fixed ConstituentsOfCharacter for Brauer character

- The variant of `ConstituentsOfCharacter` with only argument a Brauer character
  was wrong, it regarded the character as an ordinary character.

  (This bug has been reported by Gabriel Navarro.)

- Also the case of a virtual Brauer character was not handled correctly.

The two bugs are now fixed,
some tests for the variants of arguments are available,
and the documentation states which cases are admissible:
ordinary or modular characters,
ordinary of modular virtual characters.

Also, the documentation

lib/ctblfuns.gd

@@ -1393,8 +1393,13 @@ DeclareAttribute( "ClassPositionsOfCentre", IsHomogeneousList );
 ## <Attr Name="ConstituentsOfCharacter" Arg='[tbl, ]chi'/>
 ##
 ## <Description>
-## is the set of irreducible characters that occur in the decomposition of
-## the (virtual) character <A>chi</A> with nonzero coefficient.
+## Let <A>chi</A> be an ordinary or modular (virtual) character.
+## If an ordinary or modular character table <A>tbl</A> is given then
+## <A>chi</A> may also be a list of character values.
+## <P/>
+## <Ref Attr="ConstituentsOfCharacter"/> returns
+## the set of those irreducible characters that occur in the decomposition
+## of <A>chi</A> with nonzero coefficient.
 ## <P/>
 ## <Example><![CDATA[
 ## gap> nat:= NaturalCharacter( S4 );

lib/ctblfuns.gi

@@ -1832,11 +1832,10 @@ InstallMethod( ConstituentsOfCharacter,
  chi -> ConstituentsOfCharacter( UnderlyingCharacterTable( chi ), chi ) );
 
 InstallMethod( ConstituentsOfCharacter,
- "for a character",
- [ IsClassFunction and IsCharacter ],
- function( chi )
- local tbl, # underlying table of `chi'
- irr, # irreducible characters of `tbl'
+ "for an ordinary table, and a character",
+ [ IsOrdinaryTable, IsClassFunction and IsCharacter ],
+ function( tbl, chi )
+ local irr, # irreducible characters of `tbl'
  values, # character values
  deg, # degree of `chi'
  const, # list of constituents, result
@@ -1881,7 +1880,7 @@ InstallMethod( ConstituentsOfCharacter,
  scpr:= ScalarProduct( tbl, chi, i );
  if scpr <> 0 then
  Add( const, i );
- proper:= proper and IsInt( scpr ) and ( 0 < scpr );
+ proper:= proper and IsPosInt( scpr );
  fi;
  od;
 
@@ -1897,15 +1896,18 @@ InstallMethod( ConstituentsOfCharacter,
  "for a Brauer table, and a homogeneous list",
  [ IsBrauerTable, IsHomogeneousList ],
  function( tbl, chi )
- local irr, # irreducible characters of `tbl'
- dec;
+ local irr, intA, intB, dec;
 
  irr:= Irr( tbl );
- dec:= Decomposition( irr, [ chi ], "nonnegative" )[1];
+ intA:= IntegralizedMat( irr );
+ intB:= IntegralizedMat( [ chi ], intA.inforec );
+ dec:= SolutionIntMat( intA.mat, intB.mat[1] );
  if dec = fail then
- TryNextMethod();
+ Error( "<chi> is not a virtual character of <tbl>" );
  fi;
- return irr{ Filtered( [ 1 .. Length( dec ) ], i -> dec[i] <> 0 ) };
+
+ return SortedList( irr{ Filtered( [ 1 .. Length( dec ) ],
+ i -> dec[i] <> 0 ) } );
  end );
 
 

tst/teststandard/ctblfuns.tst

@@ -0,0 +1,37 @@
+#@local ordtbl, modtbl, irr, chi, const, ibr, phi
+gap> START_TEST( "ctblfuns.tst" );
+
+#
+gap> ordtbl:= CharacterTable( GL(2,3) );;
+gap> modtbl:= ordtbl mod 2;;
+gap> irr:= Irr( ordtbl );;
+gap> chi:= irr[5] * irr[5];;
+gap> const:= ConstituentsOfCharacter( chi );;
+gap> List( const, ValuesOfClassFunction );
+[ [ 1, 1, 1, 1, 1, -1, -1, -1 ], [ 3, 0, 3, 0, -1, -1, -1, 1 ] ]
+gap> const:= ConstituentsOfCharacter( -chi );;
+gap> List( const, ValuesOfClassFunction );
+[ [ 1, 1, 1, 1, 1, -1, -1, -1 ], [ 3, 0, 3, 0, -1, -1, -1, 1 ] ]
+gap> const:= ConstituentsOfCharacter( ordtbl, chi );;
+gap> List( const, ValuesOfClassFunction );
+[ [ 1, 1, 1, 1, 1, -1, -1, -1 ], [ 3, 0, 3, 0, -1, -1, -1, 1 ] ]
+gap> const:= ConstituentsOfCharacter( ordtbl, ValuesOfClassFunction( chi ) );;
+gap> List( const, ValuesOfClassFunction );
+[ [ 1, 1, 1, 1, 1, -1, -1, -1 ], [ 3, 0, 3, 0, -1, -1, -1, 1 ] ]
+gap> ibr:= Irr( modtbl );;
+gap> phi:= ibr[2] * ibr[2];;
+gap> const:= ConstituentsOfCharacter( phi );;
+gap> List( const, ValuesOfClassFunction );
+[ [ 1, 1 ], [ 2, -1 ] ]
+gap> const:= ConstituentsOfCharacter( -phi );;
+gap> List( const, ValuesOfClassFunction );
+[ [ 1, 1 ], [ 2, -1 ] ]
+gap> const:= ConstituentsOfCharacter( modtbl, phi );;
+gap> List( const, ValuesOfClassFunction );
+[ [ 1, 1 ], [ 2, -1 ] ]
+gap> const:= ConstituentsOfCharacter( modtbl, ValuesOfClassFunction( phi ) );;
+gap> List( const, ValuesOfClassFunction );
+[ [ 1, 1 ], [ 2, -1 ] ]
+
+#
+gap> STOP_TEST( "ctblfuns.tst" );