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7 <title>Mathematics
</title>
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12 <div class=
"document" id=
"mathematics">
13 <h1 class=
"title">Mathematics
</h1>
15 <p>Docutils supports inline math with the prefix or postfix
<tt class=
"docutils literal">:math:
</tt>
16 role specificator,
<span class=
"math">\(n! + \sin(x_n^
2)\)
</span> and
<span class=
"math">\(A_\text{c} =
17 \frac{\pi}{
4} d^
2\)
</span>, as well as displayed math via the
18 <cite>math
</cite> directive:
</p>
21 f(\epsilon) = \frac{
1}{
1 + \exp\left(\frac{\varepsilon}{k_\text{B}T}\right)}
24 <p>Content may start on the first line of the directive, e.g.
</p>
27 N = \frac{\text{number of apples}}{
7}
30 <p>Equations can be labeled with a reference name using the
<tt class=
"docutils literal">:name:
</tt> option.
31 See
<a class=
"reference internal" href=
"#eq-m">eq:M
</a> and
<a class=
"reference internal" href=
"#eq-schrodinger">eq:schrödinger
</a> below.
</p>
32 <p>The determinant of the matrix
</p>
33 <div class=
"math" id=
"eq-m">
35 \mathbf{M} = \left(\begin{matrix}a
&b\\c
&d\end{matrix}\right)
38 <p>is
<span class=
"math">\(|\mathbf{M}| = ad - bc\)
</span>.
</p>
39 <p>More than one display math block can be put in one math directive.
40 For example, the following sum and integral with limits:
</p>
43 \int_0^
1 x^n dx = \frac{
1}{n +
1}
48 \sum_{n=
1}^m n = \frac{m(m+
1)}{
2}
51 <p>LaTeX-supported Unicode math symbols can be used in math roles and
53 <p>The Schrödinger equation
</p>
54 <div class=
"math" id=
"eq-schrodinger">
56 i\hbar \frac{\partial }{\partial t}\Psi = \hat{H}\Psi ,
59 <p>with the
<em>wave function
</em> <span class=
"math">\(\Psi \)
</span>, describes how the quantum state of a
60 physical system changes in time.
</p>
62 <dt>Math-Accents:
</dt>
63 <dd><table border=
"1" class=
"colwidths-given borderless first last docutils">
70 <tr><td><span class=
"math">\(\acute{a}\)
</span> <tt class=
"docutils literal">\acute{a}
</tt></td>
71 <td><span class=
"math">\(\dot{t}\)
</span> <tt class=
"docutils literal">\dot{t}
</tt></td>
72 <td><span class=
"math">\(\hat{\gamma}\)
</span> <tt class=
"docutils literal"><span class=
"pre">\hat{\gamma}
</span></tt></td>
74 <tr><td><span class=
"math">\(\grave{a}\)
</span> <tt class=
"docutils literal">\grave{a}
</tt></td>
75 <td><span class=
"math">\(\ddot{t}\)
</span> <tt class=
"docutils literal">\ddot{t}
</tt></td>
76 <td><span class=
"math">\(\tilde{\alpha}\)
</span> <tt class=
"docutils literal"><span class=
"pre">\tilde{\alpha}
</span></tt></td>
78 <tr><td><span class=
"math">\(\breve{x}\)
</span> <tt class=
"docutils literal">\breve{x}
</tt></td>
79 <td><span class=
"math">\(\dddot{t}\)
</span> <tt class=
"docutils literal">\dddot{t}
</tt></td>
80 <td><span class=
"math">\(\vec{\imath}\)
</span> <tt class=
"docutils literal"><span class=
"pre">\vec{\imath}
</span></tt></td>
82 <tr><td><span class=
"math">\(\check{a}\)
</span> <tt class=
"docutils literal">\check{a}
</tt></td>
83 <td><span class=
"math">\(\bar{a}\)
</span> <tt class=
"docutils literal">\bar{a}
</tt></td>
84 <td><span class=
"math">\(\vec{R}\)
</span> <tt class=
"docutils literal">\vec{R}
</tt></td>
92 <p>Modulation Transfer Function:
</p>
95 \text{MTF} = \left|\frac{\mathcal{F}\{s(x)\}}
96 {\mathcal{F}\{ s(x)\} |_{\omega _{x}=
0}}\right|
97 = \mathrm{abs}\left(\frac
98 {\int _{-\infty }^{\infty }s(x) \mathrm{e}^{\mathrm{i}\omega _{x}x}\mathrm{d}{x}}
99 {\int _{-\infty }^{\infty }s(x)\mathrm{d}{x}}
103 <p>Math split over two lines: If a double backslash is detected outside a
104 <tt class=
"docutils literal"><span class=
"pre">\begin{...}
</span> <span class=
"pre">\end{...}
</span></tt> 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>
105 <tt class=
"docutils literal">align
</tt> environment:
</p>
108 s_{\mathrm{out}}(x)
& = s_{\mathrm{in}}(x') * s_\delta (x-x') \\
109 & = \int s_{\mathrm{in}}(x')s_\delta (x-x')\mathrm{d}x'
112 <p>Cases (
"manually
", with
<tt class=
"docutils literal">matrix
</tt> environment):
</p>
115 \mathrm{sgn}(x) = \left\{\begin{matrix}
121 <p>Cases with the
<a class=
"reference external" href=
"ftp://ftp.ams.org/ams/doc/amsmath/short-math-guide.pdf">AMSmath
</a> <tt class=
"docutils literal">cases
</tt> environment (not (yet) supported by
122 HTML writers with
<tt class=
"docutils literal"><span class=
"pre">--math-output=MathML
</span></tt>):
</p>
125 \mathrm{sgn}(x) = \begin{cases}