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import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/equation.md","filePath":"ja/api/mp_math/equation.md"}'),t={name:"ja/api/mp_math/equation.md"},l=n(`<h1 id="mbcp-mp-math-equation" tabindex="-1">mbcp.mp_math.equation <a class="header-anchor" href="#mbcp-mp-math-equation" aria-label="Permalink to &quot;mbcp.mp_math.equation&quot;"></a></h1><p><strong>説明</strong>: 本模块定义了方程相关的类和函数以及一些常用的数学函数</p><h3 id="class-curveequation" tabindex="-1"><em><strong>class</strong></em> <code>CurveEquation</code> <a class="header-anchor" href="#class-curveequation" aria-label="Permalink to &quot;***class*** \`CurveEquation\`&quot;"></a></h3><h4 id="func-init-self-x-func-onevarfunc-y-func-onevarfunc-z-func-onevarfunc" tabindex="-1"><em><strong>func</strong></em> <code>__init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc)</code> <a class="header-anchor" href="#func-init-self-x-func-onevarfunc-y-func-onevarfunc-z-func-onevarfunc" aria-label="Permalink to &quot;***func*** \`__init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc)\`&quot;"></a></h4><p><strong>説明</strong>: 曲线方程。</p><p><strong>引数</strong>:</p><blockquote><ul><li>x_func (<a href="./mp_math_typing.html#var-onevarfunc"><code>OneVarFunc</code></a>): x函数</li><li>y_func (<a href="./mp_math_typing.html#var-onevarfunc"><code>OneVarFunc</code></a>): y函数</li><li>z_func (<a href="./mp_math_typing.html#var-onevarfunc"><code>OneVarFunc</code></a>): z函数</li></ul></blockquote><details><summary><b>ソースコード</b> または <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/equation.py#L12" target="_blank">GitHubで表示</a></summary><div class="language-python vp-adaptive-theme"><button title="Copy Code" class="copy"></button><span class="lang">python</span><pre class="shiki shiki-themes github-light github-dark vp-code" tabindex="0"><code><span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">def</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> __init__</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> 曲线方程</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> Args:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> x_func ([\`OneVarFunc\`](./mp_math_typing#var-onevarfunc)): x函数</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> y_func ([\`OneVarFunc\`](./mp_math_typing#var-onevarfunc)): y函数</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> z_func ([\`OneVarFunc\`](./mp_math_typing#var-onevarfunc)): z函数</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.x_func </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> x_func</span></span>
<span class="line"><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.y_func </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> y_func</span></span>
<span class="line"><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.z_func </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> z_func</span></span></code></pre></div></details><h4 id="func-call-self-t-var-point3-tuple-point3" tabindex="-1"><em><strong>func</strong></em> <code>__call__(self, *t: Var) -&gt; Point3 | tuple[Point3, ...]</code> <a class="header-anchor" href="#func-call-self-t-var-point3-tuple-point3" aria-label="Permalink to &quot;***func*** \`__call__(self, *t: Var) -&gt; Point3 | tuple[Point3, ...]\`&quot;"></a></h4><p><strong></strong>: 线</p><p><strong></strong>:</p><blockquote><ul><li>*t:</li><li>:</li></ul></blockquote><p><strong></strong>: </p><details><summary><b></b> <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/equation.py#L24" target="_blank">GitHub</a></summary><div class="language-python vp-adaptive-theme"><button title="Copy Code" class="copy"></button><span class="lang">python</span><pre class="shiki shiki-themes github-light github-dark vp-code" tabindex="0"><code><span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">def</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> __call__</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(self, </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">t: Var) -&gt; Point3 </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">|</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> tuple[Point3, </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">...</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">]:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> 计算曲线上的点</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> Args:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> *t:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> 参数</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> Returns:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> 目标点</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> if</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> len</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(t) </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">==</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> 1</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> Point3(</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.x_func(t[</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">0</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">]), </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.y_func(t[</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">0</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">]), </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.z_func(t[</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">0</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">]))</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> else</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> tuple</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">([Point3(x, y, z) </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">for</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> x, y, z </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">in</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> zip</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.x_func(t), </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.y_func(t), </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">.z_func(t))])</span></span></code></pre></div></details><h3 id="func-get-partial-derivative-func-func-multivarsfunc-var-int-tuple-int-epsilon-number-epsilon-multivarsfunc" tabindex="-1"><em><strong>func</strong></em> <code>get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -&gt; MultiVarsFunc</code> <a class="header-anchor" href="#func-get-partial-derivative-func-func-multivarsfunc-var-int-tuple-int-epsilon-number-epsilon-multivarsfunc" aria-label="Permalink to &quot;***func*** \`get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -&gt; MultiVarsFunc\`&quot;"></a></h3><p><strong></strong>: N</p><div class="warning custom-block github-alert"><p class="custom-block-title">WARNING</p><p></p></div><p><strong></strong>:</p><blockquote><ul><li>func (<a href="./mp_math_typing.html#var-multivarsfunc"><code>MultiVarsFunc</code></a>): N</li><li>var: ()()</li><li>epsilon: </li></ul></blockquote><p><strong></strong>: </p><p><strong></strong>:</p><blockquote><ul><li>ValueError </li></ul></blockquote><details><summary><b></b> <a href="https://github.com/snowykami/mbcp/tree/main/mbcp/mp_math/equation.py#L42" target="_blank">GitHub</a></summary><div class="language-python vp-adaptive-theme"><button title="Copy Code" class="copy"></button><span class="lang">python</span><pre class="shiki shiki-themes github-light github-dark vp-code" tabindex="0"><code><span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">def</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;"> get_partial_derivative_func</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(func: MultiVarsFunc, var: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">int</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> |</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> tuple[</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">int</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">, </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">...</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">], epsilon: Number</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">EPSILON</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">) -&gt; MultiVarsFunc:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> 求N元函数一阶偏导函数这玩意不太稳定慎用</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> &gt; [!warning]</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> &gt; 目前数学界对于一个函数的导函数并没有通解的说法因此该函数的稳定性有待提升</span></span>
<span class="line"></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> Args:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> func ([\`MultiVarsFunc\`](./mp_math_typing#var-multivarsfunc)): N元函数</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> var: 变量位置可为整数(一阶偏导)或整数元组(高阶偏导)</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> epsilon: 偏移量</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> Returns:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> 偏导函数</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> Raises:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> ValueError: 无效变量类型</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> if</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> isinstance</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(var, </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">int</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">):</span></span>
<span class="line"></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> def</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;"> partial_derivative_func</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">args: Var) -&gt; Var:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> &quot;&quot;&quot;@litedoc-hide&quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> args_list_plus </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> list</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(args)</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> args_list_plus[var] </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">+=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> epsilon</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> args_list_minus </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> list</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(args)</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> args_list_minus[var] </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">-=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> epsilon</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> (func(</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">args_list_plus) </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">-</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> func(</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">args_list_minus)) </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">/</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> (</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">2</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> *</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> epsilon)</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> partial_derivative_func</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> elif</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> isinstance</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(var, </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;">tuple</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">):</span></span>
<span class="line"></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> def</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0;"> high_order_partial_derivative_func</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">args: Var) -&gt; Var:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> @litedoc-hide</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> 求高阶偏导函数</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> Args:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> *args: 参数</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> Returns:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> 高阶偏导数值</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;"> &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> result_func </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> func</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> for</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> v </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">in</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> var:</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> result_func </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> get_partial_derivative_func(result_func, v, epsilon)</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> result_func(</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">args)</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> return</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;"> high_order_partial_derivative_func</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> else</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">:</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583;"> raise</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF;"> ValueError</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">(</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF;">&#39;Invalid var type&#39;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8;">)</span></span></code></pre></div></details>`,23),p=[l];function h(k,e,r,E,c,d){return a(),i("div",null,p)}const F=s(t,[["render",h]]);export{u as __pageData,F as default};