def __init__(self, R, n, names):
"""
The free algebra on `n` generators over a base ring.
EXAMPLES::
sage: F.<x,y,z> = FreeAlgebra(QQ, 3); F # indirect doctest
Free Algebra on 3 generators (x, y, z) over Rational Field
TESTS:
Note that the following is *not* the recommended way to create
a free algebra::
sage: from sage.algebras.free_algebra import FreeAlgebra_generic
sage: FreeAlgebra_generic(ZZ, 3, 'abc')
Free Algebra on 3 generators (a, b, c) over Integer Ring
"""
if R not in Rings():
raise TypeError("Argument R must be a ring.")
self.__ngens = n
indices = FreeMonoid(n, names=names)
cat = AlgebrasWithBasis(R)
CombinatorialFreeModule.__init__(self,
R,
indices,
prefix='F',
category=cat)
self._assign_names(indices.variable_names())
def __init__(self, R, n, names):
"""
The free algebra on `n` generators over a base ring.
EXAMPLES::
sage: F.<x,y,z> = FreeAlgebra(QQ, 3); F # indirect doctet
Free Algebra on 3 generators (x, y, z) over Rational Field
TEST:
Note that the following is *not* the recommended way to create
a free algebra::
sage: from sage.algebras.free_algebra import FreeAlgebra_generic
sage: FreeAlgebra_generic(ZZ, 3, 'abc')
Free Algebra on 3 generators (a, b, c) over Integer Ring
"""
if R not in Rings():
raise TypeError("Argument R must be a ring.")
self.__ngens = n
indices = FreeMonoid(n, names=names)
cat = AlgebrasWithBasis(R)
CombinatorialFreeModule.__init__(self, R, indices, prefix='F',
category=cat)
self._assign_names(indices.variable_names())
