def __init__(self, m, n, q, bar, R):
"""
Initialize ``self``.
TESTS::
sage: O = algebras.QuantumMatrixCoordinate(4)
sage: TestSuite(O).run()
sage: O = algebras.QuantumMatrixCoordinate(10)
sage: O.variable_names()
('x0101', ..., 'x1010')
sage: O = algebras.QuantumMatrixCoordinate(11,3)
sage: O.variable_names()
('x011', ..., 'x113')
sage: O = algebras.QuantumMatrixCoordinate(3,11)
sage: O.variable_names()
('x101', ..., 'x311')
"""
gp_indices = [(i, j) for i in range(1, m + 1) for j in range(1, n + 1)]
if m == n:
cat = Bialgebras(R.category()).WithBasis()
else:
cat = Algebras(R.category()).WithBasis()
self._m = m
QuantumMatrixCoordinateAlgebra_abstract.__init__(
self, gp_indices, n, q, bar, R, cat)
# Set the names
mb = len(str(m))
nb = len(str(n))
base = 'x{{:0>{}}}{{:0>{}}}'.format(mb, nb)
names = [base.format(*k) for k in gp_indices]
self._assign_names(names)
def super_categories(self):
"""
EXAMPLES::
sage: HopfAlgebras(QQ).super_categories()
[Category of bialgebras over Rational Field]
"""
R = self.base_ring()
return [Bialgebras(R)]
def extra_super_categories(self):
"""
The algebra of a monoid is a bialgebra and a monoid.
EXAMPLES::
sage: C = Monoids().Algebras(QQ)
sage: C.extra_super_categories()
[Category of bialgebras over Rational Field,
Category of monoids]
sage: Monoids().Algebras(QQ).super_categories()
[Category of bialgebras with basis over Rational Field,
Category of semigroup algebras over Rational Field,
Category of unital magma algebras over Rational Field]
"""
from sage.categories.bialgebras import Bialgebras
return [Bialgebras(self.base_ring()), Monoids()]
def __init__(self, m, n, q, bar, R):
"""
Initialize ``self``.
TESTS::
sage: O = algebras.QuantumMatrixCoordinate(4)
sage: TestSuite(O).run()
"""
gp_indices = [(i, j) for i in range(1, m + 1) for j in range(1, n + 1)]
if m == n:
cat = Bialgebras(R.category()).WithBasis()
else:
cat = Algebras(R.category()).WithBasis()
self._m = m
QuantumMatrixCoordinateAlgebra_abstract.__init__(self, gp_indices, n, q, bar, R, cat)
# Set the names
names = ['x{}{}'.format(*k) for k in gp_indices]
self._assign_names(names)