Differences between revisions 2 and 8 (spanning 6 versions)
Revision 2 as of 2007-10-02 19:48:47
Size: 1159
Editor: MikeHansen
Comment:
Revision 8 as of 2008-03-28 01:08:58
Size: 873
Editor: MikeHansen
Comment:
Deletions are marked like this. Additions are marked like this.
Line 2: Line 2:
== Q' Basis: ==
Timing data for arithmetic with Hall-Littlewood polynomials in the Q' basis.
Line 5: Line 3:
Over ZZ: == P basis ==
{{{
sage: HallLittlewoodP(QQ)
Hall-Littlewood polynomials in the P basis over Fraction Field of Univariate Polynomial Ring in t over Rational Field
sage: HallLittlewoodP(QQ, t=-1)
Hall-Littlewood polynomials in the P basis with t=-1 over Rational Field
sage: HLP = HallLittlewoodP(QQ)
sage: s = SFASchur(HLP.base_ring())
sage: s(HLP([2,1]))
(-t^2-t)*s[1, 1, 1] + s[2, 1]
}}}
Line 7: Line 15:
The Hall-Littlewood polynomials in the P basis at $t = 0$ are the Schur functions.
Line 8: Line 17:
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
sage: HLP = HallLittlewoodP(QQ,t=0)
sage: s = SFASchur(HLP.base_ring())
sage: s(HLP([2,1])) == s([2,1])
True
Line 22: Line 22:
Over QQ:
Line 24: Line 23:
The Hall-Littlewood polynomials in the P basis at $t = 1$ are the monomial symmetric functions.
Line 25: Line 25:
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
sage: HLP = HallLittlewoodP(QQ,t=1)
sage: m = SFAMonomial(HLP.base_ring())
sage: m(HLP([2,2,1])) == m([2,2,1])
True
Line 39: Line 30:
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).

Hall-Littlewood Polynomials

P basis

sage: HallLittlewoodP(QQ)
Hall-Littlewood polynomials in the P basis over Fraction Field of Univariate Polynomial Ring in t over Rational Field
sage: HallLittlewoodP(QQ, t=-1)
Hall-Littlewood polynomials in the P basis with t=-1 over Rational Field
sage: HLP = HallLittlewoodP(QQ)
sage: s = SFASchur(HLP.base_ring())
sage: s(HLP([2,1]))
(-t^2-t)*s[1, 1, 1] + s[2, 1]

The Hall-Littlewood polynomials in the P basis at t = 0 are the Schur functions.

sage: HLP = HallLittlewoodP(QQ,t=0)
sage: s = SFASchur(HLP.base_ring())
sage: s(HLP([2,1])) == s([2,1])
True

The Hall-Littlewood polynomials in the P basis at t = 1 are the monomial symmetric functions.

sage: HLP = HallLittlewoodP(QQ,t=1)
sage: m = SFAMonomial(HLP.base_ring())
sage: m(HLP([2,2,1])) == m([2,2,1])
True

combinat/HallLittlewood (last edited 2008-11-14 13:42:03 by anonymous)