<?xml version="1.0" encoding="UTF-8"?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en"> <head> <title>GAP (NumericalSgps) - Appendix B: Random functions</title> <meta http-equiv="content-type" content="text/html; charset=UTF-8" /> <meta name="generator" content="GAPDoc2HTML" /> <link rel="stylesheet" type="text/css" href="manual.css" /> </head> <body> <div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0.html">Top</a> <a href="chap1.html">1</a> <a href="chap2.html">2</a> <a href="chap3.html">3</a> <a href="chap4.html">4</a> <a href="chap5.html">5</a> <a href="chap6.html">6</a> <a href="chap7.html">7</a> <a href="chap8.html">8</a> <a href="chap9.html">9</a> <a href="chapA.html">A</a> <a href="chapB.html">B</a> <a href="chapC.html">C</a> <a href="chapBib.html">Bib</a> <a href="chapInd.html">Ind</a> </div> <div class="chlinkprevnexttop"> <a href="chap0.html">Top of Book</a> <a href="chapA.html">Previous Chapter</a> <a href="chapC.html">Next Chapter</a> </div> <p><a id="X86746B487B54A2D6" name="X86746B487B54A2D6"></a></p> <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> </div> </div> <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> <div class="chlinkprevnextbot"> <a href="chap0.html">Top of Book</a> <a href="chapA.html">Previous Chapter</a> <a href="chapC.html">Next Chapter</a> </div> <div class="chlinkbot"><span class="chlink1">Goto Chapter: </span><a href="chap0.html">Top</a> <a href="chap1.html">1</a> <a href="chap2.html">2</a> <a href="chap3.html">3</a> <a href="chap4.html">4</a> <a href="chap5.html">5</a> <a href="chap6.html">6</a> <a href="chap7.html">7</a> <a href="chap8.html">8</a> <a href="chap9.html">9</a> <a href="chapA.html">A</a> <a href="chapB.html">B</a> <a href="chapC.html">C</a> <a href="chapBib.html">Bib</a> <a href="chapInd.html">Ind</a> </div> <hr /> <p class="foot">generated by <a href="http://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc">GAPDoc2HTML</a></p> </body> </html>