Spracherkennung für: .tst vermutete Sprache: Unknown {[0] [0] [0]} [Methode: Schwerpunktbildung, einfache Gewichte, sechs Dimensionen]
#@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:= First( irr, x -> x[1] = 2 and not ForAll( x, IsInt ) );;
gap> chi:= chi * chi;;
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:= First( ibr, x -> x[1] = 2 );;
gap> phi:= phi * phi;;
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> FrobeniusCharacterValue( E(7), 7 );
fail
gap> FrobeniusCharacterValue( 1/7, 7 );
fail
gap> FrobeniusCharacterValue( 1, 7 );
Z(7)^0
gap> FrobeniusCharacterValue( 7*E(5), 7 );
0*Z(7)
gap> FrobeniusCharacterValue( E(23), 2 );
Z(2^11)^89
gap> FrobeniusCharacterValue( E(19), 97 );
#I the Conway polynomial of degree 18 for p = 97 is not known
fail
gap> FrobeniusCharacterValue( 82*E(16)+E(16)^5, 269 );
0*Z(269)
gap> FrobeniusCharacterValue( E(16), 269 );
162+256z+143z2+219z3
# Dixon-Schneider test that also exercises MatrixObjects over Z/nZ
gap> Irr(MathieuGroup(24));;
#
gap> STOP_TEST( "ctblfuns.tst" );
