def __init__(self, A, names=None):
"""
Initialize ``self``.
TESTS::
sage: F.<x,y,z> = FreeAlgebra(QQ)
sage: J = JordanAlgebra(F)
sage: TestSuite(J).run()
sage: J.category()
Category of commutative unital algebras with basis over Rational Field
"""
R = A.base_ring()
C = MagmaticAlgebras(R)
if A not in C.Associative():
raise ValueError("A is not an associative algebra")
self._A = A
cat = C.Commutative()
if A in C.Unital():
cat = cat.Unital()
if A in C.WithBasis():
cat = cat.WithBasis()
if A in C.FiniteDimensional():
cat = cat.FiniteDimensional()
Parent.__init__(self, base=R, names=names, category=cat)
def __init__(self, A, names=None):
"""
Initialize ``self``.
TESTS::
sage: F.<x,y,z> = FreeAlgebra(QQ)
sage: J = JordanAlgebra(F)
sage: TestSuite(J).run()
sage: J.category()
Category of commutative unital algebras with basis over Rational Field
"""
R = A.base_ring()
C = MagmaticAlgebras(R)
if A not in C.Associative():
raise ValueError("A is not an associative algebra")
self._A = A
cat = C.Commutative()
if A in C.Unital():
cat = cat.Unital()
self._no_generic_basering_coercion = True
# Remove the preceding line once trac #16492 is fixed
# Removing this line will also break some of the input formats,
# see trac #16054
if A in C.WithBasis():
cat = cat.WithBasis()
if A in C.FiniteDimensional():
cat = cat.FiniteDimensional()
Parent.__init__(self, base=R, names=names, category=cat)
def __classcall_private__(cls,
k,
table,
names='e',
assume_associative=False,
category=None):
"""
Normalize input.
TESTS::
sage: table = [Matrix([[1, 0], [0, 1]]), Matrix([[0, 1], [0, 0]])]
sage: A1 = FiniteDimensionalAlgebra(GF(3), table)
sage: A2 = FiniteDimensionalAlgebra(GF(3), table, names='e')
sage: A3 = FiniteDimensionalAlgebra(GF(3), table, names=['e0', 'e1'])
sage: A1 is A2 and A2 is A3
True
The ``assume_associative`` keyword is built into the category::
sage: from sage.categories.magmatic_algebras import MagmaticAlgebras
sage: cat = MagmaticAlgebras(GF(3)).FiniteDimensional().WithBasis()
sage: A1 = FiniteDimensionalAlgebra(GF(3), table, category=cat.Associative())
sage: A2 = FiniteDimensionalAlgebra(GF(3), table, assume_associative=True)
sage: A1 is A2
True
Uniqueness depends on the category::
sage: cat = Algebras(GF(3)).FiniteDimensional().WithBasis()
sage: A1 = FiniteDimensionalAlgebra(GF(3), table)
sage: A2 = FiniteDimensionalAlgebra(GF(3), table, category=cat)
sage: A1 == A2
False
sage: A1 is A2
False
Checking that equality is still as expected::
sage: A = FiniteDimensionalAlgebra(GF(3), table)
sage: B = FiniteDimensionalAlgebra(GF(5), [Matrix([0])])
sage: A == A
True
sage: B == B
True
sage: A == B
False
sage: A != A
False
sage: B != B
False
sage: A != B
True
"""
n = len(table)
table = [b.base_extend(k) for b in table]
for b in table:
b.set_immutable()
if not (is_Matrix(b) and b.dimensions() == (n, n)):
raise ValueError("input is not a multiplication table")
table = tuple(table)
cat = MagmaticAlgebras(k).FiniteDimensional().WithBasis()
cat = cat.or_subcategory(category)
if assume_associative:
cat = cat.Associative()
names = normalize_names(n, names)
return super(FiniteDimensionalAlgebra, cls).__classcall__(cls,
k,
table,
names,
category=cat)