{"title":"微分标准基的容许序和有限准则","authors":"A. Zobnin","doi":"10.1145/1073884.1073935","DOIUrl":null,"url":null,"abstract":"We prove that any admissible ordering on ordinary differential monomials in one differential indeterminate can be specified by a canonical set of matrices. The relations between some classes of these orderings are studied. We give criteria of finiteness of differential standard bases and propose an algorithm that computes such bases if they are finite.","PeriodicalId":311546,"journal":{"name":"Proceedings of the 2005 international symposium on Symbolic and algebraic computation","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2005-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"17","resultStr":"{\"title\":\"Admissible orderings and finiteness criteria for differential standard bases\",\"authors\":\"A. Zobnin\",\"doi\":\"10.1145/1073884.1073935\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that any admissible ordering on ordinary differential monomials in one differential indeterminate can be specified by a canonical set of matrices. The relations between some classes of these orderings are studied. We give criteria of finiteness of differential standard bases and propose an algorithm that computes such bases if they are finite.\",\"PeriodicalId\":311546,\"journal\":{\"name\":\"Proceedings of the 2005 international symposium on Symbolic and algebraic computation\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2005-07-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"17\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 2005 international symposium on Symbolic and algebraic computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/1073884.1073935\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 2005 international symposium on Symbolic and algebraic computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/1073884.1073935","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Admissible orderings and finiteness criteria for differential standard bases
We prove that any admissible ordering on ordinary differential monomials in one differential indeterminate can be specified by a canonical set of matrices. The relations between some classes of these orderings are studied. We give criteria of finiteness of differential standard bases and propose an algorithm that computes such bases if they are finite.
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