在Macaulay2上证明多项式系统的近似解

ACM Commun. Comput. Algebra Pub Date : 2019-11-08 DOI:10.1145/3371991.3371995

Kisun Lee

{"title":"在Macaulay2上证明多项式系统的近似解","authors":"Kisun Lee","doi":"10.1145/3371991.3371995","DOIUrl":null,"url":null,"abstract":"We present the Macaulay2 package NumericalCertification for certifying roots of square polynomial systems. It employs the interval Krawczyk method and α-theory as main methods for certification. The package works with output data computed in Macaulay2 with no need for external software. Also, our implementation supports the Krawczyk method which uses interval arithmetic.","PeriodicalId":7093,"journal":{"name":"ACM Commun. Comput. Algebra","volume":"11 1","pages":"45-48"},"PeriodicalIF":0.0000,"publicationDate":"2019-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":"{\"title\":\"Certifying approximate solutions to polynomial systems on Macaulay2\",\"authors\":\"Kisun Lee\",\"doi\":\"10.1145/3371991.3371995\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present the Macaulay2 package NumericalCertification for certifying roots of square polynomial systems. It employs the interval Krawczyk method and α-theory as main methods for certification. The package works with output data computed in Macaulay2 with no need for external software. Also, our implementation supports the Krawczyk method which uses interval arithmetic.\",\"PeriodicalId\":7093,\"journal\":{\"name\":\"ACM Commun. Comput. Algebra\",\"volume\":\"11 1\",\"pages\":\"45-48\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-11-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACM Commun. Comput. Algebra\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3371991.3371995\",\"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/10.1145/3371991.3371995","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 8

摘要

我们提出了Macaulay2包数字认证，用于验证平方多项式系统的根。它采用区间Krawczyk法和α-理论作为主要的证明方法。该软件包使用Macaulay2计算的输出数据，不需要外部软件。此外，我们的实现支持使用区间算法的Krawczyk方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Certifying approximate solutions to polynomial systems on Macaulay2

We present the Macaulay2 package NumericalCertification for certifying roots of square polynomial systems. It employs the interval Krawczyk method and α-theory as main methods for certification. The package works with output data computed in Macaulay2 with no need for external software. Also, our implementation supports the Krawczyk method which uses interval arithmetic.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

ACM Commun. Comput. Algebra

自引率

0.00%

发文量

期刊最新文献

Multivariate ore polynomials in SageMath Certifying operator identities via noncommutative Gröbner bases A Kenzo interface for algebraic topology computations in SageMath The conference "computer algebra" in Moscow Computing generic bivariate Gröbner bases with Mathemagix