{"title":"Effective Hilbert irreducibility","authors":"Erich Kaltofen","doi":"10.1016/S0019-9958(85)80056-5","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper we prove by entirely elementary means a very effective version of the Hilbert irreducibility theorem. We then apply our theorem to construct a probabilistic irreducibility test for sparse multivariate polynomials over arbitrary perfect fields. For the usual coefficient fields the test runs in polynomial time in the input size.</p></div>","PeriodicalId":38164,"journal":{"name":"信息与控制","volume":"66 3","pages":"Pages 123-137"},"PeriodicalIF":0.0000,"publicationDate":"1985-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0019-9958(85)80056-5","citationCount":"38","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"信息与控制","FirstCategoryId":"1093","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0019995885800565","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 38
Abstract
In this paper we prove by entirely elementary means a very effective version of the Hilbert irreducibility theorem. We then apply our theorem to construct a probabilistic irreducibility test for sparse multivariate polynomials over arbitrary perfect fields. For the usual coefficient fields the test runs in polynomial time in the input size.
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