[GAP Forum] Three packages for polycyclic groups

[Charles Wright]

Dear GAP Forum subscribers –

It is a pleasure to report that the Polycyclic and Alnuth GAP 4 packages 
have attained “accepted” status. You may already be familiar with these 
packages, but let me describe them briefly.

Polycyclic provides various algorithms for computations with finite or 
infinite polycyclic groups that can defined by polycyclic presentations. 
The package contains methods to compute centralizers and normalizers of 
subgroups, complements and extensions, torsion subgroups and many more 
features. For some of its functionality, it requires the installation of 
Alnuth. The package is the work of Bettina Eick and Werner Nickel. The 
most recent version is available at

http://cayley.math.nat.tu-bs.de/software/eick/polycyclic.

Alnuth, formerly called “Kant,” provides various methods to compute with 
number fields that are given by defining polynomials or by generators. 
Some of the methods provided in the package are written in GAP code and 
some are imported from the Computer Algebra System KANT, for which 
Alnuth acts as an interface. The package requires Polycyclic, as well as 
some external programs available from the KANT web site. Methods 
included in the package allow the user to create a number field, compute 
its maximal order, compute its unit group and a presentation of this 
unit group, compute the elements of a given norm of the number field and 
determine a presentation for a finitely generated multiplicative 
subgroup. Alnuth is the work of Bettina Eick and Bjoern Assmann. The 
current version may be obtained from

http://cayley.math.nat.tu-bs.de/software/assmann/Alnuth.

Assmann has also written the Polenta package, currently under review, 
which provides methods to compute polycyclic presentations of matrix 
groups (finite or infinite). This package may be downloaded from

http://cayley.math.nat.tu-bs.de/software/assmann/Polenta.

All three of these packages require at least GAP 4.3fix4 and will be 
made available as part of the GAP 4.4 distribution.

These packages are significant additions to GAP’s capabilities in the 
areas of polycyclic groups and algebraic number theory.

Charles R.B. Wright