GAP Package Alnuth

The Alnuth package provides various methods to compute with number fields which are given by a defining polynomial or by generators. Some of the methods provided in this package are written in GAP code. The other part of the methods is imported from an another computer algebra system, currently either PARI/GP or OSCAR. Hence this package contains some GAP functions and an interface to some functions in the computer algebra systems PARI/GP and OSCAR. The main methods included in Alnuth are: creating a number field, computing its maximal order (using the external CAS), computing its unit group (using the external CAS) and a presentation of this unit group, computing the elements of a given norm of the number field (using the external CAS), determining a presentation for a finitely generated multiplicative subgroup (using the external CAS), and factoring polynomials defined over number fields (using the external CAS).

The current version of this package is version 4.0.0, released on 2026-05-14. For more information, please refer to the package manual. There is also a README file.

License: GPL-2.0-or-later

Dependencies

This package requires GAP version >= 4.8

The following other GAP packages are needed:

polycyclic >=1.1

Authors

Björn Assmann, Andreas Distler, Bettina Eick.

Citing

Please, cite this package as

[ADE26] Assmann, B., Distler, A. and Eick, B., Alnuth, ALgebraic NUmber THeory and an interface to PARI/GP and OSCAR, Version 4.0.0 (2026)
(GAP package), https://gap-packages.github.io/alnuth.

You can get more info by typing Cite("Alnuth"); in the gap prompt.

Feedback

For bug reports, feature requests and suggestions, please use the issue tracker.