I have some polynomials of high degree with coefficients of the form
a + b Sqrt where
b are integers (or at least rationals).
I want to rigorously determine when they have all real roots - that means symbolically, and not numerically.
It seems to me that
RootIntervals do actually work exactly (presumably via Sturm sequences or similar) when the polynomials have integer coefficients, but do they work correctly and exactly for ANY symbolically defined coefficients?