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add Hamilton
2023-12-02 14:12:25 +01:00
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01//EN"
"http://www.w3.org/TR/html4/strict.dtd">
<html>
<head>
<title></title>
<meta http-equiv="content-type" content="text/html; charset=utf-8">
<style type="text/css">
td.linenos { background-color: #f0f0f0; padding-right: 10px; }
span.lineno { background-color: #f0f0f0; padding: 0 5px 0 5px; }
pre { line-height: 125%; }
body .hll { background-color: #ffffcc }
body { background: #f8f8f8; }
body .c { color: #408080; font-style: italic } /* Comment */
body .err { border: 1px solid #FF0000 } /* Error */
body .k { color: #008000; font-weight: bold } /* Keyword */
body .o { color: #666666 } /* Operator */
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body .cm { color: #408080; font-style: italic } /* Comment.Multiline */
body .cp { color: #BC7A00 } /* Comment.Preproc */
body .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */
body .c1 { color: #408080; font-style: italic } /* Comment.Single */
body .cs { color: #408080; font-style: italic } /* Comment.Special */
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body .ge { font-style: italic } /* Generic.Emph */
body .gr { color: #FF0000 } /* Generic.Error */
body .gh { color: #000080; font-weight: bold } /* Generic.Heading */
body .gi { color: #00A000 } /* Generic.Inserted */
body .go { color: #888888 } /* Generic.Output */
body .gp { color: #000080; font-weight: bold } /* Generic.Prompt */
body .gs { font-weight: bold } /* Generic.Strong */
body .gu { color: #800080; font-weight: bold } /* Generic.Subheading */
body .gt { color: #0044DD } /* Generic.Traceback */
body .kc { color: #008000; font-weight: bold } /* Keyword.Constant */
body .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */
body .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */
body .kp { color: #008000 } /* Keyword.Pseudo */
body .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */
body .kt { color: #B00040 } /* Keyword.Type */
body .m { color: #666666 } /* Literal.Number */
body .s { color: #BA2121 } /* Literal.String */
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body .nf { color: #0000FF } /* Name.Function */
body .nl { color: #A0A000 } /* Name.Label */
body .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */
body .nt { color: #008000; font-weight: bold } /* Name.Tag */
body .nv { color: #19177C } /* Name.Variable */
body .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */
body .w { color: #bbbbbb } /* Text.Whitespace */
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body .il { color: #666666 } /* Literal.Number.Integer.Long */
</style>
</head>
<body>
<h2></h2>
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227</pre></div></td><td class="code"><div class="highlight"><pre><span class="ch">#!/usr/bin/env python</span>
<span class="c1"># -*- coding: utf-8 -*-</span>
<span class="n">description</span> <span class="o">=</span> <span class="s2">&quot;&quot;&quot;</span>
<span class="s2">Tento jednoduchý skript řeší poměrně otravný problém, který</span>
<span class="s2">je však snadno algoritmizovatelný. Jsou to jen opakované parciální derivace,</span>
<span class="s2">jejichž výsledky jsou dosazovány do daných výrazů. Protože se přitom člověk</span>
<span class="s2">snadno splete (hlavně ve znaménku), je lepší to nechat na programu.</span>
<span class="s2">Stačí nadefinovat potřebné symboly pro konstanty a časově závislé proměnné</span>
<span class="s2">(zobecněné souřadnice), pomocí nich pak vyjádřit lagranžián a o zbytek se postará python.</span>
<span class="s2">&quot;&quot;&quot;</span>
<span class="kn">from</span> <span class="nn">sympy.core</span> <span class="kn">import</span> <span class="n">mul</span><span class="p">,</span> <span class="n">add</span>
<span class="kn">from</span> <span class="nn">sympy.physics.vector.printing</span> <span class="kn">import</span> <span class="n">vlatex</span>
<span class="kn">from</span> <span class="nn">sympy.physics.mechanics</span> <span class="kn">import</span> <span class="n">dynamicsymbols</span>
<span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="p">(</span><span class="n">Symbol</span><span class="p">,</span> <span class="n">symbols</span><span class="p">,</span> <span class="n">Derivative</span><span class="p">,</span>
<span class="n">Eq</span><span class="p">,</span> <span class="n">pprint</span><span class="p">,</span> <span class="n">solve</span><span class="p">,</span> <span class="n">latex</span><span class="p">,</span> <span class="n">simplify</span><span class="p">,</span> <span class="n">expand</span><span class="p">)</span>
<span class="c1">################# HTML dekorace ###############################################</span>
<span class="k">class</span> <span class="nc">Tag</span><span class="p">:</span>
<span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">v</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">name</span> <span class="o">=</span> <span class="n">n</span>
<span class="bp">self</span><span class="o">.</span><span class="n">value</span> <span class="o">=</span> <span class="n">v</span>
<span class="k">def</span> <span class="nf">to_str</span> <span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="k">return</span> <span class="s1">&#39; &#39;</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">name</span> <span class="o">+</span> <span class="s1">&#39;=</span><span class="se">\&quot;</span><span class="s1">&#39;</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">value</span> <span class="o">+</span> <span class="s1">&#39;</span><span class="se">\&quot;</span><span class="s1">&#39;</span>
<span class="k">class</span> <span class="nc">Element</span><span class="p">:</span>
<span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">v</span><span class="o">=</span><span class="bp">None</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">name</span> <span class="o">=</span> <span class="n">n</span>
<span class="bp">self</span><span class="o">.</span><span class="n">value</span> <span class="o">=</span> <span class="n">v</span>
<span class="bp">self</span><span class="o">.</span><span class="n">tags</span> <span class="o">=</span> <span class="p">[]</span>
<span class="bp">self</span><span class="o">.</span><span class="n">childs</span> <span class="o">=</span> <span class="p">[]</span>
<span class="bp">self</span><span class="o">.</span><span class="n">id</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">def</span> <span class="nf">addE</span> <span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">e</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">childs</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">addT</span> <span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">t</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">tags</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">addF</span> <span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">f</span><span class="p">):</span>
<span class="n">t</span> <span class="o">=</span> <span class="n">Tag</span> <span class="p">(</span><span class="s1">&#39;class&#39;</span><span class="p">,</span><span class="s1">&#39;formulaDsp&#39;</span><span class="p">)</span>
<span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">f</span><span class="p">:</span>
<span class="n">n</span> <span class="o">=</span> <span class="n">Element</span><span class="p">(</span><span class="s1">&#39;p&#39;</span><span class="p">,</span> <span class="s1">&#39;</span><span class="se">\\</span><span class="s1">[&#39;</span> <span class="o">+</span> <span class="n">p</span> <span class="o">+</span> <span class="s1">&#39;</span><span class="se">\\</span><span class="s1">]&#39;</span><span class="p">)</span>
<span class="n">n</span><span class="o">.</span><span class="n">addT</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">addE</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">to_str</span> <span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="n">s</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">indent</span><span class="p">()</span>
<span class="n">s</span><span class="o">+=</span> <span class="s1">&#39;&lt;&#39;</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">name</span>
<span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">tags</span><span class="p">:</span> <span class="n">s</span> <span class="o">+=</span> <span class="n">n</span><span class="o">.</span><span class="n">to_str</span><span class="p">()</span>
<span class="n">s</span><span class="o">+=</span> <span class="s1">&#39;&gt;&#39;</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">value</span> <span class="o">!=</span> <span class="bp">None</span><span class="p">:</span> <span class="n">s</span> <span class="o">+=</span> <span class="bp">self</span><span class="o">.</span><span class="n">value</span>
<span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">childs</span><span class="p">:</span> <span class="n">s</span> <span class="o">+=</span> <span class="n">n</span><span class="o">.</span><span class="n">to_str</span><span class="p">()</span>
<span class="n">s</span><span class="o">+=</span> <span class="bp">self</span><span class="o">.</span><span class="n">indent</span><span class="p">()</span>
<span class="n">s</span><span class="o">+=</span> <span class="s1">&#39;&lt;/&#39;</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">name</span> <span class="o">+</span> <span class="s1">&#39;&gt;&#39;</span>
<span class="k">return</span> <span class="n">s</span>
<span class="k">def</span> <span class="nf">cal</span> <span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">k</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">id</span> <span class="o">=</span> <span class="n">k</span>
<span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">childs</span><span class="p">:</span> <span class="n">n</span><span class="o">.</span><span class="n">cal</span> <span class="p">(</span><span class="n">k</span><span class="o">+</span><span class="mi">2</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">indent</span> <span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="n">s</span> <span class="o">=</span> <span class="s1">&#39;</span><span class="se">\n</span><span class="s1">&#39;</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">id</span> <span class="o">*</span> <span class="s1">&#39; &#39;</span>
<span class="k">return</span> <span class="n">s</span>
<span class="k">def</span> <span class="nf">set_root</span> <span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">root</span><span class="p">):</span>
<span class="n">styl</span> <span class="o">=</span> <span class="n">Element</span><span class="p">(</span><span class="s1">&#39;style&#39;</span><span class="p">,</span> <span class="s1">&#39;body {background-color: rgb(192,255,255);} h2 {color: rgb(64,0,192);} h3 {color: rgb(192,0,0);} table {color: rgb(128,0,128);}&#39;</span><span class="p">)</span>
<span class="n">scfg</span> <span class="o">=</span> <span class="s1">&#39;MathJax.Hub.Config({</span><span class="se">\n</span><span class="s1"> extensions: [</span><span class="se">\&quot;</span><span class="s1">tex2jax.js</span><span class="se">\&quot;</span><span class="s1">,&quot;TeX/AMSmath.js&quot;],</span><span class="se">\n</span><span class="s1"> jax: [</span><span class="se">\&quot;</span><span class="s1">input/TeX</span><span class="se">\&quot;</span><span class="s1">,&#39;</span>
<span class="n">scfg</span><span class="o">+=</span> <span class="s1">&#39;</span><span class="se">\&quot;</span><span class="s1">output/HTML-CSS</span><span class="se">\&quot;</span><span class="s1">],</span><span class="se">\n</span><span class="s1"> tex2jax: {inlineMath: [[</span><span class="se">\&#39;</span><span class="s1">$</span><span class="se">\&#39;</span><span class="s1">,</span><span class="se">\&#39;</span><span class="s1">$</span><span class="se">\&#39;</span><span class="s1">]]},</span><span class="se">\n</span><span class="s1"> displayAlign: </span><span class="se">\&quot;</span><span class="s1">left</span><span class="se">\&quot;</span><span class="s1">});&#39;</span>
<span class="n">head</span> <span class="o">=</span> <span class="n">Element</span><span class="p">(</span><span class="s1">&#39;head&#39;</span><span class="p">)</span>
<span class="n">meta</span> <span class="o">=</span> <span class="n">Element</span><span class="p">(</span><span class="s1">&#39;META&#39;</span><span class="p">)</span>
<span class="n">titl</span> <span class="o">=</span> <span class="n">Element</span><span class="p">(</span><span class="s1">&#39;title&#39;</span><span class="p">,</span> <span class="s1">&#39;Lagrange&#39;</span><span class="p">)</span>
<span class="n">s1</span> <span class="o">=</span> <span class="n">Element</span><span class="p">(</span><span class="s1">&#39;script&#39;</span><span class="p">,</span> <span class="n">scfg</span><span class="p">)</span>
<span class="n">s2</span> <span class="o">=</span> <span class="n">Element</span><span class="p">(</span><span class="s1">&#39;script&#39;</span><span class="p">)</span>
<span class="n">s1</span><span class="o">.</span><span class="n">addT</span><span class="p">(</span><span class="n">Tag</span><span class="p">(</span><span class="s1">&#39;type&#39;</span><span class="p">,</span><span class="s1">&#39;text/x-mathjax-config&#39;</span><span class="p">))</span>
<span class="n">s2</span><span class="o">.</span><span class="n">addT</span><span class="p">(</span><span class="n">Tag</span><span class="p">(</span><span class="s1">&#39;type&#39;</span><span class="p">,</span><span class="s1">&#39;text/javascript&#39;</span><span class="p">))</span>
<span class="n">s2</span><span class="o">.</span><span class="n">addT</span><span class="p">(</span><span class="n">Tag</span><span class="p">(</span><span class="s1">&#39;src&#39;</span><span class="p">,</span><span class="s1">&#39;https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js&#39;</span><span class="p">))</span>
<span class="n">meta</span><span class="o">.</span><span class="n">addT</span><span class="p">(</span><span class="n">Tag</span><span class="p">(</span><span class="s1">&#39;HTTP-EQUIV&#39;</span><span class="p">,</span><span class="s1">&#39;CONTENT-TYPE&#39;</span><span class="p">))</span>
<span class="n">meta</span><span class="o">.</span><span class="n">addT</span><span class="p">(</span><span class="n">Tag</span><span class="p">(</span><span class="s1">&#39;CONTENT&#39;</span><span class="p">,</span><span class="s1">&#39;text/html; charset=utf-8&#39;</span><span class="p">))</span>
<span class="n">head</span><span class="o">.</span><span class="n">addE</span><span class="p">(</span><span class="n">meta</span><span class="p">)</span>
<span class="n">head</span><span class="o">.</span><span class="n">addE</span><span class="p">(</span><span class="n">titl</span><span class="p">)</span>
<span class="n">head</span><span class="o">.</span><span class="n">addE</span><span class="p">(</span><span class="n">styl</span><span class="p">)</span>
<span class="n">head</span><span class="o">.</span><span class="n">addE</span><span class="p">(</span><span class="n">s1</span><span class="p">)</span>
<span class="n">head</span><span class="o">.</span><span class="n">addE</span><span class="p">(</span><span class="n">s2</span><span class="p">)</span>
<span class="n">e</span><span class="o">.</span><span class="n">addE</span> <span class="p">(</span><span class="n">head</span><span class="p">)</span>
<span class="n">body</span> <span class="o">=</span> <span class="n">Element</span><span class="p">(</span><span class="s1">&#39;body&#39;</span><span class="p">)</span>
<span class="n">body</span><span class="o">.</span><span class="n">addE</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
<span class="n">e</span><span class="o">.</span><span class="n">addE</span> <span class="p">(</span><span class="n">body</span><span class="p">)</span>
<span class="n">e</span><span class="o">.</span><span class="n">cal</span><span class="p">()</span>
<span class="k">def</span> <span class="nf">html_head</span> <span class="p">():</span>
<span class="n">s</span> <span class="o">=</span> <span class="s1">&#39;&lt;!DOCTYPE html PUBLIC </span><span class="se">\&quot;</span><span class="s1">-//W3C//DTD XHTML 1.0 Transitional//EN</span><span class="se">\&quot;</span><span class="s1"> </span><span class="se">\&quot;</span><span class="s1">http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd</span><span class="se">\&quot;</span><span class="s1">&gt;&#39;</span>
<span class="k">return</span> <span class="n">s</span>
<span class="k">def</span> <span class="nf">CreateHTML</span> <span class="p">(</span><span class="n">filename</span><span class="p">,</span> <span class="n">html</span><span class="p">):</span>
<span class="n">s</span> <span class="o">=</span> <span class="n">html_head</span> <span class="p">()</span>
<span class="n">r</span> <span class="o">=</span> <span class="n">Element</span> <span class="p">(</span><span class="s1">&#39;html&#39;</span><span class="p">)</span>
<span class="n">set_root</span> <span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">html</span><span class="p">)</span>
<span class="n">s</span> <span class="o">+=</span> <span class="n">r</span><span class="o">.</span><span class="n">to_str</span><span class="p">()</span>
<span class="nb">file</span> <span class="o">=</span> <span class="nb">open</span> <span class="p">(</span><span class="n">filename</span><span class="p">,</span><span class="s1">&#39;w&#39;</span><span class="p">)</span>
<span class="nb">file</span><span class="o">.</span><span class="n">write</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
<span class="nb">file</span><span class="o">.</span><span class="n">close</span><span class="p">()</span>
<span class="k">def</span> <span class="nf">output</span> <span class="p">(</span><span class="n">counter</span><span class="p">,</span> <span class="n">problem</span><span class="p">,</span> <span class="n">L</span><span class="p">,</span> <span class="n">H</span><span class="p">,</span> <span class="n">hce</span><span class="p">,</span> <span class="n">lce</span><span class="p">):</span>
<span class="n">html</span> <span class="o">=</span> <span class="n">Element</span><span class="p">(</span><span class="s1">&#39;div&#39;</span><span class="p">,</span> <span class="s1">&#39;&lt;hr&gt;&#39;</span><span class="p">)</span>
<span class="n">html</span><span class="o">.</span><span class="n">addE</span><span class="p">(</span><span class="n">Element</span><span class="p">(</span><span class="s1">&#39;h2&#39;</span><span class="p">,</span><span class="s1">&#39;Řešený problém : {0:s}&#39;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">problem</span><span class="p">)))</span>
<span class="n">html</span><span class="o">.</span><span class="n">addE</span><span class="p">(</span><span class="n">Element</span><span class="p">(</span><span class="s1">&#39;h3&#39;</span><span class="p">,</span><span class="s1">&#39;{0:d}.1. Zadaný lagranžián :&#39;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">counter</span><span class="p">)))</span>
<span class="n">html</span><span class="o">.</span><span class="n">addF</span> <span class="p">([</span><span class="s1">&#39;L = &#39;</span> <span class="o">+</span> <span class="n">vlatex</span><span class="p">(</span><span class="n">L</span><span class="p">)]);</span>
<span class="n">html</span><span class="o">.</span><span class="n">addE</span><span class="p">(</span><span class="n">Element</span><span class="p">(</span><span class="s1">&#39;h3&#39;</span><span class="p">,</span><span class="s1">&#39;{0:d}.2. Lagrangeovy rovnice :&#39;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">counter</span><span class="p">)))</span>
<span class="n">html</span><span class="o">.</span><span class="n">addF</span> <span class="p">([</span><span class="n">vlatex</span><span class="p">(</span><span class="n">lce</span><span class="p">)]);</span>
<span class="n">html</span><span class="o">.</span><span class="n">addE</span><span class="p">(</span><span class="n">Element</span><span class="p">(</span><span class="s1">&#39;h3&#39;</span><span class="p">,</span><span class="s1">&#39;{0:d}.3. Hamiltonova funkce :&#39;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">counter</span><span class="p">)))</span>
<span class="n">html</span><span class="o">.</span><span class="n">addF</span> <span class="p">([</span><span class="s1">&#39;H = &#39;</span> <span class="o">+</span> <span class="n">vlatex</span><span class="p">(</span><span class="n">H</span><span class="p">)]);</span>
<span class="n">html</span><span class="o">.</span><span class="n">addE</span><span class="p">(</span><span class="n">Element</span><span class="p">(</span><span class="s1">&#39;h3&#39;</span><span class="p">,</span><span class="s1">&#39;{0:d}.4. Hamiltonovy kanonické rovnice :&#39;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">counter</span><span class="p">)))</span>
<span class="n">table</span> <span class="o">=</span> <span class="n">Element</span><span class="p">(</span><span class="s1">&#39;table&#39;</span><span class="p">)</span>
<span class="n">table</span><span class="o">.</span><span class="n">addT</span><span class="p">(</span><span class="n">Tag</span><span class="p">(</span><span class="s1">&#39;align&#39;</span><span class="p">,</span><span class="s1">&#39;center&#39;</span><span class="p">))</span>
<span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">hce</span><span class="p">:</span>
<span class="n">td</span> <span class="o">=</span> <span class="s1">&#39;&#39;</span>
<span class="k">for</span> <span class="n">q</span> <span class="ow">in</span> <span class="n">p</span><span class="p">:</span> <span class="n">td</span> <span class="o">+=</span> <span class="s1">&#39;</span><span class="se">\n</span><span class="s1">&lt;td class=&quot;formulaDsp&quot;&gt;</span><span class="se">\\</span><span class="s1">[{0:s}={1:s}\qquad</span><span class="se">\\</span><span class="s1">]&lt;/td&gt;&#39;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">vlatex</span><span class="p">(</span><span class="n">q</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">vlatex</span><span class="p">(</span><span class="n">expand</span><span class="p">(</span><span class="n">q</span><span class="p">[</span><span class="mi">1</span><span class="p">])))</span>
<span class="n">tr</span> <span class="o">=</span> <span class="n">Element</span><span class="p">(</span><span class="s1">&#39;tr&#39;</span><span class="p">,</span> <span class="n">td</span><span class="p">)</span>
<span class="n">table</span><span class="o">.</span><span class="n">addE</span><span class="p">(</span><span class="n">tr</span><span class="p">)</span>
<span class="n">html</span><span class="o">.</span><span class="n">addE</span><span class="p">(</span><span class="n">table</span><span class="p">)</span>
<span class="k">return</span> <span class="n">html</span>
<span class="c1">#################### Vlastní výpočty ##########################################</span>
<span class="n">t</span> <span class="o">=</span> <span class="n">Symbol</span><span class="p">(</span><span class="s1">&#39;t&#39;</span><span class="p">)</span> <span class="c1"># Globální symbol pro čas</span>
<span class="c1"># vykrácení konstantou uděláme ručně, ale nemusí to fungovat, v podstatě jde jen o zbytečné hmotnosti</span>
<span class="k">def</span> <span class="nf">parse</span> <span class="p">(</span><span class="n">ex</span><span class="p">):</span>
<span class="n">ex</span> <span class="o">=</span> <span class="n">expand</span> <span class="p">(</span><span class="n">ex</span><span class="p">)</span>
<span class="k">if</span> <span class="n">ex</span><span class="o">.</span><span class="n">func</span> <span class="o">!=</span> <span class="n">add</span><span class="o">.</span><span class="n">Add</span><span class="p">:</span> <span class="k">return</span> <span class="n">ex</span>
<span class="n">e1</span> <span class="o">=</span> <span class="n">ex</span><span class="o">.</span><span class="n">args</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="k">if</span> <span class="n">e1</span><span class="o">.</span><span class="n">func</span> <span class="o">!=</span> <span class="n">mul</span><span class="o">.</span><span class="n">Mul</span><span class="p">:</span> <span class="k">return</span> <span class="n">ex</span>
<span class="n">p</span> <span class="o">=</span> <span class="n">e1</span><span class="o">.</span><span class="n">args</span>
<span class="n">x</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">p</span><span class="p">:</span> <span class="n">x</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="k">for</span> <span class="n">e</span> <span class="ow">in</span> <span class="n">ex</span><span class="o">.</span><span class="n">args</span><span class="p">:</span>
<span class="k">if</span> <span class="n">e</span><span class="o">.</span><span class="n">func</span> <span class="o">!=</span> <span class="n">mul</span><span class="o">.</span><span class="n">Mul</span><span class="p">:</span> <span class="k">break</span>
<span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">e</span><span class="o">.</span><span class="n">args</span><span class="p">:</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span><span class="n">b</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">p</span><span class="p">):</span>
<span class="k">if</span> <span class="n">a</span> <span class="o">==</span> <span class="n">b</span><span class="p">:</span> <span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span> <span class="c1"># TODO: or plus power of expression</span>
<span class="n">l</span> <span class="o">=</span> <span class="nb">len</span> <span class="p">(</span><span class="n">ex</span><span class="o">.</span><span class="n">args</span><span class="p">)</span>
<span class="n">z</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span><span class="n">y</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="k">if</span> <span class="n">y</span> <span class="o">==</span> <span class="n">l</span><span class="p">:</span> <span class="n">z</span><span class="o">.</span><span class="n">append</span> <span class="p">(</span><span class="n">p</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
<span class="k">for</span> <span class="n">e</span> <span class="ow">in</span> <span class="n">z</span><span class="p">:</span> <span class="n">ex</span> <span class="o">=</span> <span class="n">ex</span> <span class="o">/</span> <span class="n">e</span>
<span class="n">ex</span> <span class="o">=</span> <span class="n">simplify</span> <span class="p">(</span><span class="n">ex</span><span class="p">)</span>
<span class="n">ex</span> <span class="o">=</span> <span class="n">expand</span> <span class="p">(</span><span class="n">ex</span><span class="p">)</span>
<span class="k">return</span> <span class="n">ex</span>
<span class="k">def</span> <span class="nf">lagrange</span> <span class="p">(</span><span class="n">L</span><span class="p">,</span> <span class="n">coord</span><span class="p">):</span>
<span class="n">lce</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">coord</span><span class="p">:</span>
<span class="n">ex</span> <span class="o">=</span> <span class="n">L</span><span class="o">.</span><span class="n">diff</span><span class="p">(</span><span class="n">c</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span><span class="o">.</span><span class="n">diff</span><span class="p">(</span><span class="n">t</span><span class="p">)</span> <span class="o">-</span> <span class="n">L</span><span class="o">.</span><span class="n">diff</span><span class="p">(</span><span class="n">c</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="c1"># výraz pro Lagrangeovu rovnici</span>
<span class="n">ex</span> <span class="o">=</span> <span class="n">parse</span> <span class="p">(</span><span class="n">ex</span><span class="p">)</span> <span class="c1"># vykrátit případné konstanty (lze i ručně)</span>
<span class="n">le</span> <span class="o">=</span> <span class="n">Eq</span> <span class="p">(</span><span class="n">ex</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span> <span class="c1"># a udělat z toho rovnici</span>
<span class="n">lce</span><span class="o">.</span><span class="n">append</span> <span class="p">(</span><span class="n">le</span><span class="p">)</span>
<span class="n">pprint</span><span class="p">(</span><span class="n">lce</span><span class="p">)</span>
<span class="k">return</span> <span class="n">lce</span>
<span class="k">def</span> <span class="nf">compute</span> <span class="p">(</span><span class="nb">input</span><span class="p">,</span> <span class="n">Counter</span><span class="p">):</span>
<span class="n">res</span> <span class="o">=</span> <span class="nb">input</span><span class="p">()</span>
<span class="n">coord__x</span> <span class="o">=</span> <span class="n">res</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">coord__p</span> <span class="o">=</span> <span class="n">res</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
<span class="n">L</span> <span class="o">=</span> <span class="n">res</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span>
<span class="n">pprint</span> <span class="p">(</span><span class="n">L</span><span class="p">)</span> <span class="c1"># Pro kontrolu</span>
<span class="n">coord_dp</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">coord__p</span><span class="p">:</span> <span class="n">coord_dp</span><span class="o">.</span><span class="n">append</span> <span class="p">(</span><span class="n">p</span><span class="o">.</span><span class="n">diff</span><span class="p">(</span><span class="n">t</span><span class="p">))</span>
<span class="n">coord_dx</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">coord__x</span><span class="p">:</span> <span class="n">coord_dx</span><span class="o">.</span><span class="n">append</span> <span class="p">(</span><span class="n">p</span><span class="o">.</span><span class="n">diff</span><span class="p">(</span><span class="n">t</span><span class="p">))</span>
<span class="n">lce</span> <span class="o">=</span> <span class="n">lagrange</span> <span class="p">(</span><span class="n">L</span><span class="p">,</span> <span class="nb">zip</span><span class="p">(</span><span class="n">coord__x</span><span class="p">,</span> <span class="n">coord_dx</span><span class="p">))</span>
<span class="n">E</span> <span class="o">=</span> <span class="o">-</span><span class="n">L</span>
<span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">coord_dx</span><span class="p">:</span> <span class="n">E</span> <span class="o">+=</span> <span class="n">L</span><span class="o">.</span><span class="n">diff</span> <span class="p">(</span><span class="n">p</span><span class="p">)</span> <span class="o">*</span> <span class="n">p</span>
<span class="n">E</span> <span class="o">=</span> <span class="n">simplify</span> <span class="p">(</span><span class="n">E</span><span class="p">)</span>
<span class="c1">#pprint (E) # Energie</span>
<span class="n">coord_ps</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">coord_dx</span><span class="p">:</span> <span class="n">coord_ps</span><span class="o">.</span><span class="n">append</span> <span class="p">(</span><span class="n">L</span><span class="o">.</span><span class="n">diff</span><span class="p">(</span><span class="n">p</span><span class="p">))</span>
<span class="n">coord__h</span> <span class="o">=</span> <span class="nb">zip</span> <span class="p">(</span><span class="n">coord__p</span><span class="p">,</span> <span class="n">coord_ps</span><span class="p">)</span>
<span class="n">eqs</span> <span class="o">=</span> <span class="p">[]</span> <span class="c1"># Legendreova duální transformace</span>
<span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">coord__h</span><span class="p">:</span> <span class="n">eqs</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">Eq</span><span class="p">(</span><span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">p</span><span class="p">[</span><span class="mi">1</span><span class="p">]))</span>
<span class="n">sol</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span><span class="n">p</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">eqs</span><span class="p">):</span> <span class="n">sol</span><span class="o">.</span><span class="n">append</span> <span class="p">(</span><span class="n">solve</span> <span class="p">([</span><span class="n">p</span><span class="p">],</span> <span class="p">[</span><span class="n">coord_dx</span><span class="p">[</span><span class="n">i</span><span class="p">]]))</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span><span class="n">p</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">sol</span><span class="p">):</span> <span class="n">E</span> <span class="o">=</span> <span class="n">E</span><span class="o">.</span><span class="n">subs</span> <span class="p">(</span><span class="n">coord_dx</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">p</span><span class="p">[</span><span class="n">coord_dx</span><span class="p">[</span><span class="n">i</span><span class="p">]])</span>
<span class="n">H</span> <span class="o">=</span> <span class="n">simplify</span> <span class="p">(</span><span class="n">E</span><span class="p">)</span>
<span class="n">H</span> <span class="o">=</span> <span class="n">expand</span> <span class="p">(</span><span class="n">H</span><span class="p">)</span> <span class="c1"># O něco čitelněji</span>
<span class="n">pprint</span> <span class="p">(</span><span class="n">H</span><span class="p">)</span> <span class="c1"># Hamiltonova funkce</span>
<span class="n">hce</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span><span class="n">p</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">coord__x</span><span class="p">):</span>
<span class="n">eqx</span> <span class="o">=</span> <span class="n">Eq</span> <span class="p">(</span><span class="o">+</span><span class="n">H</span><span class="o">.</span><span class="n">diff</span> <span class="p">(</span><span class="n">coord__p</span><span class="p">[</span><span class="n">i</span><span class="p">])</span> <span class="o">-</span> <span class="n">coord_dx</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="mi">0</span><span class="p">)</span>
<span class="n">eqx</span> <span class="o">=</span> <span class="n">solve</span> <span class="p">([</span><span class="n">eqx</span><span class="p">],[</span><span class="n">coord_dx</span><span class="p">[</span><span class="n">i</span><span class="p">]])</span>
<span class="n">eqx</span> <span class="o">=</span> <span class="p">[</span><span class="n">coord_dx</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">eqx</span><span class="p">[</span><span class="n">coord_dx</span><span class="p">[</span><span class="n">i</span><span class="p">]]]</span>
<span class="n">eqp</span> <span class="o">=</span> <span class="n">Eq</span> <span class="p">(</span><span class="o">-</span><span class="n">H</span><span class="o">.</span><span class="n">diff</span> <span class="p">(</span><span class="n">coord__x</span><span class="p">[</span><span class="n">i</span><span class="p">])</span> <span class="o">-</span> <span class="n">coord_dp</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="mi">0</span><span class="p">)</span>
<span class="n">eqp</span> <span class="o">=</span> <span class="n">solve</span> <span class="p">([</span><span class="n">eqp</span><span class="p">],[</span><span class="n">coord_dp</span><span class="p">[</span><span class="n">i</span><span class="p">]])</span>
<span class="n">eqp</span> <span class="o">=</span> <span class="p">[</span><span class="n">coord_dp</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">eqp</span><span class="p">[</span><span class="n">coord_dp</span><span class="p">[</span><span class="n">i</span><span class="p">]]]</span>
<span class="n">hce</span><span class="o">.</span><span class="n">append</span><span class="p">([</span><span class="n">eqx</span><span class="p">,</span> <span class="n">eqp</span><span class="p">])</span>
<span class="n">pprint</span> <span class="p">(</span><span class="n">hce</span><span class="p">)</span> <span class="c1"># Hamiltonovy kanonické rovnice</span>
<span class="k">return</span> <span class="n">output</span> <span class="p">(</span><span class="n">Counter</span><span class="p">,</span> <span class="n">res</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">L</span><span class="p">,</span> <span class="n">H</span><span class="p">,</span> <span class="n">hce</span><span class="p">,</span> <span class="n">lce</span><span class="p">)</span>
<span class="c1">######################## Uživatelská část #####################################</span>
<span class="k">def</span> <span class="nf">entry1</span> <span class="p">():</span>
<span class="c1">##### Zadání #####</span>
<span class="n">m</span><span class="p">,</span><span class="n">mu</span><span class="p">,</span><span class="n">C</span> <span class="o">=</span> <span class="n">symbols</span> <span class="p">(</span><span class="s1">&#39;m mu C&#39;</span><span class="p">)</span> <span class="c1"># konstanty</span>
<span class="n">x</span><span class="p">,</span> <span class="n">Q</span> <span class="o">=</span> <span class="n">dynamicsymbols</span> <span class="p">(</span><span class="s1">&#39;x Q&#39;</span><span class="p">)</span> <span class="c1"># proměnné (zobecněné souřadnice)</span>
<span class="n">px</span><span class="p">,</span><span class="n">pQ</span> <span class="o">=</span> <span class="n">dynamicsymbols</span> <span class="p">(</span><span class="s1">&#39;p_x p_Q&#39;</span><span class="p">)</span> <span class="c1"># symboly pro příslušné zobecněné hybnosti</span>
<span class="c1"># Lagranžián</span>
<span class="n">L</span> <span class="o">=</span> <span class="p">(</span><span class="n">m</span> <span class="o">*</span> <span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">diff</span><span class="p">(</span><span class="n">t</span><span class="p">))</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="p">(</span><span class="n">mu</span> <span class="o">*</span> <span class="n">x</span> <span class="o">*</span> <span class="p">(</span><span class="n">Q</span><span class="o">.</span><span class="n">diff</span><span class="p">(</span><span class="n">t</span><span class="p">))</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span> <span class="o">-</span> <span class="p">(</span><span class="n">Q</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">C</span><span class="p">)</span>
<span class="c1">#############################################################################</span>
<span class="k">return</span> <span class="p">[[</span><span class="n">x</span><span class="p">,</span> <span class="n">Q</span><span class="p">],</span> <span class="p">[</span><span class="n">px</span><span class="p">,</span> <span class="n">pQ</span><span class="p">],</span> <span class="n">L</span><span class="p">,</span> <span class="s1">&#39;Railgun&#39;</span><span class="p">]</span> <span class="c1"># Zobecníme výstup</span>
<span class="k">def</span> <span class="nf">entry2</span> <span class="p">():</span> <span class="c1"># Z učebnice - pohyb planety kolem Slunce, vychází</span>
<span class="n">G</span><span class="p">,</span><span class="n">m</span><span class="p">,</span><span class="n">M</span> <span class="o">=</span> <span class="n">symbols</span> <span class="p">(</span><span class="s1">&#39;G m M&#39;</span><span class="p">)</span> <span class="c1"># konstanty</span>
<span class="c1">##### Zadání #####</span>
<span class="n">r</span><span class="p">,</span> <span class="n">phi</span> <span class="o">=</span> <span class="n">dynamicsymbols</span> <span class="p">(</span><span class="s1">&#39;r phi&#39;</span><span class="p">)</span> <span class="c1"># proměnné (zobecněné souřadnice)</span>
<span class="n">pr</span><span class="p">,</span> <span class="n">pphi</span> <span class="o">=</span> <span class="n">dynamicsymbols</span> <span class="p">(</span><span class="s1">&#39;p_r p_phi&#39;</span><span class="p">)</span> <span class="c1"># symboly pro příslušné zobecněné hybnosti</span>
<span class="c1"># Lagranžián</span>
<span class="n">L</span> <span class="o">=</span> <span class="p">(</span><span class="n">m</span><span class="o">/</span><span class="mi">2</span> <span class="o">*</span> <span class="p">((</span><span class="n">r</span><span class="o">.</span><span class="n">diff</span><span class="p">(</span><span class="n">t</span><span class="p">))</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="p">(</span><span class="n">r</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">*</span><span class="p">((</span><span class="n">phi</span><span class="o">.</span><span class="n">diff</span><span class="p">(</span><span class="n">t</span><span class="p">))</span><span class="o">**</span><span class="mi">2</span><span class="p">)))</span> <span class="o">+</span> <span class="p">((</span><span class="n">G</span> <span class="o">*</span> <span class="n">m</span> <span class="o">*</span> <span class="n">M</span><span class="p">)</span> <span class="o">/</span> <span class="n">r</span><span class="p">)</span>
<span class="c1">#############################################################################</span>
<span class="k">return</span> <span class="p">[[</span><span class="n">r</span><span class="p">,</span> <span class="n">phi</span><span class="p">],</span> <span class="p">[</span><span class="n">pr</span><span class="p">,</span> <span class="n">pphi</span><span class="p">],</span> <span class="n">L</span><span class="p">,</span> <span class="s1">&#39;Pohyb planety&#39;</span><span class="p">]</span> <span class="c1"># Zobecníme výstup</span>
<span class="k">def</span> <span class="nf">entry3</span> <span class="p">():</span> <span class="c1"># Z učebnice - harmonický oscilátor, vychází</span>
<span class="c1">##### Zadání #####</span>
<span class="n">m</span><span class="p">,</span><span class="n">omega</span> <span class="o">=</span> <span class="n">symbols</span> <span class="p">(</span><span class="s1">&#39;m omega&#39;</span><span class="p">)</span> <span class="c1"># konstanty</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">dynamicsymbols</span> <span class="p">(</span><span class="s1">&#39;x&#39;</span><span class="p">)</span> <span class="c1"># proměnné (zobecněné souřadnice)</span>
<span class="n">px</span> <span class="o">=</span> <span class="n">dynamicsymbols</span> <span class="p">(</span><span class="s1">&#39;p_x&#39;</span><span class="p">)</span> <span class="c1"># symboly pro příslušné zobecněné hybnosti</span>
<span class="c1"># Lagranžián</span>
<span class="n">L</span> <span class="o">=</span> <span class="p">(</span><span class="n">m</span> <span class="o">*</span> <span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">diff</span><span class="p">(</span><span class="n">t</span><span class="p">))</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="n">m</span> <span class="o">*</span> <span class="n">omega</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="n">x</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span>
<span class="c1">#############################################################################</span>
<span class="k">return</span> <span class="p">[[</span><span class="n">x</span><span class="p">],</span> <span class="p">[</span><span class="n">px</span><span class="p">],</span> <span class="n">L</span><span class="p">,</span> <span class="s1">&#39;Harmonický oscilátor&#39;</span><span class="p">]</span> <span class="c1"># Zobecníme výstup</span>
<span class="c1">###############################################################################</span>
<span class="k">if</span> <span class="n">__name__</span> <span class="o">==</span> <span class="s2">&quot;__main__&quot;</span><span class="p">:</span>
<span class="n">computed</span> <span class="o">=</span> <span class="p">[</span><span class="n">entry1</span><span class="p">,</span> <span class="n">entry2</span><span class="p">,</span> <span class="n">entry3</span><span class="p">]</span> <span class="c1"># Co vše se bude počítat</span>
<span class="n">html</span> <span class="o">=</span> <span class="n">Element</span><span class="p">(</span><span class="s1">&#39;div&#39;</span><span class="p">)</span>
<span class="n">html</span><span class="o">.</span><span class="n">addE</span><span class="p">(</span><span class="n">Element</span><span class="p">(</span><span class="s1">&#39;h1&#39;</span><span class="p">,</span><span class="s1">&#39;Automatický výpočet Hamiltonových rovnic z lagranžiánu v pythonu pomocí sympy - vyzkoušené příklady.&#39;</span><span class="p">))</span>
<span class="n">html</span><span class="o">.</span><span class="n">addE</span><span class="p">(</span><span class="n">Element</span><span class="p">(</span><span class="s1">&#39;p&#39;</span><span class="p">,</span> <span class="n">description</span><span class="p">))</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span><span class="n">p</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">computed</span><span class="p">,</span> <span class="n">start</span> <span class="o">=</span> <span class="mi">1</span><span class="p">):</span> <span class="n">html</span><span class="o">.</span><span class="n">addE</span><span class="p">(</span><span class="n">compute</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">i</span><span class="p">))</span>
<span class="n">CreateHTML</span><span class="p">(</span><span class="s1">&#39;equations.html&#39;</span><span class="p">,</span> <span class="n">html</span><span class="p">)</span> <span class="c1"># převod do lidsky čitelné formy (mathjax latex v html)</span>
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