conventions about X.Graded() categories

[Vincent Delecroix]

Dear all,

While fixing #33499 I wanted to implement a generic version at the level
of categories (namely inside graded algebras). However, I did not find a
place with the specifications of the Graded axiom... In particular
- how do we specify the grading semi-ring on parents?
- how do we access the homogenous components on elements?

Best
Vincent

[Travis Scrimshaw]

Hi Vincent,

 

- how do we specify the grading semi-ring on parents?

Right now we only have graded modules (and hence algebras as well), not for (semi-)rings. So for what you want, you might have to implement these categories using the functorial construction (and it would be good to also do the filtered versions too). Unfortunately I don't know of a good way immediately to share the code between these categories, but there might be some nice way to do it with inheritance.

 

- how do we access the homogenous components on elements?

Here is an example for what you are after I believe:

sage: s = SymmetricFunctions(QQ).s()
sage: x = s.an_element(); x
2*s[] + 2*s[1] + 3*s[2]
sage: x.homogeneous_component(2)
3*s[2]
sage: x.homogeneous_component(1)
2*s[1]

Best,

Travis