GeneralizedConjugacyClasses

doc/cartan.xml

@@ -1,7 +1,7 @@
 #############################################################################
 ##
 #W  cartan.xml
-#Y  Copyright (C) 2024                                   Balthazar Charles
+#Y  Copyright (C) 2024-2026                              Balthazar Charles
 ##                                                             Joseph Ruiz
 ##
 ##  Licensing information can be found in the README file of this package.
@@ -31,14 +31,6 @@
       semigroup <A>S</A>. In a group generalized conjugacy classes coincide
       with conjugacy classes.<P/>
 
-      Note that each generalized conjugacy class as currently implemented
-      does not store a list of elements in the conjugacy class, only the representative
-      with no way to compute all the elements in the conjugacy class.
-      This means that
-      <Ref Attr="GeneralizedConjugacyClasses" Label = "for a semigroup"/> as currently
-      implemented is only as effective as
-      <Ref Attr="GeneralizedConjugacyClassesRepresentatives" Label = "for a semigroup"/>.
-
       <Example><![CDATA[
 gap> S := FullTransformationMonoid(6);;
 gap> GeneralizedConjugacyClassesRepresentatives(S);
@@ -185,13 +177,13 @@ gap> BlockDiagonalMatrixOfCharacterTables(S);
   </ManSection>
 <#/GAPDoc>
 
-<#GAPDoc Label="MonoidCharacterTable">
+<#GAPDoc Label="CharacterTable">
   <ManSection>
-    <Attr Name="MonoidCharacterTable" Arg='M[, F]'/>
+    <Oper Name="CharacterTable" Arg='M[, F]'/>
     <Returns>The character table object for <A>M</A> over <A>F</A>.</Returns>
     <Description>
       Called with a finite monoid <A>M</A> and optionally a field <A>F</A>,
-      <Ref Attr="MonoidCharacterTable"/> returns the character table of the
+      <Ref Oper="CharacterTable"/> returns the character table of the
       monoid which is defined as the matrix <M>Trace(X(m))</M>, where <M>X</M>
       runs over the simple <M>FM</M>-modules and <M>m</M> runs over the
       generalized conjugacy class representatives of <A>M</A>.<P/>
@@ -201,7 +193,7 @@ gap> BlockDiagonalMatrixOfCharacterTables(S);
       <Ref Attr="Irr" Label="for a monoid character table"/>.<P/>
 
       If <A>F</A> is not given, then
-      <Ref Attr="MonoidCharacterTable"/> returns the character table of
+      <Ref Oper="CharacterTable"/> returns the character table of
       <M>M</M> over a characteristic zero splitting field of <A>M</A>.<P/>
 
       At the moment, methods are available for the following cases:
@@ -212,7 +204,7 @@ gap> BlockDiagonalMatrixOfCharacterTables(S);
 
       <Example><![CDATA[
 gap> S := FullTransformationMonoid(3);;
-gap> ct := MonoidCharacterTable(S);;
+gap> ct := CharacterTable(S);;
 gap> Irr(ct);;
 gap> Display(ct);
     c.1 c.2 c.3 c.4 c.5 c.6
@@ -242,7 +234,7 @@ X.6   1   1   1   1   1   1
       the presentation of the monoid display inconsistently -->
       <Example><![CDATA[
 gap> M := FullBooleanMatMonoid(2);;
-gap> ct := MonoidCharacterTable(M);;
+gap> ct := CharacterTable(M);;
 gap> Irr(ct);
 [ MonoidCharacter( MonoidCharacterTable( Monoid( [ Matrix(IsBooleanMat\
 , [ [ false, true ], [ true, false ] ]), Matrix(IsBooleanMat, [ [ true\
@@ -268,23 +260,23 @@ gap> Irr(ct);
   </ManSection>
 <#/GAPDoc>
 
-<#GAPDoc Label="MonoidCartanMatrix">
+<#GAPDoc Label="CartanMatrix">
   <ManSection>
-    <Attr Name="MonoidCartanMatrix" Arg='M[, F]'/>
+    <Attr Name="CartanMatrix" Arg='M[, F]'/>
     <Returns>An object.</Returns>
     <Description>
       Called with a finite monoid <A>M</A> and a field <A>F</A>,
-      <Ref Attr="MonoidCartanMatrix"/> returns the Cartan matrix of the monoid
+      <Ref Attr="CartanMatrix"/> returns the Cartan matrix of the monoid
       algebra <M>FM</M> which is defined as the matrix
       <M>dim Hom(P,Q)/dim End(P / rad(FM))</M>, where <M>P</M> and <M>Q</M>
       run over the right indecomposable projective modules of FM.<P/>
 
       To get the Cartan matrix of a monoid to display like the example below,
       the projective indecomposable modules need to be computed first using
-      <Ref Attr="Pims" Label="for a monoid cartan matrix"/>.<P/>
+      <Ref Attr="Pims" Label="for a cartan matrix"/>.<P/>
 
       If <A>M</A> is the only argument then
-      <Ref Attr="MonoidCartanMatrix"/> returns the Cartan matrix of the monoid
+      <Ref Attr="CartanMatrix"/> returns the Cartan matrix of the monoid
       algebra <M>FM</M>, where <A>F</A> is a splitting field of <A>M</A> over
       the rationals.<P/>
 
@@ -296,7 +288,7 @@ gap> Irr(ct);
 
       <Example><![CDATA[
 gap> S := FullTransformationMonoid(3);;
-gap> cm := MonoidCartanMatrix(S);;
+gap> cm := CartanMatrix(S);;
 gap> Pims(cm);;
 gap> Display(cm);
     X.1 X.2 X.3 X.4 X.5 X.6
@@ -315,18 +307,18 @@ P.6   .   .   .   1   .   1
 <#GAPDoc Label="Pims">
   <ManSection>
     <Attr Name ="Pims" Arg="T"
-         Label = "for a monoid cartan matrix"/>
+         Label = "for a cartan matrix"/>
     <Returns>A list of monoid characters.</Returns>
     <Description>
-      <Ref Attr="Pims" Label="for a monoid cartan matrix"/> returns a
+      <Ref Attr="Pims" Label="for a cartan matrix"/> returns a
       list of the characters of the projective indecomposable
       modules of the <Ref Attr="Parent" BookName = "ref"/> monoid of the monoid character table <A>T</A>.
 
       <!-- The following example is a log because the values in the vectors and
       the presentation of the monoid display inconsistently -->
       <Example><![CDATA[
 gap> M := FullBooleanMatMonoid(2);;
-gap> cm := MonoidCartanMatrix(M);;
+gap> cm := CartanMatrix(M);;
 gap> Pims(cm);
 [ MonoidCharacter( MonoidCharacterTable( Monoid( [ Matrix(IsBooleanMat\
 , [ [ false, true ], [ true, false ] ]), Matrix(IsBooleanMat, [ [ true\

doc/z-chap11.xml

@@ -317,9 +317,9 @@
     <#Include Label="RegularRepresentationBicharacter">
     <#Include Label="RClassBicharacterOfGroupHClass">
     <#Include Label="BlockDiagonalMatrixOfCharacterTables">
-    <#Include Label="MonoidCharacterTable">
+    <#Include Label="CharacterTable">
     <#Include Label="Irr">
-    <#Include Label="MonoidCartanMatrix">
+    <#Include Label="CartanMatrix">
     <#Include Label="Pims">
 
   </Section>

gap/attributes/cartan.gd

@@ -1,31 +1,37 @@
 #############################################################################
 ##
 ##  cartan.gd
-##  Copyright (C) 2024                                   Balthazar Charles
+##  Copyright (C) 2024-2026                              Balthazar Charles
 ##                                                             Joseph Ruiz
 ##
 ##  Licensing information can be found in the README file of this package.
 ##
 #############################################################################
 ##
 
-DeclareCategory("IsGeneralizedConjugacyClass", IsObject);
+DeclareCategory("IsGeneralizedConjugacyClass", IsCollection);
 DeclareAttribute("Representative", IsGeneralizedConjugacyClass);
 DeclareAttribute("ParentAttr", IsGeneralizedConjugacyClass);
+DeclareAttribute("MapToGroupHClass", IsGeneralizedConjugacyClass);
 DeclareOperation("GeneralizedConjugacyClass",
                  [IsSemigroup, IsMultiplicativeElement]);
-DeclareAttribute("GeneralizedConjugacyClassesRepresentatives", IsSemigroup);
+DeclareOperation("GeneralizedConjugacyClass",
+                 [IsSemigroup, IsMultiplicativeElement, IsGeneralMapping]);
 DeclareAttribute("GeneralizedConjugacyClasses", IsSemigroup);
+DeclareAttribute("GeneralizedConjugacyClassesRepresentatives", IsSemigroup);
 DeclareCategory("IsMonoidCharacterTable", IsObject);
 DeclareAttribute("ParentAttr", IsMonoidCharacterTable);
-DeclareAttribute("MonoidCharacterTable", IsSemigroup);
+DeclareAttribute("CartanMatrix", IsMonoidCharacterTable);
+DeclareAttribute("OrdinaryCharacterTable", IsSemigroup);
+DeclareOperation("CharacterTable", [IsSemigroup]);
 
 DeclareCategory("IsMonoidCharacter", IsObject);
-DeclareOperation("MonoidCharacter", [IsMonoidCharacterTable, IsList]);
-DeclareOperation("PimMonoidCharacter",
+DeclareOperation("Character", [IsMonoidCharacterTable, IsList]);
+DeclareOperation("Character",
                  [IsMonoidCharacterTable, IsDenseList, IsMonoidCharacter]);
+DeclareOperation("\^", [IsMultiplicativeElement, IsMonoidCharacter]);
 DeclareAttribute("ParentAttr", IsMonoidCharacter);
-DeclareAttribute("ValuesOfMonoidClassFunction", IsMonoidCharacter);
+DeclareAttribute("ValuesOfClassFunction", IsMonoidCharacter);
 DeclareAttribute("ProjectiveCoverOf", IsMonoidCharacter);
 DeclareAttribute("ValuesOfCompositionFactorsFunction", IsMonoidCharacter);
 DeclareAttribute("DClassBicharacter", IsGreensDClass);
@@ -38,6 +44,6 @@ DeclareAttribute("Irr", IsMonoidCharacterTable);
 
 DeclareCategory("IsMonoidCartanMatrix", IsObject);
 DeclareAttribute("ParentAttr", IsMonoidCartanMatrix);
-DeclareAttribute("MonoidCartanMatrix", IsSemigroup);
+DeclareAttribute("CartanMatrix", IsSemigroup);
 
 DeclareAttribute("Pims", IsMonoidCartanMatrix);