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Mathematics
-----------
.. math:: N = \idotsint
Docutils supports inline math with the prefix or postfix ``:math:``
role specificator, :math:`n! + \sin(x_n^2)` and `A_\text{c} =
\frac{\pi}{4} d^2`:math:, as well as displayed math via the
`math` directive:
.. math::
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.
.. math:: 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
.. math:: :name: eq:M
\mathbf{M} = \left(\begin{matrix}a&b\\c&d\end{matrix}\right)
is :math:`|\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:
.. math::
\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
.. math:: :name: eq:schrödinger
i\hbar \frac{∂}{∂t}Ψ = \hat{H}Ψ,
with the *wave function* :math:`Ψ`, describes how the quantum state of a
physical system changes in time.
Math-Accents:
.. list-table::
:class: borderless
:width: 100%
* - :math:`\acute{a}` ``\acute{a}``
- :math:`\dot{t}` ``\dot{t}``
- :math:`\hat{\gamma}` ``\hat{\gamma}``
* - :math:`\grave{a}` ``\grave{a}``
- :math:`\ddot{t}` ``\ddot{t}``
- :math:`\tilde{\alpha}` ``\tilde{\alpha}``
* - :math:`\breve{x}` ``\breve{x}``
- :math:`\dddot{t}` ``\dddot{t}``
- :math:`\vec{\imath}` ``\vec{\imath}``
* - :math:`\check{a}` ``\check{a}``
- :math:`\bar{a}` ``\bar{a}``
- :math:`\vec{R}` ``\vec{R}``
..
\widetilde{xxx}
\widehat{xxx}
Modulation Transfer Function:
.. math::
\text{MTF} = \left|\frac{\mathcal{F}\{s(x)\}}
{\mathcal{F}\{ s(x)\} |_{ω_{x}=0}}\right|
= \mathrm{abs}\left(\frac
{∫_{-∞}^{∞}s(x) \mathrm{e}^{\mathrm{i}ω_{x}x}\mathrm{d}{x}}
{∫_{-∞}^{∞}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:
.. math::
s_{\mathrm{out}}(x) & = s_{\mathrm{in}}(x') * s_δ(x-x') \\
& = ∫ s_{\mathrm{in}}(x')s_δ(x-x')\mathrm{d}x'
Cases with the AMSmath_ ``cases`` environment:
.. math::
\mathrm{sgn}(x) = \begin{cases}
-1 & x<0\\
\phantom{-} 1 & x>0
\end{cases}
.. _AMSmath: ftp://ftp.ams.org/ams/doc/amsmath/short-math-guide.pdf
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