Full description
SONATA stands for "systems of nearrings and their applications." It
provides methods for the construction and the analysis of finite
nearrings:
* Methods for constructing all endomorphisms and all
fixed-point-free automorphisms of a given group.
* Methods for constructing the following nearrings of functions on
a group G: the nearring of polynomial functions of G (in the sense
of Lausch-Nöbauer); the nearring of compatible functions of G;
distributively generated nearrings such as I(G), A(G), E(G);
centralizer nearrings.
* A library of all small nearrings (up to order 15) and all small
nearrings with identity (up to order 31).
* Functions to obtain solvable fixed-point-free automorphism
groups on abelian groups, nearfields, planar nearrings, as well
as designs from those.
* Various functions to study the structure (size, ideals,
N-groups, ...) of nearrings, to determine properties of nearring
elements, and to decide whether two nearrings are isomorphic.
* If the package XGAP is installed, the lattices of one- and
two-sided ideals of a nearring can be studied interactively using
a graphical representation
Packages