Factoring Polynomials over Global Fields
نویسندگان
چکیده
We prove polynomial time complexity for a now widely used factorization algorithm for polynomials over the rationals. Our approach also yields polynomial time complexity results for bivariate polynomials over a finite field.
منابع مشابه
A Lecture on the Complexity of Factoring Polynomials over Global Fields
This paper provides an overview on existing algorithms for factoring polynomials over global fields with their complexity analysis from our experiments on the subject. It relies on our studies of the complexity of factoring parametric multivariate polynomials that is used for solving parametric polynomial systems in our PhD thesis. It is intended to be useful to two groups of people: those who ...
متن کاملA New Algorithm for Factoring Polynomials Over Finite Fields
We present a new probabilistic algorithm for factoring polynomials over finite fields.
متن کاملFactoring Polynomials over Finite Fields: Asymptotic Complexity vs. Reality
Several algorithms for factoring polynomials over nite elds are compared from the point of view of asymptotic complexity, and from a more realistic point of view: how well actual implementations perform on \moderately" sized inputs.
متن کاملFactoring Multivariate Polynomials over Algebraic Number Fields
The algorithm for factoring polynomials over the integers by Wang and Rothschild is generalized to an algorithm for the irreducible factorization of multivariate polynomials over any given algebraic number field. The extended method makes use of recent ideas in factoring univariate polynomials over large finite fields due to Berlekamp and Zassenhaus. The procedure described has been implemented...
متن کاملFactoring Multivariate Polynomials over Algebraic Number Fields
The algorithm for factoring polynomials over the integers by Wang and Rothschild is generalized to an algorithm for the irreducible factorization of multivariate polynomials over any given algebraic number field. The extended method makes use of recent ideas in factoring univariate polynomials over large finite fields due to Berlekamp and Zassenhaus. The procedure described has been implemented...
متن کامل