Root isolation is the process of constructing pairwise disjoint intervals whose endpoints are rational numbers, such that each interval contains exactly one real root of a polynomial and every real root is contained in one of the intervals. Each interval is called an isolating interval.
A squarefree factorization first separates roots of different multiplicities.
The intervals can then be found by repeated subdivision
using Sturm's theorem, Descartes'
sign rule, or continued fraction methods.
A bound on root separation
provides a sufficient final interval width. For example,
the two real roots of 
are isolated by
 |
An alternative exact representation is a Thom encoding, which identifies a real root by the signs of the successive derivatives of its polynomial.
