Given a symmetric function f, the function toP yields a representation of f as a polynomial in the power-sum symmetric functions.
If f is an element of a Schur ring S then the output fp is an element of the Symmetric ring associated to S (see symmetricRing).
i1 : R = symmetricRing 7; |
i2 : toP(h_3*e_3)
1 6 1 2 2 1 3 1 2
o2 = --p - -p p + -p p + -p
36 1 4 1 2 9 1 3 9 3
o2 : R
|
i3 : S = schurRing(s,4) o3 = S o3 : SchurRing |
i4 : toP S_{3,2,1}
1 6 1 4 1 2 2 5 3 1 1 2 1 2
o4 = --p + --p p - -p p - --p p + -p p p - -p + -p p
72 1 12 1 2 8 1 2 18 1 3 6 1 2 3 9 3 4 1 4
o4 : QQ[e ..e , p ..p , h ..h ]
1 4 1 4 1 4
|
This also works over tensor products of Symmetric/Schur rings.
i5 : R = schurRing(r, 4, EHPVariables => (a,b,c)); |
i6 : S = schurRing(R, s, 2, EHPVariables => (x,y,z)); |
i7 : T = schurRing(S, t, 3); |
i8 : A = symmetricRing T; |
i9 : f = (r_1+s_1+t_1)^2
o9 = t + t + (2r s + 2r s )t + (s + s + 2r s + (r +
2 1,1 () 1 1 () 1 2 1,1 1 1 2
------------------------------------------------------------------------
r )s )t
1,1 () ()
o9 : T
|
i10 : toP f
2 2 2
o10 = p + (2z + 2c )p + z + 2c z + c
1 1 1 1 1 1 1 1
o10 : A
|
The object toP is a method function.