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Integer polynomials and exact real-root isolation.
Conic intersections lead to a quartic whose roots are nested radicals
at best and not radicals at all in general (casus irreducibilis). So an
exact root is represented the way CGAL’s Algebraic_kernel_d does it:
a square-free integer polynomial plus a dyadic interval that contains
exactly one of its roots. Every comparison is then decided exactly:
by Sturm counts, by refining the intervals, or by a gcd when two roots
might be equal.
Coefficients are BigInt. A polynomial with dyadic coefficients is
scaled by a power of two first (IntPoly::from_dyadic), which does
not move its roots.