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.
| \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 ("manually", with matrix environment):
\mathrm{sgn}(x) = \left\{\begin{matrix}
-1 & x<0\\
1 & x>0
\end{matrix}\right.
Cases with the AMSmath cases environment (not (yet) supported by HTML writers with --math-output=MathML):
\mathrm{sgn}(x) = \begin{cases}
-1 & x<0\\
1 & x>0
\end{cases}