{"title":"关于消去理论的注释","authors":"Piotr Pragacz","doi":"10.1016/S1385-7258(87)80041-0","DOIUrl":null,"url":null,"abstract":"<div><p>We consider certain generalisation of the resultant of two polynomials in one variable. Using the Schur symmetricfunctions we describe the ideal of all polynomials in the coefficients of two equations, which vanish if these equations have<em>r</em>+1 roots in common, where <em>r</em>≥0. We discuss also related (classical)criterions giving the conditions when two equations have <em>r</em>+1 roots in common, where <em>r</em>≥0.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"90 2","pages":"Pages 215-221"},"PeriodicalIF":0.0000,"publicationDate":"1987-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(87)80041-0","citationCount":"8","resultStr":"{\"title\":\"A note on the elimination theory\",\"authors\":\"Piotr Pragacz\",\"doi\":\"10.1016/S1385-7258(87)80041-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We consider certain generalisation of the resultant of two polynomials in one variable. Using the Schur symmetricfunctions we describe the ideal of all polynomials in the coefficients of two equations, which vanish if these equations have<em>r</em>+1 roots in common, where <em>r</em>≥0. We discuss also related (classical)criterions giving the conditions when two equations have <em>r</em>+1 roots in common, where <em>r</em>≥0.</p></div>\",\"PeriodicalId\":100664,\"journal\":{\"name\":\"Indagationes Mathematicae (Proceedings)\",\"volume\":\"90 2\",\"pages\":\"Pages 215-221\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1987-06-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S1385-7258(87)80041-0\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Indagationes Mathematicae (Proceedings)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1385725887800410\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indagationes Mathematicae (Proceedings)","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1385725887800410","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We consider certain generalisation of the resultant of two polynomials in one variable. Using the Schur symmetricfunctions we describe the ideal of all polynomials in the coefficients of two equations, which vanish if these equations haver+1 roots in common, where r≥0. We discuss also related (classical)criterions giving the conditions when two equations have r+1 roots in common, where r≥0.
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