#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|  
b29f67e46e18721313330d3a6e116cf3df2eaf8e
   Dependencies:                     |     Stopgaps:
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Comment (by jhpalmieri):

 > I'll make those changes. However we can't get a descending filtration
 unless the grading set can be negated.

 You can get something mathematically equivalent to a descending
 filtration, though, and maybe that should be good enough?

 I wonder if we should use `degree` for grading and `filtration` for a
 filtration: `x.filtration()` would return `n` if `x` is in `F_n` but not
 in `F_{n-1}`. For a filtered object, `degree` would default to be
 `filtration`, but you could override it in any specific case. (Maybe these
 aren't the best names, but you get the idea.)

 If this is the first ticket with filtrations, at least in any systematic
 way, we can decide how to set it up now rather than having to fix it
 later.

--
Ticket URL: <http://trac.sagemath.org/ticket/17096#comment:38>
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