多项式的不可约性检验与因子分解

22nd Annual Symposium on Foundations of Computer Science (sfcs 1981) Pub Date : 1981-10-28 DOI:10.1109/SFCS.1981.20

L. Adleman, A. Odlyzko

{"title":"多项式的不可约性检验与因子分解","authors":"L. Adleman, A. Odlyzko","doi":"10.1109/SFCS.1981.20","DOIUrl":null,"url":null,"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.","PeriodicalId":224735,"journal":{"name":"22nd Annual Symposium on Foundations of Computer Science (sfcs 1981)","volume":"19 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1981-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"38","resultStr":"{\"title\":\"Irreducibility testing and factorization of polynomials\",\"authors\":\"L. Adleman, A. Odlyzko\",\"doi\":\"10.1109/SFCS.1981.20\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":224735,\"journal\":{\"name\":\"22nd Annual Symposium on Foundations of Computer Science (sfcs 1981)\",\"volume\":\"19 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1981-10-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"38\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"22nd Annual Symposium on Foundations of Computer Science (sfcs 1981)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SFCS.1981.20\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"22nd Annual Symposium on Foundations of Computer Science (sfcs 1981)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SFCS.1981.20","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 38

摘要

证明了在一定假设下，整数系数多项式的不可约性检验和因子分解分别多项式时间可约为整数的素数检验和因子分解。结合最近发现的快速素数测试，这产生了一个几乎多项式时间的不可约算法。该算法产生的不可约性断言总是确定的，并给出不可约性的简短证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Irreducibility testing and factorization of polynomials

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

22nd Annual Symposium on Foundations of Computer Science (sfcs 1981)

自引率

0.00%

发文量