Software

Symbolic computation can be seen as the automation and algorithmization of mathematics. Therefore, most of what we do results in concrete software.

Software

AGADE

A Maple package for computing rational general solutions of first-order algebraic ODEs

The Maple package AGADE implements several methods for computing rational general solutions of first-order algebraic ordinary differential equations and planar rational systems. An advantage of these methods, compared to the standard dsolve-routine in Maple, is that the implemented algorithms provide ...

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Bibasic Telescope

A Mathematica Implementation of a Generalization of Gosper's Algorithm to Bibasic Hypergeometric Summation

This package is part of the RISCErgoSum bundle. pqTelescope is a Mathematica implementation of a generalization of Gosper’s algorithm to indefinite bibasic hypergeometric summation. The package has been developed by Axel Riese, a former member of the RISC Combinatorics group. ...

Authors: Axel Riese
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CASA

Computer Algebra System for Algebraic Geometry

CASA is a special-purpose system for computational algebra and constructive algebraic geometry. The system has been developed since 1990, and is the ongoing product of the Computer Algebra Group under the direction of Prof. Winkler. It is built on the ...

Authors: Franz Winkler
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CharSet

Differential Characteristic Set Computations

CharSet is an Aldor package written by Christian Aistleitner for differential characteristic set computations. CharSet comes with generic implementations of reduction, Gröbner bases, and differential characteristic set algorithms. Interfaces to the command line, Mathematica and Maple are included. ...

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DAJ is a toolkit for designing, implementing, testing, simulating, and visualizing distributed algorithms in Java. ...

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DiffTools

A Mathematica Implementation of several Algorithms for Solving Linear Difference Equations with Polynomial Coefficients

DiffTools is a Mathematica implementation for solving linear difference equations with polynomial coefficients. It contains an algorithm for finding polynomial solutions (by Marko Petkovsek), the algorithm by Sergei Abramov for finding rational solutions, the algorithm of Mark van Hoeij for ...

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Paul Kainberger Short description DrawFunDoms.m is a Mathematica package for drawing fundamental domains for congruence subgroups in the modular group SL2(ℤ). It was written by Paul Kainberger as part of his master’s thesis under supervision of Univ.-Prof. Dr. ...

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Engel

A Mathematica Implementation of q-Engel Expansion

This package is part of the RISCErgoSum bundle. Engel is a Mathematica implementation of the q -Engel Expansion algorithm which expands q-series into inverse polynomial series. Examples of q-Engel Expansions include the Rogers-Ramanujan identities together with their elegant generalization by ...

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GenOmega

A Mathematica Implementation of Guo-Niu Han's General Algorithm for MacMahon's Partition Analysis

This package is part of the RISCErgoSum bundle. GenOmega is a Mathematica implementation of Guo-Niu Han’s general Algorithm for MacMahon’s Partition Analysis carried out by Manuela Wiesinger, a master student of the RISC Combinatorics group. Partition Analysis is a computational ...

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Guess

A Mathematica Package for Guessing Multivariate Recurrence Equations

This package is part of the RISCErgoSum bundle. The Guess package provides commands for guessing multivariate recurrence equations, as well as for efficiently guessing minimal order univariate recurrence, differential, or algebraic equations given the initial terms of a sequence or ...

Authors: Manuel Kauers
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HarmonicSums

The HarmonicSums package by Jakob Ablinger allows to deal with nested sums such as harmonic sums, S-sums, cyclotomic sums and cyclotmic S-sums as well as iterated integrals such as harmonic polylogarithms, multiple polylogarithms and cyclotomic polylogarithms in an algorithmic fashion. ...

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HolonomicFunctions

A Mathematica Package for dealing with Multivariate Holonomic Functions, including Closure Properties, Summation, and Integration

This package is part of the RISCErgoSum bundle. The HolonomicFunctions package 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) ...

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ModularGroup

ModularGroup.m is a Mathematica package which has been developed in the course of the diploma thesis Computer Algebra and Analysis: Complex Variables Visualized, carried out at the Research Institute for Symbolic Computation (RISC) of the Johannes Kepler University Linz ...

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MultiIntegrate

The MultiIntegrate package allows to compute multi-dimensional integrals over hyperexponential integrands in terms of (generalized) harmonic sums.

The MultiIntegrate package allows to compute multi-dimensional integrals over hyperexponential integrands in terms of (generalized) harmonic sums. This package uses variations and extensions of the multivariate Alkmkvist-Zeilberger algorithm. Registration and Legal Notices The source code for this package is password ...

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MultiSum

A Mathematica Package for Proving Hypergeometric Multi-Sum Identities

This package is part of the RISCErgoSum bundle. MultiSum is a Mathematica package for proving hypergeometric multi-sum identities. It uses an efficient generalization of Sister Celine’s technique to find a homogeneous polynomial recurrence relation for the sum. The package has ...

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Omega

A Mathematica Implementation of Partition Analysis

Omega is a Mathematica implementation of MacMahon’s Partition Analysis carried out by Axel Riese, a Postdoc of the RISC Combinatorics group. It has been developed together with George E. Andrews and Peter Paule within the frame of a project initiated ...

Authors: Axel Riese
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OreSys

A Mathematica Implementation of several Algorithms for Uncoupling Systems of Linear Ore Operator Equations

This package is part of the RISCErgoSum bundle. OreSys is a Mathematica package for uncoupling systems of linear Ore operator equations. It offers four algorithms for reducing systems of differential or (q-)difference equations to higher order equations in a single ...

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PGB

Parametric Gröbner Bases

PGB is a software package for computing parametric Gröbner bases and related objects in several domains. It is implemented in the computer algebra system Risa/Asir by Katsusuke Nabeshima. ...

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PLDESolver

The PLDESolver package is a Mathematica package to find solutions of parameterized linear difference equations in difference rings.

The PLDESolver package by Jakob Ablinger and Carsten Schneider is a Mathematica package that allows to compute solutions of non-degenerated linear difference operators in difference rings with zero-divisors by reducing it to finding solutions in difference rings that are integral ...

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PositiveSequence

A Mathematica package for showing positivity of univariate C-finite and holonomic sequences

This package is part of the RISCErgoSum bundle. See Download and Installation. Short Description The PositiveSequence package provides methods to show positivity of C-finite and holonomic sequences. Accompanying files Demo.nb Hints Type ?PositiveSequence for information. The package is developed ...

Authors: Philipp Nuspl
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QEta

A FriCAS package to compute with Dedekind eta functions

The QEta package is a collection of programs written in the FriCAS computer algebra system that allow to compute with Dedekind eta-functions and related q-series where q=exp(2 π i τ). Furthermore, we provide a number of functions connected to the ...

Authors: Ralf Hemmecke
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qFunctions

The qFunctions package is a Mathematica package for q-series and partition theory applications.

The qFunctions package by Jakob Ablinger and Ali K. Uncu is a Mathematica package for q-series and partition theory applications. This package includes both experimental and symbolic tools. The experimental set of elements includes guessers for q-shift equations and recurrences ...

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qMultiSum

A Mathematica Package for Proving q-Hypergeometric Multi-Sum Identities

This package is part of the RISCErgoSum bundle. qMultiSum is a Mathematica package for proving q-hypergeometric multiple summation identities. The package has been developed by Axel Riese, a former member of the RISC Combinatorics group. ...

Authors: Axel Riese
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qZeil

A Mathematica Implementation of q-Analogues of Gosper's and Zeilberger's Algorithm

This package is part of the RISCErgoSum bundle. qZeil is a Mathematica implementation of q-analogues of Gosper’s and Zeilberger’s algorithm for proving and finding indefinite and definite q-hypergeometric summation identities. The package has been developed by Axel Riese, a former ...

Authors: Axel Riese
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RaduRK

RaduRK: Ramanujan-Kolberg Program

RaduRK is a Mathematica implementation of an algorithm developed by Cristian-Silviu Radu. The algorithm takes as input an arithmetic sequence a(n) generated from a large class of q-Pochhammer quotients, together with a given arithmetic progression mn+j, and the level of ...

Authors: Nicolas Smoot
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RatDiff

A Mathematica Implementation of Mark van Hoeij's Algorithm for Finding Rational Solutions of Linear Difference Equations

RatDiff is a Mathematica implementation of Mark van Hoeij's algorithm for finding rational solutions of linear difference equations. The package has been developed by Axel Riese, a Postdoc of the RISC Combinatorics group during a stay at the University of ...

Authors: Axel Riese
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rec_sequences

A SageMath package to work with sequences satisfying linear recurrence equations

The SageMath package rec_sequences provides a framework to work with sequences satisfying linear recurrence equations. It can be used to work with C^2-finite sequences and to show inequalities of C- and D-finite sequences. More documentation can be found at GitHub. ...

Authors: Philipp Nuspl
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RISC ProgramExplorer

An Interactive Program Reasoning Environment

The RISC ProgramExplorer is a computer-supported program reasoning environment for a simple imperative programming language "MiniJava"; it incorporates the RISC ProofNavigator as a semi-automatic proving assistant. The environment has been developed mainly for educational purposes (see this paper for a ...

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RISC ProofNavigator

An Interactive Proof Assistant for Program/System Verification

The RISC ProofNavigator is an interactive proof assistant for supporting formal reasoning about computer programs and computing systems, see the README file and this short paper for the main ideas; it is the core reasoning component of the RISC ProgramExplorer. ...

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RISCAL

The RISC Algorithm Language: A Language and Associated Software System for Specifying and Verifying Mathematical Algorithms

The RISC Algorithm Language (RISCAL) is a specification language and associated software system for describing mathematical algorithms, formally specifying their behavior based on mathematical theories, and validating the correctness of algorithms, specifications, and theories by execution/evaluation. The software has been ...

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RLangGFun

A Maple Implementation of the Inverse Schützenberger Methodology

The inverse Schützenberger methodology transforms a rational generating function into a (pseudo-) regular expression for a corresponding regular language, and is based on Soittola's Theorem about the N-rationality of a formal power series. It is implemented in the Maple package ...

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SCSCP4Mathematica

An interface between the Symbolic Computation Software Composability Protocol and Mathematica

SCSCP4Mathematica is an interface between the Symbolic Computation Software Composability Protocol developed in the frame of the European Project SCIEnce (Symbolic Computation Infrastructure for Europe) and the computer algebra system Mathematica of Wolfram Research. ...

Authors: Károly Bósa
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Sigma

A Mathematica Package for Discovering and Proving Multi-Sum Identities

Sigma is a Mathematica package that can handle multi-sums in terms of indefinite nested sums and products. The summation principles of Sigma are: telescoping, creative telescoping and recurrence solving. The underlying machinery of Sigma is based on difference field theory. ...

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Stirling

A Mathematica Package for Computing Recurrence Equations of Sums Involving Stirling Numbers or Eulerian Numbers

This package is part of the RISCErgoSum bundle. The Stirling package provides a command for computing recurrence equations of sums involving Stirling numbers or Eulerian numbers. ...

Authors: Manuel Kauers
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SumCracker

A Mathematica Implementation of several Algorithms for Identities and Inequalities of Special Sequences, including Summation Problems

This package is part of the RISCErgoSum bundle. The SumCracker package contains routines for manipulating a large class of sequences (admissible sequences). It can prove identities and inequalities for these sequences, simplify expressions, evaluate symbolic sums, and solve certain difference ...

Authors: Manuel Kauers
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Theorema

A Mathematical Assistant System implemented in Mathematica

The present prototype version of the Theorema software system is implemented in Mathematica . The system consists of a general higher-order predicate logic prover and a collection of special provers that call each other depending on the particular proof situations. ...

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This library contains unification, matching, and anti-unification algorithms in various theories developed at RISC. Unification with sequence variables. Context sequence matching. Rigid anti-unification for unranked terms and hedges and its experimental extension with commutative symbols. Unranked second-order anti-unification and its ...

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Zeilberger

A Maxima Implementation of Gosper's and Zeilberger's Algorithm

Zeilberger is an implementatian for the free and open source Maxima computer algebra system of Gosper's and Zeilberger's algorithm for proving and finding indefinite and definite hypergeometric summation identities. The package has been developed by Fabrizio Caruso, a former Ph. ...

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