#17096: Implement categories for filtered algebras
-------------------------------------+-------------------------------------
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|
bb234ec71d1276c6cc14320074b3de6fdc606192
Dependencies: | Stopgaps:
-------------------------------------+-------------------------------------
Comment (by darij):
1) What does the `_element_constructor_` in `associated_graded.py` do? I
understand that it constructs an element of gr A from an element a of A,
but the way it does this I do not think is correct.
The "right" thing to do is this: For a given pair `(a, n)` where `n` is a
nonnegative integer and `a` is an element of the `n`-th filtered part of
`A`, the residue class of `a` modulo the `(n-1)`-th filtered part of `A`
is an element of the `n`-th graded component of `\gr A`. The `n` is part
of the input; you can try to reconstruct it as the smallest `i` such that
`a` lies in the `i`-th filtered part of `A`, but such a definition will be
ill-behaved.
2) I think you need some requirements on the basis of a
FilteredModulesWithBasis for your code to work. I would guess you want the
basis to be a sequence `(B_0, B_1, B_2, ...)` of sets such that for every
`n`, the union `B_0 \cup B_1 \cup ...\cup B_n` is a basis of the `n`-th
filtered component. Is it what you want?
--
Ticket URL: <http://trac.sagemath.org/ticket/17096#comment:4>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
