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; OEIS; gfun; Plural; DLMF; SageMath; DET; OreTools; SIGMA; ore_algebra; olga.lib; DODGSON; Axodraw; HarmonicSums; Asymptotics; SumCracker; Knot Atlas; GeneratingFunctions; DEtools Cited in: 57 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 1244.33024Koutschan, Christoph; Moll, Victor H. 2010 all top 5 Cited by 81 Authors 22 Koutschan, Christoph 8 Kauers, Manuel 5 Blümlein, Johannes 5 Pillwein, Veronika 4 Moll, Victor Hugo 4 Raab, Clemens G. 4 Thanatipanonda, Thotsaporn (Aek) 3 Bostan, Alin 3 Chen, Shaoshi 3 Garoufalidis, Stavros 3 Jiu, Lin 3 Levandovskyy, Viktor 3 Schönwald, Kay 3 Wong, Elaine 3 Zhang, Yi 2 Beuchler, Sven 2 Combot, Thierry 2 De Freitas, Abilio 2 Hoffmann, Johannes 2 Hou, Qinghu 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 Huang, Hui 1 Jaroschek, Maximilian 1 Koukouvinos, Christos 1 Kuriki, Satoshi 1 Labahn, George 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 Spahn, George 1 Spiegelhofer, Lukas 1 Straub, Armin 1 Sun, Yidong 1 Takayama, Nobuki 1 Tirrell, Jordan Olliver 1 Tõnso, Maris 1 Vignat, Christophe 1 Wang, Ronghua 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. 1 Zudilin, Wadim all top 5 Cited in 30 Serials 6 Advances in Applied Mathematics 3 Nuclear Physics. B 3 Annals of Combinatorics 2 Journal of Mathematical Physics 2 European Journal of Combinatorics 2 Journal of Symbolic Computation 2 Mathematics in Computer Science 2 Journal of Physics A: Mathematical and Theoretical 1 Bulletin of the Australian Mathematical Society 1 Discrete Mathematics 1 Information Processing Letters 1 Rocky Mountain Journal of Mathematics 1 Mathematics of Computation 1 Beiträge zur Algebra und Geometrie 1 Annales de l’Institut Fourier 1 Journal of Combinatorial Theory. Series A 1 Journal of Multivariate Analysis 1 Mathematics and Computers in Simulation 1 Numerische Mathematik 1 SIAM Journal on Discrete Mathematics 1 The Ramanujan Journal 1 Advances in Theoretical and Mathematical Physics 1 Journal of Integer Sequences 1 Algebraic & Geometric Topology 1 Central European Journal of Mathematics 1 International Journal of Number Theory 1 Scientia. Series A: Mathematical Sciences. New Series 1 ACM Communications in Computer Algebra 1 Advances in Delays and Dynamics 1 Open Mathematics all top 5 Cited in 34 Fields 20 Special functions (33-XX) 20 Computer science (68-XX) 15 Combinatorics (05-XX) 8 Number theory (11-XX) 8 Numerical analysis (65-XX) 7 Quantum theory (81-XX) 6 Associative rings and algebras (16-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 4 Ordinary differential equations (34-XX) 4 Partial differential equations (35-XX) 3 Algebraic geometry (14-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Difference and functional equations (39-XX) 3 Approximations and expansions (41-XX) 3 Manifolds and cell complexes (57-XX) 2 Field theory and polynomials (12-XX) 2 Commutative algebra (13-XX) 2 Optics, electromagnetic theory (78-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Systems theory; control (93-XX) 1 General and overarching topics; collections (00-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Sequences, series, summability (40-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 Operator theory (47-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Statistics (62-XX) 1 Mechanics of particles and systems (70-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year