FUNCTION:  Vec2FC - map a vector to the fundamental chamber by Reflections
    ,CALLING SEQUENCE:  Vec2FC(v,R);,                   Vec2FC(v,R,'w');
    ,PARAMETERS:  R = a root system data Structure
             v = a linear combination of e1,e2,...
             w = (optional) a name,SYNOPSIS:   
  A "vector" (distinct from the vector data Structure used by Maple) is a
  linear combination of the standard orthonormal basis e1,e2,e3,..., with
  coefficients that are rational or floating-point. A vector v is dominant
  relative to a set of simple roots S if it belongs to the closure of the
  fundamental chamber defined by S; i.e., Iprod(r,v) >= 0 for all r in S.

  If v is a vector, Vec2FC(v,R) returns the unique dominant vector (relative
  to Base(R)) that can be reached from v by a series of Reflections.,     
  If there is a third argument, it will be assigned the list of indices of
  the simple Reflections that were used to bring v into the fundamental
  chamber. The list is ordered so that the first item in the list Indexes
  the first Reflection applied to v. Therefore if S = Base(R) and u is
  the result returned by the function call  Vec2FC(v,R,'w'), then
  v = Reflect(seq(S[i],i=w),u).
  Among all the possible sequences of simple Reflections that send v to u,
  the one assigned to the third argument has minimum length, and is first
  in lexicographic order among all such minimum-length expressions.
  WARNING: If any floating-point coordinates occur in v or Base(R), then
  the result is only approximate in the sense that a vector u is considered
  to be on the negative side of the hyperplane orthogonal to r if and only
  if Iprod(r,u) < -epsilon ( = -0.001, by default).
  To adjust epsilon, assign a new value to Coxeter/default[epsilon].

  For a description of root system data Structures, see Coxeter[Structure].
EXAMPLES:   
  Vec2FC(-e1+2*e2,D4);             yields          2*e4+e3,  S:=Base(F4);
  Vec2FC(-S[2],S,'w'),w;           yields   e4, [2,1,3,2,4,3,2,1],    
SEE ALSO:  Base, InteriorPt, Iprod, Orbit, Rank, Reflect, Structure):
