Sturm's Theorem

Manuel Eberl 🌐

January 11, 2014

This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.


Sturm's Theorem states that polynomial sequences with certain properties, so-called Sturm sequences, can be used to count the number of real roots of a real polynomial. This work contains a proof of Sturm's Theorem and code for constructing Sturm sequences efficiently. It also provides the “sturm” proof method, which can decide certain statements about the roots of real polynomials, such as “the polynomial P has exactly n roots in the interval I” or “P(x) > Q(x) for all x ∈ ℝ”.


BSD License


Session Sturm_Sequences