#MakeLex
#
LEX:= proc(GB_org,Vars)
#################################################################
# This procedure uses the FGLM algorithm to convert from the terms order
# wdeg([1,15,15,15,15,15],[a,b,c,d,e,f]) to plex(Vars)
# and returns the resulting grobner basis
#################################################################
local GB_new, Poly_Alg, T_org,T_new,NFproc,FDproc,TMproc,FGLM,i,F;

 Poly_Alg:=poly_algebra(a,b,c,d,e,f):
 T_org:=termorder(Poly_Alg,wdeg([1,15,15,15,15,15],[a,b,c,d,e,f])):

 # Define NFproc and FDproc in view of a call to fglm. 
 NFproc:=proc(t,NF,TOrd)
  NF[t]:=normalf(t,GB_org,T_org)
 end:
 FDproc:=proc(M,NF)
  local ind_lst,term,eta,sol;
  ind_lst:=map(op,[indices(NF)]);
  for term in M do
   ind_lst:=remove(divide,ind_lst,term)
  od;
   expand(numer(normal(add(eta[term]*NF[term],term=ind_lst))));
   sol:=[solve({coeffs(%,{a,b,c,d,e,f})},
         {seq(eta[term],term=ind_lst)})];
   subs(op(1,sol),add(eta[term]*term,term=ind_lst));
       `if`(%=0,FAIL,collect(primpart(numer(subs(map(n->n=1,
        map2(op,1,select(evalb,sol[1]))),%)),
	   [a,b,c,d,e,f]),[a,b,c,d,e,f],distributed,factor))
 end:
 TMproc:=proc(border,monoideal,TOrd)
   border<>[]
 end:

 T_new:=termorder(Poly_Alg,plex(Vars[])):
 FGLM:=[fglm(NFproc,FDproc,TMproc,T_new)]:
 # Up to a sort, here is the final Groebner basis: 
 GB_new:=map(op,[entries(FGLM[2])]):
GB_new
 # for i from 1 to nops(GB_new) do
 #  if nops(indets(GB_new[i]))=1 then
 #  F:=GB_new[i]  fi:
 # od:
 # F
end: