Differences

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--- lfs [2018/08/12 12:04]
anna [A system can be represented in several forms.]
+++ lfs [2024/03/06 12:10] (current)
anna
@@ Line 1: / Line 1: @@
-====== Hypergeometric solutions for linear functional systems ======
+====== Solutions for linear functional systems ======
-The procedure **HypergeometricSolution** in the package **LFS**  (Linear Functional Systems) is an implementation in Maple 2018 of an algorithm to construct a partial __hypergeometric__ solutions for inhomogeneous systems of linear differential, difference and q-difference equations with rational-function coefficients and hypergeometric right-hand sides.
+The LFS package is for solving Linear Functional (differential, difference and q-difference) Systems of equations.
-Additionally, a procedure **RationalSolution** construct a partial rational solutions for systems with rational-function coefficients and rational-function right-hand sides.
+The procedure **RationalSolution** is an implementation in Maple 2020 of two algorithms to construct a basis of rational-function solutions for homogeneous systems with rational-function coefficients and a particular solution for inhomogeneous systems with rational-function right-hand sides. See for detail in {{:2020_12_02_slides.pdf|the slides of the talk S. Abramov, D.Khmelnov, A.Ryabenko «Searching for rational solutions of linear ordinary difference and differential systems: schemes equipped with checkpoints»}} in [[https://www.youtube.com/playlist?list=PLOaW8o20mEgjGbDZxLazmmwCasbpuhjLY|The conference "Программирование и вычислительная математика" памяти Н. П. Трифонова (1925–2020)]]. See also the abstract of this talk in pages 12-13 of   [[https://elibrary.ru/item.asp?id=44323701|Программирование и вычислительная математика. тезисы докладов конференции памяти Н. П. Трифонова / под ред. С. А. Абрамова, А. В. Столярова. – Москва : МАКС Пресс, 2020.]]
-===== A system can be represented in several forms. =====
+The procedure **HypergeometricSolution** is an implementation in Maple 2020 of an algorithm to construct a particular __hypergeometric__ solutions for inhomogeneous systems with rational-function coefficients and hypergeometric right-hand sides. See for detail in [[https://doi.org/10.1134/S0361768819020099|Ryabenko A.A. 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]]
+The procedure **LaurentSolution** is a draft implementation in Maple2023 of an algorithm to construct Laurent series solutions for homogeneous differential systems with polynomial or power series coefficients (implemented by A.A.Ryabenko, D.E.Khmelnov).
+===== Source =====
+{{:lfs.zip|lfs.zip}} – the archive with two files: lfs.ind and lfs.lib are a Maple library.
+Put these files to some directory, for example to "/usr/userlib".
+Assign **libname := "/usr/userlib", libname:** in the Maple session.
+===== A system can be represented in several forms =====
 The __matrix form__ of a full-rank system:
@@ Line 13: / Line 25: @@
 where
-   * **Ai(x)** are matrices whose entries are rational functions of **x**;
+   * **Ai(x)** are matrices whose entries are rational functions or power series of **x**;
    * **b(x)** is a column vector of finite sums of hypergeometric terms of **x**;
    * **y(x)** is a column vector of unknown functions;
@@ Line 32: / Line 44: @@
 For the q-difference case: **ξ(y(x)) = y(q x)**, where **q** is a name or an integer large then **1**.
-===== Source =====
-{{:lfs.mpl|lfs.mpl}} - the Maple code of the package (implemented by A.A.Ryabenko, D.E.Khmelnov).
+===== The procedures LaurentSolution and InducedRecurrence (a draft version) =====
+{{:essay_on_laurent_solution.mw|essay_on_laurent_solution.mw}} - сессия Maple 2023 с примерами из [[http://www.ccas.ru/ca/essay_on_laurent_solution.html|Эссе о лорановых решениях линейных дифференциальных систем]]
+{{:lfs_laurentsolution_examples.mw|lfs_laurentsolution_examples.mw}} - the Maple 2023 session file with Laurent solution examples.
+{{:lfs_laurentsolution_examples.pdf|lfs_laurentsolution_examples.pdf}} - the pdf copy of that Maple session.
+===== Two algorithms to construct rational solutions =====
+The optional argument of **RationalSolution** and **HypergeometricSolution** may be
+  * **'earlyterminate' = true**, the rational solution's algorithm with checkpoints is used, the algorithms from [[https://doi.org/10.1007/978-3-030-44559-1_1|Abramov S.A. When the Search for Solutions Can Be Terminated // In: Pillwein V., Schneider C. (eds) Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra. In Honour of Peter Paule on his 60th Birthday.Springer, Cham. 2020. P. 1–7.]] and from [[https://doi.org/10.1145/3427218.3427219|Abramov S.A., Khmelnov D.E., Ryabenko A.A. Checkpoints in searching for rational solutions of linear ordinary difference and differential systems // ACM Communications in Computer Algebra. 2020. Vol. 54. Issue 2. P. 18–29]] are used.
+  * **'earlyterminate' = false**, the algorithm from [[http://www.ccas.ru/sabramov/ps/prog12e.pdf|Abramov S.A., Khmelnov D.E. Denominators of rational solutions of linear difference systems of an arbitrary order. Progr. and Comp. Softwr, No 2, 2012, pp. 84-91]] is used.
+The default is  **'earlyterminate' = true**.
+{{:lfs_rational_examples.mw|lfs_rational_examples.mw}} - the Maple session file with rational solutions examples.
+{{:lfs_rational_examples.pdf|lfs_rational_examples.pdf}} - the pdf copy of that Maple session.
+===== The procedures HypergeometricSolution for inhomogeneous systems =====
-{{:lfs_examples.mw|lfs_examples.mw}} - the Maple session file with examples.
+{{:lfs_examples.mw|lfs_examples.mw}} - the Maple session file with hypergeometric examples.
 {{:lfs_examples.pdf|lfs_examples.pdf}} - the pdf copy of that Maple session.