# Mathematics

Docutils supports inline math with the prefix or postfix :math: role specificator, n! + sin(x2n) and Ac = (π)/(4)d2 , as well as displayed math via the math directive:

f(ϵ) = (1)/(1 + exp(ε)/(kBT))

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| = ad − bc .

More than one display math block can be put in one math directive. For example, the following sum and integral with limits:

10xndx = (1)/(n + 1)
mn = 1n = (m(m + 1))/(2)

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

The Schrödinger equation

i()/(t)Ψ = Ψ,

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

Math-Accents:
 á \acute{a} ṫ \dot{t} γ̂ \hat{\gamma} à \grave{a} ẗ \ddot{t} α̃ \tilde{\alpha} x̆ \breve{x} t⃛ \dddot{t} ı⃗ \vec{\imath} ǎ \check{a} a \bar{a} R⃗ \vec{R}

Modulation Transfer Function:

MTF = ||(ℱ{s(x)})/(ℱ{s(x)}|ωx = 0)|| =  abs( − ∞s(x)eiωxxdx)/( − ∞s(x)dx).

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:

sout(x)  = sin(x’)*sδ(x − x’)  = sin(x’)sδ(x − x’)dx

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):

sgn(x) =   − 1  x < 0        1  x > 0