#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/categoires/filtered_algebras-17096|
ad184efacc9ceabfb1179ccd4d677786f4713b01
Dependencies: | Stopgaps:
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Comment (by nthiery):
Replying to [comment:1 tscrim]:
> - Every graded algebra is a filtered algebra under the "natural"
filtration of summing over (weakly) smaller degrees (assuming total
ordering on the grading group). This is implicit in the category
structure; nothing specific is implemented.
Of course, depending on the context, the converse convention can also
sense; but maybe that's ok because eventually we will have both
filtered and descendingFiltered (or something similar) categories.
http://en.wikipedia.org/wiki/Filtration_%28mathematics%29
> - Every `graded_*` category has `filtered_*` as an immediate super
category. In particular, this is needed for `GradedAlgebrasWithBasis` not
picking up `FilteredAlgebrasWithBasis` in its super categories otherwise.
This seems like the same situation as for quotients
w.r.t. subquotients. So the same mechanism should do the job (see
`sage.categories.quotients.Quotients.default_super_categories`). Please
confirm!
> - Homogeneous elements for filtered algebras are elements in F,,i,, not
in F,,i-1,,. I don't know if this is a standard definition, but it allowed
extensions of methods from graded to filtered.
I see the point. The inconvenient is of course that this makes the set
of homogeneous elements for a given i not be a vector space. What do
you do with 0 btw?
Cheers,
Nicolas
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Ticket URL: <http://trac.sagemath.org/ticket/17096#comment:2>
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