Computation of the difference-differential Galois group and differential relations among solutions for a second-order linear difference equation
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2016
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| _version_ | 1866913745907744768 |
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| author | Arreche, Carlos E. |
| author_facet | Arreche, Carlos E. |
| contents | We apply the difference-differential Galois theory developed by Hardouin and Singer to compute the differential-algebraic relations among the solutions to a second-order homogeneous linear difference equation of the form $ y(x+2)+a(x)y(x+1)+b(x)y(x)=0,$ where the coefficients $a(x),b(x)\in \bar{\mathbb{Q}}(x)$ are rational functions in $x$ with coefficients in $\bar{\mathbb{Q}}$. We develop algorithms to compute the difference-differential Galois group associated to such an equation, and show how to deduce the differential-algebraic relations among the solutions from the defining equations of the Galois group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1606_07109 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Computation of the difference-differential Galois group and differential relations among solutions for a second-order linear difference equation Arreche, Carlos E. Commutative Algebra Algebraic Geometry Dynamical Systems Rings and Algebras 39A10, 39A06, 12H10, 12H05, 20H20 We apply the difference-differential Galois theory developed by Hardouin and Singer to compute the differential-algebraic relations among the solutions to a second-order homogeneous linear difference equation of the form $ y(x+2)+a(x)y(x+1)+b(x)y(x)=0,$ where the coefficients $a(x),b(x)\in \bar{\mathbb{Q}}(x)$ are rational functions in $x$ with coefficients in $\bar{\mathbb{Q}}$. We develop algorithms to compute the difference-differential Galois group associated to such an equation, and show how to deduce the differential-algebraic relations among the solutions from the defining equations of the Galois group. |
| title | Computation of the difference-differential Galois group and differential relations among solutions for a second-order linear difference equation |
| topic | Commutative Algebra Algebraic Geometry Dynamical Systems Rings and Algebras 39A10, 39A06, 12H10, 12H05, 20H20 |
| url | https://arxiv.org/abs/1606.07109 |