Graded algebra with finite degree

[Michael Jung]

Hello,

For my next project I need graded algebras with finite degree. So far, Sage provides commutative (graded) differential algebras:

https://doc.sagemath.org/html/en/reference/algebras/sage/algebras/commutative_dga.html

A finite degree could be obtained by using appropriate ideals from this algebra. However, I don't see how this ideal can be straightforwardly and quickly computed. Thus it might probably much faster to implement those algebras directly by using weights and CombinatorialFreeModule.

Does that sound reasonable? Is there another class I just haven't found yet but providing what I need? Otherwise, I would start working on it.

Best,
Michael

[sver...@gmail.com]

Michael,

I have been participating in writing a package for representing finitely presented modules over the Steenrod algebra (awaiting review):

https://trac.sagemath.org/ticket/30680
"
This package implements finitely presented modules over the mod p Steenrod algebra. We define classes for such finitely presented modules, their elements, and morphisms between them. Methods are provided for doing some homological algebra, e.g., computing kernels and images of morphisms, and finding free resolutions of modules.
"

As part of this we created classes within the Sage category framework for representing modules over graded algebras in a more general context.

Our focus is on modules over finite graded sub-algebras of the mod p Steenrod algebra, but the class FP_Module implemented in fp_module.py (and auxiliary classes for elements, homspaces and homomorphisms) is written with the intention that it could be used in conjunction with other graded algebras than the ones coming from the class SteenrodAlgebra.

We implement modules rather than algebras, so this is not what you are asking for, but I thought it was related and could help you put things in context.

Good luck!

Sverre