About finding roots of polynomials in specific domains

[Phoenix]

I have two polynomials $p(x)$ and $q(x)$ and I want to know if there are roots of the equation $\frac{p'}{p} = \frac{q'}{q}$ in the domain $(a,\infinity)$ - where $a = max \{ roots(p),roots(q) \}$

This is the same as asking for the roots of the polynomial, $p'q - pq' = 0$ in the same domain.

- Can something in Sage help?

[slelievre]

Note: same as this question on stackoverflow:
http://stackoverflow.com/questions/30784577/how-does-one-find-roots-of-polynomials-in-a-given-domain-in-sage

[Jeroen Demeyer]

Just compute all roots and filter out the ones which satisfy your condition.

[luisfe]

Depending on the coefficient field, the degree of the polynomials, accuracy etc. You can also take a look at Sturm's theorem and Sturm's sequence.