Algebraic number theory and an interface to PARI/GP

Version 3.2.1
Released 2022-04-05

This project is maintained by The GAP Team

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 the computer algebra system PARI/GP. Hence this package contains some GAP functions and an interface to some functions in the computer algebra system PARI/GP. The main methods included in Alnuth are: creating a number field, computing its maximal order (using PARI/GP), computing its unit group (using PARI/GP) and a presentation of this unit group, computing the elements of a given norm of the number field (using PARI/GP), determining a presentation for a finitely generated multiplicative subgroup (using PARI/GP), and factoring polynomials defined over number fields (using PARI/GP).

The current version of this package is version 3.2.1, released on 2022-04-05. For more information, please refer to the package manual. There is also a README file.

License: GPL-2.0-or-later


This package requires GAP version >= 4.8

The following other GAP packages are needed:


Björn Assmann, Andreas Distler, Bettina Eick.


Please, cite this package as

[ADET22] Assmann, B., Distler, A., Eick, B. and GAP Team, T., Alnuth, Algebraic number theory and an interface to PARI/GP, Version 3.2.1 (2022)
(Refereed GAP package),

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


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