@vv Thank you very much for you suggestions. Actually, I need strictly to rely on the elimination ordering that I have described.

Since I'm not such acquainted with definition of monomials orderings, etc, let me define better this ordering, again with a small example, to see if there is again a trick to define it. In fact, for the variables set [x,y,z,t,u,v,etc], I need the weight vector

[1,1,0,1,1,0,etc] and then pure lexicographic with x > y > z > t > u > v > etc.

@vv 

The computer algebra systems I have used to factorize my polynomial are Singular and Magma. It seems that my example gives evidence of a bug in the Maple procedure.

In fact, by using the command

infolevel[`mod`]:= 2;

I have obtained an infinte loop with this error messages

mod/Gcd:   "polyc error"

Any suggestions?