splitCharacter -- Decomposes a symmetric polynomial as a sum 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)