sonata

System of finite nearrings and their applications

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

homepage ↗ github: gap-packages/sonata