def __init__(self, group, base_ring = IntegerRing()):
r""" Create the given group algebra.
INPUT:
-- (Group) group: a generic group.
-- (Ring) base_ring: a commutative ring.
OUTPUT:
-- a GroupAlgebra instance.
EXAMPLES::
sage: from sage.algebras.group_algebra import GroupAlgebra
doctest:1: DeprecationWarning:...
sage: GroupAlgebra(GL(3, GF(7)))
Group algebra of group "General Linear Group of degree 3 over Finite
Field of size 7" over base ring Integer Ring
sage: GroupAlgebra(1)
Traceback (most recent call last):
...
TypeError: "1" is not a group
sage: GroupAlgebra(SU(2, GF(4, 'a')), IntegerModRing(12)).category()
Category of group algebras over Ring of integers modulo 12
"""
if not base_ring.is_commutative():
raise NotImplementedError("Base ring must be commutative")
if not is_Group(group):
raise TypeError('"%s" is not a group' % group)
ParentWithGens.__init__(self, base_ring, category = GroupAlgebras(base_ring))
self._formal_sum_module = FormalSums(base_ring)
self._group = group
def __init__(self, group, base_ring=IntegerRing()):
r"""
See :class:`GroupAlgebra` for full documentation.
EXAMPLES::
sage: GroupAlgebra(GL(3, GF(7)))
Group algebra of group "General Linear Group of degree 3 over Finite Field of size 7" over base ring Integer Ring
"""
from sage.groups.group import is_Group
if not base_ring.is_commutative():
raise NotImplementedError("Base ring must be commutative")
if not is_Group(group):
raise TypeError('"%s" is not a group' % group)
self._group = group
CombinatorialFreeModule.__init__(self,
base_ring,
group,
prefix='',
bracket=False,
category=GroupAlgebras(base_ring))
if not base_ring.has_coerce_map_from(group):
## some matrix groups assume that coercion is only valid to
## other matrix groups. This is a workaround
## call _element_constructor_ to coerce group elements
#try :
self._populate_coercion_lists_(coerce_list=[group])
def __init__(self, R, G):
"""
EXAMPLES::
sage: from sage.categories.examples.group_algebras import MyGroupAlgebra
sage: MyGroupAlgebra(ZZ,DihedralGroup(4)) # indirect doctest
The group algebra of the Dihedral group of order 8 as a permutation group over Integer Ring
"""
self._group = G
CombinatorialFreeModule.__init__(self, R, G, category=GroupAlgebras(R))
def __init__(self, R, n):
"""
TESTS::
sage: QS3 = SymmetricGroupAlgebra(QQ, 3)
sage: TestSuite(QS3).run()
"""
self.n = n
self._name = "Symmetric group algebra of order %s" % self.n
CombinatorialFreeModule.__init__(
self,
R,
permutation.Permutations(n),
prefix='',
latex_prefix='',
category=(GroupAlgebras(R), FiniteDimensionalAlgebrasWithBasis(R)))
# This is questionable, and won't be inherited properly
if n > 0:
S = SymmetricGroupAlgebra(R, n - 1)
self.register_coercion(S.canonical_embedding(self))