#
# redex - list all reduced expressions for a group element
#
# Calling sequence:
#  redex(w,R);
#
# Parameters:
#  R = a root system data structure
#  w = a list of integers representing an element of W(R)
#
# This procedure lists, in lexicographic order, all reduced expressions for
# an element w of the (finite) Coxeter group W(R).
#
# Example:
#  with(coxeter):
#  redex(longest_elt(A3),A3);
#
redex:=proc(w,R) local S,v,i;
  S:=coxeter['base'](R);
  v:=coxeter['interior_pt'](S);
  v:=coxeter['reflect'](seq(S[i],i=w),v);
  `redex/vec`(v,S);
end;
#
`redex/vec`:=proc(v,S) local J,i,w;
  J:=map(proc(x,y,z) if coxeter['iprod'](y[x],z)<0 then x fi end,
    [$1..nops(S)],S,v);
  if nops(J)=0 then [[]] else
    [seq(seq([i,op(w)],w=procname(coxeter['reflect'](S[i],v),S)),i=J)]
  fi
end;