Enumerate integer vectors modulo to the action of a Permutation Group

[nborie]

The goal of this ticket is to enumerate integer vectors up to the action of a Permutation Group.

This will produced a Parent : infinite enumerated set whose element are just tuple of python int (cythonize this is in my wishlist...).

depends on #8288

[nborie]

I fixed some language mistakes. I already tell reviewers that there are probably still some typos, misunderstood or mistakes. I am sorry for that... It's hard!

[nborie]

Refactoring : -> I move the code in sage/combinat/invariant_ring_perm_gps (advise form Nicolas Thiéry) -> I implemented a new class InfiniteEnumeratedSet? (with category)

There is no a shortcut in sage to IntegerVectorsUptoPermGroup? which is a user friendly parent (with hope). This code stay really strongly connected to the Invariant theory and connected with a the graded algebras of multivariate polynomial view as combination of orbit sum. This really why the code enter this new folder : sage/combinat/invariant_ring_perm_gps (other things have to come here....)

[SimonKing]

Hi!

This is not a review yet, just some remarks.

Indeed it seems to me that the comments and the documentation should be proof read by a native speaker. I am not a native speaker, I'm afraid.

I also suggest to rename some methods. For example, the purpose of "generate_list_of_sum" is not clear from that name:

• "generate" suggests a process. Therefore, I expected that the method would return an iterator. But in fact, an actual list is returned. A similar statement applies to "get_orbit". Why not simply "orbit"?
• "list_of_sums" is not clear at all. I mean, there is the notion of "partition", so, there is no reason to describe it as "list of sums". Of course, not all partitions are returned, but representatives for each permutation class of partitions.

So, I think "partition_class_representatives" or slightly less precise "partition_classes" would be clearer.

And "generate_canonicals": The return value is the list of canonical representatives of all children of the input. So, why not "children_representatives" or "canonical_children"?

Best regards, Simon

[nborie]

Hi Simon,

Thank for these advises, I start a new cleanup and will update a better version shortly!

[nborie]

The patch use now the generic code from Search Forest (breadth_first_search....). So this patch now depends on #8288

[nborie]

Add a canonical_representative method... This will perhaps help later...

[nborie]

Please apply and look only the last patch...