Abstract
We present the Mathematica package HolonomicFunctions which provides a powerful framework for the automatic manipulation of multivariate holonomic functions, in the spirit of Zeilberger's holonomic systems approach. Its top-level functionalities are: converting a mathematical expression into a holonomic description, executing holonomic closure properties, and creative telescoping for general holonomic functions. To achieve these goals, many other, lower-level, functionalities had to be implemented which were not available in the Mathematica system: finding rational solutions of linear systems of (q-) difference / differential equations, noncommutative arithmetic in Ore algebras and computing Gröbner bases in such domains.
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