# Mathematics

Docutils supports inline math with the prefix or postfix `:math:` role specificator, `n! + \sin(x_n^2)` and `A_\text{c} = \frac{\pi}{4} d^2`, as well as displayed math via the math directive:

    f(\epsilon) = \frac{1}{1 + \exp\left(\frac{\varepsilon}{k_\text{B}T}\right)}

Content may start on the first line of the directive, e.g.

    N = \frac{\text{number of apples}}{7}

Equations can be labeled with a reference name using the `:name:` option. See eq:M and eq:schrödinger below.

The determinant of the matrix

    \mathbf{M} = \left(\begin{matrix}a&b\\c&d\end{matrix}\right)

is `|\mathbf{M}| = ad - bc`.

More than one display math block can be put in one math directive. For example, the following sum and integral with limits:

    \int_0^1 x^n dx = \frac{1}{n + 1}

    \sum_{n=1}^m n = \frac{m(m+1)}{2}

LaTeX-supported Unicode math symbols can be used in math roles and directives:

The Schrödinger equation

    i\hbar \frac{\partial }{\partial t}\Psi  = \hat{H}\Psi ,

with the wave function `\Psi` , describes how the quantum state of a physical system changes in time.

Math-Accents:

  `\acute{a}` `\acute{a}` | `\dot{t}` `\dot{t}` | `\hat{\gamma}` `\hat{\gamma}`
  `\grave{a}` `\grave{a}` | `\ddot{t}` `\ddot{t}` | `\tilde{\alpha}` `\tilde{\alpha}`
  `\breve{x}` `\breve{x}` | `\dddot{t}` `\dddot{t}` | `\vec{\imath}` `\vec{\imath}`
  `\check{a}` `\check{a}` | `\bar{a}` `\bar{a}` | `\vec{R}` `\vec{R}`

Modulation Transfer Function:

    \text{MTF} = \left|\frac{\mathcal{F}\{s(x)\}}
                            {\mathcal{F}\{ s(x)\} |_{\omega _{x}=0}}\right|
               = \mathrm{abs}\left(\frac
                     {\int _{-\infty }^{\infty }s(x) \mathrm{e}^{\mathrm{i}\omega _{x}x}\mathrm{d}{x}}
                     {\int _{-\infty }^{\infty }s(x)\mathrm{d}{x}}
                 \right).

Math split over two lines: If a double backslash is detected outside a `\begin{...} \end{...}` pair, the math code is wrapped in an AMSmath `align` environment:

    s_{\mathrm{out}}(x) & = s_{\mathrm{in}}(x') * s_\delta (x-x') \\
                        & = \int  s_{\mathrm{in}}(x')s_\delta (x-x')\mathrm{d}x'

Cases with the AMSmath `cases` environment:

    \mathrm{sgn}(x) = \begin{cases}
                                 -1 & x<0\\
                        \phantom{-} 1 & x>0
                      \end{cases}