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 33 articles , 2 standard articles )

Showing results 21 to 33 of 33.
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  1. Koutschan, Christoph: Holonomic functions in Mathematica (2013) ioport
  2. Koutschan, Christoph; Thanatipanonda, Thotsaporn “Aek”: Advanced computer algebra for determinants (2013)
  3. Nakamura, Brian; Zeilberger, Doron: Using Noonan-Zeilberger functional equations to enumerate (in polynomial time!) generalized Wilf classes (2013)
  4. Amdeberhan, Tewodros; Moll, Victor H.; Vignat, Christophe: The evaluation of a quartic integral via Schwinger, Schur and Bessel (2012)
  5. Beuchler, Sven; Pillwein, Veronika; Zaglmayr, Sabine: Sparsity optimized high order finite element functions for H(div) on simplices (2012)
  6. Chen, Shaoshi; Kauers, Manuel; Singer, Michael F.: Telescopers for rational and algebraic functions via residues (2012)
  7. Combot, Thierry; Koutschan, Christoph: Third order integrability conditions for homogeneous potentials of degree $-1$ (2012)
  8. Garoufalidis, Stavros; Koutschan, Christoph: Twisting $q$-holonomic sequences by complex roots of unity (2012)
  9. Garoufalidis, Stavros; Koutschan, Christoph: The $\frak sl_3$ Jones polynomial of the trefoil: a case study of $q$-holonomic sequences (2011)
  10. Koukouvinos, Christos; Pillwein, Veronika; Simos, Dimitris E.; Zafeirakopoulos, Zafeirakis: On the average complexity for the verification of compatible sequences (2011)
  11. Levandovskyy, Viktor; Koutschan, Christoph; Motsak, Oleksandr: On two-generated non-commutative algebras subject to the affine relation. (2011)
  12. Koutschan, Christoph; Moll, Victor H.: The integrals in Gradshteyn and Ryzhik. XVIII: Some automatic proofs (2010)
  13. Koutschan, Christoph: Advanced applications of the holonomic systems approach. (Abstract of thesis) (2009)

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