2 <html xmlns=
"http://www.w3.org/1999/xhtml" xml:
lang=
"en" lang=
"en">
4 <meta charset=
"utf-8" />
5 <meta name=
"generator" content=
"Docutils 0.20: https://docutils.sourceforge.io/" />
6 <meta name=
"viewport" content=
"width=device-width, initial-scale=1" />
7 <title>Mathematics
</title>
8 <link rel=
"stylesheet" href=
"../input/data/minimal.css" type=
"text/css" />
9 <link rel=
"stylesheet" href=
"../input/data/plain.css" type=
"text/css" />
12 <main id=
"mathematics">
13 <h1 class=
"title">Mathematics
</h1>
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">
21 <mo>⁡</mo>
22 <mo stretchy=
"false">(
</mo>
28 <mo stretchy=
"false">)
</mo>
29 </math> and
<math xmlns=
"http://www.w3.org/1998/Math/MathML">
43 </math>, as well as displayed math via the
44 <cite>math
</cite> directive:
</p>
46 <math xmlns=
"http://www.w3.org/1998/Math/MathML" display=
"block">
48 <mo stretchy=
"false">(
</mo>
50 <mo stretchy=
"false">)
</mo>
58 <mo>⁡</mo>
77 <p>Content may start on the first line of the directive, e.g.
</p>
79 <math xmlns=
"http://www.w3.org/1998/Math/MathML" display=
"block">
83 <mtext>number of apples
</mtext>
88 <p>Equations can be labeled with a reference name using the
<span class=
"docutils literal">:name:
</span> option.
89 See
<a class=
"reference internal" href=
"#eq-m">eq:M
</a> and
<a class=
"reference internal" href=
"#eq-schrodinger">eq:schrödinger
</a> below.
</p>
90 <p>The determinant of the matrix
</p>
92 <math xmlns=
"http://www.w3.org/1998/Math/MathML" display=
"block">
93 <mi mathvariant=
"bold">M
</mi>
119 <p>is
<math xmlns=
"http://www.w3.org/1998/Math/MathML">
120 <mo stretchy=
"false">|
</mo>
121 <mi mathvariant=
"bold">M
</mi>
122 <mo stretchy=
"false">|
</mo>
130 <p>More than one display math block can be put in one math directive.
131 For example, the following sum and integral with limits:
</p>
133 <math xmlns=
"http://www.w3.org/1998/Math/MathML" display=
"block">
157 <math xmlns=
"http://www.w3.org/1998/Math/MathML" display=
"block">
159 <mo movablelimits=
"true">∑
</mo>
172 <mo stretchy=
"false">(
</mo>
176 <mo stretchy=
"false">)
</mo>
182 <p>LaTeX-supported Unicode math symbols can be used in math roles and
184 <p>The Schrödinger equation
</p>
185 <div id=
"eq-schrodinger">
186 <math xmlns=
"http://www.w3.org/1998/Math/MathML" display=
"block">
196 <mi class=
"capital-greek">Ψ
</mi>
200 <mo stretchy=
"false">ˆ
</mo>
202 <mi class=
"capital-greek">Ψ
</mi>
206 <p>with the
<em>wave function
</em> <math xmlns=
"http://www.w3.org/1998/Math/MathML">
207 <mi class=
"capital-greek">Ψ
</mi>
208 </math>, describes how the quantum state of a
209 physical system changes in time.
</p>
211 <dt>Math-Accents:
</dt>
212 <dd><table class=
"borderless" style=
"width: 100%;">
214 <tr><td><p><math xmlns=
"http://www.w3.org/1998/Math/MathML">
217 <mo stretchy=
"false">´
</mo>
219 </math> <span class=
"docutils literal">\acute{a}
</span></p></td>
220 <td><p><math xmlns=
"http://www.w3.org/1998/Math/MathML">
223 <mo stretchy=
"false">˙
</mo>
225 </math> <span class=
"docutils literal">\dot{t}
</span></p></td>
226 <td><p><math xmlns=
"http://www.w3.org/1998/Math/MathML">
229 <mo stretchy=
"false">ˆ
</mo>
231 </math> <span class=
"docutils literal"><span class=
"pre">\hat{\gamma}
</span></span></p></td>
233 <tr><td><p><math xmlns=
"http://www.w3.org/1998/Math/MathML">
236 <mo stretchy=
"false">`
</mo>
238 </math> <span class=
"docutils literal">\grave{a}
</span></p></td>
239 <td><p><math xmlns=
"http://www.w3.org/1998/Math/MathML">
242 <mo stretchy=
"false">¨
</mo>
244 </math> <span class=
"docutils literal">\ddot{t}
</span></p></td>
245 <td><p><math xmlns=
"http://www.w3.org/1998/Math/MathML">
248 <mo stretchy=
"false">˜
</mo>
250 </math> <span class=
"docutils literal"><span class=
"pre">\tilde{\alpha}
</span></span></p></td>
252 <tr><td><p><math xmlns=
"http://www.w3.org/1998/Math/MathML">
255 <mo stretchy=
"false">˘
</mo>
257 </math> <span class=
"docutils literal">\breve{x}
</span></p></td>
258 <td><p><math xmlns=
"http://www.w3.org/1998/Math/MathML">
261 <mo stretchy=
"false">⋯
</mo>
263 </math> <span class=
"docutils literal">\dddot{t}
</span></p></td>
264 <td><p><math xmlns=
"http://www.w3.org/1998/Math/MathML">
267 <mo stretchy=
"false" accent=
"false">→
</mo>
269 </math> <span class=
"docutils literal"><span class=
"pre">\vec{\imath}
</span></span></p></td>
271 <tr><td><p><math xmlns=
"http://www.w3.org/1998/Math/MathML">
274 <mo stretchy=
"false">ˇ
</mo>
276 </math> <span class=
"docutils literal">\check{a}
</span></p></td>
277 <td><p><math xmlns=
"http://www.w3.org/1998/Math/MathML">
280 <mo stretchy=
"false">ˉ
</mo>
282 </math> <span class=
"docutils literal">\bar{a}
</span></p></td>
283 <td><p><math xmlns=
"http://www.w3.org/1998/Math/MathML">
286 <mo stretchy=
"false" accent=
"false">→
</mo>
288 </math> <span class=
"docutils literal">\vec{R}
</span></p></td>
296 <p>Modulation Transfer Function:
</p>
298 <math xmlns=
"http://www.w3.org/1998/Math/MathML" display=
"block">
305 <mi mathvariant=
"script">F
</mi>
308 <mo stretchy=
"false">(
</mo>
310 <mo stretchy=
"false">)
</mo>
314 <mi mathvariant=
"script">F
</mi>
317 <mo stretchy=
"false">(
</mo>
319 <mo stretchy=
"false">)
</mo>
322 <mo stretchy=
"false">|
</mo>
337 <mi mathvariant=
"normal">abs
</mi>
351 <mo stretchy=
"false">(
</mo>
353 <mo stretchy=
"false">)
</mo>
355 <mi mathvariant=
"normal">e
</mi>
357 <mi mathvariant=
"normal">i
</mi>
365 <mi mathvariant=
"normal">d
</mi>
378 <mo stretchy=
"false">(
</mo>
380 <mo stretchy=
"false">)
</mo>
381 <mi mathvariant=
"normal">d
</mi>
390 <p>Math split over two lines: If a double backslash is detected outside a
391 <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>
392 <span class=
"docutils literal">align
</span> environment:
</p>
394 <math xmlns=
"http://www.w3.org/1998/Math/MathML" display=
"block">
395 <mtable class=
"align" displaystyle=
"true" columnalign=
"right left" columnspacing=
"0">
400 <mi mathvariant=
"normal">out
</mi>
402 <mo stretchy=
"false">(
</mo>
404 <mo stretchy=
"false">)
</mo>
410 <mi mathvariant=
"normal">in
</mi>
412 <mo stretchy=
"false">(
</mo>
415 <mo stretchy=
"false">)
</mo>
421 <mo stretchy=
"false">(
</mo>
426 <mo stretchy=
"false">)
</mo>
437 <mi mathvariant=
"normal">in
</mi>
439 <mo stretchy=
"false">(
</mo>
442 <mo stretchy=
"false">)
</mo>
447 <mo stretchy=
"false">(
</mo>
452 <mo stretchy=
"false">)
</mo>
453 <mi mathvariant=
"normal">d
</mi>
461 <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:
</p>
463 <math xmlns=
"http://www.w3.org/1998/Math/MathML" display=
"block">
464 <mi mathvariant=
"normal">sgn
</mi>
465 <mo stretchy=
"false">(
</mo>
467 <mo stretchy=
"false">)
</mo>
470 <mo rspace=
"0.17em">{
</mo>
471 <mtable columnalign=
"left">