[GAP Forum] Three packages for polycyclic groups
Charles Wright
wright at darkwing.uoregon.edu
Fri Jan 30 17:55:40 GMT 2004
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
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