{"title":"多项式因式分解","authors":"René Thiemann, A. Yamada","doi":"10.1201/b11066-19","DOIUrl":null,"url":null,"abstract":"This invited talk presents some developments in the history of factoring polynomials. We restrict our discussion to univariate polynomials over the integers or the integers modulo a prime, and do not strive for completeness. In the beginning was root-finding. The Babylonians had numerical algorithms for solving quadratic equations, around 1900–1600 BC. Somewhat later, they also solved cubic equations of the form ax + bx = c numerically, and had mastered quadratics symbolically. For example, to solve","PeriodicalId":280633,"journal":{"name":"Arch. Formal Proofs","volume":"25 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Polynomial Factorization\",\"authors\":\"René Thiemann, A. Yamada\",\"doi\":\"10.1201/b11066-19\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This invited talk presents some developments in the history of factoring polynomials. We restrict our discussion to univariate polynomials over the integers or the integers modulo a prime, and do not strive for completeness. In the beginning was root-finding. The Babylonians had numerical algorithms for solving quadratic equations, around 1900–1600 BC. Somewhat later, they also solved cubic equations of the form ax + bx = c numerically, and had mastered quadratics symbolically. For example, to solve\",\"PeriodicalId\":280633,\"journal\":{\"name\":\"Arch. Formal Proofs\",\"volume\":\"25 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Arch. Formal Proofs\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1201/b11066-19\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Arch. Formal Proofs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1201/b11066-19","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
This invited talk presents some developments in the history of factoring polynomials. We restrict our discussion to univariate polynomials over the integers or the integers modulo a prime, and do not strive for completeness. In the beginning was root-finding. The Babylonians had numerical algorithms for solving quadratic equations, around 1900–1600 BC. Somewhat later, they also solved cubic equations of the form ax + bx = c numerically, and had mastered quadratics symbolically. For example, to solve
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