#6670: Port group algebras to the current coercion system
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Reporter: mraum | Owner: mraum
Type: enhancement | Status: needs_work
Priority: minor | Milestone: sage-4.7.1
Component: algebra | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author: Martin Raum
Merged: | Dependencies:
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Changes (by jhpalmieri):
* status: needs_review => needs_work
Comment:
Some minor comments:
- The first line of the new file is redundant: "Group algebra of a
group". Maybe it should just be "Group algebras"?
- The new file should be added to the reference manual, by adding an
appropriate line to `sage/doc/en/reference/algebras.rst`.
More interesting:
- Can you implement coercion from R[H] to R[G] if H is a subgroup of G,
or more generally from R[H] to S[G] if there is a coercion from H to G and
from R to S? Then coercing from the base ring R to R[G] would just be the
special case where R=S and H is the trivial group.
A more important issue: I'm not sure that I agree with the implementation.
I would have it inherit from `CombinatorialFreeModule`, and then unique
representation is built in nicely so you don't have to cache the results
as you do now. You can also implement the Hopf algebra structure on the
group algebra pretty easily. For reference, you should look at the files
- `sage/categories/examples/hopf_algebras_with_basis.py` for a simple
(not very full-featured) implementation of group algebras.
- `sage/algebras/steenrod/steenrod_algebra.py` for the implementation of
the Steenrod algebra, including all of its Hopf algebra structure,
inheriting from `CombinatorialFreeModule`. This has a lot of things you
don't need, but if you want to base the implementation on the first file,
or if you want to modify the print representation of elements (which I
recommend), you might be able to use this one to help fill in some
details.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6670#comment:13>
Sage <http://www.sagemath.org>
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