### Jacobian matrix rank

Consider the following code :

R.<x,y,z> = QQ[];

p=(x-y)*(y-z)*(x-z);

J = matrix(R,[[x-y],[y]]);

J.rank();

The answer displayed is 1. This is the rank over the polynomia ring I suppose. I would like to compute rank over the field of rationals. That is if there are rational numbers ~~a ~~a,b and ~~b ~~c such that
a diff(p,x) + b diff(p,y) + c diff(p,z) =0 but ~~a,b ~~a,b,c non zero then rank should be ~~2. ~~3.

What is the way to do it ?