#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|
2aec8bdaeba3c34478807342b5659b8e8ceca2f4
Dependencies: | Stopgaps:
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Comment (by darij):
I think your doc is inconsistent. This can't be:
{{{
+We require all `F_i \setminus F_{i-1}` to be modules for all `i`.
}}}
What do you want `F_i` to be? The span of all elements UP TO degree `i`,
or the span of all elements that are added by degree `i`? So when you
consider a graded module as a filtered module, then will `F_i` be the
`i`-th graded component or the direct sum of the `0, 1, ..., i`-th graded
components? In the former case, you don't want a setminus at all. In the
latter case, setminus is the right idea but the wrong notation, and you
want to say something like `F_i = F_{i-1} \oplus G_i` where `G_i` is the
submodule spanned by the degree `i`-basis elements.
--
Ticket URL: <http://trac.sagemath.org/ticket/17096#comment:12>
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