Expose quantum Littlewood-Richardson coefficients from lrcalc #14107
Description
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