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

On Tuesday, April 13, 2021 at 5:14:10 PM UTC+2 Michael Jung wrote:

>
> 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
>

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