Fast Straightening Algorithm for Bracket Polynomials Based on Tableau Manipulations

Changpeng Shao, Hongbo Li
{"title":"Fast Straightening Algorithm for Bracket Polynomials Based on Tableau Manipulations","authors":"Changpeng Shao, Hongbo Li","doi":"10.1145/3208976.3208978","DOIUrl":null,"url":null,"abstract":"Straightening is the most fundamental symbolic manipulation in bracket algebra. Young's classical algorithm and White's more recent algorithm have poor performance in straightening bracket polynomials of degree >4. Rota's straightening algorithm based on Capelli operator is generally superior to the former two in speed, but still performs badly when the degree reaches 5. In this paper, a new operator is defined in bracket algebra based on tableau manipulations, and is simpler than Capelli operator. A new straightening algorithm is then proposed, and is superior to the above three algorithms by a speedup of two order of magnitude on average by testing over 500 examples in the past two years.","PeriodicalId":105762,"journal":{"name":"Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation","volume":"40 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3208976.3208978","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

Straightening is the most fundamental symbolic manipulation in bracket algebra. Young's classical algorithm and White's more recent algorithm have poor performance in straightening bracket polynomials of degree >4. Rota's straightening algorithm based on Capelli operator is generally superior to the former two in speed, but still performs badly when the degree reaches 5. In this paper, a new operator is defined in bracket algebra based on tableau manipulations, and is simpler than Capelli operator. A new straightening algorithm is then proposed, and is superior to the above three algorithms by a speedup of two order of magnitude on average by testing over 500 examples in the past two years.
基于Tableau操作的支架多项式快速矫直算法
矫直是括号代数中最基本的符号操作。Young的经典算法和White的最新算法在矫直次数大于4的括号多项式时表现不佳。基于Capelli算子的Rota矫直算法在速度上总体优于前两种,但在度达到5时仍然表现不佳。本文在括号代数中定义了一种新的基于表操作的算子,它比Capelli算子更简单。在此基础上提出了一种新的矫直算法,经过两年500多例的测试,该算法的平均速度比上述三种算法提高了两个数量级。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信