Implement quantum group q-numbers

[tscrim]

Split off of #15508 for better granularity and to use it to build other tickets. Implements [n]_q, [n]_q! and q-binomials that appear in quantum groups.

CC: @sagetrac-sage-combinat @darijgr @anneschilling @bsalisbury1 @AndrewAtLarge

Component: algebra

Keywords: quantum groups, q-analogs

Author: Travis Scrimshaw

Branch: e0893e0

Reviewer: Darij Grinberg

Issue created by migration from https://trac.sagemath.org/ticket/25067

[tscrim]

Commit: 67c6ba0

[tscrim]

Branch: public/quantum_groups/q_numbers-25067

[tscrim]

New commits:

67c6ba0

Adding q-analogs used in quantum groups.

[sagetrac-git]

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

e908d59

Adding q-analogs used in quantum groups.

[sagetrac-git]

Changed commit from 67c6ba0 to e908d59

[sagetrac-git]

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

e0893e0

documentation improvements

[sagetrac-git]

Changed commit from e908d59 to e0893e0

[tscrim]

Reviewer: Darij Grinberg

[tscrim]

comment:4

Discussed with Darij and says good modulo his changes, which LGTM. So positive review. Thank you!

[AndrewMathas]

comment:5

Sorry to be late to the party but are you aware of combinat/q_analogues.py? In particular, this module provides functions q_int, q_factorial and q_binomial (among others). I have not been through this ticket in detail but comparing the q_int function in this ticket appears to be less general than the existing function because, in q_analogues.py, q_int(n) allows n to be positive or negative whereas the q_int function in this ticket requires n to be non-negative. On the other hand, the quantum integer that the existing q_int returns is different to the one in this ticket.

I am not sure how much this ticket overlaps with the code that is already in sage but some one should check. At a minimum, I think that there should be some documentation links between this code and the pre-existing code and, arguably, the code should be merged so that we don't have code providing similar functionality in different places. Different function names, or a more general syntax that allows one to choose between the different quantum integers, should also be considered.

Annoyingly, the q_int defined in q_analogues.py is the natural quantum integer to use in Hecke algebras whereas the q_int defined in this ticket is what is required in the quantum group setting...so both are needed.

As I have not read through all of the code I won't set this back to needs work but my feeling is that it does need more work.

[AndrewMathas]

comment:6

Oh, I see that there are already documentation links, so feel free to ignore the above. This said, adding a link from the documentation in combinat/q_analogues.py to the code in this ticket would also be useful.

[vbraun]

Changed branch from public/quantum_groups/q_numbers-25067 to e0893e0

[fchapoton]

Changed commit from e0893e0 to none