论文信息 - On Polynomial Factorization

On Polynomial Factorization

These algorithms are probabilistic in the following sense. The time of computation depends on random choices, but the validity of the result does not depend on them. So, worst case complexity, being infinite, is meaningless and we compute average complexity. It appears that our and Cantor-Zassenhaus algorithms have the same asymptotic complexity and they are the best algorithms actually known ; with elementary multiplication and GCD computation, CantorZassenhaus algorithm is always better than ours ; with fast multiplication and GCD, it seems that ours is better, but this fact is not yet proveen.

Daniel Lazard

[1] Jacques Calmet,et al. An Improvement of Rabin's Probabilistic Algorithm for Generating Irreducible Polynomials over GF(p) , 1980, Inf. Process. Lett..

[2] Allan Borodin,et al. The computational complexity of algebraic and numeric problems , 1975, Elsevier computer science library.

[3] Philippe Flajolet,et al. A Branching Process Arising in Dynamic Hashing, Trie Searching and Polynomial Factorization , 1982, ICALP.

[4] Alfred V. Aho,et al. The Design and Analysis of Computer Algorithms , 1974 .

[5] D. Cantor,et al. A new algorithm for factoring polynomials over finite fields , 1981 .

[6] David Y. Y. Yun,et al. Computational aspects of Hensel-type univariate polynomial greatest common divisor algorithms , 1974, SIGS.

[7] M. Mignotte. An inequality about factors of polynomials , 1974 .

[8] E. Berlekamp. Factoring polynomials over large finite fields* , 1970, SYMSAC '71.

[9] Robert T. Moenck,et al. On the efficiency of algorithms for polynomial factoring , 1977 .

[10] Paul Camion. Un Algorithme De Construction Des Idempotents Primitifs D'Ideaux D'Algebres Sur Fq , 1982 .