...> ] ]
+
 # SEMIGROUPS_UnbindVariables
 gap> Unbind(a);
 gap> Unbind(b);