{"title":"Symbolic computation in algebra, geometry, and differential equations","authors":"Franz Winkler","doi":"10.1016/j.ic.2024.105200","DOIUrl":null,"url":null,"abstract":"<div><p>In this survey article we describe how symbolic computation in algebra and geometry leads to symbolic, i.e., formula solutions of algebraic differential equations. Symbolic solutions of algebraic differential equations can be derived from parametrizations of corresponding algebraic varieties. Such parametrizations in turn can be computed by elimination methods, i.e., methods for solving systems of polynomial equations.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105200"},"PeriodicalIF":0.8000,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0890540124000658/pdfft?md5=0b04bde55234c483e1cb8b3d2f7312e3&pid=1-s2.0-S0890540124000658-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Information and Computation","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0890540124000658","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
In this survey article we describe how symbolic computation in algebra and geometry leads to symbolic, i.e., formula solutions of algebraic differential equations. Symbolic solutions of algebraic differential equations can be derived from parametrizations of corresponding algebraic varieties. Such parametrizations in turn can be computed by elimination methods, i.e., methods for solving systems of polynomial equations.
期刊介绍：
Information and Computation welcomes original papers in all areas of theoretical computer science and computational applications of information theory. Survey articles of exceptional quality will also be considered. Particularly welcome are papers contributing new results in active theoretical areas such as
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Computational complexity-
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Design and analysis of algorithms-
Discrete optimization and mathematical programming-
Inductive inference and learning theory-
Logic & constraint programming-
Program verification & model checking-
Probabilistic & Quantum computation-
Semantics of programming languages-
Symbolic computation, lambda calculus, and rewriting systems-
Types and typechecking
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