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<title>GAP (NumericalSgps) - Appendix B: Random functions</title>
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<div class="ChapSects"><a href="chapB.html#X86746B487B54A2D6">B <span class="Heading">Random functions</span></a>
<div class="ContSect"><span class="nocss"> </span><a href="chapB.html#X86746B487B54A2D6">B.1 <span class="Heading">Random functions</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chapB.html#X7CC477867B00AD13">B.1-1 RandomNumericalSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chapB.html#X79E73F8787741190">B.1-2 RandomListForNS</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chapB.html#X82E22E9B843DF70F">B.1-3 RandomModularNumericalSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chapB.html#X8598F10A7CD4A135">B.1-4 RandomProportionallyModularNumericalSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chapB.html#X8665F6B08036AFFB">B.1-5 RandomListRepresentingSubAdditiveFunction</a></span>
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<h3>B <span class="Heading">Random functions</span></h3>
<p>Here we describe some functions which allow to create several "random" objects.</p>
<p><a id="X86746B487B54A2D6" name="X86746B487B54A2D6"></a></p>
<h4>B.1 <span class="Heading">Random functions</span></h4>
<p><a id="X7CC477867B00AD13" name="X7CC477867B00AD13"></a></p>
<h5>B.1-1 RandomNumericalSemigroup</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> RandomNumericalSemigroup</code>( <var class="Arg">n, m</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns a ``random" numerical semigroup with no more than <var class="Arg">n</var> generators in [1..<var class="Arg">m</var>].</p>
<table class="example">
<tr><td><pre>
gap> RandomNumericalSemigroup(3,9);
<Numerical semigroup with 3 generators>
</pre></td></tr></table>
<p><a id="X79E73F8787741190" name="X79E73F8787741190"></a></p>
<h5>B.1-2 RandomListForNS</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> RandomListForNS</code>( <var class="Arg">n, m</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns a set of length not greater than <var class="Arg">n</var> of random integers in <var class="Arg">[1..m]</var> whose GCD is 1. It is used to create "random" numerical semigroups.</p>
<table class="example">
<tr><td><pre>
gap> RandomListForNS(13,79);
[ 22, 26, 29, 31, 34, 46, 53, 61, 62, 73, 76 ]
</pre></td></tr></table>
<p><a id="X82E22E9B843DF70F" name="X82E22E9B843DF70F"></a></p>
<h5>B.1-3 RandomModularNumericalSemigroup</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> RandomModularNumericalSemigroup</code>( <var class="Arg">k</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns a ``random" modular numerical semigroup.</p>
<table class="example">
<tr><td><pre>
gap> RandomModularNumericalSemigroup(9);
<Modular numerical semigroup satisfying 5x mod 6 <= x >
</pre></td></tr></table>
<p><a id="X8598F10A7CD4A135" name="X8598F10A7CD4A135"></a></p>
<h5>B.1-4 RandomProportionallyModularNumericalSemigroup</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> RandomProportionallyModularNumericalSemigroup</code>( <var class="Arg">k</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns a ``random" proportionally modular numerical semigroup (see <a href="chap1.html#X7DFB63A97E67C0A1"><b>1.</b></a>).</p>
<table class="example">
<tr><td><pre>
gap> RandomProportionallyModularNumericalSemigroup(9);
<Proportionally modular numerical semigroup satisfying 2x mod 3 <= 2x >
</pre></td></tr></table>
<p><a id="X8665F6B08036AFFB" name="X8665F6B08036AFFB"></a></p>
<h5>B.1-5 RandomListRepresentingSubAdditiveFunction</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> RandomListRepresentingSubAdditiveFunction</code>( <var class="Arg">m, a</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Produces a ``random" list representing a subadditive function (see <a href="chap1.html#X7DFB63A97E67C0A1"><b>1.</b></a>) which is periodic with period <var class="Arg">m</var> (or less). When possible, the images are in <var class="Arg">[a..20*a]</var>. (Otherwise, the list of possible images is enlarged.)</p>
<table class="example">
<tr><td><pre>
gap> RandomListRepresentingSubAdditiveFunction(7,9);
[ 173, 114, 67, 0 ]
gap> RepresentsPeriodicSubAdditiveFunction(last);
true
</pre></td></tr></table>
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