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<div class="ChapSects"><a href="chap13_mj.html#X81EC8C8A82C15298">13 <span class="Heading">Interaction with HAP </span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap13_mj.html#X865CE53A827FBE6F">13.1 <span class="Heading">Calling HAP functions</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap13_mj.html#X8699357D7DC6279E">13.1-1 SmallCat1Group</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap13_mj.html#X7B00E3FB82DC305D">13.1-2 CatOneGroupToXMod</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap13_mj.html#X84B7160284FD454A">13.1-3 IdCat1Group</a></span>
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<h3>13 <span class="Heading">Interaction with HAP </span></h3>

<p>This chapter describes functions which allow functions in the package <strong class="pkg">HAP</strong> to be called from <strong class="pkg">XMod</strong>.</p>

<p><a id="X865CE53A827FBE6F" name="X865CE53A827FBE6F"></a></p>

<h4>13.1 <span class="Heading">Calling HAP functions</span></h4>

<p>In <strong class="pkg">HAP</strong> a cat<span class="SimpleMath">\(^1\)</span>-group is called a <code class="code">CatOneGroup</code> and the traditional terms <em>source</em> and <em>target</em> are used for the <code class="code">TailMap</code> and <code class="code">HeadMap</code>. A <code class="code">CatOneGroup</code> is a record <code class="code">C</code> with fields <code class="code">C!.sourceMap</code> and <code class="code">C!.targetMap</code>.</p>

<p><a id="X8699357D7DC6279E" name="X8699357D7DC6279E"></a></p>

<h5>13.1-1 SmallCat1Group</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; SmallCat1Group</code>( <var class="Arg">n</var>, <var class="Arg">i</var>, <var class="Arg">j</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>This operation calls the <strong class="pkg">HAP</strong> function <code class="code">SmallCatOneGroup(n,i,j)</code> which returns a <code class="code">CatOneGroup</code> from the <strong class="pkg">HAP</strong> database. This is then converted into an <strong class="pkg">XMod</strong> cat<span class="SimpleMath">\(^1\)</span>-group. Note that the numbering is not the same as that used by the <strong class="pkg">XMod</strong> operation <code class="code">Cat1Select</code>. In the example <code class="code">C12</code> is the converted form of <code class="code">H12</code>.</p>


<div class="example"><pre>

<span class="GAPprompt">gap></span> <span class="GAPinput">H12 := SmallCatOneGroup( 12, 4, 3 );</span>
Cat-1-group with underlying group Group( [ f1, f2, f3 ] ) . 
<span class="GAPprompt">gap></span> <span class="GAPinput">C12 := SmallCat1Group( 12, 4, 3 );</span>
[Group( [ f1, f2, f3 ] )=>Group( [ f1, f2, <identity> of ... ] )]

</pre></div>

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<h5>13.1-2 CatOneGroupToXMod</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; CatOneGroupToXMod</code>( <var class="Arg">C</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; Cat1GroupToHAP</code>( <var class="Arg">C</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>These two functions convert between the two alternative implementations.</p>


<div class="example"><pre>

<span class="GAPprompt">gap></span> <span class="GAPinput">C12 := CatOneGroupToXMod( H12 );    </span>
[Group( [ f1, f2, f3 ] )=>Group( [ f1, f2, <identity> of ... ] )]
<span class="GAPprompt">gap></span> <span class="GAPinput">C18 := Cat1Select( 18, 4, 3 );</span>
[(C3 x C3) : C2=>Group( [ f1, <identity> of ..., f3 ] )]
<span class="GAPprompt">gap></span> <span class="GAPinput">H18 := Cat1GroupToHAP( C18 ); </span>
Cat-1-group with underlying group (C3 x C3) : C2 . 

</pre></div>

<p><a id="X84B7160284FD454A" name="X84B7160284FD454A"></a></p>

<h5>13.1-3 IdCat1Group</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; IdCat1Group</code>( <var class="Arg">C</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>This function calls the <strong class="pkg">HAP</strong> function <code class="code">IdCatOneGroup</code> on a cat<span class="SimpleMath">\(^1\)</span>-group <span class="SimpleMath">\(C\)</span>. This returns <span class="SimpleMath">\([n,i,j]\)</span> if the cat<span class="SimpleMath">\(^1\)</span>-group is the <span class="SimpleMath">\(j\)</span>-th structure on the <code class="code">SmallGroup(n,i)</code>.</p>


<div class="example"><pre>

<span class="GAPprompt">gap></span> <span class="GAPinput">IdCatOneGroup( H18 ); </span>
[ 18, 4, 4 ]
<span class="GAPprompt">gap></span> <span class="GAPinput">IdCat1Group( C18 ); </span>
[ 18, 4, 4 ]

</pre></div>


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