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.

References in zbMATH (referenced in 26 articles , 2 standard articles )

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  1. Bostan, Alin; Bousquet-Mélou, Mireille; Kauers, Manuel; Melczer, Stephen: On 3-dimensional lattice walks confined to the positive octant (2016)
  2. Dixit, Atul; Moll, Victor H.; Pillwein, Veronika: A hypergeometric inequality (2016)
  3. Drmota, Michael; Kauers, Manuel; Spiegelhofer, Lukas: On a conjecture of Cusick concerning the sum of digits of $n$ and $n+t$ (2016)
  4. Hassani, S.; Koutschan, Ch.; Maillard, J.-M.; Zenine, N.: Lattice Green functions: the $d$-dimensional face-centered cubic lattice, $d = 8, 9, 10, 11, 12$ (2016)
  5. Koutschan, Christoph; Neumüller, Martin; Radu, Cristian-Silviu: Inverse inequality estimates with symbolic computation (2016)
  6. Bostan, A.; Boukraa, S.; Maillard, J.-M.; Weil, J.-A.: Diagonals of rational functions and selected differential Galois groups (2015)
  7. Brent, Richard P.; Johansson, Fredrik: A bound for the error term in the Brent-McMillan algorithm (2015)
  8. Kauers, Manuel; Jaroschek, Maximilian; Johansson, Fredrik: Ore polynomials in Sage (2015)
  9. Ablinger, J.; Blümlein, J.; Raab, C.G.; Schneider, C.: Iterated binomial sums and their associated iterated integrals (2014)
  10. Kauers, Manuel: Bounds for D-finite closure properties (2014)
  11. Beuchler, Sven; Pillwein, Veronika; Zaglmayr, Sabine: Sparsity optimized high order finite element functions for $H(\mathrmcurl)$ on tetrahedra (2013)
  12. Dimofte, Tudor: Quantum Riemann surfaces in Chern-Simons theory (2013)
  13. Garoufalidis, Stavros; Koutschan, Christoph: Irreducibility of $q$-difference operators and the knot $7_4$ (2013)
  14. Kauers, Manuel: The holonomic toolkit (2013)
  15. Koutschan, Christoph: Holonomic functions in Mathematica (2013) ioport
  16. Koutschan, Christoph; Thanatipanonda, Thotsaporn “Aek”: Advanced computer algebra for determinants (2013)
  17. Nakamura, Brian; Zeilberger, Doron: Using Noonan-Zeilberger functional equations to enumerate (in polynomial time!) generalized Wilf classes (2013)
  18. Amdeberhan, Tewodros; Moll, Victor H.; Vignat, Christophe: The evaluation of a quartic integral via Schwinger, Schur and Bessel (2012)
  19. Beuchler, Sven; Pillwein, Veronika; Zaglmayr, Sabine: Sparsity optimized high order finite element functions for H(div) on simplices (2012)
  20. Chen, Shaoshi; Kauers, Manuel; Singer, Michael F.: Telescopers for rational and algebraic functions via residues (2012)

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Further publications can be found at: http://www.risc.jku.at/publications/