semifp: add tests and doc for AntiIsomorphismDualFpSemigroup

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>
 

tst/standard/semigroups/semifp.tst

@@ -2572,6 +2572,36 @@ 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);