# 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 108)

Environment not supported! Supported environment: "matrix".

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