53.9 IsVirtualCharacter

IsVirtualCharacter( obj )

returns true if obj is a virtual character, and false otherwise. For a class function obj that does not know whether it is a virtual character, the scalar products with all irreducible characters of the source of obj are computed. If they are all integral then obj is turned into a virtual character record.

    gap> psi:= irr[3] - irr[1];
    VirtualCharacter( S4, [ 1, 1, -2, -1, -1 ] )
    gap> cf:= ClassFunction( S4, [ 1, 1, -2, -1, -1 ] );
    ClassFunction( S4, [ 1, 1, -2, -1, -1 ] )
    gap> IsVirtualCharacter( cf );
    true
    gap> IsCharacter( cf );
    false
    gap> cf;
    VirtualCharacter( S4, [ 1, 1, -2, -1, -1 ] ) 

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