FUNCTION:  LongestElt - longest element of a Coxeter group,    
CALLING SEQUENCE:  LongestElt(R);,    
PARAMETERS:  R = a root system data Structure,SYNOPSIS:   
  If R is a root system of Rank n, members of the Coxeter group W(R) are
  represented as lists of integers in the range 1..n. The group element
  corresponding to w = [i_1,...,i_l] is the product of the generators
  Indexed by i_1,...,i_l. The Indexing follows Base(R).
  LongestElt(R) returns a Reduced expression for the longest element w0
  of W(R); i.e., a minimum-length rePresentation of w0. Among all Reduced
  expressions for w0, the one returned is the first in lexicographic order.

  For a description of root system data Structures, see Coxeter[Structure].
EXAMPLES:   
  LongestElt(H3);                 yields   [1,2,1,2,1,3,2,1,2,1,3,2,1,2,3]
  S:=Base(A3);
  LongestElt([S[1],S[3],S[2]]);   yields            [1,2,3,1,2,3],    
SEE ALSO:  Base, LengthGF, NumRefl, Reduce, Structure):
