Nicolas,
> In your case, to implement the smash product, you probably want to
> implement a subclass of CombinatorialFreeModuleTensor, set its
> category to the join of ModulesWithBasis(QQ).TensorProducts() and
> AlgebrasWithBasis(QQ), and implement the product similarly to what's
> done for tensor products of algebras with basis.
I would dearly love to be able to construct elements in my class in an
automatically multilinear way, using the _tensor_of_elements method
for tensor products of modules. However sage won't let me.
Basically it has an overly restrictive type check which fails.
Here is a toy version of my class:
class MyTensorProductOfAlgebras(CombinatorialFreeModule_Tensor):
def __init__(self, A, B):
R = A.base_ring()
CombinatorialFreeModule_Tensor.__init__(self, [A,B], \
category=Category.join((AlgebrasWithBasis(R),ModulesWithBasis(R).TensorProducts())))
The code calling the _element_tensor method for the
vanilla instance T:
sage: L = CartanType(['A',2]).root_system().weight_lattice()
sage: A = L.algebra(ZZ)
sage: a = A.an_element()
sage: T = tensor([A,A])
sage: T._tensor_of_elements([a,a])
B[2*Lambda[1] + 2*Lambda[2]] # B[2*Lambda[1] + 2*Lambda[2]]
and the custom class TT:
sage: TT = MyTensorProductOfAlgebras(A,A)
TT._tensor_of_elements([a,a])
AssertionError
and the offending line is:
assert(sage.categories.tensor.tensor(modules) == self)
where "modules" is the list of modules to be tensored and "self"
is the instance that is invoking _tensor_of_elements.
Note that
sage: T
and
sage: TT
give the same exact description string.
Any solutions/workarounds? Surely there is no need to reimplement the
multilinearity!
--Mark
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