Expose quantum Littlewood-Richardson coefficients from lrcalc

[nthiery]

Beside Littlewood-Richardson coefficient calculations and fusion
products, Anders Buch's lrcalc C library implements quantum products,
using the rim-hook rewriting rule (this corresponds to cup products in
the cohomology of quantum Grassmanian variety). The latter
functionality needs to be exposed in Sage's interface to lrcalc.

Roadmap:

Change mult to accept a "quantum" argument:

def mult(part1, part2, maxrows=None, level=None, quantum=None):
    """

    ...

    - ``quantum`` -- an element of a ring


    ...

    EXAMPLES::

        sage: var('q')
        sage: mult([1],[2,1],2,2, quantum=q)
        {[2, 2]: 1, []: q}
        sage: mult([2,1],[2,1],2,2, quantum=q)
        {[2]: q, [1,1]: q} 
   """

If quantum is set, then maxrows and level should be
set. Looking at src/mult.c one would just need to call the
quantum_reduce function function on the result of lrcalc's
mult_c. The result is a list of hash tables, each giving one
homogeneous pieces of the result w.r.t. q.

CC: @tscrim

Component: combinatorics

Keywords: days45, lrcalc

Author: Frédéric Chapoton, Travis Scrimshaw

Branch/Commit: 4637407

Reviewer: Frédéric Chapoton

Issue created by migration from https://trac.sagemath.org/ticket/14107

[fchapoton]

Attachment: trac_14107_quantum_coho.patch.gz

[fchapoton]

comment:2

Here is a patch which is not working !

I have been unable to sort things out.

Maybe some Cython expert can help to correct it ?

[fchapoton]

New commits:

48ec624	trac_14107_quantum_coho.patch
d0e9d35	trac #14107 branch not working

[fchapoton]

Branch: u/chapoton/14107

[fchapoton]

Commit: d0e9d35

[tscrim]

Changed branch from u/chapoton/14107 to u/tscrim/quantum_LR_coeff-14107

[tscrim]

Changed commit from d0e9d35 to 37e2e9d

[tscrim]

Author: Frédéric Chapoton, Travis Scrimshaw

[tscrim]

New commits:

2b012bb	Merge branch 'u/chapoton/14107' of trac.sagemath.org:sage into u/tscrim/quantum_LR_coeff-14107
37e2e9d	Implementing the quantum product from lrcalc.

[sagetrac-git]

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

4637407

Implementing the quantum product from lrcalc and some cython cleanup.

[sagetrac-git]

Changed commit from 37e2e9d to 4637407

[tscrim]

comment:10

I also added some more explicit cdef/type info, which should result in faster code.

[fchapoton]

comment:11

Thanks a lot Travis.

ok, good to go. Next step would be to wrap that into an algebra.

[fchapoton]

Reviewer: Frédéric Chapoton

[tscrim]

comment:12

Thanks for doing the review. I could finally do this ticket now that I've learned more Cython. I agree that is definitely the next step. Will you be creating said wrapper?

(Sorry, I have to do a Matrix pun: I know CyFu. :P)

[vbraun]

Changed branch from u/tscrim/quantum_LR_coeff-14107 to 4637407