ContainedPossibleVirtualCharacters( tbl, chars, parachar )
returns the list of all elements vec of the parametrized character parachar (see More about Maps and Parametrized Maps), which have integral norm and integral scalar product with the principal character of the character table tbl and integral scalar product with all elements of the list chars of characters of tbl.
# see example in "ContainedSpecialVectors"
gap> ContainedPossibleVirtualCharacters( s, s.irreducibles, rest );
[ [ 231, 7, -9, -9, 6, 15, 15, -1, -1, 1, 6, 6, 1, 1, -2, 1, 2, 2, 0,
0, 1, 0, 0, 0, 0 ],
[ 231, 7, -9, 7, 6, 15, 15, -1, -1, 1, 6, 6, 1, 1, -2, 1, 2, 2, 0,
0, 1, 0, 0, 0, 0 ],
[ 231, 7, -9, -9, 6, 15, 15, 15, 15, 1, 6, 6, 1, 1, -2, 1, 2, 2, 0,
0, 1, 0, 0, 0, 0 ],
[ 231, 7, -9, 7, 6, 15, 15, 15, 15, 1, 6, 6, 1, 1, -2, 1, 2, 2, 0,
0, 1, 0, 0, 0, 0 ] ]
ContainedPossibleVirtualCharacters calls ContainedSpecialVectors
ContainedSpecialVectors.
ContainedPossibleVirtualCharacters successively examines all vectors
that are contained in parachar, thus it might not be useful if the
indeterminateness exceeds 10^6. For another strategy that works for
rational characters only, see ContainedDecomposables.
GAP 3.4.4