#11688: graded modules : an example and new element methods
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Reporter: chapoton | Owner: sage-
Type: enhancement | combinat
Priority: minor | Status:
Component: combinatorics | needs_review
Keywords: graded module, graded algebra | Milestone: sage-5.12
Authors: | Resolution:
Report Upstream: N/A | Merged in:
Branch: | Reviewers:
Dependencies: | Work issues:
| Commit:
| Stopgaps:
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Description changed by chapoton:
Old description:
> Currently some properties of graded modules are implemented in graded
> algebras. It is necessary to put them in their proper place.
>
> One precise reason is that one can then use these properties for operads.
> One would like to have something like that:
>
> {{{
> sage: PL=PreLieOperad(QQ)
> sage: a=PL.one()
> sage: a.is_homogeneous()
> True
> sage: a.homogeneous_component(2)
> 0
> }}}
>
> For this, one needs the "homogeneous_component" method for elements and
> not for modules. Maybe "restrict_degree" would be more adequate, like for
> power series.
New description:
Currently some properties of graded modules are implemented in graded
algebras. It is necessary to put them in their proper place.
One precise reason is that one can then use these properties for operads.
One would like to have something like that:
{{{
sage: PL=PreLieOperad(QQ)
sage: a=PL.one()
sage: a.is_homogeneous()
True
sage: a.homogeneous_component(2)
0
}}}
For this, one needs the "homogeneous_component" method for elements and
not for modules. Maybe "restrict_degree" would be more adequate, like for
power series.
This ticket also provide a simple example of graded module (over
partitions).
--
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Ticket URL: <http://trac.sagemath.org/ticket/11688#comment:11>
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