Given symmetric functions f1 and f2, the method computes the standard pairing between f1 and f2.
i1 : R = symmetricRing(QQ,5); |
i2 : S = schurRing R o2 = S o2 : SchurRing |
i3 : scalarProduct(h_5,p_5) o3 = 1 o3 : QQ |
i4 : scalarProduct(S_{4,1},p_5) o4 = -1 o4 : QQ |
Indeed, the coefficients of s_5 and s_{4,1} in the s-basis expansion of h_5 are as computed above:
i5 : R = symmetricRing(QQ,5); |
i6 : toS p_5 o6 = s - s + s - s + s 5 4,1 3,1,1 2,1,1,1 1,1,1,1,1 o6 : schurRing (QQ, s, 5) |