# Projects

Some computer packages are developed at Lehrstuhl B für Mathematik:

(visit also our software server)

### jets

Originally, the Maple package jets was an extension of the package desolv, adding to it the facility of computing generalized symmetries. Now jets is an independent package going beyond symmetries. More information on this package can be found on the homepage of Mohamed Barakat.

### Involutive and Janet

The Janet algorithm constructs certain normal forms for systems of linear partial differential equations as well as for systems of polynomial equations. Implementations of the Janet algorithm are available for Maple now. Moreover the packages Janet and Involutive offer many other functions for applications.

One of these applications is e. g. control theory.

### Thomas Decomposition

The Thomas algorithm constructs a decomposition of systems of algebraic or differential equations and inequations into simple systems. The packages can be found here.

### CoW

The CoW package for Maple implements computation of the comprehensive weight enumerator of a linear code.

### homalg

The homalg project is meant to be a continuously growing open source multi volume book about homological and homotopical algebra. homalg is an attempt to translate as much as possible of homological algebra into a language that a computer can directly understand. But homalg should, to a great extent, be readable by a mathematician, even without deep programming knowledge. For a multitude of reasons GAP4 was chosen as the language of homalg.

### conley

An application of homalg is the package conley. This package computes connection and transition matrices of Morse decompositions of a dynamical system.

### PSL

The Maple package PSL is an implementation of methods for recognizing groups of L_2-type as epimorphic images of given finitely presented groups.

### QuillenSuslin

QuillenSuslin is a Maple package which implements algorithms for the computation of bases of free modules over polynomial rings.

### CARAT

We develop a computer package called CARAT, which handles enumeration, construction, recognition and comparison problems for crystallographic groups up to dimension 6. On CARAT's homepage one can find general information about the package, examples and instructions for downloading and installation.