FUNCTION: LieTools/rhoNormalOrder
USAGE: rhoNormalOrder(gpoly);
SYNOPSIS: rhoNormalOrder(x) maps a polynomial x in S[g] to a normal-ordered 
  element in U[g] (monomials in S[g] are mapped to PBW basis elements) with 
  a rho-shift.
CAVEATS: requires a previously initialized global Lie algebra environment.
  (See LieTools[gSetup].)
EXAMPLE: 
> with(LieTools):
> gSetup(G,2);
Setting up Gtype = G   rnk = 2
> c2 := add(add(BI[i,j]*g[i]*g[j],i=1..dimg),j=1..dimg);

  c2 := 1/4 g[1] g[14] + 1/4 g[2] g[13] + 1/12 g[3] g[12]

         + 1/12 g[4] g[11] + 1/4 g[10] g[5] + 1/12 g[6] g[9]

                    2                           2
         + 1/12 g[7]  + 1/4 g[8] g[7] + 1/4 g[8]

> rhoNormalOrder(c2);

  1/4 u(g[1], g[14]) + 1/4 u(g[2], g[13]) + 1/12 u(g[3], g[12])

         + 1/12 u(g[4], g[11]) + 1/4 u(g[5], g[10])

         + 1/12 u(g[6], g[9]) + 1/12 u(g[7], g[7]) + 5/12 u(g[7])

         + 7/12 + 1/4 u(g[7], g[8]) + 3/4 u(g[8]) + 1/4 u(g[8], g[8])

SEE ALSO: 
