{"title":"实单变量三次和四分次的根构型","authors":"E. González, D. Weinberg","doi":"10.12988/IMF.2021.912181","DOIUrl":null,"url":null,"abstract":"For the general monic cubic and quartic with real coefficients, polynomial conditions on the coefficients are derived as directly and as simply as possible from the Sturm sequence that will determine the real and complex root multiplicities together with the order of the real roots with respect to multiplicity.","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2015-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Root configurations of real univariate cubics and quartics\",\"authors\":\"E. González, D. Weinberg\",\"doi\":\"10.12988/IMF.2021.912181\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For the general monic cubic and quartic with real coefficients, polynomial conditions on the coefficients are derived as directly and as simply as possible from the Sturm sequence that will determine the real and complex root multiplicities together with the order of the real roots with respect to multiplicity.\",\"PeriodicalId\":107214,\"journal\":{\"name\":\"International Mathematical Forum\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-11-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Mathematical Forum\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12988/IMF.2021.912181\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Mathematical Forum","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12988/IMF.2021.912181","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Root configurations of real univariate cubics and quartics
For the general monic cubic and quartic with real coefficients, polynomial conditions on the coefficients are derived as directly and as simply as possible from the Sturm sequence that will determine the real and complex root multiplicities together with the order of the real roots with respect to multiplicity.