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<div class="chlinkprevnexttop"> <a href="chap0_mj.html">[Top of Book]</a>   <a href="chap0_mj.html#contents">[Contents]</a>    <a href="chap4_mj.html">[Previous Chapter]</a>    <a href="chap6_mj.html">[Next Chapter]</a>   </div>

<p id="mathjaxlink" class="pcenter"><a href="chap5.html">[MathJax off]</a></p>
<p><a id="X86FA580F8055B274" name="X86FA580F8055B274"></a></p>
<div class="ChapSects"><a href="chap5_mj.html#X86FA580F8055B274">5 <span class="Heading">Functions</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X870553EF8605792F">5.1 <span class="Heading">Information about a function</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X79C3BDC4781FA0FD">5.1-1 NameFunction</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X877F03F77FD74C98">5.1-2 NumberArgumentsFunction</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X818BAB817A4FB346">5.1-3 NamesLocalVariablesFunction</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X80E108C57F90FAA3">5.1-4 FilenameFunc</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7FF7643781D2C194">5.1-5 StartlineFunc</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X844F95767C74834F">5.1-6 LocationFunc</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X845A929B83D46E01">5.1-7 PageSource</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X851B58408520700D">5.2 <span class="Heading">Calling a function with a list argument that is interpreted as
several arguments</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7CF4DDB97D65AE52">5.2-1 CallFuncList</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X83066E5A80B5FB71">5.3 <span class="Heading">Wrapping a function, so the values produced are cached</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X817ED3B280A64601">5.3-1 MemoizePosIntFunction</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X7EB0A85F7D128BE0">5.4 <span class="Heading">Functions that do nothing</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7DB422A2876CCC4D">5.4-1 ReturnTrue</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7C131FB17D7518FC">5.4-2 ReturnFalse</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7A0994DE7C258E55">5.4-3 ReturnFail</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X818EA8C47B46A634">5.4-4 ReturnNothing</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X8788D7D780FCE169">5.4-5 ReturnFirst</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X810325697BDEF899">5.4-6 IdFunc</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X80FE39D27CE3DE1B">5.5 <span class="Heading">Function Types</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X85E40340806C2B8C">5.5-1 IsFunction</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X87838FE885A9AAF9">5.5-2 FunctionsFamily</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X81F732457F7BC851">5.6 <span class="Heading">Naming Conventions</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X7A1721CD79F08E71">5.7 <span class="Heading">Code annotations (pragmas)</span></a>
</span>
</div>
</div>

<h3>5 <span class="Heading">Functions</span></h3>

<p>The section <a href="chap4_mj.html#X815F71EA7BC0EB6F"><span class="RefLink">4.11</span></a> describes how to define a function. In this chapter we describe functions that give information about functions, and various utility functions used either when defining functions or calling functions.</p>

<p><a id="X870553EF8605792F" name="X870553EF8605792F"></a></p>

<h4>5.1 <span class="Heading">Information about a function</span></h4>

<p><a id="X79C3BDC4781FA0FD" name="X79C3BDC4781FA0FD"></a></p>

<h5>5.1-1 NameFunction</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ NameFunction</code>( <var class="Arg">func</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>returns the name of a function. For operations, this is the name used in their declaration. For functions, this is the variable name they were first assigned to. (For some internal functions, this might be a name <em>different</em> from the name that is documented.) If no such name exists, the string <code class="code">"unknown"</code> is returned.</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">NameFunction(SylowSubgroup);</span>
"SylowSubgroup"
<span class="GAPprompt">gap></span> <span class="GAPinput">Blubberflutsch:=x->x;;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">HasNameFunction(Blubberflutsch);</span>
true
<span class="GAPprompt">gap></span> <span class="GAPinput">NameFunction(Blubberflutsch);</span>
"Blubberflutsch"
<span class="GAPprompt">gap></span> <span class="GAPinput">a:=Blubberflutsch;;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">NameFunction(a);</span>
"Blubberflutsch"
<span class="GAPprompt">gap></span> <span class="GAPinput">SetNameFunction(a, "f");</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">NameFunction(a);</span>
"f"
<span class="GAPprompt">gap></span> <span class="GAPinput">HasNameFunction(x->x);</span>
false
<span class="GAPprompt">gap></span> <span class="GAPinput">NameFunction(x->x);</span>
"unknown"
</pre></div>

<p><a id="X877F03F77FD74C98" name="X877F03F77FD74C98"></a></p>

<h5>5.1-2 NumberArgumentsFunction</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ NumberArgumentsFunction</code>( <var class="Arg">func</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>returns the number of arguments the function <var class="Arg">func</var> accepts. -1 is returned for all operations. For functions that use <code class="code">...</code> or <code class="code">arg</code> to take a variable number of arguments, the number returned is -1 times the total number of parameters. For attributes, 1 is returned.</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">NumberArgumentsFunction(function(a,b,c,d,e,f,g,h,i,j,k)return 1;end);</span>
11
<span class="GAPprompt">gap></span> <span class="GAPinput">NumberArgumentsFunction(Size);</span>
1
<span class="GAPprompt">gap></span> <span class="GAPinput">NumberArgumentsFunction(IsCollsCollsElms);</span>
3
<span class="GAPprompt">gap></span> <span class="GAPinput">NumberArgumentsFunction(Sum);</span>
-1
<span class="GAPprompt">gap></span> <span class="GAPinput">NumberArgumentsFunction(function(a, x...) return 1; end);</span>
-2
</pre></div>

<p><a id="X818BAB817A4FB346" name="X818BAB817A4FB346"></a></p>

<h5>5.1-3 NamesLocalVariablesFunction</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ NamesLocalVariablesFunction</code>( <var class="Arg">func</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>returns a mutable list of strings; the first entries are the names of the arguments of the function <var class="Arg">func</var>, in the same order as they were entered in the definition of <var class="Arg">func</var>, and the remaining ones are the local variables as given in the <code class="keyw">local</code> statement in <var class="Arg">func</var>. (The number of arguments can be computed with <code class="func">NumberArgumentsFunction</code> (<a href="chap5_mj.html#X877F03F77FD74C98"><span class="RefLink">5.1-2</span></a>).)</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">NamesLocalVariablesFunction(function( a, b ) local c; return 1; end);</span>
[ "a", "b", "c" ]
<span class="GAPprompt">gap></span> <span class="GAPinput">NamesLocalVariablesFunction(function( arg ) local a; return 1; end);</span>
[ "arg", "a" ]
<span class="GAPprompt">gap></span> <span class="GAPinput">NamesLocalVariablesFunction( Size );</span>
fail
</pre></div>

<p><a id="X80E108C57F90FAA3" name="X80E108C57F90FAA3"></a></p>

<h5>5.1-4 FilenameFunc</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ FilenameFunc</code>( <var class="Arg">func</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>For a function <var class="Arg">func</var>, <code class="func">FilenameFunc</code> returns either <code class="keyw">fail</code> or the absolute path of the file from which <var class="Arg">func</var> has been read. The return value <code class="keyw">fail</code> occurs if <var class="Arg">func</var> is a compiled function or an operation. For functions that have been entered interactively, the string <code class="code">"*stdin*"</code> is returned, see Section <a href="chap9_mj.html#X85EC7D9087C481B0"><span class="RefLink">9.6</span></a>.</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">FilenameFunc( LEN_LIST );  # a kernel function</span>
fail
<span class="GAPprompt">gap></span> <span class="GAPinput">FilenameFunc( Size );      # an operation</span>
fail
<span class="GAPprompt">gap></span> <span class="GAPinput">FilenameFunc( x -> x^2 );  # an interactively entered function</span>
"*stdin*"
<span class="GAPprompt">gap></span> <span class="GAPinput">meth:= ApplicableMethod( Size, [ Group( () ) ] );;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">FilenameFunc( meth );</span>
"... some path .../grpperm.gi"
</pre></div>

<p><a id="X7FF7643781D2C194" name="X7FF7643781D2C194"></a></p>

<h5>5.1-5 StartlineFunc</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ StartlineFunc</code>( <var class="Arg">func</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">‣ EndlineFunc</code>( <var class="Arg">func</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Let <var class="Arg">func</var> be a function. If <code class="func">FilenameFunc</code> (<a href="chap5_mj.html#X80E108C57F90FAA3"><span class="RefLink">5.1-4</span></a>) returns <code class="keyw">fail</code> for <var class="Arg">func</var> then also <code class="func">StartlineFunc</code> returns <code class="keyw">fail</code>. If <code class="func">FilenameFunc</code> (<a href="chap5_mj.html#X80E108C57F90FAA3"><span class="RefLink">5.1-4</span></a>) returns a filename for <var class="Arg">func</var> then <code class="func">StartlineFunc</code> returns the line number in this file where the definition of <var class="Arg">func</var> starts.</p>

<p><code class="func">EndlineFunc</code> behaves similarly and returns the line number in this file where the definition of <var class="Arg">func</var> ends.</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">meth:= ApplicableMethod( Size, [ Group( () ) ] );;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">FilenameFunc( meth );</span>
"... some path ... /lib/grpperm.gi"
<span class="GAPprompt">gap></span> <span class="GAPinput">StartlineFunc( meth );</span>
487
<span class="GAPprompt">gap></span> <span class="GAPinput">EndlineFunc( meth );</span>
487
</pre></div>

<p><a id="X844F95767C74834F" name="X844F95767C74834F"></a></p>

<h5>5.1-6 LocationFunc</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LocationFunc</code>( <var class="Arg">func</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Let <var class="Arg">func</var> be a function. Returns a string describing the location of <var class="Arg">func</var>, or <code class="keyw">fail</code> if the information cannot be found. This uses the information provided by <code class="func">FilenameFunc</code> (<a href="chap5_mj.html#X80E108C57F90FAA3"><span class="RefLink">5.1-4</span></a>) and <code class="func">StartlineFunc</code> (<a href="chap5_mj.html#X7FF7643781D2C194"><span class="RefLink">5.1-5</span></a>)</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">LocationFunc( Intersection );</span>
"... some path ... gap/lib/coll.gi:2467"
# String is an attribute, so no information is stored
<span class="GAPprompt">gap></span> <span class="GAPinput">LocationFunc( String );</span>
fail
</pre></div>

<p><a id="X845A929B83D46E01" name="X845A929B83D46E01"></a></p>

<h5>5.1-7 PageSource</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ PageSource</code>( <var class="Arg">func</var>[, <var class="Arg">nr</var>] )</td><td class="tdright">( function )</td></tr></table></div>
<p>This shows the file containing the source code of the function or method <var class="Arg">func</var> in a pager (see <code class="func">Pager</code> (<a href="chap2_mj.html#X7ED03E41792C3840"><span class="RefLink">2.4-1</span></a>)). The display starts at a line shortly before the code of <var class="Arg">func</var>.</p>

<p>For operations <var class="Arg">func</var> the function shows the source code of the declaration of <var class="Arg">func</var>. Operations can have several declarations, use the optional second argument to specify which one should be shown (in the order the declarations were read); the default is to show the first.</p>

<p>For kernel functions the function tries to show the C source code.</p>

<p>If GAP cannot find a file containing the source code this will be indicated.</p>

<p>Usage examples:<br /> <code class="code">met := ApplicableMethod(\^, [(1,2),2743527]); PageSource(met);</code><br /> <code class="code">PageSource(Combinations);</code><br /> <code class="code">PageSource(SORT_LIST); </code><br /> <code class="code">PageSource(Size, 2);</code><br /> <code class="code">ct := CharacterTable(Group((1,2,3))); </code><br /> <code class="code">met := ApplicableMethod(Size,[ct]); PageSource(met); </code></p>

<p><a id="X851B58408520700D" name="X851B58408520700D"></a></p>

<h4>5.2 <span class="Heading">Calling a function with a list argument that is interpreted as
several arguments</span></h4>

<p><a id="X7CF4DDB97D65AE52" name="X7CF4DDB97D65AE52"></a></p>

<h5>5.2-1 CallFuncList</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CallFuncList</code>( <var class="Arg">func</var>, <var class="Arg">args</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">‣ CallFuncListWrap</code>( <var class="Arg">func</var>, <var class="Arg">args</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>returns the result, when calling function <var class="Arg">func</var> with the arguments given in the list <var class="Arg">args</var>, i.e. <var class="Arg">args</var> is <q>unwrapped</q> so that <var class="Arg">args</var> appears as several arguments to <var class="Arg">func</var>.</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">CallFuncList(\+, [6, 7]);</span>
13
<span class="GAPprompt">gap></span> <span class="GAPinput">#is equivalent to:</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">\+(6, 7);</span>
13
</pre></div>

<p>A more useful application of <code class="func">CallFuncList</code> is for a function <code class="code">g</code> that is called in the body of a function <code class="code">f</code> with (a sublist of) the arguments of <code class="code">f</code>, where <code class="code">f</code> has been defined with a single formal argument <code class="code">arg</code> (see <a href="chap4_mj.html#X815F71EA7BC0EB6F"><span class="RefLink">4.11</span></a>), as in the following code fragment.</p>


<div class="example"><pre>
f := function ( arg )
       CallFuncList(g, arg);
       ...
     end;
</pre></div>

<p>In the body of <code class="code">f</code> the several arguments passed to <code class="code">f</code> become a list <code class="code">arg</code>. If <code class="code">g</code> were called instead via <code class="code">g( arg )</code> then <code class="code">g</code> would see a single list argument, so that <code class="code">g</code> would, in general, have to <q>unwrap</q> the passed list. The following (not particularly useful) example demonstrates both described possibilities for the call to <code class="code">g</code>.</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">PrintNumberFromDigits := function ( arg )</span>
<span class="GAPprompt">></span> <span class="GAPinput">    CallFuncList( Print, arg );</span>
<span class="GAPprompt">></span> <span class="GAPinput">    Print( "\n" );</span>
<span class="GAPprompt">></span> <span class="GAPinput">   end;</span>
function( arg... ) ... end
<span class="GAPprompt">gap></span> <span class="GAPinput">PrintNumberFromDigits( 1, 9, 7, 3, 2 );</span>
19732
<span class="GAPprompt">gap></span> <span class="GAPinput">PrintDigits := function ( arg )</span>
<span class="GAPprompt">></span> <span class="GAPinput">    Print( arg );</span>
<span class="GAPprompt">></span> <span class="GAPinput">    Print( "\n" );</span>
<span class="GAPprompt">></span> <span class="GAPinput">   end;</span>
function( arg... ) ... end
<span class="GAPprompt">gap></span> <span class="GAPinput">PrintDigits( 1, 9, 7, 3, 2 );</span>
[ 1, 9, 7, 3, 2 ]
</pre></div>

<p><code class="func">CallFuncListWrap</code> differs only in that the result is a list. This returned list is empty if the called function returned no value, else it contains the returned value as its single member. This allows wrapping functions which may, or may not return a value.</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">CallFuncListWrap( x -> x, [1] );</span>
[ 1 ]
<span class="GAPprompt">gap></span> <span class="GAPinput">CallFuncListWrap( function(x) end, [1] );</span>
[ ]
</pre></div>

<p><a id="X83066E5A80B5FB71" name="X83066E5A80B5FB71"></a></p>

<h4>5.3 <span class="Heading">Wrapping a function, so the values produced are cached</span></h4>

<p><a id="X817ED3B280A64601" name="X817ED3B280A64601"></a></p>

<h5>5.3-1 MemoizePosIntFunction</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MemoizePosIntFunction</code>( <var class="Arg">function</var>[, <var class="Arg">options</var>] )</td><td class="tdright">( function )</td></tr></table></div>
<p><code class="func">MemoizePosIntFunction</code> returns a function which behaves the same as <var class="Arg">function</var>, except it caches the results for any inputs that are positive integers. Thus if the new function is called multiple times with the same input, then any call after the first will return the cached value, instead of recomputing it. By default, the cache can be flushed by calling <code class="func">FlushCaches</code> (<a href="chap79_mj.html#X87A4316C818B3DE3"><span class="RefLink">79.10-4</span></a>).</p>

<p>The returned function will by default only accept positive integers.</p>

<p>This function does not promise to never call <var class="Arg">function</var> more than once for any input -- values may be removed if the cache gets too large, or if <code class="func">FlushCaches</code> (<a href="chap79_mj.html#X87A4316C818B3DE3"><span class="RefLink">79.10-4</span></a>) is called, or if multiple threads try to calculate the same value simultaneously.</p>

<p>The optional second argument is a record which provides a number of configuration options. The following options are supported.</p>


<dl>
<dt><strong class="Mark"><code class="code">defaults</code> (default an empty list)</strong></dt>
<dd><p>Used to initialise the cache, both initially and after each flush. If <code class="code">defaults[i]</code> is bound, then this is used as default value for the input <code class="code">i</code>.</p>

</dd>
<dt><strong class="Mark"><code class="code">flush</code> (default <code class="keyw">true</code>)</strong></dt>
<dd><p>If this is <code class="keyw">true</code>, the cache is emptied whenever <code class="func">FlushCaches</code> (<a href="chap79_mj.html#X87A4316C818B3DE3"><span class="RefLink">79.10-4</span></a>) is called; if false, then the cache cannot be flushed.</p>

</dd>
<dt><strong class="Mark"><code class="code">errorHandler</code> (defaults to <code class="func">Error</code> (<a href="chap6_mj.html#X7E7AD8D87EBA1A08"><span class="RefLink">6.6-1</span></a>))</strong></dt>
<dd><p>A function to be called when an input which is not a positive integer is passed to the cache. The function can either raise an error, or else return a value which is then returned by the cache. Note that such a value does not get cached itself.</p>

</dd>
</dl>

<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">f := MemoizePosIntFunction(</span>
<span class="GAPprompt">></span> <span class="GAPinput">          function(i) Print("Check: ",i,"\n"); return i*i; end,</span>
<span class="GAPprompt">></span> <span class="GAPinput">          rec(defaults := [,,50], errorHandler := x -> "Bad") );;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">f(2);</span>
Check: 2
4
<span class="GAPprompt">gap></span> <span class="GAPinput">f(2);</span>
4
<span class="GAPprompt">gap></span> <span class="GAPinput">f(3);</span>
50
<span class="GAPprompt">gap></span> <span class="GAPinput">f(-3);</span>
"Bad"
<span class="GAPprompt">gap></span> <span class="GAPinput">FlushCaches();</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">f(2);</span>
Check: 2
4
<span class="GAPprompt">gap></span> <span class="GAPinput">f(3);</span>
50
</pre></div>

<p><a id="X7EB0A85F7D128BE0" name="X7EB0A85F7D128BE0"></a></p>

<h4>5.4 <span class="Heading">Functions that do nothing</span></h4>

<p>The following functions return fixed results (or just their own argument). They can be useful in places when the syntax requires a function, but actually no functionality is required. So <code class="func">ReturnTrue</code> (<a href="chap5_mj.html#X7DB422A2876CCC4D"><span class="RefLink">5.4-1</span></a>) is often used as family predicate in <code class="func">InstallMethod</code> (<a href="chap78_mj.html#X837EFDAB7BEF290B"><span class="RefLink">78.3-1</span></a>).</p>

<p><a id="X7DB422A2876CCC4D" name="X7DB422A2876CCC4D"></a></p>

<h5>5.4-1 ReturnTrue</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ReturnTrue</code>( <var class="Arg">...</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>This function takes any number of arguments, and always returns <code class="keyw">true</code>.</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">f:=ReturnTrue;</span>
function( arg... ) ... end
<span class="GAPprompt">gap></span> <span class="GAPinput">f();</span>
true
<span class="GAPprompt">gap></span> <span class="GAPinput">f(42);</span>
true
</pre></div>

<p><a id="X7C131FB17D7518FC" name="X7C131FB17D7518FC"></a></p>

<h5>5.4-2 ReturnFalse</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ReturnFalse</code>( <var class="Arg">...</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>This function takes any number of arguments, and always returns <code class="keyw">false</code>.</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">f:=ReturnFalse;</span>
function( arg... ) ... end
<span class="GAPprompt">gap></span> <span class="GAPinput">f();</span>
false
<span class="GAPprompt">gap></span> <span class="GAPinput">f("any_string");</span>
false
</pre></div>

<p><a id="X7A0994DE7C258E55" name="X7A0994DE7C258E55"></a></p>

<h5>5.4-3 ReturnFail</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ReturnFail</code>( <var class="Arg">...</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>This function takes any number of arguments, and always returns <code class="keyw">fail</code>.</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">oops:=ReturnFail;</span>
function( arg... ) ... end
<span class="GAPprompt">gap></span> <span class="GAPinput">oops();</span>
fail
<span class="GAPprompt">gap></span> <span class="GAPinput">oops(-42);</span>
fail
</pre></div>

<p><a id="X818EA8C47B46A634" name="X818EA8C47B46A634"></a></p>

<h5>5.4-4 ReturnNothing</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ReturnNothing</code>( <var class="Arg">...</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>This function takes any number of arguments, and always returns nothing.</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">n:=ReturnNothing;</span>
function( object... ) ... end
<span class="GAPprompt">gap></span> <span class="GAPinput">n();</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">n(-42);</span>
</pre></div>

<p><a id="X8788D7D780FCE169" name="X8788D7D780FCE169"></a></p>

<h5>5.4-5 ReturnFirst</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ReturnFirst</code>( <var class="Arg">...</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>This function takes one or more arguments, and always returns the first argument. <code class="func">IdFunc</code> (<a href="chap5_mj.html#X810325697BDEF899"><span class="RefLink">5.4-6</span></a>) behaves similarly, but only accepts a single argument.</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">f:=ReturnFirst;</span>
function( first, rest... ) ... end
<span class="GAPprompt">gap></span> <span class="GAPinput">f(1);</span>
1
<span class="GAPprompt">gap></span> <span class="GAPinput">f(2,3,4);</span>
2
<span class="GAPprompt">gap></span> <span class="GAPinput">f();</span>
Error, Function: number of arguments must be at least 1 (not 0)
</pre></div>

<p><a id="X810325697BDEF899" name="X810325697BDEF899"></a></p>

<h5>5.4-6 IdFunc</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IdFunc</code>( <var class="Arg">obj</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>returns <var class="Arg">obj</var>. <code class="func">ReturnFirst</code> (<a href="chap5_mj.html#X8788D7D780FCE169"><span class="RefLink">5.4-5</span></a>) is similar, but accepts one or more arguments, returning only the first.</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">id:=IdFunc;</span>
function( object ) ... end
<span class="GAPprompt">gap></span> <span class="GAPinput">id(42);</span>
42
<span class="GAPprompt">gap></span> <span class="GAPinput">f:=id(SymmetricGroup(3));</span>
Sym( [ 1 .. 3 ] )
<span class="GAPprompt">gap></span> <span class="GAPinput">s:=One(AutomorphismGroup(SymmetricGroup(3)));</span>
IdentityMapping( Sym( [ 1 .. 3 ] ) )
<span class="GAPprompt">gap></span> <span class="GAPinput">f=s;</span>
false
</pre></div>

<p><a id="X80FE39D27CE3DE1B" name="X80FE39D27CE3DE1B"></a></p>

<h4>5.5 <span class="Heading">Function Types</span></h4>

<p>Functions are <strong class="pkg">GAP</strong> objects and thus have categories and a family.</p>

<p><a id="X85E40340806C2B8C" name="X85E40340806C2B8C"></a></p>

<h5>5.5-1 IsFunction</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsFunction</code>( <var class="Arg">obj</var> )</td><td class="tdright">( category )</td></tr></table></div>
<p>is the category of functions.</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">IsFunction(x->x^2);</span>
true
<span class="GAPprompt">gap></span> <span class="GAPinput">IsFunction(Factorial);</span>
true
<span class="GAPprompt">gap></span> <span class="GAPinput">f:=One(AutomorphismGroup(SymmetricGroup(3)));</span>
IdentityMapping( Sym( [ 1 .. 3 ] ) )
<span class="GAPprompt">gap></span> <span class="GAPinput">IsFunction(f);</span>
false
</pre></div>

<p><a id="X87838FE885A9AAF9" name="X87838FE885A9AAF9"></a></p>

<h5>5.5-2 FunctionsFamily</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ FunctionsFamily</code></td><td class="tdright">( family )</td></tr></table></div>
<p>is the family of all functions.</p>

<p><a id="X81F732457F7BC851" name="X81F732457F7BC851"></a></p>

<h4>5.6 <span class="Heading">Naming Conventions</span></h4>

<p>The way functions are named in <strong class="pkg">GAP</strong> might help to memorize or even guess names of library functions.</p>

<p>If a variable name consists of several words then the first letter of each word is capitalized.</p>

<p>If the first part of the name of a function is a verb then the function may modify its argument(s) but does not return anything, for example <code class="func">Append</code> (<a href="chap21_mj.html#X79E31DB27C82D6E1"><span class="RefLink">21.4-5</span></a>) appends the list given as second argument to the list given as first argument. Otherwise the function returns an object without changing the arguments, for example <code class="func">Concatenation</code> (<a href="chap21_mj.html#X840C55A77D1BB2E1"><span class="RefLink">21.20-1</span></a>) returns the concatenation of the lists given as arguments.</p>

<p>If the name of a function contains the word <q><code class="code">Of</code></q> then the return value is thought of as information deduced from the arguments. Usually such functions are attributes (see <a href="chap13_mj.html#X7C701DBF7BAE649A"><span class="RefLink">13.5</span></a>). Examples are <code class="func">GeneratorsOfGroup</code> (<a href="chap39_mj.html#X79C44528864044C5"><span class="RefLink">39.2-4</span></a>), which returns a list of generators for the group entered as argument, or <code class="func">DiagonalOfMat</code> (<a href="chap24_mj.html#X7A9139D686ACB7D8"><span class="RefLink">24.12-1</span></a>).</p>

<p>For the setter and tester functions of an attribute <code class="code">Attr</code> the names <code class="code">SetAttr</code> resp. <code class="code">HasAttr</code> are available (see <a href="chap13_mj.html#X7C701DBF7BAE649A"><span class="RefLink">13.5</span></a>).</p>

<p>If the name of a function contains the word <q><code class="code">By</code></q> then the return value is thought of as built in a certain way from the parts given as arguments. For example, creating a group as a factor group of a given group by a normal subgroup can be done by taking the image of <code class="func">NaturalHomomorphismByNormalSubgroup</code> (<a href="chap39_mj.html#X80FC390C7F38A13F"><span class="RefLink">39.18-1</span></a>). Other examples of <q><code class="code">By</code></q> functions are <code class="func">GroupHomomorphismByImages</code> (<a href="chap40_mj.html#X7F348F497C813BE0"><span class="RefLink">40.1-1</span></a>) and <code class="func">LaurentPolynomialByCoefficients</code> (<a href="chap66_mj.html#X8467263B7EFA013E"><span class="RefLink">66.13-1</span></a>).</p>

<p>Often such functions construct an algebraic structure given by its generators (for example, <code class="func">RingByGenerators</code> (<a href="chap56_mj.html#X7D736E027DFD8961"><span class="RefLink">56.1-4</span></a>)). In some cases, <q><code class="code">By</code></q> may be replaced by <q><code class="code">With</code></q> (like e.g. <code class="func">GroupWithGenerators</code> (<a href="chap39_mj.html#X8589EF9C7B658B94"><span class="RefLink">39.2-3</span></a>)) or even both versions of the name may be used. The difference between <code class="code">StructByGenerators</code> and <code class="code">StructWithGenerators</code> is that the latter guarantees that the <code class="code">GeneratorsOfStruct</code> value of the result is equal to the given set of generators (see <a href="chap31_mj.html#X82039A218274826F"><span class="RefLink">31.3</span></a>).</p>

<p>If the name of a function has the form <q><code class="code">AsSomething</code></q> then the return value is an object (usually a collection which has the same family of elements), which may, for example:</p>


<ul>
<li><p>know more about its own structure (and so support more operations) than its input (e.g. if the elements of the collection form a group, then this group can be constructed using <code class="func">AsGroup</code> (<a href="chap39_mj.html#X7A0747F17B50D967"><span class="RefLink">39.2-5</span></a>));</p>

</li>
<li><p>discard its additional structure (e.g. <code class="func">AsList</code> (<a href="chap30_mj.html#X8289FCCC8274C89D"><span class="RefLink">30.3-8</span></a>) applied to a group will return a list of its elements);</p>

</li>
<li><p>contain all elements of the original object without duplicates (like e.g. <code class="func">AsSet</code> (<a href="chap30_mj.html#X856D927378C33548"><span class="RefLink">30.3-10</span></a>) does if its argument is a list of elements from the same family);</p>

</li>
<li><p>remain unchanged (like e.g. <code class="func">AsSemigroup</code> (<a href="chap51_mj.html#X80ED104F85AE5134"><span class="RefLink">51.1-6</span></a>) does if its argument is a group).</p>

</li>
</ul>
<p>If <code class="code">Something</code> and the argument of <code class="code">AsSomething</code> are domains, some further rules apply as explained in <a href="../../doc/tut/chap7_mj.html#X7EA77DE17DD8A231"><span class="RefLink">Tutorial: Changing the Structure</span></a>.</p>

<p>If the name of a function <code class="code">fun1</code> ends with <q><code class="code">NC</code></q> then there is another function <code class="code">fun2</code> with the same name except that the <code class="code">NC</code> is missing. <code class="code">NC</code> stands for <q>no check</q>. When <code class="code">fun2</code> is called then it checks whether its arguments are valid, and if so then it calls <code class="code">fun1</code>. The functions <code class="func">SubgroupNC</code> (<a href="chap39_mj.html#X7C82AA387A42DCA0"><span class="RefLink">39.3-1</span></a>) and <code class="func">Subgroup</code> (<a href="chap39_mj.html#X7C82AA387A42DCA0"><span class="RefLink">39.3-1</span></a>) are a typical example.</p>

<p>The idea is that the possibly time consuming check of the arguments can be omitted if one is sure that they are unnecessary. For example, if an algorithm produces generators of the derived subgroup of a group then it is guaranteed that they lie in the original group; <code class="func">Subgroup</code> (<a href="chap39_mj.html#X7C82AA387A42DCA0"><span class="RefLink">39.3-1</span></a>) would check this, and <code class="func">SubgroupNC</code> (<a href="chap39_mj.html#X7C82AA387A42DCA0"><span class="RefLink">39.3-1</span></a>) omits the check.</p>

<p>Needless to say, all these rules are not followed slavishly, for example there is one operation <code class="func">Zero</code> (<a href="chap31_mj.html#X8040AC7A79FFC442"><span class="RefLink">31.10-3</span></a>) instead of two operations <code class="code">ZeroOfElement</code> and <code class="code">ZeroOfAdditiveGroup</code>.</p>

<p><a id="X7A1721CD79F08E71" name="X7A1721CD79F08E71"></a></p>

<h4>5.7 <span class="Heading">Code annotations (pragmas)</span></h4>

<p>GAP supports the use of code annotations (pragmas) in functions, i.e., adding comments to functions that are stored in the function object itself, unlike regular comments. Pragmas are single-line comments, starting with <code class="code">#%</code>:</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">function()</span>
<span class="GAPprompt">></span> <span class="GAPinput">      #% This is a pragma</span>
<span class="GAPprompt">></span> <span class="GAPinput">      #  This is not a pragma</span>
<span class="GAPprompt">></span> <span class="GAPinput">      return;</span>
<span class="GAPprompt">></span> <span class="GAPinput">end;;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">Display( last );</span>
function (  )
    #% This is a pragma
    return;
end
</pre></div>

<p>Pragmas can be used to mark parts of functions that should later be manipulated using <a href="chap4_mj.html#X8732D9257FFCEA1B"><span class="RefLink">4.16</span></a>.</p>

<p>Please note that heavy use of pragmas in functions slows down the execution of your function in the same way as adding empty <code class="code">;</code> statements to your code.</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">a := function( )</span>
<span class="GAPprompt">></span> <span class="GAPinput">      local i;</span>
<span class="GAPprompt">></span> <span class="GAPinput">      for i in [ 1 .. 1000000 ] do</span>
<span class="GAPprompt">></span> <span class="GAPinput">              i := i + 1;</span>
<span class="GAPprompt">></span> <span class="GAPinput">      od;</span>
<span class="GAPprompt">></span> <span class="GAPinput">end;</span>
function(  ) ... end
<span class="GAPprompt">gap></span> <span class="GAPinput">a();</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">time;</span>
14
<span class="GAPprompt">gap></span> <span class="GAPinput">b := function( )</span>
<span class="GAPprompt">></span> <span class="GAPinput">      local i;</span>
<span class="GAPprompt">></span> <span class="GAPinput">      for i in [ 1 .. 1000000 ] do</span>
<span class="GAPprompt">></span> <span class="GAPinput">              i := i + 1;</span>
<span class="GAPprompt">></span> <span class="GAPinput">              #% pragma</span>
<span class="GAPprompt">></span> <span class="GAPinput">              #% pragma</span>
<span class="GAPprompt">></span> <span class="GAPinput">              #% pragma</span>
<span class="GAPprompt">></span> <span class="GAPinput">              #% pragma</span>
<span class="GAPprompt">></span> <span class="GAPinput">              #% pragma</span>
<span class="GAPprompt">></span> <span class="GAPinput">      od;</span>
<span class="GAPprompt">></span> <span class="GAPinput">end;</span>
function(  ) ... end
<span class="GAPprompt">gap></span> <span class="GAPinput">b();</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">time;</span>
25
</pre></div>


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