def exterior_power(self, n):
r"""
Returns the anti-symmetrized product of self with itself ``n`` times.
INPUT:
- ``n`` -- a positive integer.
OUTPUT:
The ``n``-th anti-symmetrized power of ``self`` as a
:class:`ClassFunction`.
EXAMPLES::
sage: chi = ClassFunction(SymmetricGroup(4), [3, 1, -1, 0, -1])
sage: p = chi.exterior_power(3) # the highest anti-symmetric power for a 3-d character
sage: p
Character of Symmetric group of order 4! as a permutation group
sage: p.values()
[1, -1, 1, 1, -1]
sage: p == chi.determinant_character()
True
"""
n = Integer(n)
tbl = gap.UnderlyingCharacterTable(self)
return ClassFunction(self._group,
gap.AntiSymmetricParts(tbl, [self], n)[1])
def symmetric_power(self, n):
r"""
Returns the symmetrized product of self with itself ``n`` times.
INPUT:
- ``n`` -- a positive integer.
OUTPUT:
The ``n``-th symmetrized power of ``self`` as a
:class:`ClassFunction`.
EXAMPLES::
sage: chi = ClassFunction(SymmetricGroup(4), [3, 1, -1, 0, -1])
sage: p = chi.symmetric_power(3)
sage: p
Character of Symmetric group of order 4! as a permutation group
sage: p.values()
[10, 2, -2, 1, 0]
"""
n = Integer(n)
tbl = gap.UnderlyingCharacterTable(self)
return ClassFunction(self._group,
gap.SymmetricParts(tbl, [self], n)[1])