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#@local G,molser,psi,x,y,tbl,irr,lin,deg3,ser,ser2,m2
gap> START_TEST("ctblmoli.tst");
#
gap> G:= AlternatingGroup( 5 );;
gap> psi:= First( Irr( G ), x -> Degree( x ) = 3 );;
gap> molser:= MolienSeries( psi );
( 1-z^2-z^3+z^6+z^7-z^9 ) / ( (1-z^5)*(1-z^3)*(1-z^2)^2 )
gap> List( [ 0 .. 20 ], i -> ValueMolienSeries( molser, i ) );
[ 1, 0, 1, 0, 1, 0, 2, 0, 2, 0, 3, 0, 4, 0, 4, 1, 5, 1, 6, 1, 7 ]
gap> m2:=MolienSeriesWithGivenDenominator( molser, [ 2, 6, 10 ] );
( 1+z^15 ) / ( (1-z^10)*(1-z^6)*(1-z^2) )
gap> ForAll( [ 0 .. 20 ], i -> ValueMolienSeries( molser, i ) = ValueMolienSeries( m2, i ) );
true
gap> molser = m2;
true
#
gap> y:= E(3);; x:= E(3)^2;;
gap> G:= Group(
> [ [ 0, y, 0, 0, 0, 0 ],
> [ x, 0, 0, 0, 0, 0 ],
> [ 0, 0, 1, 0, 0, 0 ],
> [ 0, 0, 0, 1, 0, 0 ],
> [ 0, 0, 0, 0, 1, 0 ],
> [ 0, 0, 0, 0, 0, 1 ] ],
> PermutationMat( (1,2), 6, Rationals ),
> PermutationMat( (2,3), 6, Rationals ),
> PermutationMat( (3,4), 6, Rationals ),
> PermutationMat( (4,5), 6, Rationals ) );;
gap> Size( G );
9720
gap> MolienSeries( NaturalCharacter( G ) );
( 1 ) / ( (1-z^12)*(1-z^9)*(1-z^6)*(1-z^5)*(1-z^3)*(1-z) )
## bug 7 for fix 5
gap> tbl:= CharacterTable( SL(2,3) );; irr:= Irr( tbl );;
gap> lin:= Filtered( LinearCharacters( tbl ), x -> Order(x) = 3 );;
gap> deg3:= First( irr, x -> DegreeOfCharacter( x ) = 3 );;
gap> MolienSeries( tbl, lin[1] + deg3, lin[2] );
( 2*z^2+z^3-z^4+z^6 ) / ( (1-z^3)^2*(1-z^2)^2 )
## bug 4 for fix 6
gap> tbl:= CharacterTable( SL(2,3) );; irr:= Irr( tbl );;
gap> lin := Filtered( LinearCharacters( tbl ), x -> Order(x) = 3 );;
gap> deg3 := First( irr, x -> DegreeOfCharacter( x ) = 3 );;
gap> ser := MolienSeries( tbl, lin[1] + deg3, lin[2] );;
gap> ser2 := MolienSeriesWithGivenDenominator( ser, [ 6,6,4,4 ] );
( 2*z^2+z^3+3*z^4+6*z^5+3*z^6+7*z^7+7*z^8+3*z^9+6*z^10+4*z^11+z^12+3*z^13+z^14\
+z^16 ) / ( (1-z^6)^2*(1-z^4)^2 )
gap> ForAll( [ 0 .. 20 ], i -> ValueMolienSeries( ser, i ) = ValueMolienSeries( ser2, i ) );
true
gap> ser = ser2;
true
#
# MolienSeries used to hang when given an non-character as input
# now an error is raised
#
gap> G:=Group((1,2,3,4,5,6,7),(5,6,7));;
gap> MolienSeries(NaturalCharacter(G));
( 1-z^3+z^6-z^9+z^12-z^15+z^18 ) / ( (1-z^7)*(1-z^5)*(1-z^4)*(1-z^3)^2*(1-z^2)\
*(1-z) )
gap> MolienSeries(-NaturalCharacter(G));
Error, <ns> must be a subset of <R>
#
gap> STOP_TEST("ctblmoli.tst");
[ Dauer der Verarbeitung: 0.14 Sekunden
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