FUNCTION: LieTools/HHWVsInSgMonoSet
USAGE: HHWVsInSgMonoSet(mset)
SYNOPSIS: HHWVsInSgMonoSet(mset) yields a basis for the space of highest weight 
  vectors that are killed by the Laplacian and lie in the span of polynomials
  in mset. (It is assumed the polynomials in mset are homgeneous, of the same
  degree, and of the same weight.)
CAVEATS: requires a previously initialized global Lie algebra environment.
  (See LieTools[gSetup].)
EXAMPLE: 
> with(LieTools):
> gSetup(G,2);
Setting up Gtype = G   rnk = 2
> 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]}

> HHWVsInSgMonoSet(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]]


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