def __init__(self, A):
"""
EXAMPLES::
sage: AlgebraModules(QQ['a'])
Category of algebra modules over Univariate Polynomial Ring in a over Rational Field
sage: AlgebraModules(QQ['a,b']) # todo: not implemented (QQ['a,b'] should be in Algebras(QQ))
sage: AlgebraModules(FreeAlgebra(QQ,2,'a,b'))
Traceback (most recent call last):
...
TypeError: A (=Free Algebra on 2 generators (a, b) over Rational Field) must be a commutative algebra
sage: AlgebraModules(QQ)
Traceback (most recent call last):
...
TypeError: A (=Rational Field) must be a commutative algebra
TESTS::
sage: TestSuite(AlgebraModules(QQ['a'])).run()
"""
from sage.categories.commutative_algebras import CommutativeAlgebras
if not hasattr(A, "base_ring") or not A in CommutativeAlgebras(
A.base_ring()):
raise TypeError("A (=%s) must be a commutative algebra" % A)
Category_module.__init__(self, A)
def __init__(self, K):
"""
EXAMPLES::
sage: VectorSpaces(QQ)
Category of vector spaces over Rational Field
sage: VectorSpaces(ZZ)
Traceback (most recent call last):
...
AssertionError: The base ring must be a field.
TESTS::
sage: C = QQ^10 # vector space
sage: TestSuite(C).run()
sage: TestSuite(VectorSpaces(QQ)).run()
"""
Category_module.__init__(self, K)
def __init__(self, K):
"""
EXAMPLES::
sage: VectorSpaces(QQ)
Category of vector spaces over Rational Field
sage: VectorSpaces(ZZ)
Traceback (most recent call last):
...
AssertionError: The base ring must be a field.
TESTS::
sage: C = QQ^10 # vector space
sage: TestSuite(C).run()
sage: TestSuite(VectorSpaces(QQ)).run()
"""
Category_module.__init__(self, K)
def __init__(self, A):
"""
EXAMPLES::
sage: AlgebraModules(QQ['a'])
Category of algebra modules over Univariate Polynomial Ring in a over Rational Field
sage: AlgebraModules(QQ['a,b']) # todo: not implemented (QQ['a,b'] should be in Algebras(QQ))
sage: AlgebraModules(FreeAlgebra(QQ,2,'a,b'))
Traceback (most recent call last):
...
TypeError: A (=Free Algebra on 2 generators (a, b) over Rational Field) must be a commutative algebra
sage: AlgebraModules(QQ)
Traceback (most recent call last):
...
TypeError: A (=Rational Field) must be a commutative algebra
TESTS::
sage: TestSuite(AlgebraModules(QQ['a'])).run()
"""
from sage.categories.commutative_algebras import CommutativeAlgebras
if not hasattr(A, "base_ring") or not A in CommutativeAlgebras(A.base_ring()):
raise TypeError("A (=%s) must be a commutative algebra"%A)
Category_module.__init__(self, A)
