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
