{"title":"有限域及其循环子群的标准生成器","authors":"Frank Lübeck","doi":"10.1016/j.jsc.2022.11.001","DOIUrl":null,"url":null,"abstract":"<div><p>We define standard constructions of finite fields, and standard generators of (multiplicative) cyclic subgroups in these fields.</p><p>The motivation is to provide a substitute for Conway polynomials which can be used by various software packages and in collections of mathematical data which involve finite fields.</p></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"117 ","pages":"Pages 51-67"},"PeriodicalIF":1.1000,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Standard generators of finite fields and their cyclic subgroups\",\"authors\":\"Frank Lübeck\",\"doi\":\"10.1016/j.jsc.2022.11.001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We define standard constructions of finite fields, and standard generators of (multiplicative) cyclic subgroups in these fields.</p><p>The motivation is to provide a substitute for Conway polynomials which can be used by various software packages and in collections of mathematical data which involve finite fields.</p></div>\",\"PeriodicalId\":50031,\"journal\":{\"name\":\"Journal of Symbolic Computation\",\"volume\":\"117 \",\"pages\":\"Pages 51-67\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2023-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Symbolic Computation\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0747717122001146\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Symbolic Computation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0747717122001146","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
Standard generators of finite fields and their cyclic subgroups
We define standard constructions of finite fields, and standard generators of (multiplicative) cyclic subgroups in these fields.
The motivation is to provide a substitute for Conway polynomials which can be used by various software packages and in collections of mathematical data which involve finite fields.
期刊介绍：
An international journal, the Journal of Symbolic Computation, founded by Bruno Buchberger in 1985, is directed to mathematicians and computer scientists who have a particular interest in symbolic computation. The journal provides a forum for research in the algorithmic treatment of all types of symbolic objects: objects in formal languages (terms, formulas, programs); algebraic objects (elements in basic number domains, polynomials, residue classes, etc.); and geometrical objects.
It is the explicit goal of the journal to promote the integration of symbolic computation by establishing one common avenue of communication for researchers working in the different subareas. It is also important that the algorithmic achievements of these areas should be made available to the human problem-solver in integrated software systems for symbolic computation. To help this integration, the journal publishes invited tutorial surveys as well as Applications Letters and System Descriptions.
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