Graded algebras with maximal degree

[mjungmath]

We implement graded algebras with maximal finite degree. That is, each generator has a integer degree, and multiplications exceeding a fixed degree yield zero.

This implementation is for example useful in the case of certain cohomology rings (or subrings of such) over a field of finite dimensional CW or simplicial complexes. See for example #29581.

Follow-up: #32365

Depends on #32315

CC: @tscrim @mkoeppe @trevorkarn @jhpalmieri

Component: algebra

Author: Michael Jung

Branch/Commit: 970d295

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/32272

[mjungmath]

Branch: u/gh-mjungmath/finitely_generated_graded_algebras_with_finite_degree

[sagetrac-git]

Commit: 0813d34

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

0813d34

Trac #32272: add commutative graded algebras with finite degree

[sagetrac-git]

Changed commit from 0813d34 to 7d54a50

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

7d54a50

#32272: rearrange docstring

[sagetrac-git]

Changed commit from 7d54a50 to 2915d56

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

2915d56

#32272: link to commutative_dga

[sagetrac-git]

Changed commit from 2915d56 to f09f9ec

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

8d2874e	Trac #32272: extend docstring
28c9889	Trac #32272: add super-algebra structure
f09f9ec	Trac #32272: add ngens method

[mjungmath]

comment:6

(for the following see also https://groups.google.com/g/sage-devel/c/z5Y7BMwEUVk)

I have troubles constructing a quotient. Here is what happens without a ngens method:

sage: from sage.algebras.commutative_graded_algebra_finite import FiniteGCAlgebra
sage: A.<x,y,z> = FiniteGCAlgebra(QQ, degrees=(1,2,3), max_degree=6)
sage: I = A.ideal(y^2)
sage: A.quotient(I)
Traceback (most recent call last)
...
RuntimeError: Graded commutative algebra with generators ('x', 'y', 'z') in degrees (1, 2, 3) with maximal finite degree 6 still using old coercion framework

Adding a ngens method on the other hand causes the quotients not to function properly:

sage: from sage.algebras.commutative_graded_algebra_finite import FiniteGCAlgebra
sage: A.<x,y,z> = FiniteGCAlgebra(QQ, degrees=(1,2,3), max_degree=6)
sage: I = A.ideal(y^2)
sage: Q = A.quotient(I)
sage: Q.gen(1)^2
ybar^2

The result, however, should be zero.

What am I doing wrong?

[mjungmath]

comment:7

See https://ask.sagemath.org/question/56243/quotients-of-exterior-algebras/.