Copyright (C) 2019-2026 Yaroslav Sysak with contributions by Iryna Raievska, Maryna Raievska
LocalNR is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the license, or
(at your option) any later version.
LocalNR is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
A copy of the GNU General Public License is available in the file
GPLv3; or for later versions see https://www.gnu.org/licenses/.
You can find information on how to contact us at the end of the README file and on the front page of the documentation.
The LocalNR package contains the library of local nearrings of small
orders and some functions to analyze finite nearrings.
To check which orders are represented in the library, see the content of the Endom directory. The library is complete up to isomorphism for local nearrings of orders 4, 8, 9, 16, 25, 27, 49, 81, 121, 125, 169, 289, 343, 361 and 1331.
For local nearrings of orders 32, 64, 128, 243 and 625 the library provides classifications of some classes of nearrings, determined by their additive group.
This software is written for GAP 4. It requires an existing installation of GAP (see https://www.gap-system.org) in version 4.10.0 or higher.
The installation follows standard GAP rules as outlined in the following
steps (see ?Installing a GAP Package in GAP for further details):
-
Download archive
LocalNR-X.Y.Z.tar.gzof the most recent release from https://gap-packages.github.io/LocalNR/. -
Move the archive inside a
pkgdirectory. This can be either the mainpkgdirectory in your GAP installation or your personalpkgdirectory. -
Complete the installation by unpacking the archive, e.g. under Linux type
tar -xzf LocalNR-X.Y.Z.tar.gz
at the terminal prompt. A subdirectory LocalNR will be created inside
the pkg directory.
To use the package type
LoadPackage("LocalNR");
at the GAP prompt.
The authors of the package express their gratitude to GAP developers, especially Max Horn for useful remarks and package improvements, Chris Jefferson for converting the data to the much more compact representation, Olexandr Konovalov for permanent support.
If you use LocalNR, please tell us by sending an email to package maintainers:
raeirina@imath.kiev.ua, raemarina@imath.kiev.ua.
If you find any bugs or have any suggestions or comments, we would very much appreciate it if you would let us know either by email or via https://github.com/gap-packages/LocalNR/issues on GitHub. Also, we would like to hear about applications of this software.
Yaroslav Sysak, Iryna Raievska, Maryna Raievska
Institute of Mathematics of National Academy of Sciences of Ukraine
01024, Ukraine, Kyiv, 3, Tereshchenkivska st.