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### 1 Introduction

LOOPS is a package for GAP4 whose purpose is to:

• provide researchers in nonassociative algebra with a powerful computational tool concerning finite loops and quasigroups,

• extend GAP toward the realm of nonassociative structures.

LOOPS has been accepted as an official package of GAP in May 2015.

LOOPS is free software. You can redistribute it and/or modify it under the terms of the GNU General Public License version 3 as published by the Free Software Foundation.

#### 1.2 Installation

If you do not see the subfolder pkg/loops in the main directory of GAP then download the LOOPS package from the distribution website http://www.math.du.edu/loops and unpack the downloaded file into the pkg subfolder.

The package LOOPS can then be loaded to GAP anytime by calling LoadPackage("loops");.

If you wish to load LOOPS automatically while starting GAP, start GAP, execute the following commands,


gap> pref := UserPreference( "PackagesToLoad " );;
gap> WriteGapIniFile();;



quit GAP and restart it.

#### 1.3 Documentation

The documentation has been prepared with the GAPDoc package and is therefore available in several formats: LaTeX, pdf, ps, html, and as an inline help in GAP. All these formats have been obtained directly from the master XML documentation file. Consequently, the different formats of the documentation differ only in their appearance, not in content.

The preferred format of the documentation is html with MathJax turned on.

All formats of the documentation can be found in the doc folder of LOOPS. You can also download the documentation from the LOOPS distribution website.

The inline GAP help is available upon installing LOOPS and can be accessed in the usual way, i.e., upon typing ?command, GAP displays the section of the LOOPS manual containing information about command.

#### 1.4 Test Files

Test files conforming to GAP standards are provided for LOOPS and can be found in the folder tst. The command ReadPackage("loops","tst/testall.g") runs all tests for LOOPS.

#### 1.5 Memory Management

Some libraries of loops are loaded only upon explicit demand and can occupy a lot of memory. For instance, the library or RCC loops occupies close to 100 MB of memory when fully loaded. The command LOOPS_FreeMemory(); will attempt to free memory by unbinding on-demand library data loaded by LOOPS.

#### 1.6 Feedback

We welcome all comments and suggestions on LOOPS, especially those concerning the future development of the package. You can contact us by e-mail.

#### 1.7 Acknowledgment

We thank the following people for sending us remarks and comments, and for suggesting new functionality of the package: Muniru Asiru, Bjoern Assmann, Andreas Distler, Aleš Drápal, Graham Ellis, Steve Flammia, Kenneth W. Johnson, Michael K. Kinyon, Alexander Konovalov, Frank Lübeck, Jonathan D.H. Smith, David Stanovský and Glen Whitney.

The library of Moufang loops of order 243 was generated from data provided by Michael C. Slattery and Ashley L. Zenisek. The library of right conjugacy closed loops of order less than 28 was generated from data provided by Katharina Artic. The library of right Bruck loops of order 27, 81 was obtained jointly with Izabella Stuhl.

Gábor P. Nagy was supported by OTKA grants F042959 and T043758, and Petr Vojtěchovský was supported by the 2006 and 2016 University of Denver PROF grants and the Simons Foundation Collaboration Grant 210176.

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