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 $(a,\infty)$ , 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.
I would do as follows:
sage: r = p.derivative()*q - q*p.derivative()
sage: R_r = r.roots(RR)
This gives you the real roots of r in the variable R_r. Now to filter the roots that make sense to you, you need to compute the roots of p and q:
sage: R_p = p.roots(RR)
sage: R_q = q.roots(RR)
In R_p and R_q, you have the real roots of p and q, given as pairs with the root and the multiplicity. To find a:
sage: a = max([x[0] for x in R_p] + [x[0] for x in R_q])
And finally, the roots you want:
sage: R = [x in R_r if x[0] > a]
Alternatively
def are_there_roots(p, q):
return False
Asked: 2015-06-11 23:31:40 +0100
Seen: 563 times
Last updated: Jun 12 '15
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