Expresses a symmetric polynomial c as a linear combination of schur functions
i1 : c=character({{1,1,1},{2}},4) 3 3 4 3 2 2 3 4 3 2 2 2 2 3 2 3 3 2 3 2 3 3 3 4 4 o1 = x x + x x x + 2x x x + 2x x x + x x x + 2x x x + 2x x x + 2x x x + x x + 2x x x + 2x x x + x x + x x x + x x x 0 1 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 2 0 1 2 0 1 2 1 2 0 1 2 0 1 3 ---------------------------------------------------------------------------------------------------------------------------- 3 2 2 3 4 4 3 2 2 3 4 3 2 2 2 2 2 + 2x x x + 2x x x + x x x + x x x + 4x x x x + 5x x x x + 4x x x x + x x x + 2x x x + 5x x x x + 5x x x x + 0 1 3 0 1 3 0 1 3 0 2 3 0 1 2 3 0 1 2 3 0 1 2 3 1 2 3 0 2 3 0 1 2 3 0 1 2 3 ---------------------------------------------------------------------------------------------------------------------------- 3 2 2 3 3 2 3 4 4 3 2 2 2 2 3 2 3 2 2 2 2 2 2x x x + 2x x x + 4x x x x + 2x x x + x x x + x x x + 2x x x + 2x x x + 2x x x + 2x x x + 5x x x x + 5x x x x + 1 2 3 0 2 3 0 1 2 3 1 2 3 0 2 3 1 2 3 0 1 3 0 1 3 0 1 3 0 2 3 0 1 2 3 0 1 2 3 ---------------------------------------------------------------------------------------------------------------------------- 3 2 2 2 2 2 2 2 2 2 3 2 3 2 3 3 2 3 2 3 3 3 2 3 3 2x x x + 2x x x + 5x x x x + 2x x x + 2x x x + 2x x x + x x + 2x x x + 2x x x + x x + 2x x x + 4x x x x + 1 2 3 0 2 3 0 1 2 3 1 2 3 0 2 3 1 2 3 0 3 0 1 3 0 1 3 1 3 0 2 3 0 1 2 3 ---------------------------------------------------------------------------------------------------------------------------- 2 3 2 3 2 3 3 3 4 4 4 2x x x + 2x x x + 2x x x + x x + x x x + x x x + x x x 1 2 3 0 2 3 1 2 3 2 3 0 1 3 0 2 3 1 2 3 o1 : QQ[x ..x ] 0 3 |
i2 : splitCharacter(c) o2 = s + s 4,1,1 3,3 o2 : schurRing (QQ, s, 4) |
The object splitCharacter is a method function.