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| ====== Hypergeometric solutions for linear difference systems ====== | ====== Hypergeometric solutions for linear difference systems ====== | ||
| - | The procedure **HypergeometricSolution** in the package **LRS** (Linear Recurrence Systems) is an implementation in Maple 2015 of an algorithm to construct a general __hypergeometric__ solutions for systems of linear recurrence equations with rational-function coefficients and hypergeometric right-hand sides. | + | The procedure **HypergeometricSolution** in the package **LRS** (Linear Recurrence Systems) is an implementation in Maple 2018 of an algorithm to construct a general __hypergeometric__ solutions for systems of linear recurrence equations with rational-function coefficients and hypergeometric right-hand sides. |
| - | Additionally, a procedure **RationalSolution** construct a general rational solutions for systems of linear recurrence equations with rational-function coefficients and rational-function right-hand sides. | + | The details can be found in the paper [[https://link.springer.com/article/10.1134/S0361768819020099|A.A. Ryabenko. Particular solutions of linear differential and (q-) difference systems with hypergeometric right-hand sides // Programming and computer software. 2019. Vol. 45. No. 5. P. 298--302]]. |
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| + | Additionally, a procedure **RationalSolution** construct a general rational solutions for systems of linear recurrence equations with rational-function coefficients and rational-function right-hand sides. | ||
| ===== A system can be represented in several forms. ===== | ===== A system can be represented in several forms. ===== | ||
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| where | where | ||
| - | * **A(x)** is a matrix whose entries are rational functions of **x**. | + | * **A(x)** is a matrix whose entries are rational functions in **x**. |
| ===== Source ===== | ===== Source ===== | ||
| - | {{:lrshypergeomsols.mpl|lrshypergeomsols.mpl}} - the Maple code of the package (implemented by A.A.Ryabenko in May, 2018). | + | {{:lrshypergeomsols.mpl|lrshypergeomsols.mpl}} - the Maple code of the package (implemented by A.A.Ryabenko). |
| - | {{:lrs_exapmles_2018.mw|lrs_exapmles_2018.mw}} - the Maple session file with examples. | + | {{:lrs_exapmles_2018.mw|lrs_exapmles_2018.mw}} - the Maple session file with examples to construct hypergeometric solutions for homogeneous and inhomogeneous systems. |
| {{:lrs_exapmles_2018.pdf|lrs_exapmles_2018.pdf}} - the pdf copy of that Maple session. | {{:lrs_exapmles_2018.pdf|lrs_exapmles_2018.pdf}} - the pdf copy of that Maple session. | ||
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| The algorithm is based on the use of resolving sequences. | The algorithm is based on the use of resolving sequences. | ||
| - | The details can be found in the paper [[http://www.ccas.ru/sabramov/ps/resolving2016_13_06.pdf|S.A.Abramov, M.Petkovšek, A.A.Ryabenko. Resolving sequences of operators for linear ordinary differential and difference systems. Computational Mathematics and Mathematical Physics, 2016, Vol. 56, Issue. 5, P. 894–910.]] | + | The details can be found in the paper [[https://link.springer.com/article/10.1134/S096554251605002X|S.A.Abramov, M.Petkovšek, A.A.Ryabenko. Resolving sequences of operators for linear ordinary differential and difference systems of arbitrary order. Computational Mathematics and Mathematical Physics, 2016, Vol. 56, Issue. 5, P. 894–910.]] |
| Source: | Source: | ||
| - | {{:lrshypergeomsols2016.mpl|lrshypergeomsols2016.mpl}} - the Maple code of the package (implemented by A.A.Ryabenko in 2016). | + | {{:lrshypergeomsols.mpl|lrshypergeomsols.mpl}} - the Maple code of the package (implemented by A.A.Ryabenko). |
| {{:paper_examples_hs.mw|Paper_Examples_HS.mw}} - the Maple session file with examples from the paper. | {{:paper_examples_hs.mw|Paper_Examples_HS.mw}} - the Maple session file with examples from the paper. | ||
| Line 56: | Line 58: | ||
| {{:hypergeometricsolution.pdf|hypergeometricsolution.pdf}} - the pdf-copy of that Maple session; | {{:hypergeometricsolution.pdf|hypergeometricsolution.pdf}} - the pdf-copy of that Maple session; | ||
| - | {{:slides.pdf|slides.pdf}} - the slides of the talk [[http://compalg.jinr.ru/Dubna2015/abstracts2015_files/1218%20Ryabenko.pdf|S.A. Abramov, M. Petkovšek, A.A. Ryabenko "Hypergeometric Solutions of First-Order Linear Difference Systems with Rational-Function Coefficients"]] in [[http://compalg.jinr.ru/Dubna2015/index.html|The 18th workshop on computer algebra, May 26-27, 2015, Dubna]] | + | {{:slides.pdf|slides.pdf}} - the slides of the talk [[http://compalg.jinr.ru/Dubna2015/abstracts2015_files/1218%20Ryabenko.pdf|S.A. Abramov, M. Petkovšek, A.A. Ryabenko "Hypergeometric Solutions of First-Order Linear Difference Systems with Rational-Function Coefficients"]] in [[http://compalg.jinr.ru/Dubna2015/index.html|The 18th workshop on computer algebra, May 26-27, 2015, Dubna]] |
| - | and of the talk [[http://link.springer.com/chapter/10.1007/978-3-319-24021-3_1|S.A. Abramov, M. Petkovšek, A.A. Ryabenko "Hypergeometric Solutions of First-Order Linear Difference Systems with Rational-Function Coefficients"]] in | + | and of the talk [[http://link.springer.com/chapter/10.1007/978-3-319-24021-3_1|S.A. Abramov, M. Petkovšek, A.A. Ryabenko "Hypergeometric Solutions of First-Order Linear Difference Systems with Rational-Function Coefficients"]] in |
| [[http://www.casc.cs.uni-bonn.de/2015/|The 17th international workshop on computer algebra in scientific computing, September 14-18, 2015, Aachen, Germany]]; | [[http://www.casc.cs.uni-bonn.de/2015/|The 17th international workshop on computer algebra in scientific computing, September 14-18, 2015, Aachen, Germany]]; | ||