Austin Conner , Mateusz Michałek , Michael Schindler , Balázs Szendrői
{"title":"允许同时解的多项式系统","authors":"Austin Conner , Mateusz Michałek , Michael Schindler , Balázs Szendrői","doi":"10.1016/j.jalgebra.2024.12.015","DOIUrl":null,"url":null,"abstract":"<div><div>We provide a description of a complete set of generators for the ideal that serves as the resultant ideal for <em>n</em> univariate polynomials of degree <em>d</em>. Our generators arise as maximal minors of a set of cascading matrices formed from the coefficients of the polynomials, generalizing the classical Sylvester resultant of two polynomials.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"667 ","pages":"Pages 412-424"},"PeriodicalIF":0.8000,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Polynomial systems admitting a simultaneous solution\",\"authors\":\"Austin Conner , Mateusz Michałek , Michael Schindler , Balázs Szendrői\",\"doi\":\"10.1016/j.jalgebra.2024.12.015\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We provide a description of a complete set of generators for the ideal that serves as the resultant ideal for <em>n</em> univariate polynomials of degree <em>d</em>. Our generators arise as maximal minors of a set of cascading matrices formed from the coefficients of the polynomials, generalizing the classical Sylvester resultant of two polynomials.</div></div>\",\"PeriodicalId\":14888,\"journal\":{\"name\":\"Journal of Algebra\",\"volume\":\"667 \",\"pages\":\"Pages 412-424\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2025-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021869324006902\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2025/1/6 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021869324006902","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/1/6 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Polynomial systems admitting a simultaneous solution
We provide a description of a complete set of generators for the ideal that serves as the resultant ideal for n univariate polynomials of degree d. Our generators arise as maximal minors of a set of cascading matrices formed from the coefficients of the polynomials, generalizing the classical Sylvester resultant of two polynomials.
期刊介绍：
The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.
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