Implement an example of a graded algebra with basis, and improve the later

[jhpalmieri]

The summary says it all. See also the patch on the Sage-Combinat patch server:

 http://combinat.sagemath.org/hgwebdir.cgi/patches/file/tip/trac_9280-graded-algebras-example.patch

Thanks to Jason Bandlow and Franco Saliola who participated to the improvement of the example. It now depends on #10193.

[nthiery]

Hi John,

For the record: we went through your patches with Franco and Jason, and discussed quite a bit around it. We will post here shortly an updated patch with some little suggestions.

[jhpalmieri]

Replying to nthiery:

Hi John,

For the record: we went through your patches with Franco and Jason, and discussed quite a bit around it. We will post here shortly an updated patch with some little suggestions.

Is it "shortly" yet? :)

[jhpalmieri]

In the sage-combinat patch, there are a few typos and some other issues:

• in sage/categories/graded_algebras_with_basis.py, the docstring for "degree" says "The degree of this element in the graded polynomial algebra." Delete "polynomial".

• in sage/categories/examples/graded_algebras_with_basis.py, the docstring for "one_basis" contains '(0,...,0`), and I think this should be changed to ``(0,...,0)``.

• in sage/categories/examples/graded_algebras_with_basis.py, the docstring for the main class is now outdated: it still refers to "basis_function" and "_basis_fcn", which don't exist any more, and also to "homogeneous_component", which is now part of the default implementation, not something specific to this example.

I'm attaching a referee patch which fixes these.

There are also some doctests for "basis" in sage/categories/graded_algebras_with_basis.py which are marked as "todo: not implemented". Do we need to wait for these to be fixed, or should we consider this ready for review? It may not be ideal, but we could also change

sage: A.basis(6) # todo: not implemented (output)
Family (y^{2}, x^{3}

to

sage: A.basis(6) # todo: not implemented (output)
Family (y^{2}, x^{3}
sage: list(A.basis(6))
[y^{2}, x^{3}]

By the way, all tests pass with this patch and with the one from #10193. So perhaps we could also delete the commented-out part at the beginning of the example, where it says

# TODO: double check that we can now discard this function

[jhpalmieri]

apply on top of sage-combinat patch

[saliola]

There are a couple of patches on the sage-combinat queue experimenting with moving some of the generic methods into the category GradedAlgebraWithBasis:

• trac_9280-graded-algebras-example-review-fs.patch
• trac_9280-graded-algebras-example.patch

[vdelecroix]

Sorry for the long delay for the ticket but #10193 is now ready !!