graded modules : an example and new element methods

[fchapoton]

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).

CC: @sagetrac-sage-combinat

Component: combinatorics

Keywords: graded module, graded algebra

Author: Frédéric Chapoton

Reviewer: Travis Scrimshaw

Merged: sage-5.13.beta0

Issue created by migration from https://trac.sagemath.org/ticket/11688

[fchapoton]

Description changed:

--- 
+++ 
@@ -1,6 +1,6 @@
 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 them use these properties for operads. One would like to have something like that:
+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)

[jhpalmieri]

comment:3

It would be nice to implement the Koszul sign convention for tensor products, also.

[fchapoton]

Changed keywords from graded modules, graded algebras to graded module, graded algebra

[fchapoton]

comment:6

See rather #9280

[fchapoton]

comment:7

ok, I have cut out and cleaned the relevant part of #9280

the present patch is independant of algebras and concerned only with modules

needs review !