# Software of the Computer Algebra Group

Here is a brief listing of the software developed by the Computer Algebra Group. For more information about a package, please refer to the web site about that package.

## 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 kernel of the widely used computer algebra system Maple.

## 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.

## 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. The following objects can be computed with this package:

- Comprehensive Gröbner bases (CGB) and comprehensive Gröbner systems (CGS) in commutative polynomial rings
- CGB and CGS in rings of differential operators
- CGB and CGS for modules
- Related objects: syzygies, parametric syzygies, GB for modules, GB in polynomial rings over a polynomial ring, etc.