Hey Samuel,
I don't think there currently is a general implementation for tensor
products of rings/algebras. Although you can hack together a small subclass
of CombinatorialFreeModule:
class PolynomialAlgebra(CombinatorialFreeModule):
def __init__(self, base_ring, names):
CombinatorialFreeModule.__init__(self, base_ring, FreeAbelianMonoid(
index_set=names), category=Algebras(base_ring).WithBasis())
def gens(self):
return tuple([self.monomial(x) for x in self.indices().gens()])
def one_basis(self):
return self.monomial(self.indices().one())
def product_on_basis(self, x, y):
return self.monomial(x * y)
Sample usage:
sage: P = PolynomialAlgebra(QQ, ('x','y'))
sage: x,y = P.gens()
sage: x^3
B[F['x']^3]
sage: x^3 + 2*x*y
B[F['x']^3] + 2*B[F['x']*F['y']]
sage: tensor([P, P])
Free module generated by Free abelian monoid indexed by {'x', 'y'} over
Rational Field # Free module generated by Free abelian monoid indexed by
{'x', 'y'} over Rational Field
sage: _.an_element()
2*B[1] # B[1] + 2*B[1] # B[F['x']] + 3*B[1] # B[F['y']]
However, it won't do "fancy" things like division.
Best,
Travis
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