{"title":"差分算子的快速分解算法","authors":"Yi Zhou, M. V. Hoeij","doi":"10.1145/3377006.3377023","DOIUrl":null,"url":null,"abstract":"Beke (1894) gave an algorithm that factors any differential operator and that algorithm can be used for difference operators as well. Bronstein improved Beke’s algorithm (see [2]). To find an order-m right-hand factor of an order-n operator using Beke-Bronstein’s algorithm, we need to create a difference system of order N = ( n m ) and solve that system. Experiments show that this is practical for n ≤ 8, or n = 9 if m ≤ 3, but beyond that N becomes too large. Our goal is a new method to find factors without increasing the order.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"53 1","pages":"150 - 152"},"PeriodicalIF":0.4000,"publicationDate":"2019-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1145/3377006.3377023","citationCount":"1","resultStr":"{\"title\":\"Fast algorithm for factoring difference operators\",\"authors\":\"Yi Zhou, M. V. Hoeij\",\"doi\":\"10.1145/3377006.3377023\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Beke (1894) gave an algorithm that factors any differential operator and that algorithm can be used for difference operators as well. Bronstein improved Beke’s algorithm (see [2]). To find an order-m right-hand factor of an order-n operator using Beke-Bronstein’s algorithm, we need to create a difference system of order N = ( n m ) and solve that system. Experiments show that this is practical for n ≤ 8, or n = 9 if m ≤ 3, but beyond that N becomes too large. Our goal is a new method to find factors without increasing the order.\",\"PeriodicalId\":41965,\"journal\":{\"name\":\"ACM Communications in Computer Algebra\",\"volume\":\"53 1\",\"pages\":\"150 - 152\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2019-12-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1145/3377006.3377023\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACM Communications in Computer Algebra\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3377006.3377023\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM Communications in Computer Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3377006.3377023","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Beke (1894) gave an algorithm that factors any differential operator and that algorithm can be used for difference operators as well. Bronstein improved Beke’s algorithm (see [2]). To find an order-m right-hand factor of an order-n operator using Beke-Bronstein’s algorithm, we need to create a difference system of order N = ( n m ) and solve that system. Experiments show that this is practical for n ≤ 8, or n = 9 if m ≤ 3, but beyond that N becomes too large. Our goal is a new method to find factors without increasing the order.
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