{"title":"Reduction among bracket polynomials","authors":"Hongbo Li, Changpeng Shao, Lei Huang, Yue Liu","doi":"10.1145/2608628.2608630","DOIUrl":null,"url":null,"abstract":"In this paper, we propose an <i>SL</i>(<i>n</i>)-invariant division of <i>SL</i>(<i>n</i>)-invariant polynomials by establishing an admissible order among the invariant polynomials in normal form. The invariant division leads to an invariant Gröbner basis theory.\n The invariant division is closely related to multivariate coordinate polynomial division. This feature leads to a proof of the result that if <i>f</i><sub>1</sub>,..., <i>f</i><sub><i>k</i></sub> are <i>SL</i>(<i>n</i>,K)-invariant where K is an arbitrary field, possibly of positive characteristic, then the invariant ideal generated by them is the intersection of the ideal generated by the <i>f</i><sub><i>i</i></sub> in the polynomial ring of coordinates with the algebra of invariants.","PeriodicalId":243282,"journal":{"name":"International Symposium on Symbolic and Algebraic Computation","volume":"27 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2014-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Symposium on Symbolic and Algebraic Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/2608628.2608630","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4
Abstract
In this paper, we propose an SL(n)-invariant division of SL(n)-invariant polynomials by establishing an admissible order among the invariant polynomials in normal form. The invariant division leads to an invariant Gröbner basis theory.
The invariant division is closely related to multivariate coordinate polynomial division. This feature leads to a proof of the result that if f1,..., fk are SL(n,K)-invariant where K is an arbitrary field, possibly of positive characteristic, then the invariant ideal generated by them is the intersection of the ideal generated by the fi in the polynomial ring of coordinates with the algebra of invariants.
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