{"title":"A modular greatest common divisor algorithm for gaussian polynomials","authors":"B. Caviness, M. Rothstein","doi":"10.1145/800181.810340","DOIUrl":null,"url":null,"abstract":"In this paper the Brown-Collins modular greatest common divisor algorithm for polynomials in Z[x<subscrpt>1</subscrpt>,...,x<subscrpt>v</subscrpt>], where Z denotes the ring of rational integers, is generalized to apply to polynomials in G[x<subscrpt>1</subscrpt>,...,x<subscrpt>v</subscrpt>], where G denotes the ring of Gaussian integers, i.e., complex numbers of the form a + ib where a, b are in Z\n Under certain simplifying assumptions, a function is found that dominates the maximum computing time of the new god algorithm.","PeriodicalId":447373,"journal":{"name":"ACM '75","volume":"20 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM '75","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/800181.810340","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
In this paper the Brown-Collins modular greatest common divisor algorithm for polynomials in Z[x1,...,xv], where Z denotes the ring of rational integers, is generalized to apply to polynomials in G[x1,...,xv], where G denotes the ring of Gaussian integers, i.e., complex numbers of the form a + ib where a, b are in Z
Under certain simplifying assumptions, a function is found that dominates the maximum computing time of the new god algorithm.
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