Given a symmetric function f, the function toS yields a representation of f as a linear combination of Schur functions.
If f is an element of a Symmetric ring R and the output Schur ring S is not specified, then the output fs is an element of the Schur ring associated to R (see schurRing).
i1 : R = symmetricRing(QQ,4); |
i2 : fs = toS(e_1*h_2+p_3)
o2 = 2s + s
3 1,1,1
o2 : schurRing (QQ, s, 4)
|
i3 : S = schurRing(s,2); |
i4 : toS(fs,S)
o4 = 2s
3
o4 : S
|
This also works over tensor products of Symmetric/Schur rings.
i5 : R = symmetricRing(4, EHPVariables => (a,b,c), SVariable => r); |
i6 : S = symmetricRing(R, 2, EHPVariables => (x,y,z), SVariable => s); |
i7 : T = symmetricRing(S, 3, SVariable => t); |
i8 : A = schurRing T; |
i9 : f = a_3*x_2*e_1 - b_1*z_2*p_3
o9 = - b z p + a x e
1 2 3 3 2 1
o9 : T
|
i10 : toS f
o10 = (- r s + r s )t + (r s - r s )t + (- r s + r s )t +
1 2 1 1,1 3 1 2 1 1,1 2,1 1 2 1 1,1 1,1,1
-----------------------------------------------------------------------
r s t
1,1,1 1,1 1
o10 : A
|
The object toS is a method function.