FUNCTION:  WeightSys - dominant Weights below a given dominant weight,    
                   WeightSys(v,R,'wc');,    
PARAMETERS:  R = a crystallographic root system data Structure
             v = a linear combination of e1,e2,... representing a dominant
                 integral weight,            wc = (optional) a name
SYNOPSIS:   
  If R is a crystallographic root system, Weights are represented as
  rational linear combinations of the standard orthonormal basis e1,e2,...
  A weight v is integral if it is in the integer span of the fundamental
  Weights (i.e., WeightCoords(v,R) is integral), and it is dominant if it
  is in the nonnegative span of the fundamental Weights. The irreducible
  finite-dimensional rePresentations of LieAlg(R) are Indexed by dominant
  integral Weights.
  If v is a dominant integral weight, WeightSys(v,R) returns the list of
  all dominant integral Weights that are less than or equal to v in the
  partial ordering for which v1 < v2 whenever v2-v1 is an integral sum of
  positive roots. These are the dominant Weights that occur with nonzero
  multiplicity in the irreducible rePresentation of LieAlg(R) Indexed by v.
  If a third argument is present, it is assigned a list consisting of 
  WeightCoords(u,R) for each weight u appearing in WeightSys(v,R).
  For a description of root system data Structures, see Coxeter[Structure].
EXAMPLES:   ,  w:=Weights(C3); v:=w[1]+w[3];
  WeightSys(v,C3);            yields      [e1+e2+2*e3, 2*e3, e2+e3, 0]
  w:=Weights(G2); v:=3*w[1];
  WeightSys(v,G2,'wc'): wc;   yields  [[3,0],[1,1],[0,1],[2,0],[1,0],[0,0]]
    ,SEE ALSO:  WeightCoords, WeightMults, Weights, WeylDim,
           Coxeter[PosRoots], Coxeter[Structure]):
