Pieter Wuille pointed out to me that you can: def coeffs_from_roots(roots): coefs=[1] for r in roots: coefs=[-r*coefs[0]] + [coefs[i]-r*coefs[i

Pieter Wuille pointed out to me that you can: def coeffs_from_roots(roots): coefs=[1] for r in roots: coefs=[-r*coefs[0]] + [coefs[i]-r*coefs[i+1] for i in range(len(coefs)-1)] + [1] coefs.reverse() return coefs That's merely quadratic, rather than taking exponentially many multiplications.