University of Tehran
Journal of Algorithms and Computation
2476-2776
53
2
2021
12
01
A variant of van Hoeij's algorithm to compute hypergeometric term solutions of holonomic recurrence equations
1
32
85170
10.22059/jac.2021.85170
EN
Bertrand
Teguia Tabuguia
Department of Mathematics and Natural Sciences, University of Kassel, Heinrich-Plett-Str. 40., Kassel, Germany
0000-0001-9199-7077
Journal Article
2021
12
27
Linear and homogeneous recurrence equations having polynomial coefficients are said to be holonomic. These equations are useful for proving and discovering combinatorial and hypergeometric identities. Given a field $\mathbb{K}$ of characteristic zero, $a_n$ is a hypergeometric term with respect to $\mathbb{K}$, if the ratio $a_{n+1}/a_n$ is a rational function over $\mathbb{K}$. Two algorithms by Marko Petkov\v{s}ek (1993) and Mark van Hoeij (1999) were proposed to compute hypergeometric term solutions of holonomic recurrence equations. The latter algorithm is more efficient and was implemented by its author in the Computer Algebra System (CAS) Maple through the command \texttt{LREtools[hypergeomsols]}. We describe
a variant of van Hoeij's algorithm that performs with the same efficiency without considering certain recommendations of the original version. We implemented our algorithm in the CASes Maxima and Maple. It also appears for some particular cases that our code finds results where \texttt{LREtools[hypergeomsols]} fails.
Our implementation is part of the \texttt{FPS} software which can be downloaded at \url{http://www.mathematik.uni-kassel.de/~bteguia/FPS_webpage/FPS.htm}. The command is \texttt{HypervanHoeij} for Maxima 5.44 and \texttt{rectohyperterm} for Maple 2021.
https://jac.ut.ac.ir/article_85170_fb0789d8c397ce9d958fbd9c4cdaf5eb.pdf