<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
<meta http-equiv="X-UA-Compatible" content="IE=9"/>
<meta name="generator" content="Doxygen 1.9.1"/>
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<title>DGtal: DGtal::concepts::CEuclideanRing< T > Struct Template Reference</title>
<link href="tabs.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="jquery.js"></script>
<script type="text/javascript" src="dynsections.js"></script>
<link href="navtree.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="resize.js"></script>
<script type="text/javascript" src="navtreedata.js"></script>
<script type="text/javascript" src="navtree.js"></script>
<link href="search/search.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="search/searchdata.js"></script>
<script type="text/javascript" src="search/search.js"></script>
<script type="text/x-mathjax-config">
MathJax.Hub.Config({
extensions: ["tex2jax.js", "TeX/AMSmath.js", "TeX/AMSsymbols.js"],
jax: ["input/TeX","output/HTML-CSS"],
});
</script>
<script type="text/javascript" async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.3/MathJax.js?config=TeX-MML-AM_CHTML/MathJax.js"></script>
<link href="doxygen.css" rel="stylesheet" type="text/css" />
<link href="doxygen-awesome.css" rel="stylesheet" type="text/css"/>
</head>
<body>
<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
<div id="titlearea">
<table cellspacing="0" cellpadding="0">
<tbody>
<tr style="height: 56px;">
<td id="projectalign" style="padding-left: 0.5em;">
<div id="projectname">DGtal
 <span id="projectnumber">1.4.2</span>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<!-- end header part -->
<!-- Generated by Doxygen 1.9.1 -->
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&dn=gpl-2.0.txt GPL-v2 */
var searchBox = new SearchBox("searchBox", "search",false,'Search','.html');
/* @license-end */
</script>
<script type="text/javascript" src="menudata.js"></script>
<script type="text/javascript" src="menu.js"></script>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&dn=gpl-2.0.txt GPL-v2 */
$(function() {
initMenu('',true,false,'search.php','Search');
$(document).ready(function() { init_search(); });
});
/* @license-end */</script>
<div id="main-nav"></div>
</div><!-- top -->
<div id="side-nav" class="ui-resizable side-nav-resizable">
<div id="nav-tree">
<div id="nav-tree-contents">
<div id="nav-sync" class="sync"></div>
</div>
</div>
<div id="splitbar" style="-moz-user-select:none;"
class="ui-resizable-handle">
</div>
</div>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&dn=gpl-2.0.txt GPL-v2 */
$(document).ready(function(){initNavTree('structDGtal_1_1concepts_1_1CEuclideanRing.html',''); initResizable(); });
/* @license-end */
</script>
<div id="doc-content">
<!-- window showing the filter options -->
<div id="MSearchSelectWindow"
onmouseover="return searchBox.OnSearchSelectShow()"
onmouseout="return searchBox.OnSearchSelectHide()"
onkeydown="return searchBox.OnSearchSelectKey(event)">
</div>
<!-- iframe showing the search results (closed by default) -->
<div id="MSearchResultsWindow">
<iframe src="javascript:void(0)" frameborder="0"
name="MSearchResults" id="MSearchResults">
</iframe>
</div>
<div class="header">
<div class="summary">
<a href="#pub-methods">Public Member Functions</a> |
<a href="#pri-attribs">Private Attributes</a> </div>
<div class="headertitle">
<div class="title">DGtal::concepts::CEuclideanRing< T > Struct Template Reference<div class="ingroups"><a class="el" href="group__Concepts.html">DGtal Concepts</a></div></div> </div>
</div><!--header-->
<div class="contents">
<p>Aim: Defines the mathematical concept equivalent to a unitary commutative ring with a division operator.
<a href="structDGtal_1_1concepts_1_1CEuclideanRing.html#details">More...</a></p>
<p><code>#include <<a class="el" href="CEuclideanRing_8h_source.html">DGtal/kernel/CEuclideanRing.h</a>></code></p>
<div class="dynheader">
Inheritance diagram for DGtal::concepts::CEuclideanRing< T >:</div>
<div class="dyncontent">
<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="structDGtal_1_1concepts_1_1CEuclideanRing__inherit__graph.svg" width="100%" height="404"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
</div>
<center><span class="legend">[<a target="top" href="graph_legend.html">legend</a>]</span></center></div>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:ae84f29771dfa420f1229f9882473a722"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="structDGtal_1_1concepts_1_1CEuclideanRing.html#ae84f29771dfa420f1229f9882473a722">BOOST_CONCEPT_USAGE</a> (<a class="el" href="structDGtal_1_1concepts_1_1CEuclideanRing.html">CEuclideanRing</a>)</td></tr>
<tr class="separator:ae84f29771dfa420f1229f9882473a722"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="inherit_header pub_methods_structDGtal_1_1concepts_1_1CCommutativeRing"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_structDGtal_1_1concepts_1_1CCommutativeRing')"><img src="closed.png" alt="-"/> Public Member Functions inherited from <a class="el" href="structDGtal_1_1concepts_1_1CCommutativeRing.html">DGtal::concepts::CCommutativeRing< T ></a></td></tr>
<tr class="memitem:a98ff4992feb549ce9e19bf5b4db110b6 inherit pub_methods_structDGtal_1_1concepts_1_1CCommutativeRing"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="structDGtal_1_1concepts_1_1CCommutativeRing.html#a98ff4992feb549ce9e19bf5b4db110b6">BOOST_CONCEPT_USAGE</a> (<a class="el" href="structDGtal_1_1concepts_1_1CCommutativeRing.html">CCommutativeRing</a>)</td></tr>
<tr class="separator:a98ff4992feb549ce9e19bf5b4db110b6 inherit pub_methods_structDGtal_1_1concepts_1_1CCommutativeRing"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="inherit_header pub_methods_structDGtal_1_1concepts_1_1CSignedNumber"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_structDGtal_1_1concepts_1_1CSignedNumber')"><img src="closed.png" alt="-"/> Public Member Functions inherited from <a class="el" href="structDGtal_1_1concepts_1_1CSignedNumber.html">DGtal::concepts::CSignedNumber< T ></a></td></tr>
<tr class="memitem:aceb9270217138fda6f95a69f3048618a inherit pub_methods_structDGtal_1_1concepts_1_1CSignedNumber"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="structDGtal_1_1concepts_1_1CSignedNumber.html#aceb9270217138fda6f95a69f3048618a">BOOST_CONCEPT_USAGE</a> (<a class="el" href="structDGtal_1_1concepts_1_1CSignedNumber.html">CSignedNumber</a>)</td></tr>
<tr class="separator:aceb9270217138fda6f95a69f3048618a inherit pub_methods_structDGtal_1_1concepts_1_1CSignedNumber"><td class="memSeparator" colspan="2"> </td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pri-attribs"></a>
Private Attributes</h2></td></tr>
<tr class="memitem:aa6c7ce09b7f980a264f6b881eb58b136"><td class="memItemLeft" align="right" valign="top">T </td><td class="memItemRight" valign="bottom"><a class="el" href="structDGtal_1_1concepts_1_1CEuclideanRing.html#aa6c7ce09b7f980a264f6b881eb58b136">a</a></td></tr>
<tr class="separator:aa6c7ce09b7f980a264f6b881eb58b136"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:af4df443e751577d542c035602db45575"><td class="memItemLeft" align="right" valign="top">T </td><td class="memItemRight" valign="bottom"><a class="el" href="structDGtal_1_1concepts_1_1CEuclideanRing.html#af4df443e751577d542c035602db45575">b</a></td></tr>
<tr class="separator:af4df443e751577d542c035602db45575"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a5a9744b5f0955a16e3f3e32d55cd5e40"><td class="memItemLeft" align="right" valign="top">T </td><td class="memItemRight" valign="bottom"><a class="el" href="structDGtal_1_1concepts_1_1CEuclideanRing.html#a5a9744b5f0955a16e3f3e32d55cd5e40">c</a></td></tr>
<tr class="separator:a5a9744b5f0955a16e3f3e32d55cd5e40"><td class="memSeparator" colspan="2"> </td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><h3>template<typename T><br />
struct DGtal::concepts::CEuclideanRing< T ></h3>
<p>Aim: Defines the mathematical concept equivalent to a unitary commutative ring with a division operator. </p>
<p>Description of <b>concept</b> '<b><a class="el" href="structDGtal_1_1concepts_1_1CEuclideanRing.html" title="Aim: Defines the mathematical concept equivalent to a unitary commutative ring with a division operat...">CEuclideanRing</a>'</b> </p>
<h1><a class="anchor" id="autotoc_md534"></a>
Refinement of CCommutativeRing</h1>
<h1><a class="anchor" id="autotoc_md535"></a>
Associated types</h1>
<h1><a class="anchor" id="autotoc_md536"></a>
Notation</h1>
<ul>
<li><em>X</em> : A type that is a model of <a class="el" href="structDGtal_1_1concepts_1_1CEuclideanRing.html" title="Aim: Defines the mathematical concept equivalent to a unitary commutative ring with a division operat...">CEuclideanRing</a></li>
<li><em>x</em>, <em>y</em> : <a class="el" href="classDGtal_1_1Object.html" title="Aim: An object (or digital object) represents a set in some digital space associated with a digital t...">Object</a> of type Integer</li>
</ul>
<h1><a class="anchor" id="autotoc_md537"></a>
Definitions</h1>
<h1><a class="anchor" id="autotoc_md538"></a>
Valid expressions and semantics</h1>
<table class="markdownTable">
<tr class="markdownTableHead">
<th class="markdownTableHeadNone">Name </th><th class="markdownTableHeadNone">Expression </th><th class="markdownTableHeadNone">Type requirements </th><th class="markdownTableHeadNone">Return type </th><th class="markdownTableHeadNone">Precondition </th><th class="markdownTableHeadNone">Semantics </th><th class="markdownTableHeadNone">Postcondition </th><th class="markdownTableHeadNone">Complexity </th></tr>
<tr class="markdownTableRowOdd">
<td class="markdownTableBodyNone">Division </td><td class="markdownTableBodyNone"><em>x</em> / <em>y</em> </td><td class="markdownTableBodyNone"><em>X</em> </td><td class="markdownTableBodyNone">object of type <em>X</em> </td><td class="markdownTableBodyNone">Euclidean division of two numbers </td><td class="markdownTableBodyNone"></td><td class="markdownTableBodyNone"></td><td class="markdownTableBodyNone"></td></tr>
</table>
<h1><a class="anchor" id="autotoc_md539"></a>
Invariants</h1>
<h1><a class="anchor" id="autotoc_md540"></a>
Models</h1>
<p><a class="el" href="namespaceDGtal.html#ac1e9ac6a329319ae13c51c0c9e92486a" title="signed 32-bit integer.">DGtal::int32_t</a>, <a class="el" href="namespaceDGtal.html#a1c09e3f63904ff371f1b99f45069fc63" title="signed 94-bit integer.">DGtal::int64_t</a>, <a class="el" href="namespaceDGtal.html#ac28d51e0b1672afa52b3c218a32a6a01" title="signed 8-bit integer.">DGtal::int8_t</a>, float, double, long double, <a class="el" href="namespaceDGtal.html#ad14cde66089fcbdefb20c819562d2a0d" title="Multi-precision integer with GMP implementation.">DGtal::BigInteger</a></p>
<h1><a class="anchor" id="autotoc_md541"></a>
Notes</h1>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>the type that should be a model of commutative ring. </td></tr>
</table>
</dd>
</dl>
<p class="definition">Definition at line <a class="el" href="CEuclideanRing_8h_source.html#l00087">87</a> of file <a class="el" href="CEuclideanRing_8h_source.html">CEuclideanRing.h</a>.</p>
</div><h2 class="groupheader">Member Function Documentation</h2>
<a id="ae84f29771dfa420f1229f9882473a722"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae84f29771dfa420f1229f9882473a722">◆ </a></span>BOOST_CONCEPT_USAGE()</h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template<typename T > </div>
<table class="mlabels">
<tr>
<td class="mlabels-left">
<table class="memname">
<tr>
<td class="memname"><a class="el" href="structDGtal_1_1concepts_1_1CEuclideanRing.html">DGtal::concepts::CEuclideanRing</a>< T >::BOOST_CONCEPT_USAGE </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structDGtal_1_1concepts_1_1CEuclideanRing.html">CEuclideanRing</a>< T > </td>
<td class="paramname"></td><td>)</td>
<td></td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel">inline</span></span> </td>
</tr>
</table>
</div><div class="memdoc">
<p class="definition">Definition at line <a class="el" href="CEuclideanRing_8h_source.html#l00092">92</a> of file <a class="el" href="CEuclideanRing_8h_source.html">CEuclideanRing.h</a>.</p>
<div class="fragment"><div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  {</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <a class="code" href="namespaceDGtal_1_1concepts_1_1ConceptUtils.html#ae5eda4fcd7f26921b9335b5c7d5874e1">ConceptUtils::sameType</a>( c, T( a/b ) );</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  } </div>
<div class="ttc" id="anamespaceDGtal_1_1concepts_1_1ConceptUtils_html_ae5eda4fcd7f26921b9335b5c7d5874e1"><div class="ttname"><a href="namespaceDGtal_1_1concepts_1_1ConceptUtils.html#ae5eda4fcd7f26921b9335b5c7d5874e1">DGtal::concepts::ConceptUtils::sameType</a></div><div class="ttdeci">void sameType(const T &, const T &)</div><div class="ttdef"><b>Definition:</b> <a href="ConceptUtils_8h_source.html#l00117">ConceptUtils.h:117</a></div></div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="ConceptUtils_8h_source.html#l00117">DGtal::concepts::ConceptUtils::sameType()</a>.</p>
</div>
</div>
<h2 class="groupheader">Field Documentation</h2>
<a id="aa6c7ce09b7f980a264f6b881eb58b136"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aa6c7ce09b7f980a264f6b881eb58b136">◆ </a></span>a</h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template<typename T > </div>
<table class="mlabels">
<tr>
<td class="mlabels-left">
<table class="memname">
<tr>
<td class="memname">T <a class="el" href="structDGtal_1_1concepts_1_1CEuclideanRing.html">DGtal::concepts::CEuclideanRing</a>< T >::a</td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel">private</span></span> </td>
</tr>
</table>
</div><div class="memdoc">
<p class="definition">Definition at line <a class="el" href="CEuclideanRing_8h_source.html#l00098">98</a> of file <a class="el" href="CEuclideanRing_8h_source.html">CEuclideanRing.h</a>.</p>
</div>
</div>
<a id="af4df443e751577d542c035602db45575"></a>
<h2 class="memtitle"><span class="permalink"><a href="#af4df443e751577d542c035602db45575">◆ </a></span>b</h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template<typename T > </div>
<table class="mlabels">
<tr>
<td class="mlabels-left">
<table class="memname">
<tr>
<td class="memname">T <a class="el" href="structDGtal_1_1concepts_1_1CEuclideanRing.html">DGtal::concepts::CEuclideanRing</a>< T >::b</td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel">private</span></span> </td>
</tr>
</table>
</div><div class="memdoc">
<p class="definition">Definition at line <a class="el" href="CEuclideanRing_8h_source.html#l00098">98</a> of file <a class="el" href="CEuclideanRing_8h_source.html">CEuclideanRing.h</a>.</p>
</div>
</div>
<a id="a5a9744b5f0955a16e3f3e32d55cd5e40"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a5a9744b5f0955a16e3f3e32d55cd5e40">◆ </a></span>c</h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template<typename T > </div>
<table class="mlabels">
<tr>
<td class="mlabels-left">
<table class="memname">
<tr>
<td class="memname">T <a class="el" href="structDGtal_1_1concepts_1_1CEuclideanRing.html">DGtal::concepts::CEuclideanRing</a>< T >::c</td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel">private</span></span> </td>
</tr>
</table>
</div><div class="memdoc">
<p class="definition">Definition at line <a class="el" href="CEuclideanRing_8h_source.html#l00098">98</a> of file <a class="el" href="CEuclideanRing_8h_source.html">CEuclideanRing.h</a>.</p>
</div>
</div>
<hr/>The documentation for this struct was generated from the following file:<ul>
<li><a class="el" href="CEuclideanRing_8h_source.html">CEuclideanRing.h</a></li>
</ul>
</div><!-- contents -->
</div><!-- doc-content -->
<!-- start footer part -->
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="navelem"><a class="el" href="namespaceDGtal.html">DGtal</a></li><li class="navelem"><a class="el" href="namespaceDGtal_1_1concepts.html">concepts</a></li><li class="navelem"><a class="el" href="structDGtal_1_1concepts_1_1CEuclideanRing.html">CEuclideanRing</a></li>
<li class="footer">Generated on Mon Dec 23 2024 13:19:07 for DGtal by <a href="https://www.doxygen.org/index.html"><img class="footer" src="doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.1 </li>
</ul>
</div>
</body>
</html>