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2020-03-19 10:46:29 +0100 received badge  Popular Question (source)
2017-04-21 05:36:18 +0100 commented answer Jacobian matrix rank

I would like to compute rank over the field of rationals. That is if there are rational numbers a,b and c such that a diff(p,x) + b diff(p,y) + c diff(p,z) =0 but a,b,c non zero then rank should be 3. What is the way to code this ?

2017-04-21 03:47:04 +0100 received badge  Editor (source)
2017-04-20 21:06:36 +0100 asked a question 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,b and c such that a diff(p,x) + b diff(p,y) + c diff(p,z) =0 but a,b,c non zero then rank should be 3.

What is the way to do it ?