GAP Manual: 50.19. IrreducibleDifferences

IrreducibleDifferences( tbl, chars1, chars2 )
IrreducibleDifferences( tbl, chars1, chars2, scprmat )
IrreducibleDifferences( tbl, chars, "triangle" )
IrreducibleDifferences( tbl, chars, "triangle", scprmat )

returns the list of irreducible characters which occur as difference of two elements of chars (if "triangle" is specified) or of an element of chars1 and an element of chars2; if scprmat is not specified it will be computed (see MatScalarProducts), otherwise we must have [ scprmat[i][j] = ScalarProduct( tbl, chars[i], chars[j] ) ] resp. [ scprmat[i][j] = ScalarProduct( tbl, chars1[i], chars2[j] ) ].

    gap> t:= CharTable( "A5" );;
    gap> chars:= Sublist( t.irreducibles, [ 2 .. 4 ] );;
    gap> chars:= Set( Tensored( chars, chars ) );;
    gap> IrreducibleDifferences( t, chars, "triangle" );
    [ [ 3, -1, 0, -E(5)-E(5)^4, -E(5)^2-E(5)^3 ],
      [ 3, -1, 0, -E(5)^2-E(5)^3, -E(5)-E(5)^4 ] ]