{"title":"符号积分中的稳定性问题","authors":"Shaoshi Chen","doi":"10.1145/3476446.3535502","DOIUrl":null,"url":null,"abstract":"This paper aims at initializing a dynamical aspect of symbolic integration by studying stability problems in differential fields. We first show some basic properties of stable elementary functions and then characterize three special families of stable elementary functions including rational functions, logarithmic functions, and exponential functions. We prove that all D-finite power series are eventually stable. Some problems for future studies are proposed towards deeper dynamical studies in differential algebra.","PeriodicalId":130499,"journal":{"name":"Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation","volume":"10 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Stability Problems in Symbolic Integration\",\"authors\":\"Shaoshi Chen\",\"doi\":\"10.1145/3476446.3535502\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper aims at initializing a dynamical aspect of symbolic integration by studying stability problems in differential fields. We first show some basic properties of stable elementary functions and then characterize three special families of stable elementary functions including rational functions, logarithmic functions, and exponential functions. We prove that all D-finite power series are eventually stable. Some problems for future studies are proposed towards deeper dynamical studies in differential algebra.\",\"PeriodicalId\":130499,\"journal\":{\"name\":\"Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation\",\"volume\":\"10 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-02-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3476446.3535502\",\"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 2022 International Symposium on Symbolic and Algebraic Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3476446.3535502","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
This paper aims at initializing a dynamical aspect of symbolic integration by studying stability problems in differential fields. We first show some basic properties of stable elementary functions and then characterize three special families of stable elementary functions including rational functions, logarithmic functions, and exponential functions. We prove that all D-finite power series are eventually stable. Some problems for future studies are proposed towards deeper dynamical studies in differential algebra.
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