FUNCTION: LieTools/SgGroebnerBasis
USAGE: SgGroebnerBasis(plist);
SYNOPSIS: Finds the reduced Groebner basis for the ideal generated from the polynomials in
  plist, using Maple's tdeg term ordering.
EXAMPLE: 
> with(LieTools):
> gSetup(G,2):
Setting up Gtype = G   rnk = 2
> pbasis := SgMkRepWgtBasis([2,0],2):
> nops(pbasis);

                                  27

> gb := SgGroebnerBasis(pbasis);

              2
  gb := [g[12]  - 3 g[13] g[11] - 3 g[14] g[9],

        g[12] g[11] - 9 g[13] g[10] + 3 g[14] g[7],

        -3 g[13] g[7] + g[9] g[12] + 9 g[5] g[14] - 9 g[8] g[13],

        -3 g[6] g[13] + 2 g[12] g[7] + 3 g[4] g[14] + 3 g[12] g[8],

                                             2
        -3 g[12] g[10] + 3 g[14] g[6] + g[11] ,

        2 g[9] g[11] - 3 g[12] g[8] - 3 g[6] g[13] - 3 g[4] g[14],

        -3 g[3] g[14] - g[6] g[12] + 2 g[11] g[7] + 3 g[11] g[8],

        6 g[10] g[9] - 3 g[11] g[8] - g[6] g[12] + 3 g[3] g[14],

        9 g[10] g[8] + 9 g[2] g[14] - g[6] g[11] + 6 g[10] g[7],

            2
        g[9]  + 3 g[12] g[5] + 3 g[4] g[13],

        g[4] g[12] + 6 g[11] g[5] - 3 g[3] g[13] + 3 g[9] g[8],

        g[9] g[7] + 3 g[3] g[13] - 3 g[11] g[5], 9 g[1] g[14]

                                               2
         + 9 g[2] g[13] - 7 g[4] g[11] + 9 g[8]  - 7 g[6] g[9]

         - 10 g[3] g[12] + 36 g[10] g[5], 3 g[8] g[7] + 3 g[6] g[9]

         - 18 g[10] g[5] + 4 g[4] g[11] + 5 g[3] g[12] - 9 g[2] g[13]

        , -3 g[2] g[12] + 6 g[10] g[4] + g[3] g[11] + 3 g[8] g[6],

            2
        g[7]  - 2 g[6] g[9] + 9 g[10] g[5] - 3 g[4] g[11]

         - 3 g[3] g[12] + 9 g[2] g[13],

        3 g[2] g[12] - 3 g[10] g[4] + g[7] g[6],

        9 g[1] g[13] - g[4] g[9] + 6 g[7] g[5] + 9 g[8] g[5],

        -3 g[1] g[12] + 2 g[4] g[7] + 3 g[8] g[4] - g[9] g[3],

        3 g[1] g[11] + 2 g[7] g[3] + 3 g[3] g[8] - 3 g[2] g[9],

                                          2
        3 g[3] g[10] + 3 g[2] g[11] + g[6] ,

        -3 g[8] g[4] + 6 g[5] g[6] - g[9] g[3] + 3 g[1] g[12],

        2 g[6] g[4] - 3 g[3] g[8] - 3 g[2] g[9] - 3 g[1] g[11],

        9 g[1] g[10] - 3 g[2] g[7] - 9 g[2] g[8] + g[3] g[6],

                                        2
        3 g[1] g[9] - 3 g[3] g[5] + g[4] ,

        3 g[1] g[7] + g[3] g[4] - 9 g[2] g[5],

            2
        g[3]  - 3 g[2] g[4] - 3 g[1] g[6],

        g[11] g[4] g[14] + g[14] g[6] g[9] + g[14] g[3] g[12],

        g[4] g[13] g[11] + g[13] g[6] g[9] + g[12] g[3] g[13],

        g[2] g[4] g[11] + g[2] g[6] g[9] + g[3] g[2] g[12],

        g[1] g[4] g[11] + g[1] g[6] g[9] + g[3] g[1] g[12]]

> nops(gb);

                                  31

> SgHdim(gb);

                                  6


SEE ALSO: LieTools[SgHdim] 
