Mathematics

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

\begin{matrix} f (ϵ) = \frac{1}{1 + exp (\frac{ε}{k_{B} T})} \end{matrix}

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

\begin{matrix} N = \frac{number of apples}{7} \end{matrix}

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

The determinant of the matrix

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

is $| M | = a d - b c$ .

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

\begin{matrix} \int_{0}^{1} x^{n} d x = \frac{1}{n + 1} \end{matrix}

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

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

The Schrödinger equation

\begin{matrix} i ℏ \frac{\partial}{\partial t} Ψ = \hat{H} Ψ, \end{matrix}

with the wave function $Ψ$ , describes how the quantum state of a physical system changes in time.

Math-Accents:

$\overset{´}{a}$ `\acute{a}`	$\dot{t}$ `\dot{t}`	$\hat{γ}$ `\hat{\gamma}`
$\overset{`}{a}$ `\grave{a}`	$\ddot{t}$ `\ddot{t}`	$\tilde{α}$ `\tilde{\alpha}`
$\overset{˘}{x}$ `\breve{x}`	$\overset{⃛}{t}$ `\dddot{t}`	$\vec{ı}$ `\vec{\imath}`
$\overset{ˇ}{a}$ `\check{a}`	$\bar{a}$ `\bar{a}`	$\vec{R}$ `\vec{R}`

Modulation Transfer Function:

\begin{matrix} MTF = |\frac{ℱ {s (x)}}{ℱ {s (x)} |_{ω_{x} = 0}}| = abs (\frac{\int_{- \infty}^{\infty} s (x) e^{i ω_{x} x} d x}{\int_{- \infty}^{\infty} s (x) d x}) . \end{matrix}

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:

\begin{matrix} s_{out} (x) & = s_{in} (x') * s_{δ} (x - x') \\ = \int s_{in} (x') s_{δ} (x - x') d x' \end{matrix}

Cases ("manually", with matrix environment):

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

Cases with the AMSmath cases environment (not (yet) supported by HTML writers with --math-output=MathML):

System Message: ERROR/3 (functional/input/data/math.txt, line 107)

Environment not supported! Supported environment: "matrix".

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