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<h1>smallantimagmas</h1>


<h2>A library of antiassociative magmas of small order</h2>

<p>
    0.5.1</p>

<p>
    26 September 2025
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</div>
<p><b>
    Kamil Zabielski


  </b>
<br />Address: <br />Department of Theoretical Computer Science<br /> Białystok University of Technology<br /> Wiejska 45A<br /> 15-325 Białystok<br /> Poland<br />
</p><p><b>
    Ryszard Mazurek


  </b>
<br />Address: <br />Department of Theoretical Computer Science<br /> Białystok University of Technology<br /> Wiejska 45A<br /> 15-325 Białystok<br /> Poland<br />
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<p><a id="X81488B807F2A1CF1" name="X81488B807F2A1CF1"></a></p>
<h3>Copyright</h3>
<p>© 2024 by Kamil Zabielski</p>

<p><strong class="pkg">smallantimagmas</strong> package is free software; you can redistribute it and/or modify it under the terms of the <span class="URL"><a href="http://www.fsf.org/licenses/gpl.html">GNU General Public License</a></span> 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>We appreciate very much all past and future comments, suggestions and contributions to this package and its documentation provided by <strong class="pkg">GAP</strong> users and developers.</p>

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<div class="contents">
<h3>Contents<a id="contents" name="contents"></a></h3>

<div class="ContChap"><a href="chap1_mj.html#X7EB7BB817CC15891">1 <span class="Heading">smallantimagmas automatic generated documentation</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X78F902077A6714C4">1.1 <span class="Heading">smallantimagmas automatic generated documentation of properties</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7B8537C57970AE37">1.1-1 IsAntiassociative</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X8392BFEE78284DE1">1.1-2 IsLeftCyclic</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7BE3D1C0801AE7EA">1.1-3 IsRightCyclic</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7D377A068350EE46">1.1-4 IsLeftDistributive</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X856E2BBA7B87F209">1.1-5 IsRightDistributive</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7D994F7382127E77">1.1-6 IsLeftCancellative</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X85C01ECF83CD5484">1.1-7 IsRightCancellative</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7E58570787350F43">1.1-8 IsCancellative</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7965D94579F05D6F">1.1-9 IsLeftFPFInducted</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X866768408460130D">1.1-10 IsRightFPFInducted</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7B55200A7A734759">1.1-11 IsLeftDerangementInducted</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7E0D0CD780550E81">1.1-12 IsRightDerangementInducted</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X83147660820830E8">1.1-13 IsLeftAlternative</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7C16C7657F8B5A61">1.1-14 IsRightAlternative</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X839C88FC81394B14">1.2 <span class="Heading">smallantimagmas automatic generated documentation of attributes</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X809A477180F2A0F6">1.2-1 AssociativityIndex</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X802DA9B083E7F4A3">1.2-2 DiagonalOfMultiplicationTable</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X87FED7267EB0A068">1.2-3 CommutativityIndex</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7D32B8F780294AEC">1.2-4 AnticommutativityIndex</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X85904967802C27B4">1.2-5 SquaresIndex</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X783C01BD7B931A12">1.2-6 IdSmallAntimagma</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X78BF96667D805695">1.2-7 LeftOrder</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X850894387AD0E717">1.2-8 RightOrder</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7CDCE61679BFD1F7">1.2-9 LeftOrdersOfElements</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X84D8A5D88790F870">1.2-10 RightOrdersOfElements</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X7A4C95527CCD8524">1.3 <span class="Heading">smallantimagmas automatic generated documentation of global functions</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X8011AFA47C662D53">1.3-1 AllSubmagmas</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7BA7BE44861A8C51">1.3-2 MagmaIsomorphismInvariantsMatch</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7F7EAF23807EE984">1.3-3 IsMagmaIsomorphic</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X807BD59180325341">1.3-4 IsMagmaAntiisomorphic</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X79BF9EB48562EF6C">1.3-5 TransposedMagma</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7FD21A58851687DF">1.3-6 LeftPower</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X788005DE7947D914">1.3-7 RightPower</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7DDB92C284197B0B">1.3-8 AllSmallAntimagmas</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7E5054007A985873">1.3-9 NrSmallAntimagmas</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7903CEEA79DEBA73">1.3-10 SmallAntimagma</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X804A623879A9AC7F">1.3-11 OneSmallAntimagma</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7D0A720279246D45">1.3-12 ReallyAllSmallAntimagmas</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X796637787C216BA1">1.3-13 ReallyNrSmallAntimagmas</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X8553DA53796C81EA">1.4 <span class="Heading">smallantimagmas automatic generated documentation of methods</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X87F3EA827FF3D302">1.4-1 MagmaIsomorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7AB3F3E37D8A5687">1.4-2 MagmaAntiisomorphism</a></span>
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