FUNCTION: LieTools/CW2fwgt 
USAGE: CW2fwgt(cwgt,Gt); CW2fwgt(cwgt); CW2fwgt(cwgt,Gt)
SYNOPSIS: CW2fwgt(cwgt,Gt) takes an argument of the form
      3*e1 + 2*e2 + cdots
  (the way the Coxeter/Weyl package expresses weights) and produces a list
  of the components of the corresponding weight with respect to the basis of
  fundamental weights of Gt. 
  CW2fwgt called with a single argument, cwgt, does the same thing but
  requires a previously initialized global Lie algebra environment. (See 
  LieTools[gSetup].)  
  One can also call CW2fwgt in the form CW2swgt(cwgt,Gtype,rnk).

  fwgt2CW is the inverse of CW2fwgt: i.e. it converts the expression of a 
  weight as a list of its components with respect to the basis of fundamental
  wieghts to the linear function of the standard basis elements e1,e2...
  used by the Coxeter/Weyl package.

EXAMPLE: 
> fw := LieTools[CW2fwgt](-e1-2*e2+3*e3,G2);
                             fw := [1, 1]

> cw := LieTools[fwgt2CW](fw,G2);

                       cw := -e1 - 2 e2 + 3 e3


SEE ALSO: LieTools[fwgt2CW], LieTools[CW2swgt], LieTools[swgt2CW],  LieTools[fwgt2swgt],
          LieTools[swgt2fwgt]   


