#19397: Add support for homogeneous components of a filtered module
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Reporter: tscrim | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.10
Component: categories | Resolution:
Keywords: | Merged in:
Authors: Travis Scrimshaw | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/categories/homogeneous_components-19397|
ae81aa7c64064ba8de5598aa01210efac57088c9
Dependencies: #17096 | Stopgaps:
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Comment (by jhpalmieri):
One mathematical issue: in defining `homogeneous_component`, you have
{{{
category = ModulesWithBasis(self.category().base_ring())
}}}
A homogeneous component of an ''R''-module need not be an ''R''-module
itself in a natural way: for example, if the base ring is the graded ring
''R''=''k''[''x'', ''x''^-1^] with ''x'' in some nonzero degree, then for
any homogeneous component of any graded ''R''-module, ''x'' would have to
act trivially (because ''x'' has nonzero degree). On the other hand, ''x''
is supposed to be invertible.
It will always be a module over the degree 0 part of the base ring,
though.
--
Ticket URL: <http://trac.sagemath.org/ticket/19397#comment:7>
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