{"title":"On nonnegative invariant quartics in type A","authors":"Sebastian Debus , Charu Goel , Salma Kuhlmann , Cordian Riener","doi":"10.1016/j.jsc.2024.102393","DOIUrl":null,"url":null,"abstract":"<div><div>The equivariant nonnegativity versus sums of squares question has been solved for any infinite series of essential reflection groups but type <em>A</em>. As a first step to a classification, we analyse <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>-invariant quartics. We prove that the cones of invariant sums of squares and nonnegative forms are equal if and only if the number of variables is at most 3 or odd.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Symbolic Computation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S074771712400097X","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
The equivariant nonnegativity versus sums of squares question has been solved for any infinite series of essential reflection groups but type A. As a first step to a classification, we analyse -invariant quartics. We prove that the cones of invariant sums of squares and nonnegative forms are equal if and only if the number of variables is at most 3 or odd.
期刊介绍：
An international journal, the Journal of Symbolic Computation, founded by Bruno Buchberger in 1985, is directed to mathematicians and computer scientists who have a particular interest in symbolic computation. The journal provides a forum for research in the algorithmic treatment of all types of symbolic objects: objects in formal languages (terms, formulas, programs); algebraic objects (elements in basic number domains, polynomials, residue classes, etc.); and geometrical objects.
It is the explicit goal of the journal to promote the integration of symbolic computation by establishing one common avenue of communication for researchers working in the different subareas. It is also important that the algorithmic achievements of these areas should be made available to the human problem-solver in integrated software systems for symbolic computation. To help this integration, the journal publishes invited tutorial surveys as well as Applications Letters and System Descriptions.
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