1157
Comment:

873

Deletions are marked like this.  Additions are marked like this. 
Line 2:  Line 2: 
== Q' Basis: == Timing data for arithmetic with HallLittlewood polynomials in the Q' basis. Over ZZ: 

Line 6:  Line 3: 
== P basis ==  
Line 7:  Line 5: 
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: HallLittlewoodP(QQ) HallLittlewood polynomials in the P basis over Fraction Field of Univariate Polynomial Ring in t over Rational Field sage: HallLittlewoodP(QQ, t=1) HallLittlewood 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^2t)*s[1, 1, 1] + s[2, 1] 
Line 21:  Line 14: 
Over QQ:  
Line 23:  Line 15: 
The HallLittlewood polynomials in the P basis at $t = 0$ are the Schur functions.  
Line 24:  Line 17: 
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=0) sage: s = SFASchur(HLP.base_ring()) sage: s(HLP([2,1])) == s([2,1]) True 
Line 38:  Line 22: 
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).  The HallLittlewood 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 }}} 
HallLittlewood Polynomials
P basis
sage: HallLittlewoodP(QQ) HallLittlewood polynomials in the P basis over Fraction Field of Univariate Polynomial Ring in t over Rational Field sage: HallLittlewoodP(QQ, t=1) HallLittlewood 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^2t)*s[1, 1, 1] + s[2, 1]
The HallLittlewood 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 HallLittlewood 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