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:

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

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

N = \frac{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

𝐌 = (\begin{matrix} a & b \\ c & d \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:

\int_{0}^{1} x^{n} d x = \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 ℏ \frac{\partial}{\partial t} Ψ = \hat{H} Ψ,

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}	$\overset{ˉ}{a}$ \bar{a}	$\vec{R}$ \vec{R}

Modulation Transfer Function:

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}) .

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 with the AMSmath cases environment:

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