update to LOOPS 3.4.0
These are simply the changes as distributed.
This commit is contained in:
Glen Whitney
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58 changed files with 17724 additions and 29097 deletions
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@ -188,15 +188,15 @@
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<p>Since <code class="code">CanonicalCayleyTable</code> is called within the above operation, the resulting quasigroup will have Cayley table with distinct entries <span class="SimpleMath">\(1\)</span>, <span class="SimpleMath">\(\dots\)</span>, <span class="SimpleMath">\(n\)</span>.</p>
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<div class="example"><pre>
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<span class="GAPprompt">gap></span> <span class="GAPinput">ct := CanonicalCayleyTable( [[5,3],[3,5]] );
</span>
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[ [ 2, 1 ], [ 1, 2 ] ]
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<span class="GAPprompt">gap></span> <span class="GAPinput">NormalizedQuasigroupTable( ct );
</span>
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[ [ 1, 2 ], [ 2, 1 ] ]
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<span class="GAPprompt">gap></span> <span class="GAPinput">LoopByCayleyTable( last );
</span>
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<loop of order 2>
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<span class="GAPprompt">gap></span> <span class="GAPinput">[ IsQuasigroupTable( ct ), IsLoopTable( ct ) ];
</span>
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[ true, false ]
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<div class="example"><pre>
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<span class="GAPprompt">gap></span> <span class="GAPinput">ct := CanonicalCayleyTable( [[5,3],[3,5]] );</span>
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[ [ 2, 1 ], [ 1, 2 ] ]
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<span class="GAPprompt">gap></span> <span class="GAPinput">NormalizedQuasigroupTable( ct );</span>
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[ [ 1, 2 ], [ 2, 1 ] ]
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<span class="GAPprompt">gap></span> <span class="GAPinput">LoopByCayleyTable( last );</span>
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<loop of order 2>
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<span class="GAPprompt">gap></span> <span class="GAPinput">[ IsQuasigroupTable( ct ), IsLoopTable( ct ) ];</span>
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[ true, false ]
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</pre></div>
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<p><a id="X849944F17E2B37F8" name="X849944F17E2B37F8"></a></p>
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@ -235,56 +235,56 @@
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<p><strong class="button">Example:</strong> Data does not have to be arranged into an array of any kind.</p>
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<p class="center">\[
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\begin{array}{cccc}
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0&1&2&1\\
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2&0&2& \\
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0&1& &
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\end{array}\quad + \quad "" \quad \Longrightarrow\quad
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\begin{array}{ccc}
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1&2&3\\
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2&3&1\\
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3&1&2
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\end{array}
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<p class="center">\[
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\begin{array}{cccc}
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0&1&2&1\\
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2&0&2& \\
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0&1& &
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\end{array}\quad + \quad "" \quad \Longrightarrow\quad
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\begin{array}{ccc}
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1&2&3\\
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2&3&1\\
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3&1&2
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\end{array}
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\]</p>
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<p><strong class="button">Example:</strong> Chunks can be any strings.</p>
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<p class="center">\[
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\begin{array}{cc}
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{\rm red}&{\rm green}\\
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{\rm green}&{\rm red}\\
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\end{array}\quad + \quad "" \quad \Longrightarrow\quad
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\begin{array}{cc}
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1& 2\\
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2& 1
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\end{array}
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<p class="center">\[
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\begin{array}{cc}
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{\rm red}&{\rm green}\\
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{\rm green}&{\rm red}\\
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\end{array}\quad + \quad "" \quad \Longrightarrow\quad
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\begin{array}{cc}
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1& 2\\
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2& 1
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\end{array}
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\]</p>
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<p><strong class="button">Example:</strong> A typical table produced by <strong class="pkg">GAP</strong> is easily parsed by deleting brackets and commas.</p>
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<p class="center">\[
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[ [0, 1], [1, 0] ] \quad + \quad "[,]" \quad \Longrightarrow\quad
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\begin{array}{cc}
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1& 2\\
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2& 1
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\end{array}
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<p class="center">\[
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[ [0, 1], [1, 0] ] \quad + \quad "[,]" \quad \Longrightarrow\quad
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\begin{array}{cc}
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1& 2\\
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2& 1
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\end{array}
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\]</p>
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<p><strong class="button">Example:</strong> A typical TeX table with rows separated by lines is also easily converted. Note that we have to use <span class="SimpleMath">\(\backslash\backslash\)</span> to ensure that every occurrence of <span class="SimpleMath">\(\backslash\)</span> is deleted, since <span class="SimpleMath">\(\backslash\backslash\)</span> represents the character <span class="SimpleMath">\(\backslash\)</span> in <strong class="pkg">GAP</strong></p>
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<p class="center">\[
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\begin{array}{lll}
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x\&& y\&&\ z\backslash\backslash\cr
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y\&& z\&&\ x\backslash\backslash\cr
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z\&& x\&&\ y
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\end{array}
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\quad + \quad "\backslash\backslash\&" \quad \Longrightarrow\quad
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\begin{array}{ccc}
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1&2&3\cr
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2&3&1\cr
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3&1&2
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\end{array}
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<p class="center">\[
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\begin{array}{lll}
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x\&& y\&&\ z\backslash\backslash\cr
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y\&& z\&&\ x\backslash\backslash\cr
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z\&& x\&&\ y
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\end{array}
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\quad + \quad "\backslash\backslash\&" \quad \Longrightarrow\quad
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\begin{array}{ccc}
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1&2&3\cr
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2&3&1\cr
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3&1&2
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\end{array}
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\]</p>
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<p><a id="X81A1DB918057933E" name="X81A1DB918057933E"></a></p>
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@ -329,14 +329,14 @@
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<p>These are the dual operations to <code class="code">QuasigroupByLeftSection</code> and <code class="code">LoopByLeftSection</code>.</p>
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<div class="example"><pre>
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<span class="GAPprompt">gap></span> <span class="GAPinput">S := Subloop( MoufangLoop( 12, 1 ), [ 3 ] );;
</span>
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<span class="GAPprompt">gap></span> <span class="GAPinput">ls := LeftSection( S );
</span>
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[ (), (1,3,5), (1,5,3) ]
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<span class="GAPprompt">gap></span> <span class="GAPinput">CayleyTableByPerms( ls );
</span>
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[ [ 1, 3, 5 ], [ 3, 5, 1 ], [ 5, 1, 3 ] ]
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<span class="GAPprompt">gap></span> <span class="GAPinput">CayleyTable( LoopByLeftSection( ls ) );
</span>
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[ [ 1, 2, 3 ], [ 2, 3, 1 ], [ 3, 1, 2 ] ]
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<div class="example"><pre>
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<span class="GAPprompt">gap></span> <span class="GAPinput">S := Subloop( MoufangLoop( 12, 1 ), [ 3 ] );;</span>
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<span class="GAPprompt">gap></span> <span class="GAPinput">ls := LeftSection( S );</span>
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[ (), (1,3,5), (1,5,3) ]
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<span class="GAPprompt">gap></span> <span class="GAPinput">CayleyTableByPerms( ls );</span>
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[ [ 1, 3, 5 ], [ 3, 5, 1 ], [ 5, 1, 3 ] ]
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<span class="GAPprompt">gap></span> <span class="GAPinput">CayleyTable( LoopByLeftSection( ls ) );</span>
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[ [ 1, 2, 3 ], [ 2, 3, 1 ], [ 3, 1, 2 ] ]
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</pre></div>
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<p><a id="X85ABE99E84E5B0E8" name="X85ABE99E84E5B0E8"></a></p>
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@ -360,11 +360,11 @@
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<p>Here is a simple example in which <span class="SimpleMath">\(T\)</span> is actually the right section of the resulting loop.</p>
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<div class="example"><pre>
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<span class="GAPprompt">gap></span> <span class="GAPinput">T := [ (), (1,2)(3,4,5), (1,3,5)(2,4), (1,4,3)(2,5), (1,5,4)(2,3) ];;
</span>
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<span class="GAPprompt">gap></span> <span class="GAPinput">G := Group( T );; H := Stabilizer( G, 1 );;
</span>
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<span class="GAPprompt">gap></span> <span class="GAPinput">LoopByRightFolder( G, H, T );
</span>
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<loop of order 5>
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<div class="example"><pre>
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<span class="GAPprompt">gap></span> <span class="GAPinput">T := [ (), (1,2)(3,4,5), (1,3,5)(2,4), (1,4,3)(2,5), (1,5,4)(2,3) ];;</span>
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<span class="GAPprompt">gap></span> <span class="GAPinput">G := Group( T );; H := Stabilizer( G, 1 );;</span>
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<span class="GAPprompt">gap></span> <span class="GAPinput">LoopByRightFolder( G, H, T );</span>
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<loop of order 5>
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</pre></div>
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<p><a id="X8759431780AC81A9" name="X8759431780AC81A9"></a></p>
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@ -394,16 +394,16 @@
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<p>Returns: The extension of an abelian group <var class="Arg">K</var> by a loop <var class="Arg">F</var>, using action <var class="Arg">f</var> and cocycle <var class="Arg">t</var>. The arguments must be formatted as the output of <code class="code">NuclearExtension</code>.</p>
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<div class="example"><pre>
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<span class="GAPprompt">gap></span> <span class="GAPinput">F := IntoLoop( Group( (1,2) ) );
</span>
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<loop of order 2>
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<span class="GAPprompt">gap></span> <span class="GAPinput">K := DirectProduct( F, F );;
</span>
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<span class="GAPprompt">gap></span> <span class="GAPinput">phi := [ (), (2,3) ];;
</span>
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<span class="GAPprompt">gap></span> <span class="GAPinput">theta := [ [ 1, 1 ], [ 1, 3 ] ];;
</span>
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<span class="GAPprompt">gap></span> <span class="GAPinput">LoopByExtension( K, F, phi, theta );
</span>
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<loop of order 8>
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<span class="GAPprompt">gap></span> <span class="GAPinput">IsAssociative( last );
</span>
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false
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<div class="example"><pre>
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<span class="GAPprompt">gap></span> <span class="GAPinput">F := IntoLoop( Group( (1,2) ) );</span>
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<loop of order 2>
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<span class="GAPprompt">gap></span> <span class="GAPinput">K := DirectProduct( F, F );;</span>
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<span class="GAPprompt">gap></span> <span class="GAPinput">phi := [ (), (2,3) ];;</span>
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<span class="GAPprompt">gap></span> <span class="GAPinput">theta := [ [ 1, 1 ], [ 1, 3 ] ];;</span>
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<span class="GAPprompt">gap></span> <span class="GAPinput">LoopByExtension( K, F, phi, theta );</span>
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<loop of order 8>
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<span class="GAPprompt">gap></span> <span class="GAPinput">IsAssociative( last );</span>
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false
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</pre></div>
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<p><a id="X7AE29A1A7AA5C25A" name="X7AE29A1A7AA5C25A"></a></p>
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