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HolonomicFunctions

swMATH ID: 6666
Software Authors: Christoph Koutschan
Description: The HolonomicFunctions package by Christoph Koutschan allows to deal with multivariate holonomic functions and sequences in an algorithmic fashion. For this purpose the package can compute annihilating ideals and execute closure properties (addition, multiplication, substitutions) for such functions. An annihilating ideal represents the set of linear differential equations, linear recurrences, q-difference equations, and mixed linear equations that a given function satisfies. Summation and integration of multivariate holonomic functions can be performed via creative telescoping. As subtasks, the following functionalities have been implemented in HolonomicFunctions: computations in Ore algebras (noncommutative polynomial arithmetic with mixed difference-differential operators), noncommutative Gröbner bases, and solving of coupled linear systems of differential or difference equations.
Homepage: http://www.risc.jku.at/research/combinat/software/HolonomicFunctions/
Dependencies: Mathematica
Keywords: integrals; automatic proofs
Related Software: Mathematica; SINGULAR; gfun; Plural; OEIS; DLMF; OreTools; SageMath; SIGMA; DET; ore_algebra; olga.lib; DODGSON; Axodraw; HarmonicSums; Asymptotics; SumCracker; Knot Atlas; JAS; FORM
Referenced in: 54 Publications
Further Publications: http://www.risc.jku.at/publications/

Standard Articles

2 Publications describing the Software, including 1 Publication in zbMATH Year
Holonomic functions in Mathematica
Koutschan, Christoph
2013
The integrals in Gradshteyn and Ryzhik. XVIII: Some automatic proofs. Zbl 1244.33024
Koutschan, Christoph; Moll, Victor H.
2010
all top 5

Referenced by 76 Authors

20 Koutschan, Christoph
7 Kauers, Manuel
5 Blümlein, Johannes
5 Pillwein, Veronika
4 Moll, Victor Hugo
4 Raab, Clemens G.
4 Thanatipanonda, Thotsaporn (Aek)
3 Bostan, Alin
3 Garoufalidis, Stavros
3 Jiu, Lin
3 Levandovskyy, Viktor
3 Schönwald, K.
3 Wong, Elaine
3 Zhang, Yi
2 Beuchler, Sven
2 Chen, Shaoshi
2 Combot, Thierry
2 De Freitas, Abilio
2 Hoffmann, Johannes
2 Johansson, Fredrik
2 Maillard, Jean-Marie
2 Melczer, Stephen
2 Paule, Peter
2 Quadrat, Alban
2 Radu, Cristian-Silviu
2 Schneider, Carsten
2 Zaglmayr, Sabine
1 Ablinger, Jakob
1 Amdeberhan, Tewodros
1 Baryshnikov, Yuliy M.
1 Boukraa, Salah
1 Bousquet-Mélou, Mireille
1 Brent, Richard Peirce
1 Cai, Fangfang
1 Chen, Herman Z. Q.
1 Cluzeau, Thomas
1 Dimofte, Tudor Dan
1 Dixit, Atul
1 Drmota, Michael
1 Du, Hao
1 Georgieva, Irina
1 González, Iván
1 Görlach, Paul
1 Hassani, Saoud
1 Hofreither, Clemens
1 Hou, Qinghu
1 Jaroschek, Maximilian
1 Koukouvinos, Christos
1 Kuriki, Satoshi
1 Lehn, Christian
1 Lehrenfeld, Christoph
1 Li, Ziming
1 Motsak, Oleksandr
1 Nakamura, Brian
1 Neumüller, Martin
1 Pemantle, Robin
1 Round, Mark
1 Sattelberger, Anna-Laura
1 Schöberl, Joachim
1 Simos, Dimitris E.
1 Singer, Michael F.
1 Spiegelhofer, Lukas
1 Straub, Armin
1 Sun, Yidong
1 Takayama, Nobuki
1 Tirrell, Jordan Olliver
1 Tõnso, Maris
1 Vignat, Christophe
1 Weil, Jacques-Arthur
1 Westbury, Bruce W.
1 Wiart, Jaspar
1 Zafeirakopoulos, Zafeirakis
1 Zeilberger, Doron
1 Zenine, Nadjah
1 Zerz, Eva
1 Zhang, Philip B.

Referencing Publications by Year