Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/hap/doc/   (Algebra von RWTH Aachen Version 4.15.1©)  Datei vom 19.6.2025 mit Größe 18 kB image not shown  

Quelle  chap35.html   Sprache: HTML

 
 products/Sources/formale Sprachen/GAP/pkg/hap/doc/chap35.html


<?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 (HAP commands) - Chapter 35:  Arrays and Pseudo lists</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" />
<script src="manual.js" type="text/javascript"></script>
<script type="text/javascript">overwriteStyle();</script>
</head>
<body class="chap35"  onload="jscontent()">


<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="chap10.html">10</a>  <a href="chap11.html">11</a>  <a href="chap12.html">12</a>  <a href="chap13.html">13</a>  <a href="chap14.html">14</a>  <a href="chap15.html">15</a>  <a href="chap16.html">16</a>  <a href="chap17.html">17</a>  <a href="chap18.html">18</a>  <a href="chap19.html">19</a>  <a href="chap20.html">20</a>  <a href="chap21.html">21</a>  <a href="chap22.html">22</a>  <a href="chap23.html">23</a>  <a href="chap24.html">24</a>  <a href="chap25.html">25</a>  <a href="chap26.html">26</a>  <a href="chap27.html">27</a>  <a href="chap28.html">28</a>  <a href="chap29.html">29</a>  <a href="chap30.html">30</a>  <a href="chap31.html">31</a>  <a href="chap32.html">32</a>  <a href="chap33.html">33</a>  <a href="chap34.html">34</a>  <a href="chap35.html">35</a>  <a href="chap36.html">36</a>  <a href="chap37.html">37</a>  <a href="chap38.html">38</a>  <a href="chap39.html">39</a>  <a href="chap40.html">40</a>  <a href="chapInd.html">Ind</a>  </div>

<div class="chlinkprevnexttop"> <a href="chap0.html">[Top of Book]</a>   <a href="chap0.html#contents">[Contents]</a>    <a href="chap34.html">[Previous Chapter]</a>    <a href="chap36.html">[Next Chapter]</a>   </div>

<p id="mathjaxlink" class="pcenter"><a href="chap35_mj.html">[MathJax on]</a></p>
<p><a id="X7B71D3EA7B30ADAB" name="X7B71D3EA7B30ADAB"></a></p>
<div class="ChapSects"><a href="chap35.html#X7B71D3EA7B30ADAB">35 <span class="Heading"> Arrays and Pseudo lists</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap35.html#X7CFDEEC07F15CF82">35.1 <span class="Heading">  </span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35.html#X81B7CDF487BC322B">35.1-1 Array</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35.html#X7C8BACC87E7CB7A8">35.1-2 PermuteArray</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35.html#X82573BFC835FC676">35.1-3 ArrayDimension</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35.html#X82CFCED3782CE80C">35.1-4 ArrayDimensions</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35.html#X81EBEEDA7C5E2062">35.1-5 ArraySum</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35.html#X7C1AC8B77E8859C7">35.1-6 ArrayValue</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35.html#X8169303B7C5F779F">35.1-7 ArrayValueFunctions</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35.html#X7A64A28E84797139">35.1-8 ArrayAssign</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35.html#X79A3E1968330BB3E">35.1-9 ArrayAssignFunctions</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35.html#X86F867787E75FF68">35.1-10 ArrayIterate</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35.html#X869B32CC80D03046">35.1-11 BinaryArrayToTextFile</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35.html#X7DE8BB8D86A2D34B">35.1-12 FrameArray</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35.html#X824B37627D6B979B">35.1-13 UnframeArray</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35.html#X795EC9D67E34DAB0">35.1-14 Add</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35.html#X79E31DB27C82D6E1">35.1-15 Append</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35.html#X8308C3198094AA55">35.1-16 ListToPseudoList</a></span>
</div></div>
</div>

<h3>35 <span class="Heading"> Arrays and Pseudo lists</span></h3>

<p><a id="X7CFDEEC07F15CF82" name="X7CFDEEC07F15CF82"></a></p>

<h4>35.1 <span class="Heading">  </span></h4>

<p><a id="X81B7CDF487BC322B" name="X81B7CDF487BC322B"></a></p>

<h5>35.1-1 Array</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Array</code>( <var class="Arg">A</var>, <var class="Arg">f</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs an array <span class="SimpleMath">A</span> and a function <span class="SimpleMath">f</span>. It returns the the array obtained by applying <span class="SimpleMath">f</span> to each entry of <span class="SimpleMath">A</span> (and leaves <span class="SimpleMath">A</span> unchanged).</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap2.html">1</a></span> , <span class="URL"><a href="../tutorial/chap10.html">2</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutPeripheral.html">3</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCubical.html">4</a></span> </p>

<p><a id="X7C8BACC87E7CB7A8" name="X7C8BACC87E7CB7A8"></a></p>

<h5>35.1-2 PermuteArray</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ PermuteArray</code>( <var class="Arg">A</var>, <var class="Arg">f</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs an array <span class="SimpleMath">A</span> of dimension <span class="SimpleMath">d</span> and a permutation <span class="SimpleMath">f</span> of degree at most <span class="SimpleMath">d</span>. It returns the array <span class="SimpleMath">B</span> defined by <span class="SimpleMath">B[i1][i2]...[id] = A[f(i1)][f(i2)]...A[f(id)]</span> (and leaves <span class="SimpleMath">A</span> unchanged).</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X82573BFC835FC676" name="X82573BFC835FC676"></a></p>

<h5>35.1-3 ArrayDimension</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ArrayDimension</code>( <var class="Arg">A</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs an array <span class="SimpleMath">A</span> and returns its dimension.</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X82CFCED3782CE80C" name="X82CFCED3782CE80C"></a></p>

<h5>35.1-4 ArrayDimensions</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ArrayDimensions</code>( <var class="Arg">A</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs an array <span class="SimpleMath">A</span> and returns its dimensions.</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X81EBEEDA7C5E2062" name="X81EBEEDA7C5E2062"></a></p>

<h5>35.1-5 ArraySum</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ArraySum</code>( <var class="Arg">A</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs an array <span class="SimpleMath">A</span> and returns the sum of its entries.</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X7C1AC8B77E8859C7" name="X7C1AC8B77E8859C7"></a></p>

<h5>35.1-6 ArrayValue</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ArrayValue</code>( <var class="Arg">A</var>, <var class="Arg">x</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs an array <span class="SimpleMath">A</span> and a coordinate vector <span class="SimpleMath">x</span>. It returns the value of the entry in <span class="SimpleMath">A</span> with coordinate <span class="SimpleMath">x</span>.</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X8169303B7C5F779F" name="X8169303B7C5F779F"></a></p>

<h5>35.1-7 ArrayValueFunctions</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ArrayValueFunctions</code>( <var class="Arg">d</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a positive integer <span class="SimpleMath">d</span> and returns an efficient version of the function ArrayValue for arrays of dimension <span class="SimpleMath">d</span>.</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X7A64A28E84797139" name="X7A64A28E84797139"></a></p>

<h5>35.1-8 ArrayAssign</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ArrayAssign</code>( <var class="Arg">A</var>, <var class="Arg">x</var>, <var class="Arg">n</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs an array <span class="SimpleMath">A</span> and a coordinate vector <span class="SimpleMath">x</span> and an integer <span class="SimpleMath">n</span>. It sets the entry of <span class="SimpleMath">A</span> with coordinate <span class="SimpleMath">x</span> equal to <span class="SimpleMath">n</span>.</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X79A3E1968330BB3E" name="X79A3E1968330BB3E"></a></p>

<h5>35.1-9 ArrayAssignFunctions</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ArrayAssignFunctions</code>( <var class="Arg">d</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a positive integer <span class="SimpleMath">d</span> and returns an efficient version of the function ArrayAssign for arrays of dimension <span class="SimpleMath">d</span>.</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X86F867787E75FF68" name="X86F867787E75FF68"></a></p>

<h5>35.1-10 ArrayIterate</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ArrayIterate</code>( <var class="Arg">d</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a positive integer <span class="SimpleMath">d</span> and returns a function ArrayIt(Dimensions,f). This function inputs a list Dimensions of <span class="SimpleMath">d</span> positive integers and also a function <span class="SimpleMath">f(x)</span>. It applies the function <span class="SimpleMath">f(x)</span> to each integer list <span class="SimpleMath">x</span> of length <span class="SimpleMath">d</span> with entries <span class="SimpleMath">x[i]</span> in the range [1..Dimension[i]].</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X869B32CC80D03046" name="X869B32CC80D03046"></a></p>

<h5>35.1-11 BinaryArrayToTextFile</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ BinaryArrayToTextFile</code>( <var class="Arg">file</var>, <var class="Arg">A</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a string containing the address of a file, and an array <span class="SimpleMath">A</span> of 0s and 1s. The array represents a pure cubical complex. A representation of this complex is written to the file in a format that can be read by the CAPD (Computer Assisted Proofs in Dynamics) software developed by Marian Mrozek and others.</p>

<p>The second input <span class="SimpleMath">A</span> can also be a pure cubical complex.</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X7DE8BB8D86A2D34B" name="X7DE8BB8D86A2D34B"></a></p>

<h5>35.1-12 FrameArray</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ FrameArray</code>( <var class="Arg">A</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs an array <span class="SimpleMath">A</span> and returns the array obtained by appending a 0 to the beginning and end of each "row" of the array.</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../www/SideLinks/About/aboutPeripheral.html">1</a></span> </p>

<p><a id="X824B37627D6B979B" name="X824B37627D6B979B"></a></p>

<h5>35.1-13 UnframeArray</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ UnframeArray</code>( <var class="Arg">A</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs an array <span class="SimpleMath">A</span> and returns the array obtained by removing the first and last entry in each "row" of the array.</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X795EC9D67E34DAB0" name="X795EC9D67E34DAB0"></a></p>

<h5>35.1-14 Add</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Add</code>( <var class="Arg">L</var>, <var class="Arg">x</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Let <span class="SimpleMath">L</span> be a pseudo list of length <span class="SimpleMath">n</span>, and <span class="SimpleMath">x</span> an object compatible with the entries in <span class="SimpleMath">L</span>. If <span class="SimpleMath">x</span> is not in <span class="SimpleMath">L</span> then this operation converts <span class="SimpleMath">L</span> into a pseudo list of length n+1 by adding <span class="SimpleMath">x</span> as the final entry. If <span class="SimpleMath">x</span> is in <span class="SimpleMath">L</span> the operation has no effect on <span class="SimpleMath">L</span>.</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap4.html">1</a></span> , <span class="URL"><a href="../tutorial/chap5.html">2</a></span> , <span class="URL"><a href="../tutorial/chap10.html">3</a></span> , <span class="URL"><a href="../tutorial/chap12.html">4</a></span> , <span class="URL"><a href="../tutorial/chap13.html">5</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutBogomolov.html">6</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutQuandles2.html">7</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutQuandles.html">8</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutquasi.html">9</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutRandomComplexes.html">10</a></span> </p>

<p><a id="X79E31DB27C82D6E1" name="X79E31DB27C82D6E1"></a></p>

<h5>35.1-15 Append</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Append</code>( <var class="Arg">L</var>, <var class="Arg">K</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Let <span class="SimpleMath">L</span> be a pseudo list and <span class="SimpleMath">K</span> a list whose objects are compatible with those in <span class="SimpleMath">L</span>. This operation applies Add(L,x) for each x in <span class="SimpleMath">K</span>.</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap12.html">1</a></span> , <span class="URL"><a href="../tutorial/chap13.html">2</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutBogomolov.html">3</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutParallel.html">4</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutTensorSquare.html">5</a></span> </p>

<p><a id="X8308C3198094AA55" name="X8308C3198094AA55"></a></p>

<h5>35.1-16 ListToPseudoList</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ListToPseudoList</code>( <var class="Arg">L</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a list <span class="SimpleMath">L</span> and returns the pseudo list representation of <span class="SimpleMath">L</span>.</p>

<p><strong class="button">Examples:</strong></p>


<div class="chlinkprevnextbot"> <a href="chap0.html">[Top of Book]</a>   <a href="chap0.html#contents">[Contents]</a>    <a href="chap34.html">[Previous Chapter]</a>    <a href="chap36.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="chap10.html">10</a>  <a href="chap11.html">11</a>  <a href="chap12.html">12</a>  <a href="chap13.html">13</a>  <a href="chap14.html">14</a>  <a href="chap15.html">15</a>  <a href="chap16.html">16</a>  <a href="chap17.html">17</a>  <a href="chap18.html">18</a>  <a href="chap19.html">19</a>  <a href="chap20.html">20</a>  <a href="chap21.html">21</a>  <a href="chap22.html">22</a>  <a href="chap23.html">23</a>  <a href="chap24.html">24</a>  <a href="chap25.html">25</a>  <a href="chap26.html">26</a>  <a href="chap27.html">27</a>  <a href="chap28.html">28</a>  <a href="chap29.html">29</a>  <a href="chap30.html">30</a>  <a href="chap31.html">31</a>  <a href="chap32.html">32</a>  <a href="chap33.html">33</a>  <a href="chap34.html">34</a>  <a href="chap35.html">35</a>  <a href="chap36.html">36</a>  <a href="chap37.html">37</a>  <a href="chap38.html">38</a>  <a href="chap39.html">39</a>  <a href="chap40.html">40</a>  <a href="chapInd.html">Ind</a>  </div>

<hr />
<p class="foot">generated by <a href="https://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc">GAPDoc2HTML</a></p>
</body>
</html>

99%


¤ Dauer der Verarbeitung: 0.15 Sekunden  (vorverarbeitet)  ¤

*© Formatika GbR, Deutschland




Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung ist noch experimentell.