Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation最新文献_第6页

Irredundant Triangular Decomposition 无冗余三角分解

Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation Pub Date : 2018-02-05 DOI: 10.1145/3208976.3208996

G. Pogudin, Á. Szántó

{"title":"Irredundant Triangular Decomposition","authors":"G. Pogudin, Á. Szántó","doi":"10.1145/3208976.3208996","DOIUrl":"https://doi.org/10.1145/3208976.3208996","url":null,"abstract":"Triangular decomposition is a classic, widely used and well-developed way to represent algebraic varieties with many applications. In particular, there exist - sharp degree bounds for a single triangular set in terms of intrinsic data of the variety it represents, - powerful randomized algorithms for computing triangular decompositions using Hensel lifting in the zero-dimensional case and for irreducible varieties. However, in the general case, most of the algorithms computing triangular decompositions produce embedded components, which makes it impossible to directly apply the intrinsic degree bounds. This, in turn, is an obstacle for efficiently applying Hensel lifting due to the higher degrees of the output polynomials and the lower probability of success. In this paper, we give an algorithm to compute an irredundant triangular decomposition of an arbitrary algebraic set W defined by a set of polynomials in C[x1, x2, ..., xn]. Using this irredundant triangular decomposition, we are able to give intrinsic degree bounds for the polynomials appearing in the triangular sets and apply Hensel lifting techniques. Our decomposition algorithm is randomized, and we analyze the probability of success.","PeriodicalId":105762,"journal":{"name":"Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116952878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}