FUNCTION:  PermRep - permutation rePresentation of a Coxeter group,    
CALLING SEQUENCE:  PermRep(R);,                   PermRep(R,export);
    ,PARAMETERS:  R = a root system data Structure,SYNOPSIS:   
  PermRep(R) returns the permutation rePresentation of W(R) on cosets
  of the parabolic subgroup generated by all but the last of the simple
  Reflections, where "last" is determined by the ordering of Base(R). This
  rePresentation is faithful if and only if R is irreducible.
  The output is expressed as a "permgroup" (see group[permgroup]). More
  specifically, the result returned is an unevaluated procedure call
                permgroup(n, {s1=<perm1>, s2=<perm2>,...})
  where n is the degree of the permutation rePresentation, and the
  expression <perm_i> is a permutation of the integers 1,...,n in disjoint
  cycle format that describes the action of the i-th simple Reflection.
  For a description of disjoint cycle format, see group[permgroup].
  If 'export' is specified as a second argument, then the output is a
  sequence of commands for the GAP language that define W(R) by its
  permutation rePresentation. For more information about GAP, see
  http://www.ccs.neu.edu/mirrors/GAP/.
  For a description of root system data Structures, see Coxeter[Structure].
EXAMPLES:   ,  PermRep(B3);                    yields  
                permgroup(6,{s1=[[3,4]],s2=[[2,3],[4,5]],s3=[[1,2],[5,6]]})
  pg:=PermRep(A3*G2); with(group,grouporder);
  grouporder(pg);                  yields              12,    
SEE ALSO:  Base, MultPerm, Perm2Word, PermChar, Presentation, StabChain,
           Structure, group[permgroup], group[permrep]):
