_qqbar_roots_poly_squarefree

An annihilating polynomial with rational coefficients is the product $g = \prod (\tilde a_0 + \tilde a_1 x + \cdots + \tilde a_d x^d)$ over all combinations of conjugates $\tilde a_k$ of the coefficients. It is computed numerically, as a product of polynomials with ball coefficients by binary splitting, and multiplied by a power of the common denominator of the coefficients so that its coefficients are integers that can be read off once the precision is high enough. Then $g$ is factored and the factors are matched against the numerical roots of $f$. Since $g$ can be huge, the computation is aborted when its degree (the number of conjugate combinations) or size exceeds deg_limit or bits_limit (nonpositive values remove the limits, but the function can still fail if $g$ exceeds machine size). For polynomials that may have repeated roots, use gr_poly_roots with a qqbar context, which performs a squarefree factorisation first; gr_poly_roots_other computes algebraic roots of polynomials over other rings.