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update to LOOPS 3.4.0

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These are simply the changes as distributed.
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Glen Whitney 2017-10-29 23:54:13 -04:00
parent 7e8b3b5562
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@ -444,19 +444,19 @@
<p>The following trivial example shows some of the implications and the naming conventions of <strong class="pkg">LOOPS</strong> at work:</p>
<div class="example"><pre>
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">L := LoopByCayleyTable( [ [ 1, 2 ], [ 2, 1 ] ] ); </span>
&lt;loop of order 2&gt;
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">[ IsLeftBolLoop( L ), L ] </span>
[ true, &lt;left Bol loop of order 2&gt; ]
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">[ HasIsLeftAlternativeLoop( L ), IsLeftAlternativeLoop( L ) ]; </span>
[ true, true ]
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">[ HasIsRightBolLoop( L ), IsRightBolLoop( L ) ]; </span>
[ false, true ]
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">L; </span>
&lt;Moufang loop of order 2&gt;
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">[ IsAssociative( L ), L ]; </span>
[ true, &lt;associative loop of order 2&gt; ]
<div class="example"><pre>
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">L := LoopByCayleyTable( [ [ 1, 2 ], [ 2, 1 ] ] );</span>
&lt;loop of order 2&gt;
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">[ IsLeftBolLoop( L ), L ]</span>
[ true, &lt;left Bol loop of order 2&gt; ]
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">[ HasIsLeftAlternativeLoop( L ), IsLeftAlternativeLoop( L ) ];</span>
[ true, true ]
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">[ HasIsRightBolLoop( L ), IsRightBolLoop( L ) ];</span>
[ false, true ]
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">L;</span>
&lt;Moufang loop of order 2&gt;
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">[ IsAssociative( L ), L ];</span>
[ true, &lt;associative loop of order 2&gt; ]
</pre></div>
<p>The analogous terminology for quasigroups of Bol-Moufang type is not standard yet, and hence is not supported in <strong class="pkg">LOOPS</strong> except for the situations explicitly noted above.</p>