Irreducibility testing and factorization of polynomials

Leonard M. Adlcman; Andrew M. Odlyzko

doi:10.1090/S0025-5718-1983-0717715-6

Irreducibility testing and factorization of polynomials

Leonard M. Adlcman, Andrew M. Odlyzko

School of Mathematics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

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.

Original language	English (US)
Pages (from-to)	699-709
Number of pages	11
Journal	Mathematics of Computation
Volume	41
Issue number	164
DOIs	https://doi.org/10.1090/S0025-5718-1983-0717715-6
State	Published - Oct 1983

Publisher link

10.1090/S0025-5718-1983-0717715-6

Find It

Find It at U of M Libraries

Cite this

@article{cc0167a435a640ffaa2873d0daf48e6f,

title = "Irreducibility testing and factorization of polynomials",

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.",

author = "Adlcman, {Leonard M.} and Odlyzko, {Andrew M.}",

year = "1983",

month = oct,

doi = "10.1090/S0025-5718-1983-0717715-6",

language = "English (US)",

volume = "41",

pages = "699--709",

journal = "Mathematics of Computation",

issn = "0025-5718",

publisher = "American Mathematical Society",

number = "164",

}

TY - JOUR

T1 - Irreducibility testing and factorization of polynomials

AU - Adlcman, Leonard M.

AU - Odlyzko, Andrew M.

PY - 1983/10

Y1 - 1983/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84966206335&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966206335&partnerID=8YFLogxK

U2 - 10.1090/S0025-5718-1983-0717715-6

DO - 10.1090/S0025-5718-1983-0717715-6

M3 - Article

AN - SCOPUS:84966206335

SN - 0025-5718

VL - 41

SP - 699

EP - 709

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 164

ER -

Irreducibility testing and factorization of polynomials

Abstract

Publisher link

Find It

Other files and links

Fingerprint

Cite this