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<p><a id="X7F77634D817156B3" name="X7F77634D817156B3"></a></p>
<div class="ChapSects"><a href="chap5.html#X7F77634D817156B3">5 <span class="Heading">Technicalities of the <strong class="pkg">AtlasRep</strong> Package</span></a>
<div class="ContSect"><span class="nocss"> </span><a href="chap5.html#X7DC2B7917DC30B28">5.1 <span class="Heading">Global Variables Used by the <strong class="pkg">AtlasRep</strong> Package
</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X8006BE167EB81E16">5.1-1 InfoAtlasRep</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X78601C3A87921E08">5.1-2 InfoCMeatAxe</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X80D5EF9A7FEF124B">5.1-3 InfoBBox</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X85B6010C85A06CB6">5.1-4 CMeatAxe.FastRead</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7BEC94A6781E126E">5.1-5 AtlasOfGroupRepresentationsInfo</a></span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap5.html#X81C5B5E78215169D">5.2 <span class="Heading">How to Customize the Access to Data files</span></a>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap5.html#X7D76D4437A9646E7">5.3 <span class="Heading">Reading and Writing MeatAxe Format Files</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X83D5103780E1238F">5.3-1 ScanMeatAxeFile</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7DDD09BE87063052">5.3-2 MeatAxeString</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X79D9AE4878E9DFA6">5.3-3 FFList</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X8477AA668733255C">5.3-4 CMtxBinaryFFMatOrPerm</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X872FA00C7F791FBB">5.3-5 FFMatOrPermCMtxBinary</a></span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap5.html#X7FEE162B7F63BEA0">5.4 <span class="Heading">Reading and Writing <strong class="pkg">ATLAS</strong> Straight Line Programs</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7D6617E47B013A37">5.4-1 ScanStraightLineProgram</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X82842D807A7B7DF7">5.4-2 AtlasStringOfProgram</a></span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap5.html#X86366BF08533DA5E">5.5 <span class="Heading">Data Types Used in the <strong class="pkg">ATLAS</strong> of Group Representations</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X832AB6B97BE4CD9F">5.5-1 AGRDeclareDataType</a></span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap5.html#X7D16BE31788F0E8A">5.6 <span class="Heading">Filenames Used in the <strong class="pkg">ATLAS</strong> of Group Representations</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X85D036A07A869C54">5.6-1 AGRParseFilenameFormat</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X819839FA7A639DE2">5.6-2 AGRFileContents</a></span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap5.html#X7D66C94E7A0F2252">5.7 <span class="Heading">The Tables of Contents of the <strong class="pkg">ATLAS</strong> of Group Representations
</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X8229700C8744F09B">5.7-1 AGRGNAN</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X86698BC778570236">5.7-2 AGRRNG</a></span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap5.html#X84A565E482DBF4C1">5.8 <span class="Heading">Sanity Checks for the <strong class="pkg">ATLAS</strong> of Group Representations</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7B890AE7817446DE">5.8-1 AtlasOfGroupRepresentationsTestGroupOrders</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7999A5367E21B2CD">5.8-2 AtlasOfGroupRepresentationsTestSubgroupOrders</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X80C116968254C114">5.8-3 AtlasOfGroupRepresentationsTestStdCompatibility</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X87C41F1978086FE8">5.8-4 AtlasOfGroupRepresentationsTestCompatibleMaxes</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X8318C1AD84557495">5.8-5 AtlasOfGroupRepresentationsTestFileHeaders</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X85F8ED98805FB495">5.8-6 AtlasOfGroupRepresentationsTestWords</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X828C687579111271">5.8-7 AtlasOfGroupRepresentationsTestFiles</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X793FE3A483AA58E5">5.8-8 AtlasOfGroupRepresentationsTestClassScripts</a></span>
</div>
</div>
<h3>5 <span class="Heading">Technicalities of the <strong class="pkg">AtlasRep</strong> Package</span></h3>
<p>This chapter describes those parts of the <strong class="pkg">GAP</strong> interface to the <strong class="pkg">ATLAS</strong> of Group Representations that do not belong to the user interface (cf. Chapter <a href="chap2.html#X87EAF8E578D95793"><b>2</b></a>).</p>
<p>Besides global variables used for administrational purposes (see Section <a href="chap5.html#X7DC2B7917DC30B28"><b>5.1</b></a>) and several sanity checks (see Section <a href="chap5.html#X84A565E482DBF4C1"><b>5.8</b></a>), they can be regarded as the interface between the data actually contained in the files and the corresponding <strong class="pkg">GAP</strong> objects (see Section <a href="chap5.html#X81C5B5E78215169D"><b>5.2</b></a>, <a href="chap5.html#X7D76D4437A9646E7"><b>5.3</b></a>, <a href="chap5.html#X7FEE162B7F63BEA0"><b>5.4</b></a>, and <a href="chap5.html#X86366BF08533DA5E"><b>5.5</b></a>), and the interface between the remote and the local version of the database (see Section <a href="chap5.html#X7D16BE31788F0E8A"><b>5.6</b></a> and <a href="chap5.html#X7D66C94E7A0F2252"><b>5.7</b></a>). The former interface contains functions to read and write files in <strong class="pkg">MeatAxe</strong> format, which may be interesting for users familiar with <strong class="pkg">MeatAxe</strong> standalones (see for example <a href="chapBib.html#biBRin98">[Rin98]</a>). Other low level functions may be undocumented in the sense that they are not described in this manual. Users interested in them may look at the actual implementation in the <code class="file">gap</code> directory of the package, but it may happen that this will be changed in future versions of the package.</p>
<p><a id="X7DC2B7917DC30B28" name="X7DC2B7917DC30B28"></a></p>
<h4>5.1 <span class="Heading">Global Variables Used by the <strong class="pkg">AtlasRep</strong> Package
</span></h4>
<p>For debugging purposes, the functions from the <strong class="pkg">GAP</strong> interface to the <strong class="pkg">ATLAS</strong> of Group Representations print information depending on the info level of the info classes <code class="func">InfoAtlasRep</code> (<a href="chap5.html#X8006BE167EB81E16"><b>5.1-1</b></a>), <code class="func">InfoCMeatAxe</code> (<a href="chap5.html#X78601C3A87921E08"><b>5.1-2</b></a>), and <code class="func">InfoBBox</code> (<a href="chap5.html#X80D5EF9A7FEF124B"><b>5.1-3</b></a>) (cf. <a href="../../../doc/htm/ref/CHAP007.htm#SECT004"><b>Reference: Info Functions</b></a>).</p>
<p>The info level of an info class can be changed using <code class="func">SetInfoLevel</code> (<a href="../../../doc/htm/ref/CHAP007.htm#SECT004"><b>Reference: SetInfoLevel</b></a>). For example, the info level of <code class="func">InfoAtlasRep</code> (<a href="chap5.html#X8006BE167EB81E16"><b>5.1-1</b></a>) can be set to the nonnegative integer <var class="Arg">n</var> using <code class="code">SetInfoLevel( InfoAtlasRep, <var class="Arg">n</var> )</code>.</p>
<p>Information about files being read can be obtained by setting the value of the global variable <code class="code">InfoRead1</code> to <code class="func">Print</code> (<a href="../../../doc/htm/ref/CHAP006.htm#SECT003"><b>Reference: Print</b></a>).</p>
<p><a id="X8006BE167EB81E16" name="X8006BE167EB81E16"></a></p>
<h5>5.1-1 InfoAtlasRep</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> InfoAtlasRep</code></td><td class="tdright">( info class )</td></tr></table></div>
<p>If the info level of <code class="func">InfoAtlasRep</code> is at least 1 then information about <code class="keyw">fail</code> results of functions in the <strong class="pkg">AtlasRep</strong> package is printed. If the info level is at least 2 then information about calls to external programs is printed. The default level is 0, no information is printed on this level.</p>
<p><a id="X78601C3A87921E08" name="X78601C3A87921E08"></a></p>
<h5>5.1-2 InfoCMeatAxe</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> InfoCMeatAxe</code></td><td class="tdright">( info class )</td></tr></table></div>
<p>If the info level of <code class="func">InfoCMeatAxe</code> is at least 1 then information about <code class="keyw">fail</code> results of <code class="code">C</code>-<strong class="pkg">MeatAxe</strong> functions is printed. The default level is zero, no information is printed on this level.</p>
<p><a id="X80D5EF9A7FEF124B" name="X80D5EF9A7FEF124B"></a></p>
<h5>5.1-3 InfoBBox</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> InfoBBox</code></td><td class="tdright">( info class )</td></tr></table></div>
<p>If the info level of <code class="func">InfoBBox</code> is at least 1 then information about <code class="keyw">fail</code> results of functions dealing with black box programs (see Section <a href="chap4.html#X7BE856BC785A9E8F"><b>4.2</b></a>) is printed. The default level is 0, no information is printed on this level.</p>
<p><a id="X85B6010C85A06CB6" name="X85B6010C85A06CB6"></a></p>
<h5>5.1-4 CMeatAxe.FastRead</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> CMeatAxe.FastRead</code></td><td class="tdright">( global variable )</td></tr></table></div>
<p>If this component is bound and has the value <code class="keyw">true</code> then <code class="func">ScanMeatAxeFile</code> (<a href="chap5.html#X83D5103780E1238F"><b>5.3-1</b></a>) reads text files via <code class="func">StringFile</code> (<a href="../../../pkg/gapdoc/doc/chap6.html#X7E14D32181FBC3C3"><b>GAPDoc: StringFile</b></a>). Otherwise each file containing a matrix over a finite field is read line by line via <code class="func">ReadLine</code> (<a href="../../../doc/htm/ref/CHAP010.htm#SECT003"><b>Reference: ReadLine</b></a>), and the <strong class="pkg">GAP</strong> matrix is constructed line by line, in a compressed representation (see <a href="../../../doc/htm/ref/CHAP023.htm#SECT002"><b>Reference: Row Vectors over Finite Fields</b></a> and <a href="../../../doc/htm/ref/CHAP024.htm#SECT013"><b>Reference: Matrices over Finite Fields</b></a>), which makes it possible to read large matrices in a reasonable amount of space. The <code class="func">StringFile</code> (<a href="../../../pkg/gapdoc/doc/chap6.html#X7E14D32181FBC3C3"><b>GAPDoc: StringFile</b></a>) approach is faster but needs more intermediate space when text files containing matrices over finite fields are read.</p>
<p><a id="X7BEC94A6781E126E" name="X7BEC94A6781E126E"></a></p>
<h5>5.1-5 AtlasOfGroupRepresentationsInfo</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> AtlasOfGroupRepresentationsInfo</code></td><td class="tdright">( global variable )</td></tr></table></div>
<p>This is a record that is defined in the file <code class="file">gap/types.g</code> of the package, with the following components.</p>
<p>Components corresponding to <em>user parameters</em> (see Section <a href="chap1.html#X7B04D2287CC44DE5"><b>1.7</b></a>) are</p>
<dl>
<dt><strong class="Mark"><code class="code">remote</code></strong></dt>
<dd><p>a boolean that controls what files are available; if the value is <code class="keyw">true</code> then <strong class="pkg">GAP</strong> is allowed to try remotely accessing any <strong class="pkg">ATLAS</strong> file from the servers (see below) and thus all files listed in the global table of contents are available, if the value is <code class="keyw">false</code> then <strong class="pkg">GAP</strong> may access only those files that are stored in the database directories of the local <strong class="pkg">GAP</strong> installation (see Section <a href="chap1.html#X7E1934D2780D108F"><b>1.7-1</b></a>),</p>
</dd>
<dt><strong class="Mark"><code class="code">servers</code></strong></dt>
<dd><p>a list of pairs <code class="code">[ </code><var class="Arg">server</var><code class="code">, </code><var class="Arg">path</var><code class="code"> ]</code>, where <var class="Arg">server</var> is a string denoting the <code class="file">http</code> address of a server where files can be fetched that are not stored in the local database, and <var class="Arg">path</var> is a string describing the path where the data directories on the server reside,</p>
</dd>
<dt><strong class="Mark"><code class="code">wget</code></strong></dt>
<dd><p>a boolean that controls whether the <strong class="pkg">GAP</strong> package <strong class="pkg">IO</strong><a href="chapBib.html#biBIO">[Neu07]</a> or the external program <code class="file">wget</code> is used to fetch data files, see <a href="chap1.html#X7CB4D8F887BE5E84"><b>1.7-3</b></a>,</p>
</dd>
<dt><strong class="Mark"><code class="code">compress</code></strong></dt>
<dd><p>a boolean that controls whether <strong class="pkg">MeatAxe</strong> format text files are stored in compressed form; if the value is <code class="keyw">true</code> then these files are compressed with <code class="file">gzip</code> after they have been fetched from a server, see Section <a href="chap1.html#X7E0AC1127B4363E7"><b>1.7-4</b></a>,</p>
</dd>
<dt><strong class="Mark"><code class="code">displayFunction</code></strong></dt>
<dd><p>the function that is used by <code class="func">DisplayAtlasInfo</code> (<a href="chap2.html#X79DACFFA7E2D1A99"><b>2.5-1</b></a>) for printing the formatted data, see Section <a href="chap1.html#X83EE129B7A7650F2"><b>1.7-5</b></a>,</p>
</dd>
<dt><strong class="Mark"><code class="code">accessFunctions</code></strong></dt>
<dd><p>a list of records, each describing how to access the data files, see Sections <a href="chap1.html#X7FA485E479F6C3A0"><b>1.7-6</b></a> and <a href="chap5.html#X81C5B5E78215169D"><b>5.2</b></a>.</p>
</dd>
<dt><strong class="Mark"><code class="code">markprivate</code></strong></dt>
<dd><p>a string used in <code class="func">DisplayAtlasInfo</code> (<a href="chap2.html#X79DACFFA7E2D1A99"><b>2.5-1</b></a>) to mark private data, see Section <a href="chap3.html#X7E186BFA7E59BD47"><b>3.2</b></a>, and</p>
</dd>
</dl>
<p><em>System components</em> (which are computed automatically) are</p>
<dl>
<dt><strong class="Mark"><code class="code">GAPnames</code></strong></dt>
<dd><p>a list of pairs, each containing the <strong class="pkg">GAP</strong> name and the <strong class="pkg">ATLAS</strong>-file name of a group, see Section <a href="chap2.html#X81BF52FC7B8C08D4"><b>2.2</b></a>,</p>
</dd>
<dt><strong class="Mark"><code class="code">groupnames</code></strong></dt>
<dd><p>a list of triples, each containing at the first position the name of the directory on each server that contains data about the group G in question, at the second position the name of the (usually simple) group for which a subdirectory exists that contains the data about G, and at the third position the <strong class="pkg">ATLAS</strong>-file name used for G, see Section <a href="chap5.html#X7D16BE31788F0E8A"><b>5.6</b></a>,</p>
</dd>
<dt><strong class="Mark"><code class="code">ringinfo</code></strong></dt>
<dd><p>a list of triples, each containing at the first position the name of a file with the matrix generators, at the second position a string describing the ring generated by the matrix entries, and at the third position this ring itself; <code class="func">DisplayAtlasInfo</code> (<a href="chap2.html#X79DACFFA7E2D1A99"><b>2.5-1</b></a>) displays this information for example for representations over proper extensions of the rational number field only if the representation is mentioned in the <code class="code">ringinfo</code> list,</p>
</dd>
<dt><strong class="Mark"><code class="code">private</code></strong></dt>
<dd><p>a list of pairs of strings used for administrating private data (see Chapter <a href="chap3.html#X7DF711157F9EFA28"><b>3</b></a>); the value is changed by <code class="func">AtlasOfGroupRepresentationsNotifyPrivateDirectory</code> (<a href="chap3.html#X825AF58885A48520"><b>3.1-1</b></a>) and <code class="func">AtlasOfGroupRepresentationsForgetPrivateDirectory</code> (<a href="chap3.html#X8748A8BB7C7089EE"><b>3.1-2</b></a>),</p>
</dd>
<dt><strong class="Mark"><code class="code">TableOfContents</code></strong></dt>
<dd><p>a record with at most the components <code class="code">local</code>, <code class="code">remote</code>, <code class="code">types</code>, and the names of private data directories. The values of the components <code class="code">local</code> and <code class="code">remote</code> can be computed automatically by <code class="func">ReloadAtlasTableOfContents</code> (<a href="chap1.html#X7AC3EA317EDBDA0E"><b>1.6-1</b></a>), the value of the component <code class="code">types</code> is set in <code class="func">AGRDeclareDataType</code> (<a href="chap5.html#X832AB6B97BE4CD9F"><b>5.5-1</b></a>), and the values of the components for local data directories are created by <code class="func">AtlasOfGroupRepresentationsNotifyPrivateDirectory</code> (<a href="chap3.html#X825AF58885A48520"><b>3.1-1</b></a>).</p>
</dd>
</dl>
<p><a id="X81C5B5E78215169D" name="X81C5B5E78215169D"></a></p>
<h4>5.2 <span class="Heading">How to Customize the Access to Data files</span></h4>
<p>We discuss the three steps listed in Section <a href="chap1.html#X7FA485E479F6C3A0"><b>1.7-6</b></a>.</p>
<p>For creating an overview of the locally available data, the first of these steps must be available independent of actually accessing the file in question. For updating the local copy of the server data, the second of the above steps must be available independent of the third one. Therefore, the package provides the possibility to extend the default behaviour by adding new records to the <code class="code">accessFunctions</code> component of <code class="func">AtlasOfGroupRepresentationsInfo</code> (<a href="chap5.html#X7BEC94A6781E126E"><b>5.1-5</b></a>), the components of which are as follows.</p>
<dl>
<dt><strong class="Mark">
<code class="code">location( <var class="Arg">filename</var>, <var class="Arg">groupname</var>, <var class="Arg">dirname</var>,
<var class="Arg">type</var> )</code>
</strong></dt>
<dd><p>Let <var class="Arg">filename</var> be the default filename (without path) of the required file, or a list of such filenames. Let <var class="Arg">groupname</var> be the <strong class="pkg">ATLAS</strong> name of the group to which the data in these files belong, <var class="Arg">dirname</var> be the default directory name (one of <code class="code">"datagens"</code>, <code class="code">"dataword"</code>, or the <var class="Arg">dirid</var> value of a private directory, see <code class="func">AtlasOfGroupRepresentationsNotifyPrivateDirectory</code> (<a href="chap3.html#X825AF58885A48520"><b>3.1-1</b></a>)), and <var class="Arg">type</var> be the data type (see <code class="func">AGRDeclareDataType</code> (<a href="chap5.html#X832AB6B97BE4CD9F"><b>5.5-1</b></a>)). This function must return either the absolute path(s) where the mechanism implemented by the current record expects the local version of the given file(s), or <code class="keyw">fail</code> if this function does not feel responsible for these file(s). In the latter case, the <code class="code">location</code> function in another record will know a path.</p>
<p>The file(s) is/are regarded as not locally available if all installed <code class="code">location</code> functions return either <code class="keyw">fail</code> or paths of nonexisting files, in the sense of <code class="func">IsExistingFile</code> (<a href="../../../doc/htm/ref/CHAP009.htm#SECT006"><b>Reference: IsExistingFile</b></a>).</p>
</dd>
<dt><strong class="Mark">
<code class="code">fetch( <var class="Arg">filepath</var>, <var class="Arg">filename</var>, <var class="Arg">groupname</var>,
<var class="Arg">dirname</var>, <var class="Arg">type</var> )</code>
</strong></dt>
<dd><p>This function is called when a file is not locally available and if the <code class="code">location</code> function in the current record has returned a path or a list of paths. The arguments <var class="Arg">dirname</var> and <var class="Arg">type</var> must be the same as for the <code class="code">location</code> function, and <var class="Arg">filepath</var> and <var class="Arg">filename</var> must be strings (<em>not</em> lists of strings).</p>
<p>The return value must be <code class="keyw">true</code> if the function succeeded with making the file locally available (including postprocessing if applicable), and <code class="keyw">false</code> otherwise.</p>
</dd>
<dt><strong class="Mark"><code class="code">contents( <var class="Arg">filepath</var>, <var class="Arg">type</var> )</code></strong></dt>
<dd><p>This function is called when the <code class="code">location</code> function in the current record has returned the path(s) <var class="Arg">filepath</var>, and if either these are paths of existing files or the <code class="code">fetch</code> function in the current record has been called for these paths, and the return value was <code class="keyw">true</code>. The argument <var class="Arg">type</var> must be the same as for the <code class="code">location</code> and the <code class="code">fetch</code> functions.</p>
<p>The return value must be the contents of the file(s), in the sense that the <strong class="pkg">GAP</strong> matrix, matrix list, permutation, permutation list, or program described by the file(s) is returned. This means that besides reading the file(s) via the appropriate function, it may be necessary to interpret the contents.</p>
</dd>
<dt><strong class="Mark"><code class="code">description</code></strong></dt>
<dd><p>This must be a short string that describes for which kinds of files the functions in the current record are intended, which file formats are supported etc. The value is shown when <code class="func">AtlasOfGroupRepresentationsShowUserParameters</code> (<a href="chap1.html#X80126409815DE5B6"><b>1.7-8</b></a>) is called.</p>
</dd>
<dt><strong class="Mark"><code class="code">active</code></strong></dt>
<dd><p>The current <code class="code">accessFunctions</code> record is ignored by <code class="func">AGRFileContents</code> (<a href="chap5.html#X819839FA7A639DE2"><b>5.6-2</b></a>) if the value is not <code class="keyw">true</code>.</p>
</dd>
</dl>
<p>In <code class="func">AGRFileContents</code> (<a href="chap5.html#X819839FA7A639DE2"><b>5.6-2</b></a>), the records in the <code class="code">accessFunctions</code> component of <code class="func">AtlasOfGroupRepresentationsInfo</code> (<a href="chap5.html#X7BEC94A6781E126E"><b>5.1-5</b></a>) are considered in reversed order.</p>
<p>By default, the <code class="code">accessFunctions</code> list contains three records. Only for one of them, the <code class="code">active</code> component has the value <code class="keyw">true</code>. One of the other two records can be used to change the access to permutation representations and to matrix representations over finite fields such that <strong class="pkg">MeatAxe</strong> binary files are transferred and read instead of <strong class="pkg">MeatAxe</strong> text files. The fourth record makes sense only if a local server is accessible, i. e., if the server files can be read directly, without being transferred into the data directories of the package.</p>
<p><a id="X7D76D4437A9646E7" name="X7D76D4437A9646E7"></a></p>
<h4>5.3 <span class="Heading">Reading and Writing MeatAxe Format Files</span></h4>
<p><a id="X83D5103780E1238F" name="X83D5103780E1238F"></a></p>
<h5>5.3-1 ScanMeatAxeFile</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> ScanMeatAxeFile</code>( <var class="Arg">filename[, q][, "string"]</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p><b>Returns: </b>the matrix or list of permutations stored in the file or encoded by the string.</p>
<p>Let <var class="Arg">filename</var> be the name of a <strong class="pkg">GAP</strong> readable file (see <a href="../../../doc/htm/ref/CHAP009.htm#SECT004"><b>Reference: Filename</b></a>) that contains a matrix or a permutation or a list of permutations in <strong class="pkg">MeatAxe</strong> text format (see the section about the program <code class="file">zcv</code> in the <strong class="pkg">MeatAxe</strong> manual <a href="chapBib.html#biBRin98">[Rin98]</a>), and let <var class="Arg">q</var> be a prime power. <code class="func">ScanMeatAxeFile</code> returns the corresponding <strong class="pkg">GAP</strong> matrix or list of permutations, respectively.</p>
<p>If the file contains a matrix then the way how it is read by <code class="func">ScanMeatAxeFile</code> depends on the value of the global variable <code class="func">CMeatAxe.FastRead</code> (<a href="chap5.html#X85B6010C85A06CB6"><b>5.1-4</b></a>). If the parameter <var class="Arg">q</var> is given then the result matrix is represented over the field with <var class="Arg">q</var> elements, the default for <var class="Arg">q</var> is the field size stored in the file.</p>
<p>If the file contains a list of permutations then it is read with <code class="func">StringFile</code> (<a href="../../../pkg/gapdoc/doc/chap6.html#X7E14D32181FBC3C3"><b>GAPDoc: StringFile</b></a>); the parameter <var class="Arg">q</var>, if given, is ignored in this case.</p>
<p>If the string <code class="code">"string"</code> is entered as the third argument then the first argument must be a string as obtained by reading a file in <strong class="pkg">MeatAxe</strong> text format as a text stream (see <code class="func">InputTextFile</code> (<a href="../../../doc/htm/ref/CHAP010.htm#SECT005"><b>Reference: InputTextFile</b></a>)). Also in this case, <code class="func">ScanMeatAxeFile</code> returns the corresponding <strong class="pkg">GAP</strong> matrix or list of permutations, respectively.</p>
<p><a id="X7DDD09BE87063052" name="X7DDD09BE87063052"></a></p>
<h5>5.3-2 MeatAxeString</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> MeatAxeString</code>( <var class="Arg">mat, q</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">> MeatAxeString</code>( <var class="Arg">perms, degree</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">> MeatAxeString</code>( <var class="Arg">perm, q, dims</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p><b>Returns: </b>a string encoding the <strong class="pkg">GAP</strong> objects given as input in <strong class="pkg">MeatAxe</strong> format.</p>
<p>In the first form, for a matrix <var class="Arg">mat</var> whose entries lie in the finite field with <var class="Arg">q</var> elements, <code class="func">MeatAxeString</code> returns a string that encodes <var class="Arg">mat</var> as a matrix over <code class="code">GF(<var class="Arg">q</var>)</code>, in <strong class="pkg">MeatAxe</strong> text format.</p>
<p>In the second form, for a nonempty list <var class="Arg">perms</var> of permutations that move only points up to the positive integer <var class="Arg">degree</var>, <code class="func">MeatAxeString</code> returns a string that encodes <var class="Arg">perms</var> as permutations of degree <var class="Arg">degree</var>, in <strong class="pkg">MeatAxe</strong> text format (see <a href="chapBib.html#biBRin98">[Rin98]</a>).</p>
<p>In the third form, for a permutation <var class="Arg">perm</var> with largest moved point n, say, a prime power <var class="Arg">q</var>, and a list <var class="Arg">dims</var> of length 2 containing two positive integers larger than or equal to n, <code class="func">MeatAxeString</code> returns a string that encodes <var class="Arg">perm</var> as a matrix over <code class="code">GF(<var class="Arg">q</var>)</code>, of dimensions <var class="Arg">dims</var>, whose first n rows and columns describe the permutation matrix corresponding to <var class="Arg">perm</var>, and the remaining rows and columns are zero.</p>
<p>When strings are printed to files using <code class="func">PrintTo</code> (<a href="../../../doc/htm/ref/CHAP009.htm#SECT007"><b>Reference: PrintTo</b></a>) or <code class="func">AppendTo</code> (<a href="../../../doc/htm/ref/CHAP009.htm#SECT007"><b>Reference: AppendTo</b></a>) then line breaks are inserted whenever lines exceed the number of characters given by the second entry of the list returned by <code class="func">SizeScreen</code> (<a href="../../../doc/htm/ref/CHAP006.htm#SECT012"><b>Reference: SizeScreen</b></a>), see <a href="../../../doc/htm/ref/CHAP010.htm#SECT004"><b>Reference: Operations for Output Streams</b></a>. This behaviour is not desirable for creating data files. So the recommended functions for printing the result of <code class="func">MeatAxeString</code> to a file are <code class="func">FileString</code> (<a href="../../../pkg/gapdoc/doc/chap6.html#X7E14D32181FBC3C3"><b>GAPDoc: FileString</b></a>) and <code class="func">WriteAll</code> (<a href="../../../doc/htm/ref/CHAP010.htm#SECT004"><b>Reference: WriteAll</b></a>).</p>
<table class="example">
<tr><td><pre>
gap> mat:= [ [ 1, -1 ], [ 0, 1 ] ] * Z(3)^0;;
gap> str:= MeatAxeString( mat, 3 );
"1 3 2 2\n12\n01\n"
gap> mat = ScanMeatAxeFile( str, "string" );
true
gap> str:= MeatAxeString( mat, 9 );
"1 9 2 2\n12\n01\n"
gap> mat = ScanMeatAxeFile( str, "string" );
true
gap> perms:= [ (1,2,3)(5,6) ];;
gap> str:= MeatAxeString( perms, 6 );
"12 1 6 1\n2\n3\n1\n4\n6\n5\n"
gap> perms = ScanMeatAxeFile( str, "string" );
true
gap> str:= MeatAxeString( perms, 8 );
"12 1 8 1\n2\n3\n1\n4\n6\n5\n7\n8\n"
gap> perms = ScanMeatAxeFile( str, "string" );
true
gap> perm:= (1,2,4);;
gap> str:= MeatAxeString( perm, 3, [ 5, 6 ] );
"2 3 5 6\n2\n4\n3\n1\n5\n"
gap> mat:= ScanMeatAxeFile( str, "string" );; Print( mat, "\n" );
[ [ 0*Z(3), Z(3)^0, 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ],
[ 0*Z(3), 0*Z(3), 0*Z(3), Z(3)^0, 0*Z(3), 0*Z(3) ],
[ 0*Z(3), 0*Z(3), Z(3)^0, 0*Z(3), 0*Z(3), 0*Z(3) ],
[ Z(3)^0, 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ],
[ 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), Z(3)^0, 0*Z(3) ] ]
gap> MeatAxeString( mat, 3 ) = str;
true
</pre></td></tr></table>
<p><a id="X79D9AE4878E9DFA6" name="X79D9AE4878E9DFA6"></a></p>
<h5>5.3-3 FFList</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> FFList</code>( <var class="Arg">F</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p><b>Returns: </b>a list of elements in the given finite field.</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> FFLists</code></td><td class="tdright">( global variable )</td></tr></table></div>
<p><code class="func">FFList</code> is a utility program for the conversion of vectors and matrices from <strong class="pkg">MeatAxe</strong> format to <strong class="pkg">GAP</strong> format and vice versa. It is used by <code class="func">ScanMeatAxeFile</code> (<a href="chap5.html#X83D5103780E1238F"><b>5.3-1</b></a>) and <code class="func">MeatAxeString</code> (<a href="chap5.html#X7DDD09BE87063052"><b>5.3-2</b></a>).</p>
<p>For a finite field <var class="Arg">F</var>, <code class="func">FFList</code> returns a list <var class="Arg">l</var> giving the correspondence between the <strong class="pkg">MeatAxe</strong> numbering and the <strong class="pkg">GAP</strong> numbering of the elements in <var class="Arg">F</var>.</p>
<p>The element of <var class="Arg">F</var> corresponding to <strong class="pkg">MeatAxe</strong> number <var class="Arg">n</var> is <var class="Arg">l</var>[ <var class="Arg">n</var>+1 ], and the <strong class="pkg">MeatAxe</strong> number of the field element <var class="Arg">z</var> is <code class="code">Position( </code><var class="Arg">l</var><code class="code">, </code><var class="Arg">z</var><code class="code"> ) - 1</code>.</p>
<p>The global variable <code class="func">FFLists</code> is used to store the information about <var class="Arg">F</var> once it has been computed.</p>
<table class="example">
<tr><td><pre>
gap> FFList( GF(4) );
[ 0*Z(2), Z(2)^0, Z(2^2), Z(2^2)^2 ]
gap> IsBound( FFLists[4] );
true
</pre></td></tr></table>
<p><a id="X8477AA668733255C" name="X8477AA668733255C"></a></p>
<h5>5.3-4 CMtxBinaryFFMatOrPerm</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> CMtxBinaryFFMatOrPerm</code>( <var class="Arg">elm, def, outfile</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Let the pair (<var class="Arg">elm</var>, <var class="Arg">def</var>) be either of the form (M, q) where M is a matrix over a finite field F, say, with q <= 256 elements, or of the form (pi, n) where pi is a permutation with largest moved point at most n. Let <var class="Arg">outfile</var> be a string. <code class="func">CMtxBinaryFFMatOrPerm</code> writes the <code class="code">C</code>-<strong class="pkg">MeatAxe</strong> binary format of M, viewed as a matrix over F, or of pi, viewed as a permutation on the points up to n, to the file with name <var class="Arg">outfile</var>.</p>
<p>(The binary format is described in the <code class="code">C</code>-<strong class="pkg">MeatAxe</strong> manual <a href="chapBib.html#biBRin98">[Rin98]</a>.)</p>
<table class="example">
<tr><td><pre>
gap> tmpdir:= DirectoryTemporary();;
gap> mat:= Filename( tmpdir, "mat" );;
gap> q:= 4;;
gap> mats:= GeneratorsOfGroup( GL(10,q) );;
gap> CMtxBinaryFFMatOrPerm( mats[1], q, Concatenation( mat, "1" ) );
gap> CMtxBinaryFFMatOrPerm( mats[2], q, Concatenation( mat, "2" ) );
gap> prm:= Filename( tmpdir, "prm" );;
gap> n:= 200;;
gap> perms:= GeneratorsOfGroup( SymmetricGroup( n ) );;
gap> CMtxBinaryFFMatOrPerm( perms[1], n, Concatenation( prm, "1" ) );
gap> CMtxBinaryFFMatOrPerm( perms[2], n, Concatenation( prm, "2" ) );
</pre></td></tr></table>
<p><a id="X872FA00C7F791FBB" name="X872FA00C7F791FBB"></a></p>
<h5>5.3-5 FFMatOrPermCMtxBinary</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> FFMatOrPermCMtxBinary</code>( <var class="Arg">fname</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p><b>Returns: </b>the matrix or permutation stored in the file.</p>
<p>Let <var class="Arg">fname</var> be the name of a file that contains the <code class="code">C</code>-<strong class="pkg">MeatAxe</strong> binary format of a matrix over a finite field or of a permutation, as is described in <a href="chapBib.html#biBRin98">[Rin98]</a>. <code class="func">FFMatOrPermCMtxBinary</code> returns the corresponding <strong class="pkg">GAP</strong> matrix or permutation.</p>
<table class="example">
<tr><td><pre>
gap> FFMatOrPermCMtxBinary( Concatenation( mat, "1" ) ) = mats[1];
true
gap> FFMatOrPermCMtxBinary( Concatenation( mat, "2" ) ) = mats[2];
true
gap> FFMatOrPermCMtxBinary( Concatenation( prm, "1" ) ) = perms[1];
true
gap> FFMatOrPermCMtxBinary( Concatenation( prm, "2" ) ) = perms[2];
true
</pre></td></tr></table>
<p><a id="X7FEE162B7F63BEA0" name="X7FEE162B7F63BEA0"></a></p>
<h4>5.4 <span class="Heading">Reading and Writing <strong class="pkg">ATLAS</strong> Straight Line Programs</span></h4>
<p><a id="X7D6617E47B013A37" name="X7D6617E47B013A37"></a></p>
<h5>5.4-1 ScanStraightLineProgram</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> ScanStraightLineProgram</code>( <var class="Arg">filename[, "string"]</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p><b>Returns: </b>a record containing the straight line program.</p>
<p>Let <var class="Arg">filename</var> be the name of a file that contains a straight line program in the sense that it consists only of lines in the following form.</p>
<dl>
<dt><strong class="Mark"><code class="code">#<var class="Arg">anything</var></code></strong></dt>
<dd><p>lines starting with a hash sign <code class="code">#</code> are ignored,</p>
</dd>
<dt><strong class="Mark"><code class="code">echo <var class="Arg">anything</var></code></strong></dt>
<dd><p>lines starting with <code class="code">echo</code> are ignored for the <code class="code">program</code> component of the result record (see below), they are used to set up the bijection between the labels used in the program and conjugacy class names in the case that the program computes dedicated class representatives,</p>
</dd>
<dt><strong class="Mark"><code class="code">inp <var class="Arg">n</var></code></strong></dt>
<dd><p>means that there are <var class="Arg">n</var> inputs, referred to via the labels <code class="code">1</code>, <code class="code">2</code>, ..., <var class="Arg">n</var>,</p>
</dd>
<dt><strong class="Mark"><code class="code">inp <var class="Arg">k</var> <var class="Arg">a1</var> <var class="Arg">a2</var> ... <var class="Arg">ak</var></code></strong></dt>
<dd><p>means that the next <var class="Arg">k</var> inputs are referred to via the labels <var class="Arg">a1</var>, <var class="Arg">a2</var>, ..., <var class="Arg">ak</var>,</p>
</dd>
<dt><strong class="Mark"><code class="code">cjr <var class="Arg">a</var> <var class="Arg">b</var></code></strong></dt>
<dd><p>means that <var class="Arg">a</var> is replaced by <code class="code"><var class="Arg">b</var>^(-1) * <var class="Arg">a</var> * <var class="Arg">b</var></code>,</p>
</dd>
<dt><strong class="Mark"><code class="code">cj <var class="Arg">a</var> <var class="Arg">b</var> <var class="Arg">c</var></code></strong></dt>
<dd><p>means that <var class="Arg">c</var> is defined as <code class="code"><var class="Arg">b</var>^(-1) * <var class="Arg">a</var> * <var class="Arg">b</var></code>,</p>
</dd>
<dt><strong class="Mark"><code class="code">com <var class="Arg">a</var> <var class="Arg">b</var> <var class="Arg">c</var></code></strong></dt>
<dd><p>means that <var class="Arg">c</var> is defined as <code class="code"><var class="Arg">a</var>^(-1) * <var class="Arg">b</var>^(-1) * <var class="Arg">a</var> * <var class="Arg">b</var></code>,</p>
</dd>
<dt><strong class="Mark"><code class="code">iv <var class="Arg">a</var> <var class="Arg">b</var></code></strong></dt>
<dd><p>means that <var class="Arg">b</var> is defined as <code class="code"><var class="Arg">a</var>^(-1)</code>,</p>
</dd>
<dt><strong class="Mark"><code class="code">mu <var class="Arg">a</var> <var class="Arg">b</var> <var class="Arg">c</var></code></strong></dt>
<dd><p>means that <var class="Arg">c</var> is defined as <code class="code"><var class="Arg">a</var> * <var class="Arg">b</var></code>,</p>
</dd>
<dt><strong class="Mark"><code class="code">pwr <var class="Arg">a</var> <var class="Arg">b</var> <var class="Arg">c</var></code></strong></dt>
<dd><p>means that <var class="Arg">c</var> is defined as <code class="code"><var class="Arg">b</var>^<var class="Arg">a</var></code>,</p>
</dd>
<dt><strong class="Mark"><code class="code">cp <var class="Arg">a</var> <var class="Arg">b</var></code></strong></dt>
<dd><p>means that <var class="Arg">b</var> is defined as a copy of <var class="Arg">a</var>,</p>
</dd>
<dt><strong class="Mark"><code class="code">oup <var class="Arg">l</var></code></strong></dt>
<dd><p>means that there are <var class="Arg">l</var> outputs, stored in the labels <code class="code">1</code>, <code class="code">2</code>, ..., <var class="Arg">l</var>, and</p>
</dd>
<dt><strong class="Mark"><code class="code">oup <var class="Arg">l</var> <var class="Arg">b1</var> <var class="Arg">b2</var> ... <var class="Arg">bl</var></code></strong></dt>
<dd><p>means that the next <var class="Arg">l</var> outputs are stored in the labels <var class="Arg">b1</var>, <var class="Arg">b2</var>, ... <var class="Arg">bl</var>.</p>
</dd>
</dl>
<p>Each of the labels <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">c</var> can be any nonempty sequence of digits and alphabet characters, except that the first argument of <code class="code">pwr</code> must denote an integer.</p>
<p>If the <code class="code">inp</code> or <code class="code">oup</code> statements are missing then the input or output, respectively, is assumed to be given by the labels <code class="code">1</code> and <code class="code">2</code>. There can be multiple <code class="code">inp</code> lines at the beginning of the program and multiple <code class="code">oup</code> lines at the end of the program. Only the first <code class="code">inp</code> or <code class="code">oup</code> line may omit the names of the elements. For example, an empty file <var class="Arg">filename</var> or an empty string <var class="Arg">string</var> represent a straight line program with two inputs that are returned as outputs.</p>
<p>No command except <code class="code">cjr</code> may overwrite its own input. For example, the line <code class="code">mu a b a</code> is not legal. (This is not checked.)</p>
<p><code class="func">ScanStraightLineProgram</code> returns a record containing as the value of its component <code class="code">program</code> the corresponding <strong class="pkg">GAP</strong> straight line program (see <code class="func">IsStraightLineProgram</code> (<a href="../../../doc/htm/ref/CHAP035.htm#SECT008"><b>Reference: IsStraightLineProgram</b></a>)) if the input string satisfies the syntax rules stated above, and returns <code class="keyw">fail</code> otherwise. In the latter case, information about the first corrupted line of the program is printed if the info level of <code class="func">InfoCMeatAxe</code> (<a href="chap5.html#X78601C3A87921E08"><b>5.1-2</b></a>) is at least 1.</p>
<p>If the string <code class="code">"string"</code> is entered as the second argument then the first argument must be a string as obtained by reading a file in <strong class="pkg">MeatAxe</strong> text format as a text stream (see <code class="func">InputTextFile</code> (<a href="../../../doc/htm/ref/CHAP010.htm#SECT005"><b>Reference: InputTextFile</b></a>)). Also in this case, <code class="func">ScanStraightLineProgram</code> returns either a record with the corresponding <strong class="pkg">GAP</strong> straight line program or <code class="keyw">fail</code>.</p>
<p>If the input describes a straight line program that computes certain class representatives of the group in question then the result record also contains the component <code class="code">outputs</code>. Its value is a list of strings, the entry at position i denoting the name of the class in which the i output of the straight line program lies; see Section <a href="chap2.html#X861CD545803B97E8"><b>2.4</b></a> for the definition of the class names that occur.</p>
<p>Such straight line programs must end with a sequence of output specifications of the following form.</p>
<table class="example">
<tr><td><pre>
echo "Classes 1A 2A 3A 5A 5B"
oup 5 3 1 2 4 5
</pre></td></tr></table>
<p>This example means that the list of outputs of the program contains elements of the classes <code class="code">1A</code>, <code class="code">2A</code>, <code class="code">3A</code>, <code class="code">5A</code>, and <code class="code">5B</code> (in this order), and that inside the program, these elements are referred to by the names <code class="code">3</code>, <code class="code">1</code>, <code class="code">2</code>, <code class="code">4</code>, and <code class="code">5</code>.</p>
<p><a id="X82842D807A7B7DF7" name="X82842D807A7B7DF7"></a></p>
<h5>5.4-2 AtlasStringOfProgram</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> AtlasStringOfProgram</code>( <var class="Arg">prog[, outputnames]</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">> AtlasStringOfProgram</code>( <var class="Arg">prog[, "mtx"]</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p><b>Returns: </b>a string encoding the straight line program/decision in the format used in <strong class="pkg">ATLAS</strong> files.</p>
<p>For a straight line program or straight line decision <var class="Arg">prog</var> (see <code class="func">IsStraightLineProgram</code> (<a href="../../../doc/htm/ref/CHAP035.htm#SECT008"><b>Reference: IsStraightLineProgram</b></a>) and <code class="func">IsStraightLineDecision</code> (<a href="chap4.html#X8787E2EC7DB85A89"><b>4.1-1</b></a>)), this function returns a string describing the input format of an equivalent straight line program or straight line decision as used in the <strong class="pkg">ATLAS</strong> of Group Representations, that is, the lines are of the form described in <code class="func">ScanStraightLineProgram</code> (<a href="chap5.html#X7D6617E47B013A37"><b>5.4-1</b></a>).</p>
<p>A list of strings that is given as the optional second argument <var class="Arg">outputnames</var> is interpreted as the class names corresponding to the outputs; this argument has the effect that appropriate <code class="code">echo</code> statements appear in the result string.</p>
<p>If the string <code class="code">"mtx"</code> is given as the second argument then the result has the format used in the <code class="code">C</code>-<strong class="pkg">MeatAxe</strong> (see <a href="chapBib.html#biBRin98">[Rin98]</a>) rather than the format described in Section <a href="chap5.html#X7FEE162B7F63BEA0"><b>5.4</b></a>. (Note that the <code class="code">C</code>-<strong class="pkg">MeatAxe</strong> format does not make sense if the argument <var class="Arg">outputnames</var> is given, and that this format does not support <code class="code">inp</code> and <code class="code">oup</code> statements.)</p>
<p>The argument <var class="Arg">prog</var> must not be a black box program (see <code class="func">IsBBoxProgram</code> (<a href="chap4.html#X87CAF2DE870D0E3B"><b>4.2-1</b></a>)).</p>
<table class="example">
<tr><td><pre>
gap> str:= "inp 2\nmu 1 2 3\nmu 3 1 2\niv 2 1\noup 2 1 2";;
gap> prg:= ScanStraightLineProgram( str, "string" );
rec( program := <straight line program> )
gap> prg:= prg.program;;
gap> Display( prg );
# input:
r:= [ g1, g2 ];
# program:
r[3]:= r[1]*r[2];
r[2]:= r[3]*r[1];
r[1]:= r[2]^-1;
# return values:
[ r[1], r[2] ]
gap> StringOfResultOfStraightLineProgram( prg, [ "a", "b" ] );
"[ (aba)^-1, aba ]"
gap> AtlasStringOfProgram( prg );
"inp 2\nmu 1 2 3\nmu 3 1 2\niv 2 1\noup 2\n"
gap> prg:= StraightLineProgram( "(a^2b^3)^-1", [ "a", "b" ] );
<straight line program>
gap> Print( AtlasStringOfProgram( prg ) );
inp 2
pwr 2 1 4
pwr 3 2 5
mu 4 5 3
iv 3 4
oup 1 4
gap> prg:= StraightLineProgram( [ [2,3], [ [3,1,1,4], [1,2,3,1] ] ], 2 );
<straight line program>
gap> Print( AtlasStringOfProgram( prg ) );
inp 2
pwr 3 2 3
pwr 4 1 5
mu 3 5 4
pwr 2 1 6
mu 6 3 5
oup 2 4 5
gap> Print( AtlasStringOfProgram( prg, "mtx" ) );
# inputs are expected in 1 2
zsm pwr3 2 3
zsm pwr4 1 5
zmu 3 5 4
zsm pwr2 1 6
zmu 6 3 5
echo "outputs are in 4 5"
gap> str:= "inp 2\nchor 1 2\nchor 2 3\nmu 1 2 3\nchor 3 5";;
gap> prg:= ScanStraightLineDecision( str );;
gap> AtlasStringOfProgram( prg.program );
"inp 2\nchor 1 2\nchor 2 3\nmu 1 2 3\nchor 3 5\n"
</pre></td></tr></table>
<p><a id="X86366BF08533DA5E" name="X86366BF08533DA5E"></a></p>
<h4>5.5 <span class="Heading">Data Types Used in the <strong class="pkg">ATLAS</strong> of Group Representations</span></h4>
<p>Each representation or program that is administrated by the <strong class="pkg">AtlasRep</strong> package belongs to a unique <em>data type</em>. Informally, examples of data types are "permutation representation", "matrix representation over the integers", or "straight line program for computing class representatives".</p>
<p>The idea is that for each data type, there can be</p>
<ul>
<li><p>a column of its own in the output produced by <code class="func">DisplayAtlasInfo</code> (<a href="chap2.html#X79DACFFA7E2D1A99"><b>2.5-1</b></a>) when called without arguments or with only argument a list of group names,</p>
</li>
<li><p>a line format of its own for the output produced by <code class="func">DisplayAtlasInfo</code> (<a href="chap2.html#X79DACFFA7E2D1A99"><b>2.5-1</b></a>) when called with first argument a group name,</p>
</li>
<li><p>an input format of its own for <code class="func">AtlasProgram</code> (<a href="chap2.html#X801F2E657C8A79ED"><b>2.5-3</b></a>),</p>
</li>
<li><p>an input format of its own for <code class="func">OneAtlasGeneratingSetInfo</code> (<a href="chap2.html#X841478AB7CD06D44"><b>2.5-4</b></a>), and</p>
</li>
<li><p>specific tests for the data of this data type; these functions are used by the global tests described in Section <a href="chap5.html#X84A565E482DBF4C1"><b>5.8</b></a>.</p>
</li>
</ul>
<p>Formally, a data type is defined by a record whose components are used by the interface functions. The details are described in the following.</p>
<p><a id="X832AB6B97BE4CD9F" name="X832AB6B97BE4CD9F"></a></p>
<h5>5.5-1 AGRDeclareDataType</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> AGRDeclareDataType</code>( <var class="Arg">kind, name, record</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Let <var class="Arg">kind</var> be one of the strings <code class="code">"rep"</code> or <code class="code">"prg"</code>, and <var class="Arg">record</var> be a record. <code class="func">AGRDeclareDataType</code> declares a new data type of representations (if <var class="Arg">kind</var> is <code class="code">"rep"</code>) or of programs (if <var class="Arg">kind</var> is <code class="code">"prg"</code>). For each group used in the <strong class="pkg">AtlasRep</strong> package, the record that contains the information about the data will have a component <var class="Arg">name</var> whose value is a list containing the data about the new type. Examples of <var class="Arg">name</var> are <code class="code">"perm"</code>, <code class="code">"matff"</code>, and <code class="code">"classes"</code>.</p>
<p><em>Mandatory components</em> of <var class="Arg">record</var> are</p>
<dl>
<dt><strong class="Mark"><code class="code">FilenameFormat</code></strong></dt>
<dd><p>This defines the format of the filenames containing data of the type in question. The value must be a list that can be used as the second argument of <code class="func">AGRParseFilenameFormat</code> (<a href="chap5.html#X85D036A07A869C54"><b>5.6-1</b></a>), such that only filenames of the type in question match. (It is not checked whether this "detection function" matches exactly one type, so one must be very careful here when declaring a new type.)</p>
</dd>
<dt><strong class="Mark"><code class="code">AddFileInfo</code></strong></dt>
<dd><p>This defines the information stored in the table of contents for the data of the type. The value must be a function that takes three arguments (the current list of data for the type and the given group, a list returned by <code class="func">AGRParseFilenameFormat</code> (<a href="chap5.html#X85D036A07A869C54"><b>5.6-1</b></a>) for the given type, and a filename). This function adds the necessary parts of the data entry to the list, and returns <code class="keyw">true</code> if the data belongs to the type, otherwise <code class="keyw">false</code> is returned; note that the latter case occurs if the filename matches the format description but additional conditions on the parts of the name are not satisfied (for example integer parts may be required to be positive or prime powers).</p>
</dd>
<dt><strong class="Mark"><code class="code">ReadAndInterpretDefault</code></strong></dt>
<dd><p>This is the function that does the work for the default <code class="code">contents</code> value of the <code class="code">accessFunctions</code> component of <code class="func">AtlasOfGroupRepresentationsInfo</code> (<a href="chap5.html#X7BEC94A6781E126E"><b>5.1-5</b></a>), see Section <a href="chap5.html#X81C5B5E78215169D"><b>5.2</b></a>. This function must take a path and return the <strong class="pkg">GAP</strong> object given by this file.</p>
</dd>
<dt><strong class="Mark"><code class="code">AddDescribingComponents</code> (for <code class="code">rep</code> only)</strong></dt>
<dd><p>This function takes two arguments, a record (that will be returned by <code class="func">AtlasGenerators</code> (<a href="chap2.html#X7D1CCCF8852DFF39"><b>2.5-2</b></a>), <code class="func">OneAtlasGeneratingSetInfo</code> (<a href="chap2.html#X841478AB7CD06D44"><b>2.5-4</b></a>), or <code class="func">AllAtlasGeneratingSetInfos</code> (<a href="chap2.html#X84C2D76482E60E42"><b>2.5-5</b></a>)) and the type record <var class="Arg">record</var>. It sets the components <code class="code">p</code>, <code class="code">dim</code>, <code class="code">id</code>, and <code class="code">ring</code> that are promised for return values of the abovementioned three functions.</p>
</dd>
<dt><strong class="Mark"><code class="code">DisplayGroup</code> (for <code class="code">rep</code> only)</strong></dt>
<dd><p>This defines the format of the lines printed by <code class="func">DisplayAtlasInfo</code> (<a href="chap2.html#X79DACFFA7E2D1A99"><b>2.5-1</b></a>) for a given group. The value must be a function that takes a list as returned by the function given in the component <code class="code">AddFileInfo</code>, and returns the string to be printed for the representation in question.</p>
</dd>
</dl>
<p><em>Optional components</em> of <var class="Arg">record</var> are</p>
<dl>
<dt><strong class="Mark"><code class="code">DisplayOverviewInfo</code></strong></dt>
<dd><p>This is used to introduce a new column in the output of <code class="func">DisplayAtlasInfo</code> (<a href="chap2.html#X79DACFFA7E2D1A99"><b>2.5-1</b></a>) when this is called without arguments or with a list of group names as its only argument. The value must be a list of length three, containing at its first position a string used as the header of the column, at its second position one of the strings <code class="code">"r"</code> or <code class="code">"l"</code>, denoting right or left aligned column entries, and at its third position a function that takes two arguments (a list of tables of contents of the <strong class="pkg">AtlasRep</strong> package and a group name), and returns a list of length two, containing the string to be printed as the column value and <code class="keyw">true</code> or <code class="keyw">false</code>, depending on whether private data is involved or not. (The default is to print no column for the data type.)</p>
</dd>
<dt><strong class="Mark"><code class="code">DisplayPRG</code> (for <code class="code">prg</code> only)</strong></dt>
<dd><p>This is used in <code class="func">DisplayAtlasInfo</code> (<a href="chap2.html#X79DACFFA7E2D1A99"><b>2.5-1</b></a>) for <strong class="pkg">ATLAS</strong> programs. The value must be a function that takes four arguments (a list of tables of contents to examine, the name of the given group, a list of integers or <code class="keyw">true</code> for the required standardization, and a list of all available standardizations), and returns the list of lines (strings) to be printed as the information about the available programs of the current type and for the given group. (The default is to return an empty list.)</p>
</dd>
<dt><strong class="Mark"><code class="code">AccessGroupCondition</code> (for <code class="code">rep</code> only)</strong></dt>
<dd><p>This is used in <code class="func">DisplayAtlasInfo</code> (<a href="chap2.html#X79DACFFA7E2D1A99"><b>2.5-1</b></a>) and <code class="func">OneAtlasGeneratingSetInfo</code> (<a href="chap2.html#X841478AB7CD06D44"><b>2.5-4</b></a>). The value must be a function that takes two arguments (a list as returned by <code class="func">AGRParseFilenameFormat</code> (<a href="chap5.html#X85D036A07A869C54"><b>5.6-1</b></a>), and a list of conditions), and returns <code class="keyw">true</code> or <code class="keyw">false</code>, depending on whether the first argument satisfies the conditions. (The default value is <code class="func">ReturnFalse</code> (<a href="../../../doc/htm/ref/CHAP005.htm#SECT003"><b>Reference: ReturnFalse</b></a>).)</p>
<p>The function must support conditions such as <code class="code">[ IsPermGroup, true ]</code> and <code class="code">[ NrMovedPoints, [ 5, 6 ] ]</code>, in general a list of functions followed by a prescribed value, a list of prescribed values, another (unary) function, or the string <code class="code">"minimal"</code>. For an overview of the interesting functions, see <code class="func">DisplayAtlasInfo</code> (<a href="chap2.html#X79DACFFA7E2D1A99"><b>2.5-1</b></a>).</p>
</dd>
<dt><strong class="Mark"><code class="code">AccessPRG</code> (for <code class="code">prg</code> only)</strong></dt>
<dd><p>This is used in <code class="func">AtlasProgram</code> (<a href="chap2.html#X801F2E657C8A79ED"><b>2.5-3</b></a>). The value must be a function that takes three arguments (the record with the information about the given group in the current table of contents, an integer or a list of integers or <code class="keyw">true</code> for the required standardization, and a list of conditions given by the optional arguments of <code class="func">AtlasProgram</code> (<a href="chap2.html#X801F2E657C8A79ED"><b>2.5-3</b></a>)), and returns either <code class="keyw">fail</code> or a list that together with the group name forms the identifier of a program that matches the conditions. (The default value is <code class="func">ReturnFail</code> (<a href="../../../doc/htm/ref/CHAP005.htm#SECT003"><b>Reference: ReturnFail</b></a>).)</p>
</dd>
<dt><strong class="Mark"><code class="code">AtlasProgram</code> (for <code class="code">prg</code> only)</strong></dt>
<dd><p>This is used in <code class="func">AtlasProgram</code> (<a href="chap2.html#X801F2E657C8A79ED"><b>2.5-3</b></a>) to create the result value from the identifier. (The default value is <code class="code">AtlasProgramDefault</code>, which works whenever the second entry of the identifier is the filename; this is not the case for example if the program is the composition of several programs.)</p>
</dd>
<dt><strong class="Mark"><code class="code">TOCEntryString</code></strong></dt>
<dd><p>This is used in <code class="func">StoreAtlasTableOfContents</code> (<a href="chap1.html#X7E3E52D380C20363"><b>1.6-2</b></a>). The value must be a function that takes two arguments (the name <var class="Arg">name</var> of the type and a list as returned by <code class="func">AGRParseFilenameFormat</code> (<a href="chap5.html#X85D036A07A869C54"><b>5.6-1</b></a>) and returns a string that describes the appropriate function call. (The default value is <code class="code">TOCEntryStringDefault</code>.)</p>
</dd>
<dt><strong class="Mark"><code class="code">PostprocessFileInfo</code></strong></dt>
<dd><p>This is used in the construction of a table of contents via <code class="func">ReloadAtlasTableOfContents</code> (<a href="chap1.html#X7AC3EA317EDBDA0E"><b>1.6-1</b></a>), for testing or rearranging the data of the current table of contents. The value must be a function that takes two arguments, the table of contents record and the record in it that belongs to one fixed group. (The default function does nothing.)</p>
</dd>
<dt><strong class="Mark"><code class="code">SortTOCEntries</code></strong></dt>
<dd><p>This is used in the construction of a table of contents (see <code class="func">ReloadAtlasTableOfContents</code> (<a href="chap1.html#X7AC3EA317EDBDA0E"><b>1.6-1</b></a>)), for sorting the entries after they have been added and after the value of the component <code class="code">PostprocessFileInfo</code> has been called. The value must be a function that takes a list as returned by <code class="func">AGRParseFilenameFormat</code> (<a href="chap5.html#X85D036A07A869C54"><b>5.6-1</b></a>), and returns the sorting key. (There is no default value, which means that no sorting is needed.)</p>
</dd>
<dt><strong class="Mark"><code class="code">TestFileHeaders</code> (for <code class="code">rep</code> only)</strong></dt>
<dd><p>This is used in the function <code class="func">AtlasOfGroupRepresentationsTestFileHeaders</code> (<a href="chap5.html#X8318C1AD84557495"><b>5.8-5</b></a>). The value must be a function that takes the same four arguments as <code class="func">AGRFileContents</code> (<a href="chap5.html#X819839FA7A639DE2"><b>5.6-2</b></a>), except that the first argument <code class="code">"datagens"</code> can be replaced by <code class="code">"local"</code> and that the third argument is a list as returned by <code class="func">AGRParseFilenameFormat</code> (<a href="chap5.html#X85D036A07A869C54"><b>5.6-1</b></a>). (The default value is <code class="func">ReturnTrue</code> (<a href="../../../doc/htm/ref/CHAP005.htm#SECT003"><b>Reference: ReturnTrue</b></a>).)</p>
</dd>
<dt><strong class="Mark"><code class="code">TestFiles</code> (for <code class="code">rep</code> only)</strong></dt>
<dd><p>This is used in the function <code class="func">AtlasOfGroupRepresentationsTestFiles</code> (<a href="chap5.html#X828C687579111271"><b>5.8-7</b></a>). The format of the value and the default are the same as for the value of the component <code class="code">TestFileHeaders</code>.</p>
</dd>
<dt><strong class="Mark"><code class="code">TestWords</code> (for <code class="code">prg</code> only)</strong></dt>
<dd><p>This is used in the function <code class="func">AtlasOfGroupRepresentationsTestWords</code> (<a href="chap5.html#X85F8ED98805FB495"><b>5.8-6</b></a>). The value must be a function that takes five arguments where the first four are the same arguments as for <code class="func">AGRFileContents</code> (<a href="chap5.html#X819839FA7A639DE2"><b>5.6-2</b></a>), except that the first argument <code class="code">"dataword"</code> can be replaced by <code class="code">"local"</code>, and the fifth argument is <code class="keyw">true</code> or <code class="keyw">false</code>, indicating verbose mode or not.</p>
</dd>
</dl>
<p><a id="X7D16BE31788F0E8A" name="X7D16BE31788F0E8A"></a></p>
<h4>5.6 <span class="Heading">Filenames Used in the <strong class="pkg">ATLAS</strong> of Group Representations</span></h4>
<p>The data of each local <strong class="pkg">GAP</strong> version of the <strong class="pkg">ATLAS</strong> of Group Representations is either private (see Chapter <a href="chap3.html#X7DF711157F9EFA28"><b>3</b></a>) or is stored in the two directories <code class="file">datagens</code> and <code class="file">dataword</code>. In the following, we describe the format of filenames in the latter two directories, as a reference of the "official" part of the <strong class="pkg">ATLAS</strong>.</p>
<p>In the directory <code class="file">datagens</code>, the generators for the <em>representations</em> available are stored, the directory <code class="file">dataword</code> contains the <em>programs</em> to compute conjugacy class representatives, generators of maximal subgroups, images of generators under automorphisms of a given group G from standard generators of G, and to check and compute standard generators (see Section <a href="chap2.html#X795DB7E486E0817D"><b>2.3</b></a>).</p>
<p>The name of each data file in the <strong class="pkg">ATLAS</strong> of Group Representations describes the contents of the file. This section lists the definitions of the filenames used.</p>
<p>Each filename consists of two parts, separated by a minus sign <code class="code">-</code>. The first part is always of the form <var class="Arg">groupname</var><code class="code">G</code><var class="Arg">i</var>, where the integer <var class="Arg">i</var> denotes the <var class="Arg">i</var>-th set of standard generators for the group G, say, with <strong class="pkg">ATLAS</strong>-file name <var class="Arg">groupname</var> (see <a href="chap2.html#X81BF52FC7B8C08D4"><b>2.2</b></a>). The translations of the name <var class="Arg">groupname</var> to the name(s) used within <strong class="pkg">GAP</strong> is given by the component <code class="code">GAPnames</code> of <code class="func">AtlasOfGroupRepresentationsInfo</code> (<a href="chap5.html#X7BEC94A6781E126E"><b>5.1-5</b></a>).</p>
<p>The filenames in the directory <code class="file">dataword</code> have one of the following forms. In each of these cases, the suffix <code class="code">W</code><var class="Arg">n</var> means that <var class="Arg">n</var> is the version number of the program.</p>
<dl>
<dt><strong class="Mark"><code class="code"><var class="Arg">groupname</var>G<var class="Arg">i</var>-cycW<var class="Arg">n</var></code></strong></dt>
<dd><p>In this case, the file contains a straight line program that returns a list of representatives of generators of maximally cyclic subgroups of G. An example is <code class="code">Co1G1-cycW1</code>.</p>
</dd>
<dt><strong class="Mark"><code class="code"><var class="Arg">groupname</var>G<var class="Arg">i</var>-cclsW<var class="Arg">n</var></code></strong></dt>
<dd><p>In this case, the file contains a straight line program that returns a list of conjugacy class representatives of G. An example is <code class="code">RuG1-cclsW1</code>.</p>
</dd>
<dt><strong class="Mark"><code class="code"><var class="Arg">groupname</var>G<var class="Arg">i</var>cycW<var class="Arg">n</var>-cclsW<var class="Arg">m</var></code></strong></dt>
<dd><p>In this case, the file contains a straight line program that takes the return value of the program in the file <var class="Arg">groupname</var><code class="code">G</code><var class="Arg">i</var><code class="code">-cycW</code><var class="Arg">n</var> (see above), and returns a list of conjugacy class representatives of G. An example is <code class="code">M11G1cycW1-cclsW1</code>.</p>
</dd>
<dt><strong class="Mark"><code class="code"><var class="Arg">groupname</var>G<var class="Arg">i</var>-max<var class="Arg">k</var>W<var class="Arg">n</var></code></strong></dt>
<dd><p>In this case, the file contains a straight line program that takes generators of G w.r.t. the <var class="Arg">i</var>-th set of standard generators, and returns a list of generators (in general <em>not</em> standard generators) for a subgroup U in the <var class="Arg">k</var>-th class of maximal subgroups of G. An example is <code class="code">J1G1-max7W1</code>.</p>
</dd>
<dt><strong class="Mark"><code class="code"><var class="Arg">groupname</var>G<var class="Arg">i</var>max<var class="Arg">k</var>W<var class="Arg">n</var>-<var class="Arg">subgroupname</var>G<var class="Arg">j</var>W<var class="Arg">m</var></code></strong></dt>
<dd><p>In this case, the file contains a straight line program that takes the return value of the program in the file <var class="Arg">groupname</var><code class="code">G</code><var class="Arg">i</var><code class="code">-max</code><var class="Arg">k</var><code class="code">W</code><var class="Arg">n</var> (see above), which are generators for a group U, say; <var class="Arg">subgroupname</var> is a name for U, and the return value is a list of standard generators for U, w.r.t. the <var class="Arg">j</var>-th set of standard generators. (Of course this implies that the groups in the <var class="Arg">k</var>-th class of maximal subgroups of G are isomorphic to the group with name <var class="Arg">subgroupname</var>.) An example is <code class="code">J1G1max1W1-L211G1W1</code>; the first class of maximal subgroups of the Janko group J_1 consists of groups isomorphic to the linear group L_2(11), for which standard generators are defined.</p>
</dd>
<dt><strong class="Mark"><code class="code"><var class="Arg">groupname</var>G<var class="Arg">i</var>-a<var class="Arg">outname</var>W<var class="Arg">n</var></code></strong></dt>
<dd><p>In this case, the file contains a straight line program that takes generators of G w.r.t. the <var class="Arg">i</var>-th set of standard generators, and returns the list of their images under the outer automorphism alpha of G given by the name <var class="Arg">outname</var>; if this name is empty then alpha is the unique nontrivial outer automorphism of G; if it is a positive integer k then alpha is a generator of the unique cyclic order k subgroup of the outer automorphism group of G; if it is of the form <code class="code">2_1</code> or <code class="code">2a</code>, <code class="code">4_2</code> or <code class="code">4b</code>, <code class="code">3_3</code> or <code class="code">3c</code> ... then alpha generates the cyclic group of automorphisms induced on G by G.2_1, G.4_2, G.3_3 ...; finally, if it is of the form <var class="Arg">k</var><code class="code">p</code><var class="Arg">d</var>, with <var class="Arg">k</var> one of the above forms and <var class="Arg">d</var> an integer then <var class="Arg">d</var> denotes the number of dashes appended to the automorphism described by <var class="Arg">k</var>; if <var class="Arg">d</var> = 1 then <var class="Arg">d</var> can be omitted. Examples are <code class="code">A5G1-aW1</code>, <code class="code">L34G1-a2_1W1</code>, <code class="code">U43G1-a2_3pW1</code>, and <code class="code">O8p3G1-a2_2p5W1</code>; these file names describe the outer order 2 automorphism of A_5 (induced by the action of S_5) and the order 2 automorphisms of L_3(4), U_4(3), and O_8^+(3) induced by the actions of L_3(4).2_1, U_4(3).2_2^', and O_8^+(3).2_2^{'''''}, respectively.</p>
</dd>
<dt><strong class="Mark"><code class="code"><var class="Arg">groupname</var>G<var class="Arg">i</var>-G<var class="Arg">j</var>W<var class="Arg">n</var></code></strong></dt>
<dd><p>In this case, the file contains a straight line program that takes generators of G w.r.t. the <var class="Arg">i</var>-th set of standard generators, and returns standard generators of G w.r.t. the <var class="Arg">j</var>-th set of standard generators. An example is <code class="code">L35G1-G2W1</code>.</p>
</dd>
<dt><strong class="Mark"><code class="code"><var class="Arg">groupname</var>G<var class="Arg">i</var>-check<var class="Arg">n</var></code></strong></dt>
<dd><p>In this case, the file contains a straight line decision that takes generators of G, and returns <code class="keyw">true</code> if these generators are standard generators w.r.t. the <var class="Arg">i</var>-th standardization, and <code class="keyw">false</code> otherwise.</p>
</dd>
<dt><strong class="Mark"><code class="code"><var class="Arg">groupname</var>G<var class="Arg">i</var>-P<var class="Arg">n</var></code></strong></dt>
<dd><p>In this case, the file contains a straight line decision that takes some group elements, and returns <code class="keyw">true</code> if these elements are standard generators for <var class="Arg">G</var>, w.r.t. the <var class="Arg">i</var>-th standardization, and <code class="keyw">false</code> otherwise.</p>
</dd>
<dt><strong class="Mark"><code class="code"><var class="Arg">groupname</var>G<var class="Arg">i</var>-find<var class="Arg">n</var></code></strong></dt>
<dd><p>In this case, the file contains a black box program that takes a group, and returns (if it is successful) a set of standard generators for <var class="Arg">G</var>, w.r.t. the <var class="Arg">i</var>-th standardization.</p>
</dd>
<dt><strong class="Mark"><code class="code"><var class="Arg">groupname</var>G<var class="Arg">i</var>-X<var class="Arg">descr</var>W<var class="Arg">n</var></code></strong></dt>
<dd><p>In this case, the file contains a straight line program that takes generators of G w.r.t. the <var class="Arg">i</var>-th set of standard generators, and whose return value corresponds to <var class="Arg">descr</var>. This format is used only in private extensions (see Chapter <a href="chap3.html#X7DF711157F9EFA28"><b>3</b></a>), such a script can be accessed with <var class="Arg">descr</var> as the third argument of <code class="func">AtlasProgram</code> (<a href="chap2.html#X801F2E657C8A79ED"><b>2.5-3</b></a>).</p>
</dd>
</dl>
<p>The filenames in the directory <code class="file">datagens</code> have one of the following forms. In each of these cases, <var class="Arg">id</var> is a (possibly empty) string that starts with a lowercase alphabet letter (see <code class="func">IsLowerAlphaChar</code> (<a href="../../../doc/htm/ref/CHAP026.htm#SECT003"><b>Reference: IsLowerAlphaChar</b></a>)), and <var class="Arg">m</var> is a nonnegative integer, meaning that the generators are written w.r.t. the <var class="Arg">m</var>-th basis (the meaning is defined by the <strong class="pkg">ATLAS</strong> developers).</p>
<dl>
<dt><strong class="Mark"><code class="code"><var class="Arg">groupname</var>G<var class="Arg">i</var>-f<var class="Arg">q</var>r<var class="Arg">dim</var><var class="Arg">id</var>B<var class="Arg">m</var>.m<var class="Arg">nr</var></code></strong></dt>
<dd><p>a file in <strong class="pkg">MeatAxe</strong> text file format containing the <var class="Arg">nr</var>-th generator of a matrix representation over the field with <var class="Arg">q</var> elements, of dimension <var class="Arg">dim</var>. An example is <code class="code">S5G1-f2r4aB0.m1</code>.</p>
</dd>
<dt><strong class="Mark"><code class="code"><var class="Arg">groupname</var>G<var class="Arg">i</var>-p<var class="Arg">n</var><var class="Arg">id</var>B<var class="Arg">m</var>.m<var class="Arg">nr</var></code></strong></dt>
<dd><p>a file in <strong class="pkg">MeatAxe</strong> text file format containing the <var class="Arg">nr</var>-th generator of a permutation representation on <var class="Arg">n</var> points. An example is <code class="code">M11G1-p11B0.m1</code>.</p>
</dd>
<dt><strong class="Mark"><code class="code"><var class="Arg">groupname</var>G<var class="Arg">i</var>-Ar<var class="Arg">dim</var><var class="Arg">id</var>B<var class="Arg">m</var>.g</code></strong></dt>
<dd><p>a <strong class="pkg">GAP</strong> readable file containing all generators of a matrix representation of dimension <var class="Arg">dim</var> over an algebraic number field not specified further. An example is <code class="code">A5G1-Ar3aB0.g</code>.</p>
</dd>
<dt><strong class="Mark"><code class="code"><var class="Arg">groupname</var>G<var class="Arg">i</var>-Zr<var class="Arg">dim</var><var class="Arg">id</var>B<var class="Arg">m</var>.g</code></strong></dt>
<dd><p>a <strong class="pkg">GAP</strong> readable file containing all generators of a matrix representation over the integers, of dimension <var class="Arg">dim</var>. An example is <code class="code">A5G1-Zr4B0.g</code>.</p>
</dd>
<dt><strong class="Mark"><code class="code"><var class="Arg">groupname</var>G<var class="Arg">i</var>-Hr<var class="Arg">dim</var><var class="Arg">id</var>B<var class="Arg">m</var>.g</code></strong></dt>
<dd><p>a <strong class="pkg">GAP</strong> readable file containing all generators of a matrix representation over a quaternion algebra over an algebraic number field, of dimension <var class="Arg">dim</var>. An example is <code class="code">2A6G1-Hr2aB0.g</code>.</p>
</dd>
<dt><strong class="Mark"><code class="code"><var class="Arg">groupname</var>G<var class="Arg">i</var>-Z<var class="Arg">n</var>r<var class="Arg">dim</var><var class="Arg">id</var>B<var class="Arg">m</var>.g</code></strong></dt>
<dd><p>a <strong class="pkg">GAP</strong> readable file containing all generators of a matrix representation of dimension <var class="Arg">dim</var> over the ring of integers mod <var class="Arg">n</var>. An example is <code class="code">2A8G1-Z4r4aB0.g</code>.</p>
</dd>
</dl>
<p><a id="X85D036A07A869C54" name="X85D036A07A869C54"></a></p>
<h5>5.6-1 AGRParseFilenameFormat</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> AGRParseFilenameFormat</code>( <var class="Arg">string, format</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p><b>Returns: </b>a list of strings and integers if <var class="Arg">string</var> matches <var class="Arg">format</var>, and <code class="keyw">fail</code> otherwise.</p>
<p>Let <var class="Arg">string</var> be a filename, and <var class="Arg">format</var> be a list [ [ c_1, c_2, ..., c_n ], [ f_1, f_2, ..., f_n ] ] such that each entry c_i is a list of strings and of functions that take a character as their argument and return <code class="file">true</code> or <code class="file">false</code>, and such that each entry f_i is a function for parsing a filename, such as the currently undocumented functions <code class="code">ParseForwards</code> and <code class="code">ParseBackwards</code>.</p>
<p><code class="func">AGRParseFilenameFormat</code> returns a list of strings and integers such that the concatenation of their <code class="func">String</code> (<a href="../../../doc/htm/ref/CHAP026.htm#SECT005"><b>Reference: String</b></a>) values yields <var class="Arg">string</var> if <var class="Arg">string</var> matches <var class="Arg">format</var>, and <code class="keyw">fail</code> otherwise. Matching is defined as follows. Splitting <var class="Arg">string</var> at each minus character (<code class="code">-</code>) yields m parts s_1, s_2, ..., s_m. The string <var class="Arg">string</var> matches <var class="Arg">format</var> if s_i matches the conditions in c_i, for 1 <= i <= n, in the sense that applying f_i to s_i and c_i yields a non-<code class="keyw">fail</code> result.</p>
<table class="example">
<tr><td><pre>
gap> format:= [ [ [ IsChar, "G", IsDigitChar ],
> [ "p", IsDigitChar, IsLowerAlphaOrDigitChar,
> "B", IsDigitChar, ".m", IsDigitChar ] ],
> [ ParseBackwards, ParseForwards ] ];;
gap> AGRParseFilenameFormat( "A6G1-p10B0.m1", format );
[ "A6", "G", 1, "p", 10, "", "B", 0, ".m", 1 ]
gap> AGRParseFilenameFormat( "A6G1-p15aB0.m1", format );
[ "A6", "G", 1, "p", 15, "a", "B", 0, ".m", 1 ]
gap> AGRParseFilenameFormat( "A6G1-f2r16B0.m1", format );
fail
</pre></td></tr></table>
<p><a id="X819839FA7A639DE2" name="X819839FA7A639DE2"></a></p>
<h5>5.6-2 AGRFileContents</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> AGRFileContents</code>( <var class="Arg">dirname, groupname, filename, type</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p><b>Returns: </b>the <strong class="pkg">GAP</strong> object obtained from reading and interpreting the file(s) with name(s) <var class="Arg">filename</var>.</p>
<p>Let <var class="Arg">dirname</var> and <var class="Arg">groupname</var> be strings, <var class="Arg">filename</var> be a string or a list of strings, and <var class="Arg">type</var> be a data type (see <code class="func">AGRDeclareDataType</code> (<a href="chap5.html#X832AB6B97BE4CD9F"><b>5.5-1</b></a>)). <var class="Arg">dirname</var> must be one of <code class="code">"datagens"</code>, <code class="code">"dataword"</code>, or the <var class="Arg">dirid</var> value of a private directory, see <code class="func">AtlasOfGroupRepresentationsNotifyPrivateDirectory</code> (<a href="chap3.html#X825AF58885A48520"><b>3.1-1</b></a>). If <var class="Arg">groupname</var> is the <strong class="pkg">ATLAS</strong>-file name of a group G (see Section <a href="chap2.html#X81BF52FC7B8C08D4"><b>2.2</b></a>), and if <var class="Arg">filename</var> is either the name of an accessible file in the <var class="Arg">dirname</var> directory of the <strong class="pkg">ATLAS</strong>, or a list of such filenames, with data concerning G and for the data type <code class="code">type</code>, then <code class="func">AGRFileContents</code> returns the contents of the corresponding file(s), in the sense that the file(s) (or equivalent ones, see Section <a href="chap1.html#X7FA485E479F6C3A0"><b>1.7-6</b></a>) is/are read, and the result is interpreted if necessary; otherwise <code class="keyw">fail</code> is returned.</p>
<p>Note that if <var class="Arg">filename</var> refers to file(s) already stored in the <var class="Arg">dirname</var> directory then <code class="func">AGRFileContents</code> does <em>not</em> check whether the table of contents of the <strong class="pkg">ATLAS</strong> of Group Representations actually contains <var class="Arg">filename</var>.</p>
<p><a id="X7D66C94E7A0F2252" name="X7D66C94E7A0F2252"></a></p>
<h4>5.7 <span class="Heading">The Tables of Contents of the <strong class="pkg">ATLAS</strong> of Group Representations
</span></h4>
<p>The list of data currently available is stored in several <em>tables of contents</em>, one for the local <strong class="pkg">GAP</strong> data, one for the data on remote servers, and one for each private data directory. These tables of contents are created by <code class="func">ReloadAtlasTableOfContents</code> (<a href="chap1.html#X7AC3EA317EDBDA0E"><b>1.6-1</b></a>).</p>
<p>It is assumed that the local data directories contain only files that are also available on servers. Private extensions to the database (cf. Section <a href="chap1.html#X7FB64AD37D4620E6"><b>1.8</b></a> and Chapter <a href="chap3.html#X7DF711157F9EFA28"><b>3</b></a>) cannot be handled by putting the data files into the local directories.</p>
<p>Each table of contents is represented by a record whose components are the <strong class="pkg">ATLAS</strong>-file names of the groups (see Section <a href="chap2.html#X81BF52FC7B8C08D4"><b>2.2</b></a>) and <code class="code">lastupdated</code>, a string describing the date of the last update of this table of contents. The value for each group name is a record whose components are the names of those data types (see Section <a href="chap5.html#X86366BF08533DA5E"><b>5.5</b></a>) for which data are available.</p>
<p>Note that the name mapping between the <strong class="pkg">ATLAS</strong>-file and <strong class="pkg">GAP</strong> names of the groups is provided by the <code class="code">groupnames</code> component of <code class="func">AtlasOfGroupRepresentationsInfo</code> (<a href="chap5.html#X7BEC94A6781E126E"><b>5.1-5</b></a>), and information about the base rings of matrix representations is provided by the <code class="code">ringinfo</code> component. Group names are notified with <code class="func">AGRGNAN</code> (<a href="chap5.html#X8229700C8744F09B"><b>5.7-1</b></a>), and base ring information can be notified with <code class="func">AGRRNG</code> (<a href="chap5.html#X86698BC778570236"><b>5.7-2</b></a>); these two administrational functions may be useful for private extensions of the package (see Chapter <a href="chap3.html#X7DF711157F9EFA28"><b>3</b></a>).</p>
<p><a id="X8229700C8744F09B" name="X8229700C8744F09B"></a></p>
<h5>5.7-1 AGRGNAN</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> AGRGNAN</code>( <var class="Arg">gapname, atlasname[, size[, maxessize[, "all"[, compatinfo]]]]</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Let <var class="Arg">gapname</var> be a string denoting a <strong class="pkg">GAP</strong> group name, and <var class="Arg">atlasname</var> be a string denoting the corresponding <strong class="pkg">ATLAS</strong>-file name used in filenames of the <strong class="pkg">ATLAS</strong> of Group Representations. The following optional arguments are supported.</p>
<dl>
<dt><strong class="Mark"><var class="Arg">size</var></strong></dt>
<dd><p>the order of the corresponding group,</p>
</dd>
<dt><strong class="Mark"><var class="Arg">maxessizes</var></strong></dt>
<dd><p>a (not necessarily dense) list of orders of the maximal subgroups of this group</p>
</dd>
<dt><strong class="Mark"><var class="Arg">complete</var></strong></dt>
<dd><p>the string <code class="code">"all"</code> if the <var class="Arg">maxessizes</var> list is complete,</p>
</dd>
<dt><strong class="Mark"><var class="Arg">compatinfo</var></strong></dt>
<dd><p>a list of entries of the form <code class="code">[ std, factname, factstd, flag ]</code> meaning that mapping standard generators of standardization <code class="code">std</code> to the factor group with <strong class="pkg">GAP</strong> group name <code class="code">factname</code>, via the natural epimorphism, yields standard generators of standardization <code class="code">factstd</code> if <code class="code">flag</code> is <code class="keyw">true</code>.</p>
</dd>
</dl>
<p><code class="func">AGRGNAN</code> adds the list of its arguments to the list stored in the <code class="code">GAPnames</code> component of <code class="func">AtlasOfGroupRepresentationsInfo</code> (<a href="chap5.html#X7BEC94A6781E126E"><b>5.1-5</b></a>), making the <strong class="pkg">ATLAS</strong> data involving <var class="Arg">atlasname</var> accessible for the group with name <var class="Arg">gapname</var>.</p>
<p>An example of a valid call is <code class="code">AGRGNAN("A6.2_2","PGL29",360)</code>, see also Section <a href="chap3.html#X86CC8CDD866A1FC3"><b>3.3</b></a>.</p>
<p><a id="X86698BC778570236" name="X86698BC778570236"></a></p>
<h5>5.7-2 AGRRNG</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> AGRRNG</code>( <var class="Arg">filename, descr</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Let <var class="Arg">filename</var> be a string denoting the name of a file containing the generators of a matrix representation over a ring that is not determined by the filename, and let <var class="Arg">descr</var> be a string describing this ring <var class="Arg">R</var>, say. <code class="func">AGRRNG</code> adds the triple <code class="code">[ <var class="Arg">filename</var>, <var class="Arg">descr</var>, <var class="Arg">R</var> ]</code> to the list stored in the <code class="code">ringinfo</code> component of <code class="func">AtlasOfGroupRepresentationsInfo</code> (<a href="chap5.html#X7BEC94A6781E126E"><b>5.1-5</b></a>).</p>
<p>An example of a valid call is <code class="code">AGRRNG("A5G1-Ar3aB0","Field([Sqrt(5)])")</code>.</p>
<p><a id="X84A565E482DBF4C1" name="X84A565E482DBF4C1"></a></p>
<h4>5.8 <span class="Heading">Sanity Checks for the <strong class="pkg">ATLAS</strong> of Group Representations</span></h4>
<p>The fact that the <strong class="pkg">ATLAS</strong> of Group Representations is designed as an open database (see Section <a href="chap1.html#X7E1934D2780D108F"><b>1.7-1</b></a>) makes it especially desirable to have consistency checks available which can be run automatically whenever new data are added by the developers of the <strong class="pkg">ATLAS</strong>. The tests described in the following can also be used for private extensions of the package (see Chapter <a href="chap3.html#X7DF711157F9EFA28"><b>3</b></a>).</p>
<p>The file <code class="file">tst/testall.g</code> of the package contains <code class="func">ReadTest</code> (<a href="../../../doc/htm/ref/CHAP007.htm#SECT009"><b>Reference: ReadTest</b></a>) statements for executing a collection of such sanity checks; one can run them by starting <strong class="pkg">GAP</strong> in the <code class="file">tst</code> directory, and then calling <code class="code">Read( "testall.g" )</code>. If no problem occurs then <strong class="pkg">GAP</strong> prints only lines starting with one of the following.</p>
<table class="example">
<tr><td><pre>
+ $Id:
+ GAP4stones:
</pre></td></tr></table>
<p>The required space and time for running these tests depends on the amount of locally available data.</p>
<p>The examples in this manual form a part of these tests, they are collected in the file <code class="file">tst/docxpl.tst</code> of the package.</p>
<p>The file <code class="file">tst/atlasrep.tst</code> contains calls to the functions <code class="func">AtlasOfGroupRepresentationsTestGroupOrders</code> (<a href="chap5.html#X7B890AE7817446DE"><b>5.8-1</b></a>), which checks the consistency of the stored group orders and the actual data, <code class="func">AtlasOfGroupRepresentationsTestFileHeaders</code> (<a href="chap5.html#X8318C1AD84557495"><b>5.8-5</b></a>), which checks the consistency of the names of <strong class="pkg">MeatAxe</strong> text files and the first lines of the files, and <code class="func">AtlasOfGroupRepresentationsTestWords</code> (<a href="chap5.html#X85F8ED98805FB495"><b>5.8-6</b></a>), which checks whether the available programs do what they promise.</p>
<p>The calls to <code class="func">AtlasOfGroupRepresentationsTestFiles</code> (<a href="chap5.html#X828C687579111271"><b>5.8-7</b></a>), <code class="func">AtlasOfGroupRepresentationsTestClassScripts</code> (<a href="chap5.html#X793FE3A483AA58E5"><b>5.8-8</b></a>), and <code class="func">AGR_TestMinimalDegrees</code> (<a href="chap4.html#X85217A9578DA034A"><b>4.3-5</b></a>) are not part of the tests that are run by reading <code class="file">tst/testall.g</code>.</p>
<p>All these tests apply only to the <em>local</em> table of contents (see Section <a href="chap5.html#X7D66C94E7A0F2252"><b>5.7</b></a>), that is, only those data files are checked that are actually available in the local <strong class="pkg">GAP</strong> installation. No files are fetched from servers during these tests.</p>
<p>Further tests, such as the consistency of different versions of server data, exist but are not part of the distributed package.</p>
<p><a id="X7B890AE7817446DE" name="X7B890AE7817446DE"></a></p>
<h5>5.8-1 AtlasOfGroupRepresentationsTestGroupOrders</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> AtlasOfGroupRepresentationsTestGroupOrders</code>( <var class="Arg"></var> )</td><td class="tdright">( function )</td></tr></table></div>
<p><b>Returns: </b><code class="keyw">false</code> if a contradiction was found, <code class="keyw">true</code> otherwise.</p>
<p>This function checks whether the group orders stored in the <code class="code">GAPnames</code> component of <code class="func">AtlasOfGroupRepresentationsInfo</code> (<a href="chap5.html#X7BEC94A6781E126E"><b>5.1-5</b></a>) coincide with the orders computed from an <strong class="pkg">ATLAS</strong> permutation representation of degree up to 10^4, from the character table or the table of marks with the given name, or from the inner structure of the name (supported is a splitting of the name at the first dot (<code class="code">.</code>), where the two parts of the name are examined with the same criteria in order to derive the group order).</p>
<p>A message is printed for each group name for which no order is stored (and perhaps now can be stored), for which the stored group order cannot be verified, for which a contradiction was found.</p>
<p><a id="X7999A5367E21B2CD" name="X7999A5367E21B2CD"></a></p>
<h5>5.8-2 AtlasOfGroupRepresentationsTestSubgroupOrders</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> AtlasOfGroupRepresentationsTestSubgroupOrders</code>( <var class="Arg"></var> )</td><td class="tdright">( function )</td></tr></table></div>
<p><b>Returns: </b><code class="keyw">false</code> if a contradiction was found, <code class="keyw">true</code> otherwise.</p>
<p>This function checks whether the orders of maximal subgroups stored in the <code class="code">GAPnames</code> component of <code class="func">AtlasOfGroupRepresentationsInfo</code> (<a href="chap5.html#X7BEC94A6781E126E"><b>5.1-5</b></a>) coincide with the orders computed from an <strong class="pkg">ATLAS</strong> permutation representation of degree up to 10^4, from the character table or the table of marks with the given name, or from the information about maximal subgroups of a factor group modulo a central subgroup that is contained in the derived subgroup.</p>
<p>A message is printed for each group name for which no order is stored (and perhaps now can be stored), for which the stored group order cannot be verified, for which a contradiction was found.</p>
<p><a id="X80C116968254C114" name="X80C116968254C114"></a></p>
<h5>5.8-3 AtlasOfGroupRepresentationsTestStdCompatibility</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> AtlasOfGroupRepresentationsTestStdCompatibility</code>( <var class="Arg"></var> )</td><td class="tdright">( function )</td></tr></table></div>
<p><b>Returns: </b><code class="keyw">false</code> if a contradiction was found, <code class="keyw">true</code> otherwise.</p>
<p>This function checks whether the compatibility info stored in the <code class="code">GAPnames</code> component of <code class="func">AtlasOfGroupRepresentationsInfo</code> (<a href="chap5.html#X7BEC94A6781E126E"><b>5.1-5</b></a>) coincide with computed values.</p>
<p>The following criterion is used for computing the value for a group G. Use the <strong class="pkg">GAP</strong> Character Table Library to determine factor groups F of G for which standard generators are defined and moreover a presentation in terms of these standard generators is known. Evaluate the relators of the presentation in the standard generators of G, and let N be the normal closure of these elements in G. Then mapping the standard generators of F to the Ncosets of the standard generators of G is an epimorphism. If |G/N| = |F| holds then G/N and F are isomorphic, and the standard generators of G and F are compatible in the sense that mapping the standard generators of G to their N-cosets yields standard generators of F.</p>
<p>A message is printed for each group name for which no compatibility info was stored and now can be stored, for which the stored info cannot be verified, for which a contradiction was found.</p>
<p><a id="X87C41F1978086FE8" name="X87C41F1978086FE8"></a></p>
<h5>5.8-4 AtlasOfGroupRepresentationsTestCompatibleMaxes</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> AtlasOfGroupRepresentationsTestCompatibleMaxes</code>( <var class="Arg"></var> )</td><td class="tdright">( function )</td></tr></table></div>
<p><b>Returns: </b><code class="keyw">false</code> if a contradiction was found, <code class="keyw">true</code> otherwise.</p>
<p>This function checks whether the information about maximal subgroups stored in the <code class="code">maxext</code> components of the records stored in the <code class="code">TableOfContents.remote</code> component of <code class="func">AtlasOfGroupRepresentationsInfo</code> (<a href="chap5.html#X7BEC94A6781E126E"><b>5.1-5</b></a>) coincide with computed values.</p>
<p>The following criterion is used for computing the value for a group G. If F is a factor group of G such that the standard generators of G and F are compatible (see <code class="func">AtlasOfGroupRepresentationsTestStdCompatibility</code> (<a href="chap5.html#X80C116968254C114"><b>5.8-3</b></a>)) and if there are a presentation for F and a permutation representation of G then it is checked whether the <code class="code">"maxes"</code> type scripts for F can be used to compute also generators for the maximal subgroups of G; if not then words in terms of the standard generators are computed such that the results of the script for F together with the images of these words describe the corresponding maximal subgroup of G.</p>
<p>A message is printed for each group name for which no compatibility info was stored and now can be stored, for which the stored info cannot be verified, for which a contradiction was found.</p>
<p><a id="X8318C1AD84557495" name="X8318C1AD84557495"></a></p>
<h5>5.8-5 AtlasOfGroupRepresentationsTestFileHeaders</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> AtlasOfGroupRepresentationsTestFileHeaders</code>( <var class="Arg">[tocid[, groupname]]</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p><b>Returns: </b><code class="keyw">false</code> if an error occurs, otherwise <code class="keyw">true</code>.</p>
<p>First suppose that this function is called with two arguments <var class="Arg">tocid</var>, the identifier of a directory (see Section <code class="func">sect:Adding a Private Data Directory</code> (<a href="chap3.html#X8072E5C9825D6CCE"><b>3.1</b></a>)), and <var class="Arg">groupname</var>, an <strong class="pkg">ATLAS</strong>-file name that occurs as a component name in the table of contents of the directory. The function checks for those data files for <var class="Arg">groupname</var> in the <var class="Arg">tocid</var> directory that are in <strong class="pkg">MeatAxe</strong> text format whether the filename and the header line are consistent; it checks the data file in <strong class="pkg">GAP</strong> format whether the file name is consistent with the contents of the file.</p>
<p>If only one argument <var class="Arg">tocid</var> is given then all representations available for <var class="Arg">groupname</var> are checked with the three argument version.</p>
<p>If only one argument <var class="Arg">tocid</var> is given then all available groups in the directory with identifier <var class="Arg">tocid</var> are checked; the contents of the local <code class="code">dataword</code> directory can be checked by entering <code class="code">"local"</code>, which is also the default for <var class="Arg">tocid</var>.</p>
<p><a id="X85F8ED98805FB495" name="X85F8ED98805FB495"></a></p>
<h5>5.8-6 AtlasOfGroupRepresentationsTestWords</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> AtlasOfGroupRepresentationsTestWords</code>( <var class="Arg">[tocid[, groupname]]</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p><b>Returns: </b><code class="keyw">false</code> if an error occurs, otherwise <code class="keyw">true</code>.</p>
<p>Called with one argument <var class="Arg">tocid</var>, a string, <code class="func">AtlasOfGroupRepresentationsTestWords</code> processes all programs that are stored in the directory with identifier <var class="Arg">tocid</var> (see Section <code class="func">sect:Adding a Private Data Directory</code> (<a href="chap3.html#X8072E5C9825D6CCE"><b>3.1</b></a>)), using the function stored in the <code class="code">TestWords</code> component of the data type in question. The contents of the local <code class="file">dataword</code> directory can be checked by entering <code class="code">"local"</code>, which is also the default.</p>
<p>If the string <var class="Arg">groupname</var>, an <strong class="pkg">ATLAS</strong>-file name that occurs as a component name in the table of contents of the directory, is given as the second argument then only the data files for this group are tested.</p>
<p><a id="X828C687579111271" name="X828C687579111271"></a></p>
<h5>5.8-7 AtlasOfGroupRepresentationsTestFiles</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> AtlasOfGroupRepresentationsTestFiles</code>( <var class="Arg">[tocid[, groupname]]</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p><b>Returns: </b><code class="keyw">false</code> if an error occurs, otherwise <code class="keyw">true</code>.</p>
<p>This function is an analogue of <code class="func">AtlasOfGroupRepresentationsTestFileHeaders</code> (<a href="chap5.html#X8318C1AD84557495"><b>5.8-5</b></a>). It checks whether reading <strong class="pkg">MeatAxe</strong> text files with <code class="func">ScanMeatAxeFile</code> (<a href="chap5.html#X83D5103780E1238F"><b>5.3-1</b></a>) returns non-<code class="keyw">fail</code> results. It does not check whether the first line of a <strong class="pkg">MeatAxe</strong> text file is consistent with the filename, since this is tested by <code class="func">AtlasOfGroupRepresentationsTestFileHeaders</code> (<a href="chap5.html#X8318C1AD84557495"><b>5.8-5</b></a>).</p>
<p><a id="X793FE3A483AA58E5" name="X793FE3A483AA58E5"></a></p>
<h5>5.8-8 AtlasOfGroupRepresentationsTestClassScripts</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> AtlasOfGroupRepresentationsTestClassScripts</code>( <var class="Arg">[groupname]</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p><b>Returns: </b><code class="keyw">false</code> if an error occurs, otherwise <code class="keyw">true</code>.</p>
<p>First suppose that <code class="func">AtlasOfGroupRepresentationsTestClassScripts</code> is called with one argument <var class="Arg">groupname</var>, the name of a component in <code class="code">AtlasOfGroupRepresentationsInfo.TableOfContents.( "local" )</code>. If the <strong class="pkg">GAP</strong> table library contains an ordinary character table with <code class="func">Identifier</code> (<a href="../../../doc/htm/ref/CHAP069.htm#SECT008"><b>Reference: Identifier!for character tables</b></a>) value the <strong class="pkg">GAP</strong> name corresponding to <var class="Arg">groupname</var> then it is checked whether all those straight line programs for this group that return class representatives are consistent with the character table in the sense that the class names used occur for the table, and that the element orders and centralizer orders for the classes are correct.</p>
<p>If no argument is given then all available groups are checked with the one argument version.</p>
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