sandbox/gitpull/web_stylesheet_and_menu/test/functional/expected/math_output_mathml.xhtml

   1 <?xml version="1.0" encoding="utf-8" ?>
   2 <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN" "http://www.w3.org/Math/DTD/mathml2/xhtml-math11-f.dtd">
   3 <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en">
   4 <head>
   5 <meta http-equiv="Content-Type" content="application/xhtml+xml; charset=utf-8" />
   6 <meta name="generator" content="Docutils 0.13: http://docutils.sourceforge.net/" />
   7 <title>Mathematics</title>
   8 <link rel="stylesheet" href="../input/data/html-base.css" type="text/css" />
   9 <link rel="stylesheet" href="../input/data/xhtml11.css" type="text/css" />
  10 </head>
  11 <body>
  12 <div class="document" id="mathematics">
  13 <h1 class="title">Mathematics</h1>
  14
  15 <p>Docutils supports inline math with the prefix or postfix <span class="docutils literal">:math:</span>
  16 role specificator, <math xmlns="http://www.w3.org/1998/Math/MathML">
  17 <mrow><mi>n</mi><mo>!</mo><mo>+</mo><mo>sin</mo><mo>(</mo><msubsup><mi>x</mi><mi>n</mi><mn>2</mn></msubsup><mo>)</mo></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML">
  18 <mrow><msub><mi>A</mi><mtext>c</mtext></msub><mo>=</mo><mfrac>
  19 <mrow><mi>π</mi></mrow>
  20 <mrow><mn>4</mn></mrow></mfrac><msup><mi>d</mi><mn>2</mn></msup></mrow></math>, as well as displayed math via the
  21 <cite>math</cite> directive:</p>
  22 <div>
  23 <math xmlns="http://www.w3.org/1998/Math/MathML" mode="display">
  24 <mtable>
  25 <mtr>
  26 <mtd><mi>f</mi><mo>(</mo><mi>ϵ</mi><mo>)</mo><mo>=</mo><mfrac>
  27 <mrow><mn>1</mn></mrow>
  28 <mrow><mn>1</mn><mo>+</mo><mo>exp</mo><mfenced open="(" close=")">
  29 <mrow><mfrac>
  30 <mrow><mi>ε</mi></mrow>
  31 <mrow><msub><mi>k</mi><mtext>B</mtext></msub><mi>T</mi></mrow></mfrac></mrow></mfenced></mrow></mfrac></mtd></mtr></mtable></math>
  32 </div>
  33 <p>Content may start on the first line of the directive, e.g.</p>
  34 <div>
  35 <math xmlns="http://www.w3.org/1998/Math/MathML" mode="display">
  36 <mtable>
  37 <mtr>
  38 <mtd><mi>N</mi><mo>=</mo><mfrac>
  39 <mrow><mtext>number of apples</mtext></mrow>
  40 <mrow><mn>7</mn></mrow></mfrac></mtd></mtr></mtable></math>
  41 </div>
  42 <p>Equations can be labeled with a reference name using the <span class="docutils literal">:name:</span> option.
  43 See <a class="reference internal" href="#eq-m">eq:M</a> and <a class="reference internal" href="#eq-schrodinger">eq:schrödinger</a> below.</p>
  44 <p>The determinant of the matrix</p>
  45 <div id="eq-m">
  46 <math xmlns="http://www.w3.org/1998/Math/MathML" mode="display">
  47 <mtable>
  48 <mtr>
  49 <mtd><mstyle fontweight="bold">
  50 <mrow><mi>M</mi></mrow></mstyle><mo>=</mo><mfenced open="(" close=")">
  51 <mrow>
  52 <mtable>
  53 <mtr>
  54 <mtd><mi>a</mi></mtd>
  55 <mtd><mi>b</mi></mtd></mtr>
  56 <mtr>
  57 <mtd><mi>c</mi></mtd>
  58 <mtd><mi>d</mi></mtd></mtr></mtable></mrow></mfenced></mtd></mtr></mtable></math>
  59 </div>
  60 <p>is <math xmlns="http://www.w3.org/1998/Math/MathML">
  61 <mrow><mo>|</mo><mstyle fontweight="bold">
  62 <mrow><mi>M</mi></mrow></mstyle><mo>|</mo><mo>=</mo><mi>a</mi><mi>d</mi><mo>-</mo><mi>b</mi><mi>c</mi></mrow></math>.</p>
  63 <p>More than one display math block can be put in one math directive.
  64 For example, the following sum and integral with limits:</p>
  65 <div>
  66 <math xmlns="http://www.w3.org/1998/Math/MathML" mode="display">
  67 <mtable>
  68 <mtr>
  69 <mtd><munderover><mo>∫</mo><mn>0</mn><mn>1</mn></munderover><msup><mi>x</mi><mi>n</mi></msup><mi>d</mi><mi>x</mi><mo>=</mo><mfrac>
  70 <mrow><mn>1</mn></mrow>
  71 <mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfrac></mtd></mtr></mtable></math>
  72 </div>
  73 <div>
  74 <math xmlns="http://www.w3.org/1998/Math/MathML" mode="display">
  75 <mtable>
  76 <mtr>
  77 <mtd><munderover><mo>∑</mo>
  78 <mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mi>m</mi></munderover><mi>n</mi><mo>=</mo><mfrac>
  79 <mrow><mi>m</mi><mo>(</mo><mi>m</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow>
  80 <mrow><mn>2</mn></mrow></mfrac></mtd></mtr></mtable></math>
  81 </div>
  82 <p>LaTeX-supported Unicode math symbols can be used in math roles and
  83 directives:</p>
  84 <p>The Schrödinger equation</p>
  85 <div id="eq-schrodinger">
  86 <math xmlns="http://www.w3.org/1998/Math/MathML" mode="display">
  87 <mtable>
  88 <mtr>
  89 <mtd><mi>i</mi><mi>ℏ</mi><mfrac>
  90 <mrow><mo>∂</mo></mrow>
  91 <mrow><mo>∂</mo><mi>t</mi></mrow></mfrac><mo>Ψ</mo><mo>=</mo><mover>
  92 <mrow><mi>H</mi></mrow><mo>^</mo></mover><mo>Ψ</mo><mo>,</mo></mtd></mtr></mtable></math>
  93 </div>
  94 <p>with the <em>wave function</em> <math xmlns="http://www.w3.org/1998/Math/MathML">
  95 <mrow><mo>Ψ</mo></mrow></math>, describes how the quantum state of a
  96 physical system changes in time.</p>
  97 <dl>
  98 <dt>Math-Accents:</dt>
  99 <dd><table class="borderless">
 100 <colgroup>
 101 <col style="width: 33%" />
 102 <col style="width: 33%" />
 103 <col style="width: 33%" />
 104 </colgroup>
 105 <tbody>
 106 <tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
 107 <mrow><mover>
 108 <mrow><mi>a</mi></mrow><mo>´</mo></mover></mrow></math>      <span class="docutils literal">\acute{a}</span></p></td>
 109 <td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
 110 <mrow><mover>
 111 <mrow><mi>t</mi></mrow><mo>˙</mo></mover></mrow></math>        <span class="docutils literal">\dot{t}</span></p></td>
 112 <td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
 113 <mrow><mover>
 114 <mrow><mi>γ</mi></mrow><mo>^</mo></mover></mrow></math>   <span class="docutils literal"><span class="pre">\hat{\gamma}</span></span></p></td>
 115 </tr>
 116 <tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
 117 <mrow><mover>
 118 <mrow><mi>a</mi></mrow><mo>`</mo></mover></mrow></math>      <span class="docutils literal">\grave{a}</span></p></td>
 119 <td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
 120 <mrow><mover>
 121 <mrow><mi>t</mi></mrow><mo>¨</mo></mover></mrow></math>       <span class="docutils literal">\ddot{t}</span></p></td>
 122 <td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
 123 <mrow><mover>
 124 <mrow><mi>α</mi></mrow><mo>˜</mo></mover></mrow></math> <span class="docutils literal"><span class="pre">\tilde{\alpha}</span></span></p></td>
 125 </tr>
 126 <tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
 127 <mrow><mover>
 128 <mrow><mi>x</mi></mrow><mo>˘</mo></mover></mrow></math>      <span class="docutils literal">\breve{x}</span></p></td>
 129 <td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
 130 <mrow><mover>
 131 <mrow><mi>t</mi></mrow><mo>⃛</mo></mover></mrow></math>      <span class="docutils literal">\dddot{t}</span></p></td>
 132 <td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
 133 <mrow><mover>
 134 <mrow><mi>ı</mi></mrow><mo>⃗</mo></mover></mrow></math>   <span class="docutils literal"><span class="pre">\vec{\imath}</span></span></p></td>
 135 </tr>
 136 <tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
 137 <mrow><mover>
 138 <mrow><mi>a</mi></mrow><mo>ˇ</mo></mover></mrow></math>      <span class="docutils literal">\check{a}</span></p></td>
 139 <td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
 140 <mrow><mover>
 141 <mrow><mi>a</mi></mrow><mo>¯</mo></mover></mrow></math>        <span class="docutils literal">\bar{a}</span></p></td>
 142 <td><p><math xmlns="http://www.w3.org/1998/Math/MathML">
 143 <mrow><mover>
 144 <mrow><mi>R</mi></mrow><mo>⃗</mo></mover></mrow></math>        <span class="docutils literal">\vec{R}</span></p></td>
 145 </tr>
 146 </tbody>
 147 </table>
 148 </dd>
 149 </dl>
 150 <!-- \widetilde{xxx}
 151 \widehat{xxx} -->
 152 <p>Modulation Transfer Function:</p>
 153 <div>
 154 <math xmlns="http://www.w3.org/1998/Math/MathML" mode="display">
 155 <mtable>
 156 <mtr>
 157 <mtd><mtext>MTF</mtext><mo>=</mo><mfenced open="|" close="|">
 158 <mrow><mfrac>
 159 <mrow><mi>ℱ</mi><mo>{</mo><mi>s</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>}</mo></mrow>
 160 <mrow><mi>ℱ</mi><mo>{</mo><mi>s</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>}</mo><msub><mo>|</mo>
 161 <mrow><msub><mi>ω</mi>
 162 <mrow><mi>x</mi></mrow></msub><mo>=</mo><mn>0</mn></mrow></msub></mrow></mfrac></mrow></mfenced><mo>=</mo><mtext>abs</mtext><mfenced open="(" close=")">
 163 <mrow><mfrac>
 164 <mrow><munderover><mo>∫</mo>
 165 <mrow><mo>-</mo><mo>∞</mo></mrow>
 166 <mrow><mo>∞</mo></mrow></munderover><mi>s</mi><mo>(</mo><mi>x</mi><mo>)</mo><msup><mtext>e</mtext>
 167 <mrow><mtext>i</mtext><msub><mi>ω</mi>
 168 <mrow><mi>x</mi></mrow></msub><mi>x</mi></mrow></msup><mtext>d</mtext>
 169 <mrow><mi>x</mi></mrow></mrow>
 170 <mrow><munderover><mo>∫</mo>
 171 <mrow><mo>-</mo><mo>∞</mo></mrow>
 172 <mrow><mo>∞</mo></mrow></munderover><mi>s</mi><mo>(</mo><mi>x</mi><mo>)</mo><mtext>d</mtext>
 173 <mrow><mi>x</mi></mrow></mrow></mfrac></mrow></mfenced><mo>.</mo></mtd></mtr></mtable></math>
 174 </div>
 175 <p>Math split over two lines: If a double backslash is detected outside a
 176 <span class="docutils literal"><span class="pre">\begin{...}</span> <span class="pre">\end{...}</span></span> pair, the math code is wrapped in an <a class="reference external" href="ftp://ftp.ams.org/ams/doc/amsmath/short-math-guide.pdf">AMSmath</a>
 177 <span class="docutils literal">align</span> environment:</p>
 178 <div>
 179 <math xmlns="http://www.w3.org/1998/Math/MathML" mode="display">
 180 <mtable>
 181 <mtr>
 182 <mtd><msub><mi>s</mi>
 183 <mrow><mtext>out</mtext></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo></mtd>
 184 <mtd><mo>=</mo><msub><mi>s</mi>
 185 <mrow><mtext>in</mtext></mrow></msub><mo>(</mo><mi>x</mi><mo>'</mo><mo>)</mo><mo>*</mo><msub><mi>s</mi><mi>δ</mi></msub><mo>(</mo><mi>x</mi><mo>-</mo><mi>x</mi><mo>'</mo><mo>)</mo></mtd></mtr>
 186 <mtr>
 187 <mtd></mtd>
 188 <mtd><mo>=</mo><mo>∫</mo><msub><mi>s</mi>
 189 <mrow><mtext>in</mtext></mrow></msub><mo>(</mo><mi>x</mi><mo>'</mo><mo>)</mo><msub><mi>s</mi><mi>δ</mi></msub><mo>(</mo><mi>x</mi><mo>-</mo><mi>x</mi><mo>'</mo><mo>)</mo><mtext>d</mtext><mi>x</mi><mo>'</mo></mtd></mtr></mtable></math>
 190 </div>
 191 <p>Cases (&quot;manually&quot;, with <span class="docutils literal">matrix</span> environment):</p>
 192 <div>
 193 <math xmlns="http://www.w3.org/1998/Math/MathML" mode="display">
 194 <mtable>
 195 <mtr>
 196 <mtd><mtext>sgn</mtext><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mfenced open="{" close="">
 197 <mrow>
 198 <mtable>
 199 <mtr>
 200 <mtd><mo>-</mo><mn>1</mn></mtd>
 201 <mtd><mi>x</mi><mo>&lt;</mo><mn>0</mn></mtd></mtr>
 202 <mtr>
 203 <mtd><mn>1</mn></mtd>
 204 <mtd><mi>x</mi><mo>&gt;</mo><mn>0</mn></mtd></mtr></mtable></mrow></mfenced></mtd></mtr></mtable></math>
 205 </div>
 206 <p>Cases with the <a class="reference external" href="ftp://ftp.ams.org/ams/doc/amsmath/short-math-guide.pdf">AMSmath</a> <span class="docutils literal">cases</span> environment (not (yet) supported by
 207 HTML writers with <span class="docutils literal"><span class="pre">--math-output=MathML</span></span>):</p>
 208 <div class="system-message">
 209 <p class="system-message-title">System Message: ERROR/3 (<span class="docutils literal">functional/input/data/math.txt</span>, line 107)</p>
 210 <p>
 211 Environment not supported! Supported environment: "matrix".</p>
 212 <pre class="literal-block">
 213 \mathrm{sgn}(x) = \begin{cases}
 214                     -1 &amp; x&lt;0\\
 215                      1 &amp; x&gt;0
 216                   \end{cases}
 217 </pre>
 218 </div>
 219 </div>
 220 </body>
 221 </html>