SONATA

System of nearrings and their applications

Version 2.9.1
Released 2018-10-07

This project is maintained by Erhard Aichinger, Peter Mayr

GAP Package SONATA

The SONATA package provides methods for the construction and analysis of finite nearrings.

The current version of this package is version 2.9.1, released on 2018-10-07. For more information, please refer to the package manual. There is also a README file and a tutorial.

Dependencies

This package requires GAP version >=4.9

The following additional GAP packages are not required, but suggested:

Authors

Erhard Aichinger, Franz Binder, Jürgen Ecker, Peter Mayr, Christof Nöbauer.

Introduction

SONATA stands for “systems of nearrings and their applications”. It provides methods for the construction and the analysis of finite nearrings. A left nearring is an algebra (N;+,.), where (N,+) is a (not necessarily abelian) group, (N,.) is a semigroup, and x(y+z) = xy + xz holds for all x,y,z in N.

As a typical example of a nearring, we may consider the set of all mappings from a group G into G, where the addition is the pointwise addition of mappings in G, and the multiplication is composition of functions. If functions are written on the right of their arguments, then the left distributive law holds, while the right distributive law is not satisfied for non-trivial G.

The SONATA package provides methods for the construction and analysis of finite nearrings.

References

Citing

Please, cite this package as

[ABEMN18] Aichinger, E., Binder, F., Ecker, J., Mayr, P. and Nöbauer, C., SONATA, System of nearrings and their applications, Version 2.9.1 (2018)
(Refereed GAP package), https://gap-packages.github.io/sonata/.

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

Feedback

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