{"title":"实现验证多项式因式分解","authors":"James H. Davenport","doi":"arxiv-2409.09533","DOIUrl":null,"url":null,"abstract":"Computer algebra systems are really good at factoring polynomials, i.e.\nwriting f as a product of irreducible factors. It is relatively easy to verify\nthat we have a factorisation, but verifying that these factors are irreducible\nis a much harder problem. This paper reports work-in-progress to do such\nverification in Lean.","PeriodicalId":501033,"journal":{"name":"arXiv - CS - Symbolic Computation","volume":"66 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Towards Verified Polynomial Factorisation\",\"authors\":\"James H. Davenport\",\"doi\":\"arxiv-2409.09533\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Computer algebra systems are really good at factoring polynomials, i.e.\\nwriting f as a product of irreducible factors. It is relatively easy to verify\\nthat we have a factorisation, but verifying that these factors are irreducible\\nis a much harder problem. This paper reports work-in-progress to do such\\nverification in Lean.\",\"PeriodicalId\":501033,\"journal\":{\"name\":\"arXiv - CS - Symbolic Computation\",\"volume\":\"66 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - CS - Symbolic Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.09533\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Symbolic Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09533","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
计算机代数系统非常擅长对多项式进行因式分解，即把 f 写成不可还原因式的乘积。验证我们是否有因式分解相对容易，但验证这些因式是否不可还原却是一个难得多的问题。本文报告了在 Lean 中进行这种验证的工作进展。
Computer algebra systems are really good at factoring polynomials, i.e.
writing f as a product of irreducible factors. It is relatively easy to verify
that we have a factorisation, but verifying that these factors are irreducible
is a much harder problem. This paper reports work-in-progress to do such
verification in Lean.
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