#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 jhpalmieri):
Replying to [comment:37 tscrim]:
> @jhpalmieri
> I'll make those changes. However we can't get a descending filtration
unless the grading set can be negated. As for algebras that are both
filtered and graded, it's the same issue as when an algebra has 2 natural
gradings (as we use `degree` for both filtration and grading). Although as
things evolve and the filtration can be generalized from using `degree`,
this can be rectified. For now, you have to choose the "best" one for
`degree` (or have it be an optional arg like how I'm doing for Clifford
algebras).
I still don't understand this design choice. Why not separate filtrations
and gradings? A graded object without additional filtration could still be
considered to be filtered (by having the filtration method default to
calling `degree`), but this wouldn't have to be the only choice.
Replying to [comment:60 darij]:
> 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.
"Have a ring to it". Heh.
I would object to calling a module an "algebra" if there is no
multiplicative structure. "Associated graded module" is just fine, or
"associated graded object" more generally.
--
Ticket URL: <http://trac.sagemath.org/ticket/17096#comment:61>
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