Let's say we have a rational polynomial in k variables. We are only interested in rational solutions. If k = 1, name the variables {x}, if k = 2, name them {x,y}.
For k = 1, it can be done very fast. The Rational Root Theorem gives a set of candidates, see http://en.wikipedia.org/wiki/Rational_root_theorem. But what for k=2? How can I split a polynomial into factors in this case?
Example: x^2-y^2 should be split to (x-y)(x+y). Post also available on https://math.stackexchange.com/questions/181699/roots-of-rational-equation-with-multiple-variables.
