#15726: Implement tensor modules and algebras
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Reporter: tscrim | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.3
Component: algebra | Resolution:
Keywords: tensor module | Merged in:
algebra | Reviewers:
Authors: Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | 3920f5b76fe6f53ef21f28896d2a97bd820be647
public/algebras/tensor_algebra-15726| Stopgaps:
Dependencies: #15289 |
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Comment (by tscrim):
I've removed `TensorModule` and just made it into `TensorAlgebra` since we
always have a natural algebra structure. I've also made some fixes based
upon the changes in #15289.
There is one feature that `TensorAlgebra` has different from
`FreeAlgebra`, and that is handling coercions from finite tensor products
of modules (which all coerce into the base module of `TensorAlgebra`).
`TensorAlgebra` also has the Hopf algebra structure defined on it.
However they probably should be some subclassing of `FreeAlgebra` and/or
`CombinatorialFreeModule_Tensor`. I haven't made it a functorial
construction yet. Also `tensor` should not be the multiplication of two
tensor algebra elements, but instead return the element in the tensor
product of tensor algebras (this is not isomorphic to the tensor algebra
since `(1 # b) * (c # 1) = (c # 1) * (1 # b)` where `b,c` are any elements
the tensor algebra). So there is still room for improvement.
--
Ticket URL: <http://trac.sagemath.org/ticket/15726#comment:17>
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