{"title":"代数常微分方程的代数通解","authors":"J. M. Aroca, J. Cano, Ruyong Feng, X. Gao","doi":"10.1145/1073884.1073891","DOIUrl":null,"url":null,"abstract":"In this paper, we give a necessary and sufficient condition for an algebraic ODE to have an algebraic general solution. For a first order autonomous ODE, we give an optimal bound for the degree of its algebraic general solutions and a polynomial-time algorithm to compute an algebraic general solution if it exists. Here an algebraic ODE means that an ODE given by a differential polynomial.","PeriodicalId":311546,"journal":{"name":"Proceedings of the 2005 international symposium on Symbolic and algebraic computation","volume":"36 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2005-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"32","resultStr":"{\"title\":\"Algebraic general solutions of algebraic ordinary differential equations\",\"authors\":\"J. M. Aroca, J. Cano, Ruyong Feng, X. Gao\",\"doi\":\"10.1145/1073884.1073891\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we give a necessary and sufficient condition for an algebraic ODE to have an algebraic general solution. For a first order autonomous ODE, we give an optimal bound for the degree of its algebraic general solutions and a polynomial-time algorithm to compute an algebraic general solution if it exists. Here an algebraic ODE means that an ODE given by a differential polynomial.\",\"PeriodicalId\":311546,\"journal\":{\"name\":\"Proceedings of the 2005 international symposium on Symbolic and algebraic computation\",\"volume\":\"36 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2005-07-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"32\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 2005 international symposium on Symbolic and algebraic computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/1073884.1073891\",\"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/10.1145/1073884.1073891","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Algebraic general solutions of algebraic ordinary differential equations
In this paper, we give a necessary and sufficient condition for an algebraic ODE to have an algebraic general solution. For a first order autonomous ODE, we give an optimal bound for the degree of its algebraic general solutions and a polynomial-time algorithm to compute an algebraic general solution if it exists. Here an algebraic ODE means that an ODE given by a differential polynomial.
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