Factorization of Polynomials With Algebraic Coefficients

Manuel Eberl 🌐 and RenĂ© Thiemann 📧

November 8, 2021

Abstract

The AFP already contains a verified implementation of algebraic numbers. However, it is has a severe limitation in its factorization algorithm of real and complex polynomials: the factorization is only guaranteed to succeed if the coefficients of the polynomial are rational numbers. In this work, we verify an algorithm to factor all real and complex polynomials whose coefficients are algebraic. The existence of such an algorithm proves in a constructive way that the set of complex algebraic numbers is algebraically closed. Internally, the algorithm is based on resultants of multivariate polynomials and an approximation algorithm using interval arithmetic.
BSD License

Topics

Theories of Factor_Algebraic_Polynomial