GAP (Utils) - Contents

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# utils

## Utility functions in GAP

0.92

11 September 2025

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

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

Max Horn
Email: mhorn@rptu.de
Homepage: https://github.com/mhorn

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

Pedro García-Sánchez
Email: pedro@ugr.es
Homepage: http://www.ugr.es/local/pedro

Christopher Jefferson
Email: caj21@st-andrews.ac.uk
Homepage: https://caj.host.cs.st-andrews.ac.uk/

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: cdwensley.maths@btinternet.com
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 cdwensley.maths@btinternet.com or submit an issue at the GitHub repository https://github.com/gap-packages/utils/issues/.

### Copyright

© 2015-2025, 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 Matrices
6.1 Some operations for matrices
6.1-1 DirectSumDecompositionMatrices
7 Iterators
7.1 Some iterators for groups and their isomorphisms
7.1-1 AllIsomorphismsIterator
7.1-2 AllSubgroupsIterator
7.2 Operations on iterators
7.2-1 CartesianIterator
7.2-2 UnorderedPairsIterator
8 Records
8.1 Functions for records
8.1-1 AssignGlobals
8.2 Option records for functions
8.2-1 OptionRecordWithDefaults
9 Web Downloads
9.1 Functions for downloading files from the web
9.1-1 Download
9.1-2 User preference `DownloadVerifyCertificate`
9.1-3 User preference `DownloadMaxTime`
10 Various other functions
10.1 File operations
10.1-1 Log2HTML
10.2 LaTeX strings
10.2-1 IntOrOnfinityToLaTeX
10.2-2 LaTeXStringFactorsInt
10.3 Conversion to Magma strings
10.3-1 ConvertToMagmaInputString
11 Obsolete functions
11.1 Operations from AutoDoc
11.2 Functions for printing
11.3 Other obsolete functions
11.3-1 Applicable Methods
11.3-2 ExponentOfPrime
12 The transfer procedure
References
Index
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