#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):
@nbruin: Thanks for the explanations. So it is what I feared. Someone
please remove the @cached_methods; it appears there is no easy way to get
rid of the performance issues.
Caching these maps relating A to gr(A) on gr(A) was my first idea (and I
think Travis wanted to implement them as conversions), but it conflicts
with Travis's design decision (which is a good one!) to allow overriding
`graded_algebra` with simpler stuff than the default `AssociatedGraded`
construction. Many different complicated algebras A will end up having the
same simple gr(A) (for example, for every universal enveloping algebra A =
U(g) of a Lie algebra g over a field, we have gr(A) \cong S(g)), and gr(A)
is not supposed to "know" anything about A. Overriding
`_element_constructor` of gr(A) would be messy and unscalable.
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Ticket URL: <http://trac.sagemath.org/ticket/17096#comment:66>
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