[isabelle] new AFP entry: Factorization of Polynomials with Algebraic Coefficients

Factorization of Polynomials with Algebraic Coefficients
by Manuel Eberl and René Thiemann

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.



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