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<div class="ChapSects"><a href="chap5_mj.html#X842C13C27B941744">5 <span class="Heading">Interactive ANUPQ functions</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X7935CDAD7936CA0A">5.1 <span class="Heading">Starting and Stopping Interactive ANUPQ Processes</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X83B2EC237F37623C">5.1-1 PqStart</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X79DB761185BAB9C8">5.1-2 PqQuit</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X7FF8F2657B1B008E">5.1-3 PqQuitAll</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X7EE8000A800CEE2D">5.2 <span class="Heading">Interactive ANUPQ Process Utility Functions</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X8558B20A80B999AE">5.2-1 PqProcessIndex</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X7E4A56D67C865291">5.2-2 PqProcessIndices</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X7C103DF78435AEC7">5.2-3 IsPqProcessAlive</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X823D2BBF7C4515D4">5.3 <span class="Heading">Interactive Versions of Non-interactive ANUPQ Functions</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X85408C4C790439E7">5.3-1 Pq</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X839E6F578227A8EA">5.3-2 PqEpimorphism</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X7AA64A2F8509A39A">5.3-3 PqPCover</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X805F32618005C087">5.3-4 PqStandardPresentation</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X791392977B2D692D">5.3-5 EpimorphismPqStandardPresentation</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X795817217C53AB89">5.3-6 PqDescendants</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X80CCF6D379E5A3B4">5.3-7 PqSetPQuotientToGroup</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X857F050C832A1FE4">5.4 <span class="Heading">Low-level Interactive ANUPQ functions based on menu items of the
pq program</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X868B10557D470CF6">5.5 <span class="Heading">General commands</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X7DE2F6C686C672DD">5.5-1 PqNrPcGenerators</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X87FF98867E8FFB3C">5.5-2 PqFactoredOrder</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X7B4FC9E380001A71">5.5-3 PqOrder</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X87C7F7EB7C10DC4B">5.5-4 PqPClass</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X7EA3B6917908C20A">5.5-5 PqWeight</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X79862B83817E20E1">5.5-6 PqCurrentGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X805A50687D82B9EC">5.5-7 PqDisplayPcPresentation</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X80410979854280E1">5.5-8 PqSetOutputLevel</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X7B8C72B37AE667F7">5.5-9 PqEvaluateIdentities</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X7BDD5B278719C630">5.6 <span class="Heading">Commands from the Main <span class="SimpleMath">\(p\)</span>-Quotient menu</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X7BF135DD84A781EB">5.6-1 PqPcPresentation</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X7D947CEA82C44898">5.6-2 PqSavePcPresentation</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X7FD001C0798EF219">5.6-3 PqRestorePcPresentation</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X832F69597C095A27">5.6-4 PqNextClass</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X7CF9DF7A84D387CB">5.6-5 PqComputePCover</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X7D27BE937B1DE16E">5.7 <span class="Heading">Commands from the Advanced <span class="SimpleMath">\(p\)</span>-Quotient menu</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X8633356078CA4115">5.7-1 PqCollect</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X86CCB77281FDC0FC">5.7-2 PqSolveEquation</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X789B120B7E2F3017">5.7-3 PqCommutator</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X7A61A15E78F52743">5.7-4 PqSetupTablesForNextClass</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X84F7DD8582B368D3">5.7-5 PqTails</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X8389F6437ED634B8">5.7-6 PqComputeTails</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X83CD6D888372DFB8">5.7-7 PqAddTails</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X82AA8FAE85826BB9">5.7-8 PqDoConsistencyChecks</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X7A01EE0382689928">5.7-9 PqCollectDefiningRelations</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X7C2B4C1E7BEB19D5">5.7-10 PqCollectWordInDefiningGenerators</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X7DB05AA587D7A052">5.7-11 PqCommutatorDefiningGenerators</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X80E563A97EDE083E">5.7-12 PqDoExponentChecks</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X7BBAB2787B305516">5.7-13 PqEliminateRedundantGenerators</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X783E53B5853F45E6">5.7-14 PqRevertToPreviousClass</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X8265A6DB81CD24DB">5.7-15 PqSetMaximalOccurrences</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X87A35ABB7E11595E">5.7-16 PqSetMetabelian</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X7C7D17F878AA1BAA">5.7-17 PqDoConsistencyCheck</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X843953F48319FDE1">5.7-18 PqCompact</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X80344EEC78A09ACF">5.7-19 PqEchelonise</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X852947327FC39DDF">5.7-20 PqSupplyAutomorphisms</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X7B919B537C042DAD">5.7-21 PqExtendAutomorphisms</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X7CFD54657DE4BD39">5.7-22 PqApplyAutomorphisms</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X81A3D5BF87A34934">5.7-23 PqDisplayStructure</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X853834B478C4EEE2">5.7-24 PqDisplayAutomorphisms</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X80687A138626EB2D">5.7-25 PqWritePcPresentation</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X7B94EDA385FDD904">5.8 <span class="Heading">Commands from the Standard Presentation menu</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X78D1963D85C71B7B">5.8-1 PqSPComputePcpAndPCover</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X876F30187E89E467">5.8-2 PqSPStandardPresentation</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X7E1B2B088322F48A">5.8-3 PqSPSavePresentation</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X81D2F9FF7C241D1E">5.8-4 PqSPCompareTwoFilePresentations</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X7D1277E584590ECE">5.8-5 PqSPIsomorphism</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X8490031B7AA7F237">5.9 <span class="Heading">Commands from the Main <span class="SimpleMath">\(p\)</span>-Group Generation menu</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X794A8D667A9D725A">5.9-1 PqPGSupplyAutomorphisms</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X87F251077C65B6DD">5.9-2 PqPGExtendAutomorphisms</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X82FD51A27D269E43">5.9-3 PqPGConstructDescendants</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X7E9D511385D48A98">5.9-4 PqPGSetDescendantToPcp</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X7E8FBC2D83C43481">5.10 <span class="Heading">Commands from the Advanced <span class="SimpleMath">\(p\)</span>-Group Generation menu</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X7E539E4B78A6CE8D">5.10-1 PqAPGDegree</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X7F1182A77AB7650C">5.10-2 PqAPGPermutations</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X7DD9E7507AA888CC">5.10-3 PqAPGOrbits</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X795A756C78BE5923">5.10-4 PqAPGOrbitRepresentatives</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X7E5D6D5782FE190E">5.10-5 PqAPGSingleStage</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X84A92E8087762DEE">5.11 <span class="Heading">Primitive Interactive ANUPQ Process Read/Write Functions</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X8464AF7E83A523C1">5.11-1 PqRead</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X7ADD82207D049A87">5.11-2 PqReadAll</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X7EBF3C3681671879">5.11-3 PqReadUntil</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5_mj.html#X83CBE77F78057E21">5.11-4 PqWrite</a></span>
</div></div>
</div>
<h3>5 <span class="Heading">Interactive ANUPQ functions</span></h3>
<p>Here we describe the interactive functions defined by the <strong class="pkg">ANUPQ</strong> package, i.e. the functions that manipulate and initiate interactive <strong class="pkg">ANUPQ</strong> processes. These are functions that extract information via a dialogue with a running <code class="code">pq</code> process (process used in the UNIX sense). Occasionally, a user needs the <q>next step</q>; the functions provided in this chapter make use of data from previous steps retained by the <code class="code">pq</code> program, thus allowing the user to interact with the <code class="code">pq</code> program like one can when one uses the <code class="code">pq</code> program as a stand-alone (see <code class="code">guide.dvi</code> in the <code class="code">standalone-doc</code> directory).</p>
<p>An interactive <strong class="pkg">ANUPQ</strong> process is initiated by <code class="code">PqStart</code> and terminated via <code class="code">PqQuit</code>; these functions are described in ection <a href="chap5_mj.html#X7935CDAD7936CA0A"><span class="RefLink"><span class="Heading">Starting and Stopping Interactive ANUPQ Processes</span></span></a>.</p>
<p>Each interactive <strong class="pkg">ANUPQ</strong> function that manipulates an already started interactive <strong class="pkg">ANUPQ</strong> process, has a form where the first argument is the integer <var class="Arg">i</var> returned by the initiating <code class="code">PqStart</code> command, and a second form with one argument fewer (where the integer <var class="Arg">i</var> is discovered by a default mechanism, namely by determining the least integer <var class="Arg">i</var> for which there is a currently active interactive <strong class="pkg">ANUPQ</strong> process). We will thus commonly say that <q>for the <var class="Arg">i</var>th (or default) interactive <strong class="pkg">ANUPQ</strong> process</q> a certain function performs a given action. In each case, it is an error if <var class="Arg">i</var> is not the index of an active interactive process, or there are no current active interactive processes.</p>
<p><em>Notes</em>: The global method of passing options (via <code class="code">PushOptions</code>), should not be used with any of the interactive functions. In fact, the <code class="code">OptionsStack</code> should be empty at the time any of the interactive functions is called.</p>
<p>On <code class="keyw">quit</code>ting <strong class="pkg">GAP</strong>, <code class="code">PqQuitAll();</code> is executed, which terminates all active interactive <strong class="pkg">ANUPQ</strong> processes. If <strong class="pkg">GAP</strong> is killed without <code class="keyw">quit</code>ting, before all interactive <strong class="pkg">ANUPQ</strong> processes are terminated, <em>zombie</em> processes (still living <em>child</em> processes whose <em>parents</em> have died), may result. Since zombie processes do consume resources, in such an event, the responsible computer user should seek out and terminate those zombie processes (e.g. on Linux: <code class="code">ps xw | grep pq</code> gives you information on the <code class="code">pq</code> processes corresponding to any interactive <strong class="pkg">ANUPQ</strong> processes started in a <strong class="pkg">GAP</strong> session; you can then do <code class="code">kill <var class="Arg">N</var></code> for each number <var class="Arg">N</var> appearing in the first column of this output).</p>
<p><a id="X7935CDAD7936CA0A" name="X7935CDAD7936CA0A"></a></p>
<h4>5.1 <span class="Heading">Starting and Stopping Interactive ANUPQ Processes</span></h4>
<p><a id="X83B2EC237F37623C" name="X83B2EC237F37623C"></a></p>
<h5>5.1-1 PqStart</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ PqStart</code>( <var class="Arg">G</var>, <var class="Arg">workspace:</var> <var class="Arg">options</var> )</td><td class="tdright">( function )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ PqStart</code>( <var class="Arg">G:</var> <var class="Arg">options</var> )</td><td class="tdright">( function )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ PqStart</code>( <var class="Arg">workspace:</var> <var class="Arg">options</var> )</td><td class="tdright">( function )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ PqStart</code>( <var class="Arg">:</var> <var class="Arg">options</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>activate an iostream for an interactive <strong class="pkg">ANUPQ</strong> process (i.e. <code class="code">PqStart</code> starts up a <code class="code">pq</code> process and opens a <strong class="pkg">GAP</strong> iostream to <q>talk</q> to that process) and returns an integer <var class="Arg">i</var> that can be used to identify that process. The argument <var class="Arg">G</var> should be an <em>fp group</em> or <em>pc group</em> that the user intends to manipulate using interactive <strong class="pkg">ANUPQ</strong> functions. If the function is called without specifying <var class="Arg">G</var>, a group can be read in by using the function <code class="code">PqRestorePcPresentation</code> (see <code class="func">PqRestorePcPresentation</code> (<a href="chap5_mj.html#X7FD001C0798EF219"><span class="RefLink">5.6-3</span></a>)). If <code class="code">PqStart</code> is given an integer argument <var class="Arg">workspace</var>, then the <code class="code">pq</code> program is started up with a workspace (an integer array) of size <var class="Arg">workspace</var> (i.e. <span class="SimpleMath">\(4 \times \textit{workspace}\)</span> bytes in a 32-bit environment); otherwise, the <code class="code">pq</code> program sets a default workspace of <span class="SimpleMath">\(10000000\)</span>.</p>
<p>The only <var class="Arg">options</var> currently recognised by <code class="code">PqStart</code> are <code class="code">Prime</code>, <code class="code">Exponent</code> and <code class="code">Relators</code> (see Chapter <a href="chap6_mj.html#X7B0946E97E7EB359"><span class="RefLink"><span class="Heading">ANUPQ Options</span></span></a> for detailed descriptions of these options) and if provided they are essentially global for the interactive <strong class="pkg">ANUPQ</strong> process, except that any interactive function interacting with the process and passing new values for these options will over-ride the global values.</p>
<p><a id="X79DB761185BAB9C8" name="X79DB761185BAB9C8"></a></p>
<h5>5.1-2 PqQuit</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ PqQuit</code>( <var class="Arg">i</var> )</td><td class="tdright">( function )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ PqQuit</code>( )</td><td class="tdright">( function )</td></tr></table></div>
<p>closes the stream of the <var class="Arg">i</var>th or default interactive <strong class="pkg">ANUPQ</strong> process and unbinds its <code class="code">ANUPQData.io</code> record.</p>
<p><em>Note:</em> It can happen that the <code class="code">pq</code> process, and hence the <strong class="pkg">GAP</strong> iostream assigned to communicate with it, can die, e.g. by the user typing a <code class="code">Ctrl-C</code> while the <code class="code">pq</code> process is engaged in a long calculation. <code class="code">IsPqProcessAlive</code> (see <code class="func">IsPqProcessAlive</code> (<a href="chap5_mj.html#X7C103DF78435AEC7"><span class="RefLink">5.2-3</span></a>)) is provided to check the status of the <strong class="pkg">GAP</strong> iostream (and hence the status of the <code class="code">pq</code> process it was communicating with).</p>
<p><a id="X7FF8F2657B1B008E" name="X7FF8F2657B1B008E"></a></p>
<h5>5.1-3 PqQuitAll</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ PqQuitAll</code>( )</td><td class="tdright">( function )</td></tr></table></div>
<p>is provided as a convenience, to terminate all active interactive <strong class="pkg">ANUPQ</strong> processes with a single command. It is equivalent to executing <code class="code">PqQuit(<var class="Arg">i</var>)</code> for all active interactive <strong class="pkg">ANUPQ</strong> processes <var class="Arg">i</var> (see <code class="func">PqQuit</code> (<a href="chap5_mj.html#X79DB761185BAB9C8"><span class="RefLink">5.1-2</span></a>)).</p>
<p><a id="X7EE8000A800CEE2D" name="X7EE8000A800CEE2D"></a></p>
<h4>5.2 <span class="Heading">Interactive ANUPQ Process Utility Functions</span></h4>
<p><a id="X8558B20A80B999AE" name="X8558B20A80B999AE"></a></p>
<h5>5.2-1 PqProcessIndex</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ PqProcessIndex</code>( <var class="Arg">i</var> )</td><td class="tdright">( function )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ PqProcessIndex</code>( )</td><td class="tdright">( function )</td></tr></table></div>
<p>With argument <var class="Arg">i</var>, which must be a positive integer, <code class="code">PqProcessIndex</code> returns <var class="Arg">i</var> if it corresponds to an active interactive process, or raises an error. With no arguments it returns the default active interactive process or returns <code class="keyw">fail</code> and emits a warning message to <code class="code">Info</code> at <code class="code">InfoANUPQ</code> or <code class="code">InfoWarning</code> level 1.</p>
<p><em>Note:</em> Essentially, an interactive <strong class="pkg">ANUPQ</strong> process <var class="Arg">i</var> is <q>active</q> if <code class="code">ANUPQData.io[<var class="Arg">i</var>]</code> is bound (i.e. we still have some data telling us about it). Also see <code class="func">PqStart</code> (<a href="chap5_mj.html#X83B2EC237F37623C"><span class="RefLink">5.1-1</span></a>).</p>
<p><a id="X7E4A56D67C865291" name="X7E4A56D67C865291"></a></p>
<h5>5.2-2 PqProcessIndices</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ PqProcessIndices</code>( )</td><td class="tdright">( function )</td></tr></table></div>
<p>returns the list of integer indices of all active interactive <strong class="pkg">ANUPQ</strong> processes (see <code class="func">PqProcessIndex</code> (<a href="chap5_mj.html#X8558B20A80B999AE"><span class="RefLink">5.2-1</span></a>) for the meaning of <q>active</q>).</p>
<p><a id="X7C103DF78435AEC7" name="X7C103DF78435AEC7"></a></p>
<h5>5.2-3 IsPqProcessAlive</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsPqProcessAlive</code>( <var class="Arg">i</var> )</td><td class="tdright">( function )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsPqProcessAlive</code>( )</td><td class="tdright">( function )</td></tr></table></div>
<p>return <code class="keyw">true</code> if the <strong class="pkg">GAP</strong> iostream of the <var class="Arg">i</var>th (or default) interactive <strong class="pkg">ANUPQ</strong> process started by <code class="code">PqStart</code> is alive (i.e. can still be written to), or <code class="keyw">false</code>, otherwise. (See the notes for <code class="func">PqStart</code> (<a href="chap5_mj.html#X83B2EC237F37623C"><span class="RefLink">5.1-1</span></a>) and <code class="func">PqQuit</code> (<a href="chap5_mj.html#X79DB761185BAB9C8"><span class="RefLink">5.1-2</span></a>).)</p>
<p>If the user does not yet have a <code class="code">gap></code> prompt then usually the <code class="code">pq</code> program is still away doing something and an <strong class="pkg">ANUPQ</strong> interface function is still waiting for a reply. Typing a <code class="code">Ctrl-C</code> (i.e. holding down the <code class="code">Ctrl</code> key and typing <code class="code">c</code>) will stop the waiting and send <strong class="pkg">GAP</strong> into a <code class="code">break</code>-loop, from which one has no option but to <code class="code">quit;</code>. The typing of <code class="code">Ctrl-C</code>, in such a circumstance, usually causes the stream of the interactive <strong class="pkg">ANUPQ</strong> process to die; to check this we provide <code class="code">IsPqProcessAlive</code> (see <code class="func">IsPqProcessAlive</code>).</p>
<p>The <strong class="pkg">GAP</strong> iostream of an interactive <strong class="pkg">ANUPQ</strong> process will also die if the <code class="code">pq</code> program has a segmentation fault. We do hope that this never happens to you, but if it does and the failure is reproducible, then it's a bug and we'd like to know about it. Please read the <code class="code">README</code> that comes with the <strong class="pkg">ANUPQ</strong> package to find out what to include in a bug report and who to email it to.</p>
<p><a id="X823D2BBF7C4515D4" name="X823D2BBF7C4515D4"></a></p>
<h4>5.3 <span class="Heading">Interactive Versions of Non-interactive ANUPQ Functions</span></h4>
<p><a id="X85408C4C790439E7" name="X85408C4C790439E7"></a></p>
<h5>5.3-1 Pq</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Pq</code>( <var class="Arg">i:</var> <var class="Arg">options</var> )</td><td class="tdright">( function )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Pq</code>( <var class="Arg">:</var> <var class="Arg">options</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>return, for the fp or pc group (let us call it <var class="Arg">F</var>), of the <var class="Arg">i</var>th or default interactive <strong class="pkg">ANUPQ</strong> process, the <span class="SimpleMath">\(p\)</span>-quotient of <var class="Arg">F</var> specified by <var class="Arg">options</var>, as a pc group; <var class="Arg">F</var> must previously have been given (as first argument) to <code class="code">PqStart</code> to start the interactive <strong class="pkg">ANUPQ</strong> process (see <code class="func">PqStart</code> (<a href="chap5_mj.html#X83B2EC237F37623C"><span class="RefLink">5.1-1</span></a>)) or restored from file using the function <code class="code">PqRestorePcPresentation</code> (see <code class="func">PqRestorePcPresentation</code> (<a href="chap5_mj.html#X7FD001C0798EF219"><span class="RefLink">5.6-3</span></a>)). Following the colon <var class="Arg">options</var> is a selection of the options listed for the non-interactive <code class="code">Pq</code> function (see <code class="func">Pq</code> (<a href="chap4_mj.html#X86DD32D5803CF2C8"><span class="RefLink">4.1-1</span></a>)), separated by commas like record components (see Section <a href="../../../doc/ref/chap4_mj.html#X867D54987EF86D1D"><span class="RefLink">Reference: Function Call With Options</span></a> in the <strong class="pkg">GAP</strong> Reference Manual), except that the options <code class="code">SetupFile</code> or <code class="code">PqWorkspace</code> are ignored by the interactive <code class="code">Pq</code>, and <code class="code">RedoPcp</code> is an option only recognised by the interactive <code class="code">Pq</code> i.e. the following options are recognised by the interactive <code class="code">Pq</code> function:</p>
<ul>
<li><p><code class="code">Prime := <var class="Arg">p</var></code></p>
</li>
<li><p><code class="code">ClassBound := <var class="Arg">n</var></code></p>
</li>
<li><p><code class="code">Exponent := <var class="Arg">n</var></code></p>
</li>
<li><p><code class="code">Relators := <var class="Arg">rels</var></code></p>
</li>
<li><p><code class="code">Metabelian</code></p>
</li>
<li><p><code class="code">Identities := <var class="Arg">funcs</var></code></p>
</li>
<li><p><code class="code">GroupName := <var class="Arg">name</var></code></p>
</li>
<li><p><code class="code">OutputLevel := <var class="Arg">n</var></code></p>
</li>
<li><p><code class="code">RedoPcp</code></p>
</li>
</ul>
<p>Detailed descriptions of the above options may be found in Chapter <a href="chap6_mj.html#X7B0946E97E7EB359"><span class="RefLink"><span class="Heading">ANUPQ Options</span></span></a>.</p>
<p>As a minimum the <code class="code">Pq</code> function <em>must</em> have a value for the <code class="code">Prime</code> option, though <code class="code">Prime</code> need not be passed again in the case it has previously been provided, e.g. to <code class="code">PqStart</code> (see <code class="func">PqStart</code> (<a href="chap5_mj.html#X83B2EC237F37623C"><span class="RefLink">5.1-1</span></a>)) when starting the interactive process.</p>
<p>The behaviour of the interactive <code class="code">Pq</code> function depends on the current state of the pc presentation stored by the <code class="code">pq</code> program:</p>
<ol>
<li><p>If no pc presentation has yet been computed (the case immediately after the <code class="code">PqStart</code> call initiating the process) then the quotient group of the input group of the process of largest lower exponent-<var class="Arg">p</var> class bounded by the value of the <code class="code">ClassBound</code> option (see <a href="chap6_mj.html#X87EE6DD67C9996A3"><span class="RefLink">6.2</span></a>) is returned.</p>
</li>
<li><p>If the current pc presentation of the process was determined by a previous call to <code class="code">Pq</code> or <code class="code">PqEpimorphism</code>, and the current call has a larger value <code class="code">ClassBound</code> then the class is extended as much as is possible and the quotient group of the input group of the process of the new lower exponent-<var class="Arg">p</var> class is returned.</p>
</li>
<li><p>If the current pc presentation of the process was determined by a previous call to <code class="code">PqPCover</code> then a consistent pc presentation of a quotient for the current class is determined before proceeding as in 2.</p>
</li>
<li><p>If the <code class="code">RedoPcp</code> option is supplied the current pc presentation is scrapped, all options must be re-supplied (in particular, <code class="code">Prime</code> <em>must</em> be supplied) and then the <code class="code">Pq</code> function proceeds as in 1.</p>
</li>
</ol>
<p>See Section <a href="chap3_mj.html#X818175EF85CAA807"><span class="RefLink"><span class="Heading">Attributes and a Property for fp and pc p-groups</span></span></a> for the attributes and property <code class="code">NuclearRank</code>, <code class="code">MultiplicatorRank</code> and <code class="code">IsCapable</code> which may be applied to the group returned by <code class="code">Pq</code>.</p>
<p>The following is one of the examples for the non-interactive <code class="code">Pq</code> redone with the interactive version. Also, we set the option <code class="code">OutputLevel</code> to 1 (see <a href="chap6_mj.html#X87EE6DD67C9996A3"><span class="RefLink">6.2</span></a>), in order to see the orders of the quotients of all the classes determined, and we set the <code class="code">InfoANUPQ</code> level to 2 (see <code class="func">InfoANUPQ</code> (<a href="chap3_mj.html#X7CBC9B458497BFF1"><span class="RefLink">3.3-1</span></a>)), so that we catch the timing information.</p>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">F := FreeGroup("a", "b");; a := F.1;; b := F.2;;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">G := F / [a^4, b^4];</span>
<fp group on the generators [ a, b ]>
<span class="GAPprompt">gap></span> <span class="GAPinput">PqStart(G);</span>
1
<span class="GAPprompt">gap></span> <span class="GAPinput">SetInfoLevel(InfoANUPQ, 2); #To see timing information</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">Pq(: Prime := 2, ClassBound := 3, OutputLevel := 1 );</span>
#I Lower exponent-2 central series for [grp]
#I Group: [grp] to lower exponent-2 central class 1 has order 2^2
#I Group: [grp] to lower exponent-2 central class 2 has order 2^5
#I Group: [grp] to lower exponent-2 central class 3 has order 2^8
#I Computation of presentation took 0.00 seconds
<pc group of size 256 with 8 generators>
</pre></div>
<p><a id="X839E6F578227A8EA" name="X839E6F578227A8EA"></a></p>
<h5>5.3-2 PqEpimorphism</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ PqEpimorphism</code>( <var class="Arg">i:</var> <var class="Arg">options</var> )</td><td class="tdright">( function )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ PqEpimorphism</code>( <var class="Arg">:</var> <var class="Arg">options</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>return, for the fp or pc group (let us call it <var class="Arg">F</var>), of the <var class="Arg">i</var>th or default interactive <strong class="pkg">ANUPQ</strong> process, an epimorphism from <var class="Arg">F</var> onto the <span class="SimpleMath">\(p\)</span>-quotient of <var class="Arg">F</var> specified by <var class="Arg">options</var>; <var class="Arg">F</var> must previously have been given (as first argument) to <code class="code">PqStart</code> to start the interactive <strong class="pkg">ANUPQ</strong> process (see <code class="func">PqStart</code> (<a href="chap5_mj.html#X83B2EC237F37623C"><span class="RefLink">5.1-1</span></a>)). Since the underlying interactions with the <code class="code">pq</code> program effected by the interactive <code class="code">PqEpimorphism</code> are identical to those effected by the interactive <code class="code">Pq</code>, everything said regarding the requirements and behaviour of the interactive <code class="code">Pq</code> function (see <code class="func">Pq</code> (<a href="chap5_mj.html#X85408C4C790439E7"><span class="RefLink">5.3-1</span></a>)) is also the case for the interactive <code class="code">PqEpimorphism</code>.</p>
<p><em>Note:</em> See Section <a href="chap3_mj.html#X818175EF85CAA807"><span class="RefLink"><span class="Heading">Attributes and a Property for fp and pc p-groups</span></span></a> for the attributes and property <code class="code">NuclearRank</code>, <code class="code">MultiplicatorRank</code> and <code class="code">IsCapable</code> which may be applied to the image group of the epimorphism returned by <code class="code">PqEpimorphism</code>.</p>
<p><a id="X7AA64A2F8509A39A" name="X7AA64A2F8509A39A"></a></p>
<h5>5.3-3 PqPCover</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ PqPCover</code>( <var class="Arg">i:</var> <var class="Arg">options</var> )</td><td class="tdright">( function )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ PqPCover</code>( <var class="Arg">:</var> <var class="Arg">options</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>return, for the fp or pc group of the <var class="Arg">i</var>th or default interactive <strong class="pkg">ANUPQ</strong> process, the <span class="SimpleMath">\(p\)</span>-covering group of the <span class="SimpleMath">\(p\)</span>-quotient <code class="code">Pq(<var class="Arg">i</var> : <var class="Arg">options</var>)</code> or <code class="code">Pq(: <var class="Arg">options</var>)</code>, modulo the following:</p>
<ol>
<li><p>If no pc presentation has yet been computed (the case immediately after the <code class="code">PqStart</code> call initiating the process) and the group <var class="Arg">F</var> of the process is already a <span class="SimpleMath">\(p\)</span>-group, in the sense that <code class="code">HasIsPGroup(<var class="Arg">F</var>) and IsPGroup(<var class="Arg">F</var>)</code> is <code class="keyw">true</code>, then</p>
<dl>
<dt><strong class="Mark"><code class="code">Prime</code></strong></dt>
<dd><p>defaults to <code class="code">PrimePGroup(<var class="Arg">F</var>)</code>, if not supplied and <code class="code">HasPrimePGroup(<var class="Arg">F</var>) = true</code>; and</p>
</dd>
<dt><strong class="Mark"><code class="code">ClassBound</code></strong></dt>
<dd><p>defaults to <code class="code">PClassPGroup(<var class="Arg">F</var>)</code> if <code class="code">HasPClassPGroup(<var class="Arg">F</var>) = true</code> if not supplied, or to the usual default of 63, otherwise.</p>
</dd>
</dl>
</li>
<li><p>If a pc presentation has been computed and none of <var class="Arg">options</var> is <code class="code">RedoPcp</code> or if no pc presentation has yet been computed but 1. does not apply then <code class="code">PqPCover(<var class="Arg">i</var> : <var class="Arg">options</var>);</code> is equivalent to:</p>
<div class="example"><pre>
Pq(i : options);
PqPCover(i);
</pre></div>
</li>
<li><p>If the <code class="code">RedoPcp</code> option is supplied the current pc presentation is scrapped, and <code class="code">PqPCover</code> proceeds as in 1. or 2. but without the <code class="code">RedoPcp</code> option.</p>
</li>
</ol>
<p><a id="X805F32618005C087" name="X805F32618005C087"></a></p>
<h5>5.3-4 PqStandardPresentation</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ PqStandardPresentation</code>( [<var class="Arg">i</var>]<var class="Arg">:</var> <var class="Arg">options</var> )</td><td class="tdright">( function )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ StandardPresentation</code>( [<var class="Arg">i</var>]<var class="Arg">:</var> <var class="Arg">options</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>return, for the <var class="Arg">i</var>th or default interactive <strong class="pkg">ANUPQ</strong> process, the <var class="Arg">p</var>-quotient of the group <var class="Arg">F</var> of the process, specified by <var class="Arg">options</var>, as an <em>fp group</em> which has a standard presentation. Here <var class="Arg">options</var> is a selection of the options from the following list (see Chapter <a href="chap6_mj.html#X7B0946E97E7EB359"><span class="RefLink"><span class="Heading">ANUPQ Options</span></span></a> for detailed descriptions); this list is the same as for the non-interactive version of <code class="code">PqStandardPresentation</code> except for the omission of options <code class="code">SetupFile</code> and <code class="code">PqWorkspace</code> (see <code class="func">PqStandardPresentation</code> (<a href="chap4_mj.html#X86C9575D7CB65FBB"><span class="RefLink">4.2-1</span></a>)).</p>
<ul>
<li><p><code class="code">Prime := <var class="Arg">p</var></code></p>
</li>
<li><p><code class="code">pQuotient := <var class="Arg">Q</var></code></p>
</li>
<li><p><code class="code">ClassBound := <var class="Arg">n</var></code></p>
</li>
<li><p><code class="code">Exponent := <var class="Arg">n</var></code></p>
</li>
<li><p><code class="code">Metabelian</code></p>
</li>
<li><p><code class="code">GroupName := <var class="Arg">name</var></code></p>
</li>
<li><p><code class="code">OutputLevel := <var class="Arg">n</var></code></p>
</li>
<li><p><code class="code">StandardPresentationFile := <var class="Arg">filename</var></code></p>
</li>
</ul>
<p>Unless <var class="Arg">F</var> is a pc <var class="Arg">p</var>-group, or the option <code class="code">Prime</code> has been passed to a previous interactive function for the process to compute a <var class="Arg">p</var>-quotient for <var class="Arg">F</var>, the user <em>must</em> supply either the option <code class="code">Prime</code> or the option <code class="code">pQuotient</code> (if both <code class="code">Prime</code> and <code class="code">pQuotient</code> are supplied, the prime <var class="Arg">p</var> is determined by applying <code class="code">PrimePGroup</code> (see <code class="func">PrimePGroup</code> (<a href="../../../doc/ref/chap39_mj.html#X87356BAA7E9E2142"><span class="RefLink">Reference: PrimePGroup</span></a>) in the Reference Manual) to the value of <code class="code">pQuotient</code>).</p>
<p>Taking one of the examples for the non-interactive version of <code class="code">StandardPresentation</code> (see <code class="func">StandardPresentation</code> (<a href="chap4_mj.html#X86C9575D7CB65FBB"><span class="RefLink">4.2-1</span></a>)) that required two separate calls to the <code class="code">pq</code> program, we now show how it can be done by setting up a dialogue with just the one <code class="code">pq</code> process, using the interactive version of <code class="code">StandardPresentation</code>:</p>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">F4 := FreeGroup( "a", "b", "c", "d" );;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">a := F4.1;; b := F4.2;; c := F4.3;; d := F4.4;;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">G4 := F4 / [ b^4, b^2 / Comm(Comm (b, a), a), d^16,</span>
<span class="GAPprompt">></span> <span class="GAPinput"> a^16 / (c * d), b^8 / (d * c^4) ];</span>
<fp group on the generators [ a, b, c, d ]>
<span class="GAPprompt">gap></span> <span class="GAPinput">SetInfoLevel(InfoANUPQ, 1); #Only essential Info please</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">PqStart(G4); #Start a new interactive process for a new group</span>
2
<span class="GAPprompt">gap></span> <span class="GAPinput">K := Pq( 2 : Prime := 2, ClassBound := 1 ); #`pq' process no. is 2</span>
<pc group of size 4 with 2 generators>
<span class="GAPprompt">gap></span> <span class="GAPinput">StandardPresentation( 2 : pQuotient := K, ClassBound := 14 );</span>
<fp group with 53 generators>
</pre></div>
<p><em>Notes</em></p>
<p>In contrast to the function <code class="code">Pq</code> (see <code class="func">Pq</code> (<a href="chap4_mj.html#X86DD32D5803CF2C8"><span class="RefLink">4.1-1</span></a>)) which returns a pc group, <code class="code">PqStandardPresentation</code> or <code class="code">StandardPresentation</code> returns an fp group. This is because the output is mainly used for isomorphism testing for which an fp group is enough. However, the presentation is a polycyclic presentation and if you need to do any further computation with this group (e.g. to find the order) you can use the function <code class="code">PcGroupFpGroup</code> (see <code class="func">PcGroupFpGroup</code> (<a href="../../../doc/ref/chap46_mj.html#X84C10D1F7CB5274F"><span class="RefLink">Reference: PcGroupFpGroup</span></a>) in the <strong class="pkg">GAP</strong> Reference Manual) to form a pc group.</p>
<p>If the user does not supply a <var class="Arg">p</var>-quotient <var class="Arg">Q</var> via the <code class="code">pQuotient</code> option, and the prime <var class="Arg">p</var> is either supplied, stored, or <var class="Arg">F</var> is a pc <var class="Arg">p</var>-group, then a <var class="Arg">p</var>-quotient <var class="Arg">Q</var> is computed. (The value of the prime <var class="Arg">p</var> is stored if passed initially to <code class="code">PqStart</code> or to a subsequent interactive process.) Note that a stored value for <code class="code">pQuotient</code> (from a prior call to <code class="code">Pq</code>) does <em>not</em> have precedence over a value for the prime <var class="Arg">p</var>. If the user does supply a <var class="Arg">p</var>-quotient <var class="Arg">Q</var> via the <code class="code">pQuotient</code> option, the package <strong class="pkg">AutPGrp</strong> is called to compute the automorphism group of <var class="Arg">Q</var>; an error will occur that asks the user to install the package <strong class="pkg">AutPGrp</strong> if the automorphism group cannot be computed.</p>
<p>If any of the interactive functions <code class="code">PqStandardPresentation</code>, <code class="code">StandardPresentation</code>, <code class="code">EpimorphismPqStandardPresentation</code> or <code class="code">EpimorphismStandardPresentation</code> has been called previously for an interactive process, a subsequent call to any of these functions for the same process returns the previously computed value. Note that all these functions compute both an epimorphism and an fp group and store the results in the <code class="code">SPepi</code> and <code class="code">SP</code> fields of the data record associated with the process. See the example for the interactive <code class="code">EpimorphismStandardPresentation</code> (<code class="func">EpimorphismStandardPresentation</code> (<a href="chap5_mj.html#X791392977B2D692D"><span class="RefLink">5.3-5</span></a>)).</p>
<p>The attributes and property <code class="code">NuclearRank</code>, <code class="code">MultiplicatorRank</code> and <code class="code">IsCapable</code> are set for the group returned by <code class="code">PqStandardPresentation</code> or <code class="code">StandardPresentation</code> (see Section <a href="chap3_mj.html#X818175EF85CAA807"><span class="RefLink"><span class="Heading">Attributes and a Property for fp and pc p-groups</span></span></a>).</p>
<p><a id="X791392977B2D692D" name="X791392977B2D692D"></a></p>
<h5>5.3-5 EpimorphismPqStandardPresentation</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ EpimorphismPqStandardPresentation</code>( [<var class="Arg">i</var>]<var class="Arg">:</var> <var class="Arg">options</var> )</td><td class="tdright">( function )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ EpimorphismStandardPresentation</code>( [<var class="Arg">i</var>]<var class="Arg">:</var> <var class="Arg">options</var> )</td><td class="tdright">( method )</td></tr></table></div>
<p>Each of the above functions accepts the same arguments and options as the interactive form of <code class="code">StandardPresentation</code> (see <code class="func">StandardPresentation</code> (<a href="chap5_mj.html#X805F32618005C087"><span class="RefLink">5.3-4</span></a>)) and returns an epimorphism from the fp or pc group <var class="Arg">F</var> of the <var class="Arg">i</var>th or default interactive <strong class="pkg">ANUPQ</strong> process onto the finitely presented group given by a standard presentation, i.e. if <var class="Arg">S</var> is the standard presentation computed for the <span class="SimpleMath">\(p\)</span>-quotient of <var class="Arg">F</var> by <code class="code">StandardPresentation</code> then <code class="code">EpimorphismStandardPresentation</code> returns the epimorphism from <var class="Arg">F</var> to the group with presentation <var class="Arg">S</var>. The group <var class="Arg">F</var> must have been given (as first argument) to <code class="code">PqStart</code> to start the interactive <strong class="pkg">ANUPQ</strong> process (see <code class="func">PqStart</code> (<a href="chap5_mj.html#X83B2EC237F37623C"><span class="RefLink">5.1-1</span></a>)).</p>
<p>Taking our earlier non-interactive example (see <code class="func">EpimorphismPqStandardPresentation</code> (<a href="chap4_mj.html#X828C06D083C0D089"><span class="RefLink">4.2-2</span></a>)) and modifying it a little, we illustrate, as for the interactive <code class="code">StandardPresentation</code> (see <code class="func">StandardPresentation</code> (<a href="chap5_mj.html#X805F32618005C087"><span class="RefLink">5.3-4</span></a>)), how something that required two separate calls to the <code class="code">pq</code> program can now be achieved with a dialogue with just one <code class="code">pq</code> process. Also, observe that calls to one of the standard presentation functions (as mentioned in the notes of <code class="func">StandardPresentation</code> (<a href="chap5_mj.html#X805F32618005C087"><span class="RefLink">5.3-4</span></a>)) computes and stores both an fp group with a standard presentation and an epimorphism; subsequent calls to a standard presentation function for the same process simply return the appropriate stored value.</p>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">F := FreeGroup(6, "F");;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">x := F.1;; y := F.2;; z := F.3;; w := F.4;; a := F.5;; b := F.6;;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">R := [x^3 / w, y^3 / w * a^2 * b^2, w^3 / b,</span>
<span class="GAPprompt">></span> <span class="GAPinput"> Comm (y, x) / z, Comm (z, x), Comm (z, y) / a, z^3 ];</span>
[ F1^3*F4^-1, F2^3*F4^-1*F5^2*F6^2, F4^3*F6^-1, F2^-1*F1^-1*F2*F1*F3^-1,
F3^-1*F1^-1*F3*F1, F3^-1*F2^-1*F3*F2*F5^-1, F3^3 ]
<span class="GAPprompt">gap></span> <span class="GAPinput">Q := F / R;</span>
<fp group on the generators [ F1, F2, F3, F4, F5, F6 ]>
<span class="GAPprompt">gap></span> <span class="GAPinput">PqStart( Q );</span>
3
<span class="GAPprompt">gap></span> <span class="GAPinput">G := Pq( 3 : Prime := 3, ClassBound := 3 );</span>
<pc group of size 729 with 6 generators>
<span class="GAPprompt">gap></span> <span class="GAPinput">lev := InfoLevel(InfoANUPQ);; # Save current InfoANUPQ level</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">SetInfoLevel(InfoANUPQ, 2); # To see computation times</span>
<span class="GAPprompt">gap></span> <span class="GAPinput"># It is not necessary to pass the `Prime' option to</span>
<span class="GAPprompt">gap></span> <span class="GAPinput"># `EpimorphismStandardPresentation' since it was previously</span>
<span class="GAPprompt">gap></span> <span class="GAPinput"># passed to `Pq':</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">phi := EpimorphismStandardPresentation( 3 : ClassBound := 3 );</span>
#I Class 1 3-quotient and its 3-covering group computed in 0.00 seconds
#I Order of GL subgroup is 48
#I No. of soluble autos is 0
#I dim U = 1 dim N = 3 dim M = 3
#I nice stabilizer with perm rep
#I Computing standard presentation for class 2 took 0.00 seconds
#I Computing standard presentation for class 3 took 0.01 seconds
[ F1, F2, F3, F4, F5, F6 ] -> [ f1*f2^2*f3*f4^2*f5^2, f1*f2*f3*f5, f3^2,
f4*f6^2, f5, f6 ]
<span class="GAPprompt">gap></span> <span class="GAPinput"># Image of phi should be isomorphic to G ...</span>
<span class="GAPprompt">gap></span> <span class="GAPinput"># let's check the order is correct:</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">Size( Image(phi) );</span>
729
<span class="GAPprompt">gap></span> <span class="GAPinput"># `StandardPresentation' and `EpimorphismStandardPresentation'</span>
<span class="GAPprompt">gap></span> <span class="GAPinput"># behave like attributes, so no computation is done when</span>
<span class="GAPprompt">gap></span> <span class="GAPinput"># either is called again for the same process ...</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">StandardPresentation( 3 : ClassBound := 3 );</span>
<fp group of size 729 on the generators [ f1, f2, f3, f4, f5, f6 ]>
<span class="GAPprompt">gap></span> <span class="GAPinput"># No timing data was Info-ed since no computation was done</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">SetInfoLevel(InfoANUPQ, lev); # Restore previous InfoANUPQ level</span>
</pre></div>
<p>A very similar (essential details are the same) example to the above may be executed live, by typing: <code class="code">PqExample( "EpimorphismStandardPresentation-i" );</code>.</p>
<p><em>Note:</em> The notes for <code class="code">PqStandardPresentation</code> or <code class="code">StandardPresentation</code> (see <code class="func">PqStandardPresentation</code> (<a href="chap5_mj.html#X805F32618005C087"><span class="RefLink">5.3-4</span></a>)) apply also to <code class="code">EpimorphismPqStandardPresentation</code> or <code class="code">EpimorphismStandardPresentation</code> except that their return value is an <em>epimorphism onto</em> an fp group, i.e. one should interpret the phrase <q>returns an fp group</q> as <q>returns an epimorphism onto an fp group</q> etc.</p>
<p><a id="X795817217C53AB89" name="X795817217C53AB89"></a></p>
<h5>5.3-6 PqDescendants</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ PqDescendants</code>( <var class="Arg">i:</var> <var class="Arg">options</var> )</td><td class="tdright">( function )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ PqDescendants</code>( <var class="Arg">:</var> <var class="Arg">options</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>return for the pc group <var class="Arg">G</var> of the <var class="Arg">i</var>th or default interactive <strong class="pkg">ANUPQ</strong> process, which must be of prime power order with a confluent pc presentation (see <code class="func">IsConfluent</code> (<a href="../../../doc/ref/chap46_mj.html#X7DF4835F79667099"><span class="RefLink">Reference: IsConfluent for pc groups</span></a>) in the <strong class="pkg">GAP</strong> Reference Manual), a list of descendants (pc groups) of <var class="Arg">G</var>. The group <var class="Arg">G</var> is usually given as first argument to <code class="code">PqStart</code> when starting the interactive <strong class="pkg">ANUPQ</strong> process (see <code class="func">PqStart</code> (<a href="chap5_mj.html#X83B2EC237F37623C"><span class="RefLink">5.1-1</span></a>)). Alternatively, one may initiate the process with an fp group, use <code class="code">Pq</code> interactively (see <code class="func">Pq</code> (<a href= | |
