The complexity of factoring univariatepolynomials over the rationals: tutorial abstract

Authors:
Mark van Hoeij
Affiliations:
Florida State University, Tallahassee, USA
Venue:
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
Year:
2013

Citing 5
Cited 0

Factorization of Univariate Integer Polynomials by Diophantine Aproximation and an Improved Basis Reduction Algorithm

Proceedings of the 11th Colloquium on Automata, Languages and Programming
Complexity issues in bivariate polynomial factorization

ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Factoring univariate polynomials over the rationals

Factoring univariate polynomials over the rationals
Practical polynomial factoring in polynomial time

Proceedings of the 36th international symposium on Symbolic and algebraic computation
Gradual sub-lattice reduction and a new complexity for factoring polynomials

LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics

Quantified Score

Hi-index	0.00

Visualization

Abstract

This tutorial will explain the algorithm behind the currently fastest implementations for univariate factorization over the rationals. The complexity will be analyzed; it turns out that modifications were needed in order to prove a polynomial time complexity while preserving the best practical performance. The complexity analysis leads to two results: (1) it shows that the practical performance on common inputs can be improved without harming the worst case performance, and (2) it leads to an improved complexity, not only for factoring, but for LLL reduction as well.