# 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 ˆ 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 ˆ \hat{\gamma}
  a ` \grave{a} | t ¨ \ddot{t} | α ~ \tilde{\alpha}
  x ˘ \breve{x} | t ˙˙˙ \dddot{t} | ı → \vec{\imath}
  a ˇ \check{a} | a ˉ \bar{a} | R → \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 with the AMSmath cases environment:

sgn ( x ) = { − 1 x < 0 − 1 x > 0