{"title":"线性微分系统形式不变量的计算算法","authors":"A. Hilali, A. Wazner","doi":"10.1145/32439.32478","DOIUrl":null,"url":null,"abstract":"This paper deals with the system of n linear differential equations (*) y'(x) = A(x)y where A(x) is a matrix with formal series coefficients. A sequence of formal invariants related to (*) is defined. An algorithm which reduces (*) by means of meromorphic transformations to a “super-irreducible” form is given. The computation of these invariants follows directly from this form. This algorithm is implemented in Reduce.","PeriodicalId":314618,"journal":{"name":"Symposium on Symbolic and Algebraic Manipulation","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1986-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Algorithm for computing formal invariants of linear differential systems\",\"authors\":\"A. Hilali, A. Wazner\",\"doi\":\"10.1145/32439.32478\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper deals with the system of n linear differential equations (*) y'(x) = A(x)y where A(x) is a matrix with formal series coefficients. A sequence of formal invariants related to (*) is defined. An algorithm which reduces (*) by means of meromorphic transformations to a “super-irreducible” form is given. The computation of these invariants follows directly from this form. This algorithm is implemented in Reduce.\",\"PeriodicalId\":314618,\"journal\":{\"name\":\"Symposium on Symbolic and Algebraic Manipulation\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1986-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Symposium on Symbolic and Algebraic Manipulation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/32439.32478\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Symposium on Symbolic and Algebraic Manipulation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/32439.32478","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Algorithm for computing formal invariants of linear differential systems
This paper deals with the system of n linear differential equations (*) y'(x) = A(x)y where A(x) is a matrix with formal series coefficients. A sequence of formal invariants related to (*) is defined. An algorithm which reduces (*) by means of meromorphic transformations to a “super-irreducible” form is given. The computation of these invariants follows directly from this form. This algorithm is implemented in Reduce.
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