#17096: Implement categories for filtered algebras
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Reporter: tscrim | Owner: tscrim
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.4
Component: categories | Resolution:
Keywords: filtered algebras | Merged in:
Authors: Travis Scrimshaw | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/categories/filtered_algebras-17096|
8a747c073e706950d1b14e77458539e126ff0550
Dependencies: | Stopgaps:
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Comment (by darij):
Enough for now (FPSAC deadline is approaching). I have now checked all of
the non-Clifford/Weyl part of this patch, and here is all that I'd like to
be done before the merge of this part:
- TODO: Formulate an interface and a contract for
`FilteredModulesWithBasis` objects. Is a `CombinatorialFreeModule` with a
`degree_on_basis` method enough? Or is `basis` still needed? (See the
`FIXME` in `src/sage/categories/examples/filtered_modules_with_basis.py`.)
- TODO: Make sense of `A.basis(d)` for `A` a filtered module and `d` an
integer. This has always been broken and we can leave it for later, but it
then needs a trac ticket.
- TODO: doctesting `A.basis(d)` for `A` graded. Very easy once above is
fixed.
- TODO: overriding the `to_graded_conversion`, `from_graded_conversion`
and `projection` methods on graded algebras for the sake of speed, or
deciding not to.
- Generalizing `graded_algebra` to modules. This doesn't seem too
difficult; I am in favor of keeping the name "associated graded *algebra*"
even for modules, as it seems to have a ring to it that algebraists
recognize, but maybe some discussion is in order.
--
Ticket URL: <http://trac.sagemath.org/ticket/17096#comment:60>
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