{"title":"A condition for associativity of univariate resultants","authors":"D.A. Wolfram","doi":"10.1016/j.exco.2023.100113","DOIUrl":null,"url":null,"abstract":"<div><p>We provide a condition on the occurrences of variables in polynomials and show that it ensures associativity of univariate resultants in non-trivial cases. We give examples involving transformations and arithmetic with the zeros of polynomials. Associativity enables the composition of functions on the zeros of a polynomial by using resultants. The result is generalised to finite systems of polynomials.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"3 ","pages":"Article 100113"},"PeriodicalIF":0.0000,"publicationDate":"2023-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Examples and Counterexamples","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2666657X23000150","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We provide a condition on the occurrences of variables in polynomials and show that it ensures associativity of univariate resultants in non-trivial cases. We give examples involving transformations and arithmetic with the zeros of polynomials. Associativity enables the composition of functions on the zeros of a polynomial by using resultants. The result is generalised to finite systems of polynomials.
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