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# utils

## Utility functions in GAP

0.77

25 September 2022

Thomas Breuer
Email: sam@math.rwth-aachen.de
Homepage: https://www.math.rwth-aachen.de/~Thomas.Breuer

Sebastian Gutsche
Email: gutsche@mathematik.uni-seigen.de
Homepage: https://sebasguts.github.io/

Max Horn
Email: horn@mathematik.uni-kl.de
Homepage: https://github.com/mhorn

Alexander Hulpke
Email: hulpke@math.colostate.edu
Homepage: https://www.math.colostate.edu/~hulpke

Stefan Kohl
Email: stefan@mcs.st-and.ac.uk
Homepage: https://www.gap-system.org/DevelopersPages/StefanKohl/

Frank Lübeck
Email: Frank.Luebeck@Math.RWTH-Aachen.De
Homepage: https://www.math.rwth-aachen.de/~Frank.Luebeck

Chris Wensley
Email: c.d.wensley@bangor.ac.uk
Homepage: https://github.com/cdwensley

### Abstract

The Utils package provides a space for utility functions in a variety of GAP packages to be collected together into a single package. In this way it is hoped that they will become more visible to package authors.

Any package author who transfers a function to Utils will become an author of Utils.

If deemed appropriate, functions may also be transferred from the main library.

Bug reports, suggestions and comments are, of course, welcome. Please contact the last author at c.d.wensley@bangor.ac.uk or submit an issue at the GitHub repository https://github.com/gap-packages/utils/issues/.

### Copyright

© 2015-2022, The GAP Group.

The Utils package 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 2 of the License, or (at your option) any later version.

### Acknowledgements

This documentation was prepared using the GAPDoc [LN17] and AutoDoc [GH16] packages.

The procedure used to produce new releases uses the package GitHubPagesForGAP [Hor17] and the package ReleaseTools.

### Contents

1 Introduction
1.1 Information for package authors
2 Printing Lists and Iterators
2.1 Printing selected items
2.1-1 PrintSelection
3 Lists, Sets and Strings
3.1 Functions for lists
3.1-1 DifferencesList
3.1-2 QuotientsList
3.1-3 SearchCycle
3.1-4 RandomCombination
3.2 Distinct and Common Representatives
3.2-1 DistinctRepresentatives
3.3 Functions for strings
3.3-1 BlankFreeString
4 Number-theoretic functions
4.1 Functions for integers
4.1-1 AllSmoothIntegers
4.1-2 AllProducts
4.1-3 RestrictedPartitionsWithoutRepetitions
4.1-4 NextProbablyPrimeInt
4.1-5 PrimeNumbersIterator
5 Groups and homomorphisms
5.1 Functions for groups
5.1-1 Comm
5.1-2 IsCommuting
5.1-3 ListOfPowers
5.1-4 GeneratorsAndInverses
5.1-5 UpperFittingSeries
5.2 Left Cosets for Groups
5.2-1 LeftCoset
5.2-2 Inverse
5.3 Functions for group homomorphisms
5.3-1 EpimorphismByGenerators
5.3-2 Pullback
5.3-3 CentralProduct
5.3-4 IdempotentEndomorphisms
5.3-5 DirectProductOfFunctions
5.3-6 DirectProductOfAutomorphismGroups
6 Iterators
6.1 Some iterators for groups and their isomorphisms
6.1-1 AllIsomorphismsIterator
6.1-2 AllSubgroupsIterator
6.2 Operations on iterators
6.2-1 CartesianIterator
6.2-2 UnorderedPairsIterator
7 Records
7.1 Functions for records
7.1-1 AssignGlobals
8 Web Downloads
8.1 Functions for downloading files from the web
8.1-1 Download
8.1-2 User preference `DownloadVerifyCertificate`
9 Various other functions
9.1 File operations
9.1-1 Log2HTML
9.2 LaTeX strings
9.2-1 IntOrOnfinityToLaTeX
9.2-2 LaTeXStringFactorsInt
9.3 Conversion to Magma string
9.3-1 ConvertToMagmaInputString
10 Obsolete functions
10.1 Operations from AutoDoc
10.2 Functions for printing
10.3 Other obsolete functions
10.3-1 Applicable Methods
10.3-2 ExponentOfPrime
11 The transfer procedure
References
Index
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