Hall-Littlewood Polynomials

Q' Basis:

Timing data for arithmetic with Hall-Littlewood polynomials in the Q' basis.

Over ZZ:

sage: Qp = HallLittlewood_qp(ZZ)
sage: time c = Qp([2,2])^2
CPU times: user 0.54 s, sys: 0.01 s, total: 0.55 s
Wall time: 0.55
sage: time c = Qp([3,2,1])^2
CPU times: user 11.52 s, sys: 0.24 s, total: 11.76 s
Wall time: 11.78
sage: time c = Qp([2,2])^2
CPU times: user 0.21 s, sys: 0.01 s, total: 0.22 s
Wall time: 0.22
sage: time c = Qp([3,2,1])^2
CPU times: user 1.16 s, sys: 0.02 s, total: 1.18 s
Wall time: 1.18

Over QQ:

sage: Qp = HallLittlewood_qp(QQ)
sage: time c = Qp([2,2])^2
CPU times: user 0.77 s, sys: 0.01 s, total: 0.78 s
Wall time: 0.78
sage: time c = Qp([3,2,1])^2
CPU times: user 14.00 s, sys: 0.24 s, total: 14.24 s
Wall time: 14.26
sage: time c = Qp([2,2])^2
CPU times: user 0.55 s, sys: 0.01 s, total: 0.56 s
Wall time: 0.56
sage: time c = Qp([3,2,1])^2
CPU times: user 3.57 s, sys: 0.08 s, total: 3.65 s
Wall time: 3.66

The majority of time spent in the second one is due to coercion from ZZ['t'] to QQ('t') (which should really be much faster).