<?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 (ToolsForHomalg) - Chapter
9: Trees</
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=
"chap9" 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="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="chap8.html">[Previous Chapter]</a> <a href="chap10.html">[Next Chapter]</a> </div>
<p id="mathjaxlink" class="pcenter"><a href="chap9_mj.html">[MathJax on]</a></p>
<p><a id="X82EAC5E57CAA5FC5" name="X82EAC5E57CAA5FC5"></a></p>
<div class="ChapSects"><a href="chap9.html#X82EAC5E57CAA5FC5">9 <span class="Heading">Trees</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X82EAC5E57CAA5FC5">9.1 <span class="Heading">Trees</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X7ACE7DC5811BC3E6">9.1-1 IsTree</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X7F3BD31F8167E2AD">9.1-2 Content</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X87364E1880BAFD86">9.1-3 ListOfSuccessors</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X7963601778389D55">9.1-4 Predecessor</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X7DBFDC727BD18391">9.1-5 ListOfSentinels</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X82C8BE577AF4389D">9.1-6 RemoveHead</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X81853D90786ACF86">9.1-7 Tree</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X822ED357788C5AE8">9.1-8 Tree</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X7C9C3B5F81D1B816">9.1-9 Add</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X874C552787D43D73">9.1-10 ContentListFromSentinelToHead</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X851053447BC5684C">9.1-11 PostOrder</a></span>
</div></div>
</div>
<h3>9 <span class="Heading">Trees</span></h3>
<p>The trees are used in ToDoLists. They are a technical feature, and fairly general, so they also can be used somewhere else.</p>
<p><a id="X82EAC5E57CAA5FC5" name="X82EAC5E57CAA5FC5"></a></p>
<h4>9.1 <span class="Heading">Trees</span></h4>
<p><a id="X7ACE7DC5811BC3E6" name="X7ACE7DC5811BC3E6"></a></p>
<h5>9.1-1 IsTree</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">an style='color: green'>8227; IsTree</code>( <var class="Arg">arg</var> )</td><td class="tdright">( filter )</td></tr></table></div>
<p>Returns: <code class="keyw">true</code> or <code class="keyw">false</code></p>
<p>The category of trees. A tree may have a content, a list of successors, a predecessor and it knows if it is a leave of a tree or not.</p>
<p><a id="X7F3BD31F8167E2AD" name="X7F3BD31F8167E2AD"></a></p>
<h5>9.1-2 Content</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">an style='color: green'>8227; Content</code>( <var class="Arg">arg</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: object</p>
<p>The content of the tree. May be any object.</p>
<p><a id="X87364E1880BAFD86" name="X87364E1880BAFD86"></a></p>
<h5>9.1-3 ListOfSuccessors</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">an style='color: green'>8227; ListOfSuccessors</code>( <var class="Arg">arg</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a list of trees</p>
<p>Returns the list of successors of a tree.</p>
<p><a id="X7963601778389D55" name="X7963601778389D55"></a></p>
<h5>9.1-4 Predecessor</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">an style='color: green'>8227; Predecessor</code>( <var class="Arg">arg</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a tree or fail</p>
<p>Returns the predecessor of a tree, or fail if there is none.</p>
<p><a id="X7DBFDC727BD18391" name="X7DBFDC727BD18391"></a></p>
<h5>9.1-5 ListOfSentinels</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">an style='color: green'>8227; ListOfSentinels</code>( <var class="Arg">arg</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a list</p>
<p>Returns a list of leaves of the tree.</p>
<p><a id="X82C8BE577AF4389D" name="X82C8BE577AF4389D"></a></p>
<h5>9.1-6 RemoveHead</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">an style='color: green'>8227; RemoveHead</code>( <var class="Arg">arg</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a tree</p>
<p>Returns the first successor of the tree, and adds all other successors of the tree to the tree that is returned. If the tree is a leave, it returns an empty tree. If the tree is empty, it returns the tree itself.</p>
<p><a id="X81853D90786ACF86" name="X81853D90786ACF86"></a></p>
<h5>9.1-7 Tree</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">an style='color: green'>8227; Tree</code>( )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a tree</p>
<p>Returns an empty tree.</p>
<p><a id="X822ED357788C5AE8" name="X822ED357788C5AE8"></a></p>
<h5>9.1-8 Tree</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">an style='color: green'>8227; Tree</code>( <var class="Arg">obj</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a tree</p>
<p>Returns a tree with argument <var class="Arg">obj</var>.</p>
<p><a id="X7C9C3B5F81D1B816" name="X7C9C3B5F81D1B816"></a></p>
<h5>9.1-9 Add</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">an style='color: green'>8227; Add</code>( <var class="Arg">tree</var>, <var class="Arg">new_tree</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>
<p>Adds the [list of] tree[s] <var class="Arg">new_tree</var> as successor to the tree <var class="Arg">tree</var>.</p>
<p><a id="X874C552787D43D73" name="X874C552787D43D73"></a></p>
<h5>9.1-10 ContentListFromSentinelToHead</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">an style='color: green'>8227; ContentListFromSentinelToHead</code>( <var class="Arg">sent</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a list</p>
<p>Returns a list of the contents of the trees from the leave <var class="Arg">sent</var> up to the content of the head of the tree.</p>
<p><a id="X851053447BC5684C" name="X851053447BC5684C"></a></p>
<h5>9.1-11 PostOrder</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">an style='color: green'>8227; PostOrder</code>( <var class="Arg">arg</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a list</p>
<p>Returns the contents of the nodes of the tree in post-order.</p>
<div class="chlinkprevnextbot"> <a href="chap0.html">[Top of Book]</a> <a href="chap0.html#contents">[Contents]</a> <a href="chap8.html">[Previous Chapter]</a> <a href="chap10.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="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>
¤ Dauer der Verarbeitung: 0.1 Sekunden
(vorverarbeitet am 2026-11-04)
¤
*© Formatika GbR, Deutschland