#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 tscrim):
How is that any different for objects with multiple natural gradings? The
point I'm trying to make is `GradedAlgebra` is not an algebra that has
''some'' grading (all algebras have a trivial grading), but that they have
a ''distinguished'' grading, just like
(`FiniteDimensional`)`AlgebrasWithBasis` are algebras with a distinguished
basis (can replace grading by filtered).
The main reason why I chose to use `grading` is so we don't have to
duplicate all of the code for graded algebras but just replacing `degree`
by `smallest_filtered_component` (or whatever name you want to call it).
For the Clifford algebras, we don't yet have the category framework in
place (I know how I want to do it, but I haven't done so yet). Perhaps it
is a bad choice to give Clifford algebras that option right now for the
future outlook. Also now that we have the filtered algebras, we don't need
the graded algebras to get extra features.
This relates to John's suggestion, and that we probably need something at
the ''class'' level, not the ''category'' level which is what this ticket
is about, which set's the degree function. I want to stress that the
category has a distinguished filtration/grading (perhaps I forgot to
reflect this in the documentation).
I will take a more detailed look at all of the changes later tonight.
--
Ticket URL: <http://trac.sagemath.org/ticket/17096#comment:64>
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