{"title":"Computing the differential Galois group of a parameterized second-order linear differential equation","authors":"Carlos E. Arreche","doi":"10.1145/2608628.2608680","DOIUrl":null,"url":null,"abstract":"We develop algorithms to compute the differential Galois group <i>G</i> associated to a parameterized second-order homogeneous linear differential equation of the form\n [EQUATION]\n where the coefficients <i>r</i><sub>1</sub>, <i>r</i><sub>0</sub> ∈ <i>F</i>(<i>x</i>) are rational functions in <i>x</i> with coefficients in a partial differential field <i>F</i> of characteristic zero. This work relies on earlier procedures developed by Dreyfus and by the present author to compute <i>G</i> when <i>r</i><sub>1</sub> = 0. By reinterpreting a classical change-of-variables procedure in Galois-theoretic terms, we complete these algorithms to compute <i>G</i> with no restrictions on <i>r</i><sub>1</sub>.","PeriodicalId":243282,"journal":{"name":"International Symposium on Symbolic and Algebraic Computation","volume":"33 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2014-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Symposium on Symbolic and Algebraic Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/2608628.2608680","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 11
Abstract
We develop algorithms to compute the differential Galois group G associated to a parameterized second-order homogeneous linear differential equation of the form
[EQUATION]
where the coefficients r1, r0 ∈ F(x) are rational functions in x with coefficients in a partial differential field F of characteristic zero. This work relies on earlier procedures developed by Dreyfus and by the present author to compute G when r1 = 0. By reinterpreting a classical change-of-variables procedure in Galois-theoretic terms, we complete these algorithms to compute G with no restrictions on r1.
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