Irreducibility testing and factorization of polynomials-Reference-Cited by-同舟云学术

Irreducibility testing and factorization of polynomials

Published:1983 Issue:164 Volume:41 Page:699-709
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Adleman Leonard M.,Odlyzko Andrew M.

Abstract

It is shown that under certain hypotheses, irreducibility testing and factorization of polynomials with integer coefficients are polynomial time reducible to primality testing and factorization of integers, respectively. Combined with recently discovered fast primality tests, this yields an almost polynomial time irreducibility algorithm. The assertions of irreducibility produced by this algorithm are always certain and yield short proofs of irreducibility.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1983-41-164/S0025-5718-1983-0717715-6/S0025-5718-1983-0717715-6.pdf

Reference31 articles.

1. L. M. Adleman, On Distinguishing Prime Numbers from Composite Numbers, Proc. 21st Annual IEEE Found. Comp. Sci. Conference, IEEE, 1980, pp. 387-406.

2. L. M. Adleman & A. M. Odlyzko, Irreducibility Testing and Factorization of Polynomials, (extended abstract), Proc. 22nd Annual IEEE Found. Comp. Sci. Conference, IEEE, 1981, pp. 409-418.

3. On distinguishing prime numbers from composite numbers;Adleman, Leonard M.;Ann. of Math. (2),1983

4. A heuristic asymptotic formula concerning the distribution of prime numbers;Bateman, Paul T.;Math. Comp.,1962

5. Primes represented by irreducible polynomials in one variable;Bateman, Paul T.,1965

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