Implement LeftSemigroupIdeal and RightSemigroupIdeal

doc/ideals.xml

@@ -98,6 +98,56 @@ gap> I := SemigroupIdeal(S, I, Idempotents(S));
   </ManSection>
 <#/GAPDoc>
 
+<#GAPDoc Label="LeftSemigroupIdeal">
+  <ManSection>
+    <Func Name = "LeftSemigroupIdeal" Arg = "S, obj1, obj2, .. . "/>
+    <Returns>
+      A left ideal of a semigroup.
+    </Returns>
+    <Description>
+      If <A>obj1</A>, <A>obj2</A>, .. . are (any combination) of elements of the
+      semigroup <A>S</A> or collections of elements of <A>S</A> (including
+      subsemigroups and ideals of <A>S</A>),  then <C>LeftSemigroupIdeal</C> returns the
+      left ideal of the semigroup <A>S</A> generated by the union of
+      <A>obj1</A>,  <A>obj2</A>, .. .. <P/>
+
+      The <Ref Func = "Parent" BookName = "ref"/> of the ideal returned by this
+      function is <A>S</A>.
+
+      <Example><![CDATA[
+gap> S := SymmetricInverseMonoid(10);
+<symmetric inverse monoid of degree 10>
+gap> I := LeftSemigroupIdeal(S, PartialPerm([1, 2]));
+<LeftMagmaIdeal with 1 generator>]]></Example>
+    </Description>
+  </ManSection>
+<#/GAPDoc>
+
+<#GAPDoc Label="RightSemigroupIdeal">
+  <ManSection>
+    <Func Name = "RightSemigroupIdeal" Arg = "S, obj1, obj2, .. . "/>
+    <Returns>
+      A Right ideal of a semigroup.
+    </Returns>
+    <Description>
+      If <A>obj1</A>, <A>obj2</A>, .. . are (any combination) of elements of the
+      semigroup <A>S</A> or collections of elements of <A>S</A> (including
+      subsemigroups and ideals of <A>S</A>),  then <C>RightSemigroupIdeal</C> returns the
+      Right ideal of the semigroup <A>S</A> generated by the union of
+      <A>obj1</A>,  <A>obj2</A>, .. .. <P/>
+
+      The <Ref Func = "Parent" BookName = "ref"/> of the ideal returned by this
+      function is <A>S</A>.
+
+      <Example><![CDATA[
+gap> S := SymmetricInverseMonoid(10);
+<symmetric inverse monoid of degree 10>
+gap> I := RightSemigroupIdeal(S, PartialPerm([1, 2]));
+<RightMagmaIdeal with 1 generator>]]></Example>
+    </Description>
+  </ManSection>
+<#/GAPDoc>
+
 <#GAPDoc Label="SupersemigroupOfIdeal">
   <ManSection>
     <Attr Name = "SupersemigroupOfIdeal" Arg = "I"/>

doc/semicons.xml

@@ -147,6 +147,61 @@ true]]></Example>
   </ManSection>
 <#/GAPDoc>
 
+<#GAPDoc Label="FreeSemilattice">
+  <ManSection>
+    <Func Name="FreeSemilattice" Arg="[filt, ] n"/>
+    <Returns>
+      A free semilattice with <A>n</A> generators.
+    </Returns>
+    <Description>
+      If <A>n</A> is a positive integer, then this function returns a free
+      semilattice with <A>n</A> generators in the representation given by the
+      filter <A>filt</A>.
+
+      The optional argument <A>filt</A> may be one of the following:
+      <List>
+        <Item><C>IsTransformationSemigroup</C>
+          (the default, if <A>filt</A> is not specified),</Item>
+        <Item><C>IsTransformationMonoid</C>,</Item>
+        <Item><C>IsPartialPermSemigroup</C>,</Item>
+        <Item><C>IsPartialPermMonoid</C>,</Item>
+        <Item><C>IsFpSemigroup</C>,</Item>
+        <Item><C>IsFpMonoid</C>,</Item>
+        <Item><C>IsBipartitionSemigroup</C>,</Item>
+        <Item><C>IsBipartitionMonoid</C>,</Item>
+        <Item><C>IsPBRSemigroup</C>,</Item>
+        <Item><C>IsPBRMonoid</C>,</Item>
+        <Item><C>IsBooleanMatSemigroup</C>,</Item>
+        <Item><C>IsBooleanMatMonoid</C>,</Item>
+        <Item><C>IsNTPMatrixSemigroup</C>,</Item>
+        <Item><C>IsNTPMatrixMonoid</C>,</Item>
+        <Item><C>IsMaxPlusMatrixSemigroup</C>,</Item>
+        <Item><C>IsMaxPlusMatrixMonoid</C>,</Item>
+        <Item><C>IsMinPlusMatrixSemigroup</C>,</Item>
+        <Item><C>IsMinPlusMatrixMonoid</C>,</Item>
+        <Item><C>IsTropicalMaxPlusMatrixSemigroup</C>,</Item>
+        <Item><C>IsTropicalMaxPlusMatrixMonoid</C>,</Item>
+        <Item><C>IsTropicalMinPlusMatrixSemigroup</C>,</Item>
+        <Item><C>IsTropicalMinPlusMatrixMonoid</C>,</Item>
+        <Item><C>IsProjectiveMaxPlusMatrixSemigroup</C>,</Item>
+        <Item><C>IsProjectiveMaxPlusMatrixMonoid</C>,</Item>
+        <Item><C>IsIntegerMatrixSemigroup.</C></Item>
+        <Item><C>IsIntegerMatrixMonoid.</C></Item>
+      </List>
+
+      <Example><![CDATA[
+gap> S := FreeSemilattice(IsTransformationSemigroup, 5);
+<inverse transformation semigroup of size 31, degree 6 with 5 
+ generators>
+gap> T := FreeSemilattice(IsPartialPermSemigroup, 3);
+<inverse partial perm semigroup of size 7, rank 3 with 3 generators>
+gap> U := FreeSemilattice(IsBooleanMatSemigroup, 4);
+<inverse semigroup of size 15, 5x5 boolean matrices with 4 generators>
+]]></Example>
+    </Description>
+  </ManSection>
+<#/GAPDoc>
+
 <#GAPDoc Label="ZeroSemigroup">
   <ManSection>
     <Func Name="ZeroSemigroup" Arg="[filt, ]n"/>

doc/z-chap07.xml

@@ -155,6 +155,7 @@
     <#Include Label = "TrivialSemigroup">
     <#Include Label = "MonogenicSemigroup">
     <#Include Label = "RectangularBand">
+    <#Include Label = "FreeSemilattice">
     <#Include Label = "ZeroSemigroup">
     <#Include Label = "LeftZeroSemigroup">
     <#Include Label = "BrandtSemigroup">

doc/z-chap09.xml

@@ -29,6 +29,8 @@
     </Heading>
 
     <#Include Label = "SemigroupIdeal">
+    <#Include Label = "LeftSemigroupIdeal">
+    <#Include Label = "RightSemigroupIdeal">
     <#Include Label = "Ideals">
   </Section>
 

gap/ideals/froidure-pin.gd

@@ -9,3 +9,5 @@
 ##
 
 DeclareAttribute("PositionsInSupersemigroup", IsSemigroupIdeal);
+DeclareAttribute("PositionsInSupersemigroup", IsLeftSemigroupIdeal);
+DeclareAttribute("PositionsInSupersemigroup", IsRightSemigroupIdeal);

gap/ideals/froidure-pin.gi

@@ -39,6 +39,48 @@ function(I)
   return result;
 end);
 
+InstallMethod(PositionsInSupersemigroup,
+"for a left semigroup ideal with known generators",
+[IsLeftSemigroupIdeal and HasGeneratorsOfSemigroupIdeal and
+ CanUseFroidurePin],
+function(I)
+  local S, L, result, pos, x;
+  S := SupersemigroupOfIdeal(I);
+  L := LeftCayleyDigraph(S);
+
+  result := [];
+  for x in GeneratorsOfSemigroupIdeal(I) do
+    pos := PositionCanonical(S, x);
+    if not pos in result then
+      AddSet(result, pos);
+      UniteSet(result, VerticesReachableFrom(L, pos));
+    fi;
+  od;
+
+  return result;
+end);
+
+InstallMethod(PositionsInSupersemigroup,
+"for a right semigroup ideal with known generators",
+[IsRightSemigroupIdeal and HasGeneratorsOfSemigroupIdeal and
+ CanUseFroidurePin],
+function(I)
+  local S, R, result, pos, x;
+  S := SupersemigroupOfIdeal(I);
+  R := RightCayleyDigraph(S);
+
+  result := [];
+  for x in GeneratorsOfSemigroupIdeal(I) do
+    pos := PositionCanonical(S, x);
+    if not pos in result then
+      AddSet(result, pos);
+      UniteSet(result, VerticesReachableFrom(R, pos));
+    fi;
+  od;
+
+  return result;
+end);
+
 InstallMethod(GeneratorsOfInverseSemigroup,
 "for an inverse semigroup ideal with inverse op and generators",
 [IsSemigroupIdeal and IsInverseSemigroup

gap/ideals/ideals.gd

@@ -8,7 +8,20 @@
 #############################################################################
 
 DeclareSynonymAttr("GeneratorsOfSemigroupIdeal", GeneratorsOfMagmaIdeal);
+
 DeclareGlobalFunction("SemigroupIdeal");
+DeclareGlobalFunction("LeftSemigroupIdeal");
+DeclareGlobalFunction("RightSemigroupIdeal");
+DeclareGlobalFunction("AnySemigroupIdealInputParsing");
+
+DeclareOperation("AnySemigroupIdealByGenerators",
+                 [IsSemigroup, IsOperation, IsListOrCollection]);
+
+DeclareOperation("AnySemigroupIdealByGenerators",
+                 [IsSemigroup, IsOperation, IsListOrCollection, IsRecord]);
+
+DeclareOperation("AnySemigroupIdealByGeneratorsNC",
+                 [IsSemigroup, IsOperation, IsListOrCollection, IsRecord]);
 
 DeclareOperation("SemigroupIdealByGenerators",
                  [IsSemigroup, IsListOrCollection]);
@@ -40,6 +53,6 @@ DeclareAttribute("MinimalIdealGeneratingSet", IsSemigroupIdeal);
 
 DeclareAttribute("SupersemigroupOfIdeal", IsSemigroupIdeal);
 
-InstallTrueMethod(IsSemigroup, IsSemigroupIdeal);
+InstallTrueMethod(IsSemigroup, IsSemigroupIdeal);  # Duplicate with ideal.gi?
 
 DeclareAttribute("Ideals", IsSemigroup);