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<h1>utils</h1>
<h2>Utility functions in <strong class="pkg">GAP</strong></h2>
<p>
0.92</p>
<p>
11 September 2025
</p>
</div>
<p><b>
Thomas Breuer
</b>
<br />Email: <span class="URL"><a href="mailto:sam@math.rwth-aachen.de">sam@math.rwth-aachen.de</a></span>
<br />Homepage: <span class="URL"><a href="https://www.math.rwth-aachen.de/~Thomas.Breuer">https://www.math.rwth-aachen.de/~Thomas.Breuer</a></span>
</p><p><b>
Sebastian Gutsche
</b>
<br />Email: <span class="URL"><a href="mailto:gutsche@mathematik.uni-siegen.de">gutsche@mathematik.uni-siegen.de</a></span>
<br />Homepage: <span class="URL"><a href="https://sebasguts.github.io/">https://sebasguts.github.io/</a></span>
</p><p><b>
Max Horn
</b>
<br />Email: <span class="URL"><a href="mailto:mhorn@rptu.de">mhorn@rptu.de</a></span>
<br />Homepage: <span class="URL"><a href="https://github.com/mhorn">https://github.com/mhorn</a></span>
</p><p><b>
Alexander Hulpke
</b>
<br />Email: <span class="URL"><a href="mailto:hulpke@math.colostate.edu">hulpke@math.colostate.edu</a></span>
<br />Homepage: <span class="URL"><a href="https://www.math.colostate.edu/~hulpke">https://www.math.colostate.edu/~hulpke</a></span>
</p><p><b>
Pedro García-Sánchez
</b>
<br />Email: <span class="URL"><a href="mailto:pedro@ugr.es">pedro@ugr.es</a></span>
<br />Homepage: <span class="URL"><a href="http://www.ugr.es/local/pedro">http://www.ugr.es/local/pedro</a></span>
</p><p><b>
Christopher Jefferson
</b>
<br />Email: <span class="URL"><a href="mailto:caj21@st-andrews.ac.uk">caj21@st-andrews.ac.uk</a></span>
<br />Homepage: <span class="URL"><a href="https://caj.host.cs.st-andrews.ac.uk/">https://caj.host.cs.st-andrews.ac.uk/</a></span>
</p><p><b>
Stefan Kohl
</b>
<br />Email: <span class="URL"><a href="mailto:stefan@mcs.st-and.ac.uk">stefan@mcs.st-and.ac.uk</a></span>
<br />Homepage: <span class="URL"><a href="https://www.gap-system.org/DevelopersPages/StefanKohl/">https://www.gap-system.org/DevelopersPages/StefanKohl/</a></span>
</p><p><b>
Frank Lübeck
</b>
<br />Email: <span class="URL"><a href="mailto:Frank.Luebeck@Math.RWTH-Aachen.De">Frank.Luebeck@Math.RWTH-Aachen.De</a></span>
<br />Homepage: <span class="URL"><a href="https://www.math.rwth-aachen.de/~Frank.Luebeck">https://www.math.rwth-aachen.de/~Frank.Luebeck</a></span>
</p><p><b>
Chris Wensley
</b>
<br />Email: <span class="URL"><a href="mailto:cdwensley.maths@btinternet.com">cdwensley.maths@btinternet.com</a></span>
<br />Homepage: <span class="URL"><a href="https://github.com/cdwensley">https://github.com/cdwensley</a></span>
</p>
<p><a id="X7AA6C5737B711C89" name="X7AA6C5737B711C89"></a></p>
<h3>Abstract</h3>
<p>The <strong class="pkg">Utils</strong> package provides a space for utility functions in a variety of <strong class="pkg">GAP</strong> packages to be collected together into a single package. In this way it is hoped that they will become more visible to package authors.</p>
<p>Any package author who transfers a function to <strong class="pkg">Utils</strong> will become an author of <strong class="pkg">Utils</strong>.</p>
<p>If deemed appropriate, functions may also be transferred from the main library.</p>
<p>Bug reports, suggestions and comments are, of course, welcome. Please contact the last author at <span class="URL"><a href="mailto:cdwensley.maths@btinternet.com">cdwensley.maths@btinternet.com</a></span> or submit an issue at the GitHub repository <span class="URL"><a href="https://github.com/gap-packages/utils/issues/">https://github.com/gap-packages/utils/issues/</a></span>.</p>
<p><a id="X81488B807F2A1CF1" name="X81488B807F2A1CF1"></a></p>
<h3>Copyright</h3>
<p>© 2015-2025, The GAP Group.</p>
<p>The <strong class="pkg">Utils</strong> 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.</p>
<p><a id="X82A988D47DFAFCFA" name="X82A988D47DFAFCFA"></a></p>
<h3>Acknowledgements</h3>
<p>This documentation was prepared using the <strong class="pkg">GAPDoc</strong> <a href="chapBib.html#biBGAPDoc">[LN17]</a> and <strong class="pkg">AutoDoc</strong> <a href="chapBib.html#biBAutoDoc">[GH16]</a> packages.</p>
<p>The procedure used to produce new releases uses the package <strong class="pkg">GitHubPagesForGAP</strong> <a href="chapBib.html#biBGitHubPagesForGAP">[Hor17]</a> and the package <strong class="pkg">ReleaseTools</strong>.</p>
<p><a id="X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8"></a></p>
<div class="contents">
<h3>Contents<a id="contents" name="contents"></a></h3>
<div class="ContChap"><a href="chap1.html#X7DFB63A97E67C0A1">1 <span class="Heading">Introduction</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X8508AD637B79CEE8">1.1 <span class="Heading">Information for package authors</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap2.html#X83686EE47E4D4F66">2 <span class="Heading">Printing Lists and Iterators</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7F6817927F86240F">2.1 <span class="Heading">Printing selected items</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X784638AC84D49870">2.1-1 PrintSelection</a></span>
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</div>
<div class="ContChap"><a href="chap3.html#X7AE6EFC086C0EB3C">3 <span class="Heading">Lists, Sets and Strings</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7C3F1E7D878AAA65">3.1 <span class="Heading">Functions for lists</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X78B7C92681D2F13C">3.1-1 DifferencesList</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X7975371E865B89BC">3.1-2 QuotientsList</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X86096E73858CFABD">3.1-3 SearchCycle</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X7EF06CAD7F35245D">3.1-4 RandomCombination</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X82F443FF84B8FCE3">3.2 <span class="Heading">Distinct and Common Representatives</span></a>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X78105CAA847A888C">3.2-1 DistinctRepresentatives</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X8033A2FE80FC2F2A">3.3 <span class="Heading">Functions for strings</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X870C964E7804B266">3.3-1 BlankFreeString</a></span>
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</div>
<div class="ContChap"><a href="chap4.html#X86E71C1687F2D0AD">4 <span class="Heading">Number-theoretic functions</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X7D33B5B17BF785CA">4.1 <span class="Heading">Functions for integers</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X8191A031788AC7C0">4.1-1 AllSmoothIntegers</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X78BE6B8B878D250D">4.1-2 AllProducts</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X845F46E579CEA43F">4.1-3 RestrictedPartitionsWithoutRepetitions</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X81708BF4858505E8">4.1-4 NextProbablyPrimeInt</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X8021EEE5787FCA37">4.1-5 PrimeNumbersIterator</a></span>
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<div class="ContChap"><a href="chap5.html#X8171DAF2833FF728">5 <span class="Heading">Groups and homomorphisms</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X7E21E6D285E6B12C">5.1 <span class="Heading">Functions for groups</span></a>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X80761843831B468E">5.1-1 Comm</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X803A050C7A183CCC">5.1-2 IsCommuting</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X87A8F01286548037">5.1-3 ListOfPowers</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X820B71307E41BEE5">5.1-4 GeneratorsAndInverses</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X84CF95227F9D562F">5.1-5 UpperFittingSeries</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X7FE4848B7DE6B3FD">5.2 <span class="Heading">Left Cosets for Groups</span></a>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X8340B4537F17DCD3">5.2-1 LeftCoset</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X793E48267EF5FD77">5.2-2 <span class="Heading">Inverse</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X80A512877F515DE7">5.3 <span class="Heading">Functions for group homomorphisms</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X80C9A0B583FEA7B9">5.3-1 EpimorphismByGenerators</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7C705F2A79F8E43C">5.3-2 Pullback</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X78DD2C617B992BE2">5.3-3 CentralProduct</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X801038CB808FC956">5.3-4 IdempotentEndomorphisms</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X81FA9E6C7F3B9238">5.3-5 DirectProductOfFunctions</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7CB2D5F27F4182AF">5.3-6 DirectProductOfAutomorphismGroups</a></span>
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<div class="ContChap"><a href="chap6.html#X812CCAB278643A59">6 <span class="Heading">Matrices</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X802118FB7C94D6BA">6.1 <span class="Heading">Some operations for matrices</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X787B89237E1398B6">6.1-1 DirectSumDecompositionMatrices</a></span>
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<div class="ContChap"><a href="chap7.html#X85A3F00985453F95">7 <span class="Heading">Iterators</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#X7BB5350081B27D17">7.1 <span class="Heading">Some iterators for groups and their isomorphisms</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7F8B54D1806C762D">7.1-1 AllIsomorphismsIterator</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X831DA5AE8437578F">7.1-2 AllSubgroupsIterator</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#X85413EED812C6497">7.2 <span class="Heading">Operations on iterators</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X87395A9181A35301">7.2-1 CartesianIterator</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7C95E27987A812EA">7.2-2 UnorderedPairsIterator</a></span>
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<div class="ContChap"><a href="chap8.html#X7AA1073C7E943DD7">8 <span class="Heading">Records</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8.html#X82B3D1D583CDF0E5">8.1 <span class="Heading">Functions for records</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap8.html#X84D82EB579B2ACCD">8.1-1 AssignGlobals</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8.html#X7E6207B47B9AA30C">8.2 <span class="Heading">Option records for functions</span></a>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap8.html#X8322B9377CC590D2">8.2-1 OptionRecordWithDefaults</a></span>
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<div class="ContChap"><a href="chap9.html#X815B0C4B7EBE6E1E">9 <span class="Heading">Web Downloads</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X8758CB7F79EFB6ED">9.1 <span class="Heading">Functions for downloading files from the web</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X7A7438AE8448635E">9.1-1 Download</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X85182BA486E3C2AA">9.1-2 <span class="Heading">User preference <code class="code">DownloadVerifyCertificate</code></span></a>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X79E10E5B83EF929F">9.1-3 <span class="Heading">User preference <code class="code">DownloadMaxTime</code></span></a>
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<div class="ContChap"><a href="chap10.html#X83EFC3178180D918">10 <span class="Heading">Various other functions</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap10.html#X81A0A4FF842B039B">10.1 <span class="Heading">File operations</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X7B7ECADF85F748BE">10.1-1 Log2HTML</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap10.html#X84D2922D87EDE9E9">10.2 <span class="Heading">LaTeX strings</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X87DEB2B58266F858">10.2-1 IntOrOnfinityToLaTeX</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X7DC642B97CD02F4E">10.2-2 LaTeXStringFactorsInt</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap10.html#X79F021B1830B68F6">10.3 <span class="Heading">Conversion to <span class="SimpleMath">Magma</span> strings</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X8768D7707B4CBBD4">10.3-1 ConvertToMagmaInputString</a></span>
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<div class="ContChap"><a href="chap11.html#X7F561B1D803182FF">11 <span class="Heading">Obsolete functions</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap11.html#X7A6BB3D084912F35">11.1 <span class="Heading">Operations from AutoDoc</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap11.html#X86F322FC7DECE36F">11.2 <span class="Heading">Functions for printing</span></a>
</span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap11.html#X84A4F0B281FA0F94">11.3 <span class="Heading">Other obsolete functions</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X78B7D1A982BE9866">11.3-1 <span class="Heading">Applicable Methods</span></a>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X7C1AF2467FB55D79">11.3-2 <span class="Heading">ExponentOfPrime</span></a>
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<div class="ContChap"><a href="chap12.html#X84AC9613842F014C">12 <span class="Heading">The transfer procedure</span></a>
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<div class="ContChap"><a href="chapBib.html"><span class="Heading">References</span></a></div>
<div class="ContChap"><a href="chapInd.html"><span class="Heading">Index</span></a></div>
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