Math Rendering Examples#

The examples start always with a code box showing the commands, which is followed by the resulting Sphinx output.

Inline math#

Some inline math :math:`x_1 + x_2 + ... + x_n, n \in \mathbb{Z}`,
followed by text.

Some inline math x1+x2+...+xn,n∈Zx_1 + x_2 + ... + x_n, n \in \mathbb{Z}, followed by text.

Macros#

You can define macros directly in your math directive.

.. math::

    \def \x {\mathbf{x}}
    \def \w {\omega}
    \def \d {\operatorname{d}\!}

    P(\x,\w) = \oint_{\partial V} D(\x_0,\w) G(\x-\x_0,\w) \d A(\x_0)
P(x,ω)=∮∂VD(x0,ω)G(x−x0,ω)d⁡ ⁣A(x0)\def \x {\mathbf{x}} \def \w {\omega} \def \d {\operatorname{d}\!} P(\x,\w) = \oint_{\partial V} D(\x_0,\w) G(\x-\x_0,\w) \d A(\x_0)

If you want to use them in the whole document, the best is to define them in conf.py as part of the katex_options, see LaTeX Macros. Afterwards, you can use them in every math directive.

Aligned environment#

.. math::

    \begin{aligned}
        \dot{x} & = \sigma(y-x) \\
        \dot{y} & = \rho x - y - xz \\
        \dot{z} & = -\beta z + xy
    \end{aligned}
x˙=σ(y−x)y˙=ρx−y−xzz˙=−βz+xy\begin{aligned} \dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho x - y - xz \\ \dot{z} & = -\beta z + xy \end{aligned}

Array environment#

.. math::

    \begin{array}{c:c:c:c:c:c}
        \Gamma & \Delta & \Theta & \Lambda & \Xi & \Pi \\ \hdashline
        \gamma & \delta & \theta & \lambda & \xi & \pi
    \end{array}
ΓΔΘΛΞΠγδθλξπ\begin{array}{c:c:c:c:c:c} \Gamma & \Delta & \Theta & \Lambda & \Xi & \Pi \\ \hdashline \gamma & \delta & \theta & \lambda & \xi & \pi \end{array}

Case definitions#

.. math::

    f(n) = \begin{cases}
        \frac{n}{2}, & \text{if } n\text{ is even} \\
        3n+1,        & \text{if } n\text{ is odd}
    \end{cases}
f(n)={n2,if n is even2n+1,if n is odd f(n) = \begin{cases} \frac{n}{2}, & \text{if } n\text{ is even} \\ 2n+1, & \text{if } n\text{ is odd} \end{cases}

Matrices#

A simple matrix defined with the pmatrix environment:

.. math::

    \begin{pmatrix}
        a_{11} & a_{12} & a_{13}\\
        a_{21} & a_{22} & a_{23}\\
        a_{31} & a_{32} & a_{33}
    \end{pmatrix}
(a11a12a13a21a22a23a31a32a33)\begin{pmatrix} a_{11} & a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33} \end{pmatrix}

The pmatrix* environment is not available, but you can use the array environment for more complex matrices:

.. math::

    \def \msum {-\textstyle\sum}
    \def \psum {\phantom{-}\textstyle\sum}
    I_{ik} = \left(
    \begin{array}{lll}
        \psum m (y^2+z^2) & \msum m x y       & \msum m x z         \\
        \msum m y x       & \psum m (x^2+z^2) & \msum m y z         \\
        \msum m z x       & \msum m z y       & \psum m (x^2 + y^2)
    \end{array}
    \right)
Iik=(−∑m(y2+z2)−∑mxy−∑mxz−∑myx−∑m(x2+z2)−∑myz−∑mzx−∑mzy−∑m(x2+y2))\def \msum {-\textstyle\sum} \def \psum {\phantom{-}\textstyle\sum} I_{ik} = \left( \begin{array}{lll} \psum m (y^2+z^2) & \msum m x y & \msum m x z \\ \msum m y x & \psum m (x^2+z^2) & \msum m y z \\ \msum m z x & \msum m z y & \psum m (x^2 + y^2) \end{array} \right)

Equation numbers#

Some of Maxwell’s equations are given in (1), (2), and (3).

.. math::
    :label: gauss-law

    \nabla \cdot \mathbf{E} = 4 \pi \rho

.. math::
    :label: gauss-law-magnetism

    \nabla \cdot \mathbf{B} = 0

.. math::
    :label: maxwell-faraday-equation

    \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}
(1)#∇⋅E=4πρ\nabla \cdot \mathbf{E} = 4 \pi \rho
(2)#∇⋅B=0\nabla \cdot \mathbf{B} = 0
(3)#∇×E=−∂B∂t\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}

Fraction#

.. math::

    1 - 2 \phi_{i,j} = \frac{4 N^{AA,aa}_{i,j}
                             + N^{Aa}_{i}
                             + N^{Aa}_{j}
                             - 2 N^{Aa,Aa}_{i,j}}
                            {\sum_{s \in S_{i,j}} 4 p_s (1 - p_s)}
1−2ϕi,j=4Ni,jAA,aa+NiAa+NjAa−2Ni,jAa,Aa∑s∈Si,j4ps(1−ps)1 - 2 \phi_{i,j} = \frac{4 N^{AA,aa}_{i,j} + N^{Aa}_{i} + N^{Aa}_{j} - 2 N^{Aa,Aa}_{i,j}} {\sum_{s \in S_{i,j}} 4 p_s (1 - p_s)}