# Mathematics

Docutils supports inline math with the prefix or postfix `:math:` role specificator, n!+sin(x n 2) and A c= π 4 d 2, as well as displayed math via the math directive:

f(ϵ)= 1 1+exp ε k B T

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

N= 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= a b c d

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:

∫0 1 x n d x= 1 n+1
∑ n=1 m n= m(m+1) 2

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

The Schrödinger equation

i ℏ ∂ ∂t Ψ= H^Ψ,

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

Math-Accents:

  a´ `\acute{a}` | t˙ `\dot{t}` | γ^ `\hat{\gamma}`
  a` `\grave{a}` | t¨ `\ddot{t}` | α˜ `\tilde{\alpha}`
  x˘ `\breve{x}` | t⃛ `\dddot{t}` | ı⃗ `\vec{\imath}`
  a ˇ `\check{a}` | a¯ `\bar{a}` | R⃗ `\vec{R}`

Modulation Transfer Function:

MTF= ℱ{s(x)} ℱ{s(x)}| ω x=0=abs ∫ -∞ ∞s(x)e i ω x x d x ∫ -∞ ∞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:

s out(x) =s in(x')*s δ(x-x') =∫s in(x')s δ(x-x')d x'

Cases ("manually", with `matrix` environment):

sgn(x)= -1 x<0 1 x>0

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}