Ludovic Brieulle, L. Feo, Javad Doliskani, J. Flori, É. Schost
{"title":"有限域的同构计算与嵌入","authors":"Ludovic Brieulle, L. Feo, Javad Doliskani, J. Flori, É. Schost","doi":"10.1090/mcom/3363","DOIUrl":null,"url":null,"abstract":"Let <i>q</i> be a prime power and let F<sub><i>q</i></sub> be a field with <i>q</i> elements. Let <i>f</i> and <i>g</i> be irreducible polynomials in F<sub><i>q</i></sub>[<i>X</i>], with deg <i>f</i> dividing deg <i>g.</i> Define <i>k</i> = F<sub><i>q</i></sub>[<i>X</i>]/<i>f</i> and <i>K</i> = F<sub><i>q</i></sub>[<i>X</i>]/<i>g</i>, then there is an embedding <i>φ</i> : <i>k</i> [EQUATION] <i>K</i>, unique up to F<sub><i>q</i></sub>-automorphisms of <i>k.</i> Our goal is to describe algorithms to efficiently represent and evaluate one such embedding.","PeriodicalId":7093,"journal":{"name":"ACM Commun. Comput. Algebra","volume":"12 1","pages":"117-119"},"PeriodicalIF":0.0000,"publicationDate":"2017-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"Computing isomorphisms and embeddings of finite fields\",\"authors\":\"Ludovic Brieulle, L. Feo, Javad Doliskani, J. Flori, É. Schost\",\"doi\":\"10.1090/mcom/3363\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let <i>q</i> be a prime power and let F<sub><i>q</i></sub> be a field with <i>q</i> elements. Let <i>f</i> and <i>g</i> be irreducible polynomials in F<sub><i>q</i></sub>[<i>X</i>], with deg <i>f</i> dividing deg <i>g.</i> Define <i>k</i> = F<sub><i>q</i></sub>[<i>X</i>]/<i>f</i> and <i>K</i> = F<sub><i>q</i></sub>[<i>X</i>]/<i>g</i>, then there is an embedding <i>φ</i> : <i>k</i> [EQUATION] <i>K</i>, unique up to F<sub><i>q</i></sub>-automorphisms of <i>k.</i> Our goal is to describe algorithms to efficiently represent and evaluate one such embedding.\",\"PeriodicalId\":7093,\"journal\":{\"name\":\"ACM Commun. Comput. Algebra\",\"volume\":\"12 1\",\"pages\":\"117-119\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-05-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACM Commun. Comput. Algebra\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/mcom/3363\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM Commun. Comput. Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/mcom/3363","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Computing isomorphisms and embeddings of finite fields
Let q be a prime power and let Fq be a field with q elements. Let f and g be irreducible polynomials in Fq[X], with deg f dividing deg g. Define k = Fq[X]/f and K = Fq[X]/g, then there is an embedding φ : k [EQUATION] K, unique up to Fq-automorphisms of k. Our goal is to describe algorithms to efficiently represent and evaluate one such embedding.
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