FUNCTION: LieTools/HWVsInSgWgtSet
USAGE: HWVsInSgWgtSet(wset)
SYNOPSIS: HHWVsInSgWgtSet(wset) finds the highest weight vectors residing
  in the span of a set wset of polynomials in S[g] of fixed degree and weight. 
CAVEATS: requires a previously initialized global Lie algebra environment.
  (See LieTools[gSetup].)
EXAMPLE: 
> gSetup(G,2);
Setting up Gtype = G   rnk = 2
> DecompSg(3,G2);

         XX[0, 3] + XX[2, 1] + XX[3, 0] + XX[0, 1] + XX[1, 0]

> mset := fwgt2SgMonoSet([1,0],3);

  mset := {g[6] g[9] g[12], g[9] g[8] g[11], g[7] g[8] g[12],

        g[3] g[11] g[13], g[4] g[7] g[14], g[4] g[11] g[12],

        g[6] g[7] g[13], g[3] g[9] g[14], g[10] g[4] g[13],

        g[9] g[7] g[11], g[4] g[8] g[14], g[2] g[12] g[13],

        g[5] g[10] g[12], g[1] g[12] g[14], g[6] g[8] g[13],

                                   2      2            2
        g[5] g[6] g[14], g[5] g[11] , g[8]  g[12], g[7]  g[12],

                  2      2
        g[3] g[12] , g[9]  g[10]}

> HHWVsInSgWgtSet(mset);

  {-3 g[3] g[11] g[13] + g[4] g[11] g[12] - 9 g[10] g[4] g[13]

                                            2             2
         - 9 g[5] g[10] g[12] + 3 g[5] g[11]  + g[3] g[12]

         + 3 g[4] g[7] g[14] - 3 g[3] g[9] g[14] + 9 g[5] g[6] g[14]

         + g[6] g[9] g[12] + 3 g[9] g[8] g[11] + 3 g[7] g[8] g[12]

                                                       2
         - 3 g[6] g[7] g[13] - 9 g[6] g[8] g[13] + g[7]  g[12]

                 2
         - 3 g[9]  g[10]}

> nops(%);

                                  1


SEE ALSO: LieTools[HHWVsInSgMonoSet], LieTools[HWVsInSgMonoSet],
          LieTools[HLWVsInSgMonoSet], LieTools[HLWVsinSgWgtSet],
          LieTools[fwgt2SgMonoSet]
