{"title":"一种多项式分解算法","authors":"David R. Barton, R. Zippel","doi":"10.1145/800205.806356","DOIUrl":null,"url":null,"abstract":"This paper presents an efficient, effective algorithm for decomposing a polynomial <italic>f(x)</italic> into an irreducible representation of the form <italic>f(x) &equil; g<subscrpt>1</subscrpt>(g<subscrpt>2</subscrpt>( ... g<subscrpt>n</subscrpt>(x) ... ))</italic>. This decomposition is used as an aid in solving high degree metacyclic equations in radicals and preconditioning polynomials for evaluation.","PeriodicalId":314618,"journal":{"name":"Symposium on Symbolic and Algebraic Manipulation","volume":"364 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1976-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"26","resultStr":"{\"title\":\"A polynomial decomposition algorithm\",\"authors\":\"David R. Barton, R. Zippel\",\"doi\":\"10.1145/800205.806356\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper presents an efficient, effective algorithm for decomposing a polynomial <italic>f(x)</italic> into an irreducible representation of the form <italic>f(x) &equil; g<subscrpt>1</subscrpt>(g<subscrpt>2</subscrpt>( ... g<subscrpt>n</subscrpt>(x) ... ))</italic>. This decomposition is used as an aid in solving high degree metacyclic equations in radicals and preconditioning polynomials for evaluation.\",\"PeriodicalId\":314618,\"journal\":{\"name\":\"Symposium on Symbolic and Algebraic Manipulation\",\"volume\":\"364 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1976-08-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"26\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Symposium on Symbolic and Algebraic Manipulation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/800205.806356\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Symposium on Symbolic and Algebraic Manipulation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/800205.806356","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
This paper presents an efficient, effective algorithm for decomposing a polynomial f(x) into an irreducible representation of the form f(x) &equil; g1(g2( ... gn(x) ... )). This decomposition is used as an aid in solving high degree metacyclic equations in radicals and preconditioning polynomials for evaluation.
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