Computing the differential Galois group of a parameterized second-order linear differential equation
Computing the differential Galois group of a parameterized second-order linear differential equation
复制标题
计算参数化二阶线性微分方程的微分伽罗瓦群
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Carlos E. Arreche
中科院分区：
文献类型：
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作者：
Carlos E. Arreche
我们开发了计算与以下形式的参数二阶齐次线性微分方程相关的微分Galois群的算法
[方程式]
其中系数r1、r0、∈(Xx)是x中的有理函数，其系数在特征为零的偏微分场中。这项工作依赖于Dreyfus和本作者开发的早期程序来计算当r1=0时G。通过用Galois理论重新解释一个经典的变量变换过程，我们完成了这些算法来计算<i>G</i>而不受<i>r</i><sub>1</sub>的限制。
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
[EQUATION]
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>.