The Markdown parser included in IPython is MathJax-aware. This means that you can freely mix in mathematical expressions using the MathJax subset of Tex and LaTeX. Some examples from the MathJax site are reproduced below, as well as the Markdown+TeX source.
Motivating Examples¶
The Lorenz Equations¶
Source¶
\begin{aligned}
\dot{x} & = \sigma(y-x) \\
\dot{y} & = \rho x - y - xz \\
\dot{z} & = -\beta z + xy
\end{aligned}
Display¶
\begin{aligned} \dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho x - y - xz \\ \dot{z} & = -\beta z + xy \end{aligned}The Cauchy-Schwarz Inequality¶
Source¶
\begin{equation*}
\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)
\end{equation*}
Display¶
\begin{equation*} \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \end{equation*}A Cross Product Formula¶
Source¶
\begin{equation*}
\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix}
\mathbf{i} & \mathbf{j} & \mathbf{k} \\
\frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\
\frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0
\end{vmatrix}
\end{equation*}
Display¶
\begin{equation*} \mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \end{vmatrix} \end{equation*}An Identity of Ramanujan¶
Source¶
\begin{equation*}
\frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
{1+\frac{e^{-8\pi}} {1+\ldots} } } }
\end{equation*}
Display¶
\begin{equation*} \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} = 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\ldots} } } } \end{equation*}A Rogers-Ramanujan Identity¶
Source¶
\begin{equation*}
1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
\prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})},
\quad\quad \text{for $|q|<1$}.
\end{equation*}
Display¶
\begin{equation*} 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots = \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, \quad\quad \text{for $|q|<1$}. \end{equation*}Maxwell's Equations¶
Source¶
\begin{aligned}
\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\
\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\
\nabla \cdot \vec{\mathbf{B}} & = 0
\end{aligned}
Display¶
\begin{aligned} \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\ \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\ \nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}Equation Numbering and References¶
These equation reference examples are adapted from an example page in the MathJax documentation. Note that it's okay to reference equations across cells. Click inside this cell to see the source.
Labeled equations and references¶
Here is a labeled equation: \begin{equation} x+1\over\sqrt{1-x^2}\label{ref1} \end{equation}
with a reference to ref1: \ref{ref1}, and another numbered one with no label: \begin{equation} x+1\over\sqrt{1-x^2} \end{equation}
\nonumber and equation*¶
This one uses \nonumber: \begin{equation} x+1\over\sqrt{1-x^2}\nonumber \end{equation}
Here's one with the equation* environment: \begin{equation*} x+1\over\sqrt{1-x^2} \end{equation*}
Forward references¶
This is a forward reference [\ref{ref2}] and another \eqref{ref2} for the following equation:
\begin{equation} x+1\over\sqrt{1-x^2}\label{ref2} \end{equation}More math: \begin{equation} x+1\over\sqrt{1-x^2} \end{equation}
References inline and in environments¶
Here is a ref inside math: $\ref{ref2}+1$ and text after it.
\begin{align} x& = y_1-y_2+y_3-y_5+y_8-\dots && \text{by \eqref{ref1}}\\ & = y'\circ y^* && \text{(by \eqref{ref3})}\\ & = y(0) y' && \text {by Axiom 1.} \end{align}Missing references¶
Here's a bad ref [\ref{ref4}] to a nonexistent label.
Numbering align environments¶
An alignment: \begin{align} a&=b\label{ref3}\cr &=c+d \end{align} and a starred one: \begin{align*} a&=b\cr &=c+d \end{align*}
Inline Typesetting (Mixing Markdown and TeX)¶
While display equations look good for a page of samples, the ability to mix math and formatted text in a paragraph is also important.
Source¶
This
Display¶
This expression $\sqrt{3x-1}+(1+x)^2$ is an example of a TeX inline equation in a Markdown-formatted sentence.
Other Syntax¶
You will notice in other places on the web that $$ are needed explicitly to begin and end MathJax typesetting. This is not required if you will be using TeX environments, but the IPython notebook will accept this syntax on legacy notebooks.
Source¶
$$
\begin{array}{c}
y_1 \\\
y_2 \mathtt{t}_i \\\
z_{3,4}
\end{array}
$$
$$
\begin{array}{c}
y_1 \cr
y_2 \mathtt{t}_i \cr
y_{3}
\end{array}
$$
$$\begin{eqnarray}
x' &=& &x \sin\phi &+& z \cos\phi \\
z' &=& - &x \cos\phi &+& z \sin\phi \\
\end{eqnarray}$$
$$
x=4
$$
Display¶
$$ \begin{array}{c} y_1 \\\ y_2 \mathtt{t}_i \\\ z_{3,4} \end{array} $$$$ \begin{array}{c} y_1 \cr y_2 \mathtt{t}_i \cr y_{3} \end{array} $$$$\begin{eqnarray} x' &=& &x \sin\phi &+& z \cos\phi \\ z' &=& - &x \cos\phi &+& z \sin\phi \\ \end{eqnarray}$$$$ x=4 $$