{"title":"Isabelle/HOL中单变量实多项式的一个决策过程","authors":"Manuel Eberl","doi":"10.1145/2676724.2693166","DOIUrl":null,"url":null,"abstract":"Sturm sequences are a method for computing the number of real roots of a univariate real polynomial inside a given interval efficiently. In this paper, this fact and a number of methods to construct Sturm sequences efficiently have been formalised with the interactive theorem prover Isabelle/HOL. Building upon this, an Isabelle/HOL proof method was then implemented to prove interesting statements about the number of real roots of a univariate real polynomial and related properties such as non-negativity and monotonicity.","PeriodicalId":187702,"journal":{"name":"Proceedings of the 2015 Conference on Certified Programs and Proofs","volume":"81 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2015-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"20","resultStr":"{\"title\":\"A Decision Procedure for Univariate Real Polynomials in Isabelle/HOL\",\"authors\":\"Manuel Eberl\",\"doi\":\"10.1145/2676724.2693166\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Sturm sequences are a method for computing the number of real roots of a univariate real polynomial inside a given interval efficiently. In this paper, this fact and a number of methods to construct Sturm sequences efficiently have been formalised with the interactive theorem prover Isabelle/HOL. Building upon this, an Isabelle/HOL proof method was then implemented to prove interesting statements about the number of real roots of a univariate real polynomial and related properties such as non-negativity and monotonicity.\",\"PeriodicalId\":187702,\"journal\":{\"name\":\"Proceedings of the 2015 Conference on Certified Programs and Proofs\",\"volume\":\"81 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-01-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"20\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 2015 Conference on Certified Programs and Proofs\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/2676724.2693166\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 2015 Conference on Certified Programs and Proofs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/2676724.2693166","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A Decision Procedure for Univariate Real Polynomials in Isabelle/HOL
Sturm sequences are a method for computing the number of real roots of a univariate real polynomial inside a given interval efficiently. In this paper, this fact and a number of methods to construct Sturm sequences efficiently have been formalised with the interactive theorem prover Isabelle/HOL. Building upon this, an Isabelle/HOL proof method was then implemented to prove interesting statements about the number of real roots of a univariate real polynomial and related properties such as non-negativity and monotonicity.
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