regarding finding purely real roots within a given fixed interval

[Tanmay Chavan]

Hi,
I am working on a project which requires me to find all real roots of a
polynomial within a specific interval. In GSL, I found the
gsl_poly_complex_solve function. However, it provides all complex roots
present. As opposed to the balanced QR-reduction method used here,
SagMath's algorithm provides quicker answers as one can set intervals and
find purely real roots. I believe this could cause significant overhead if
many operations are to be done quickly. I tried to understand the
implementation and come up with a better method, but I failed to do so. Is
there any way to find purely real roots (preferably in an interval)
directly in GSL? If not, what modifications should I do for the method in
GSL so as to optimize it for my purposes? Any help would be greatly
appreciated.

Best wishes,
Tanmay