# How can I format mathematical expressions here, using MathJax?

Blatantly ripped off from chem.SE, this post is meant to help people understand how to use MathJax formatting of mathematical expressions here on Robotics.

## Getting started with MathJax

On Robotics Stack Exchange, we use MathJax to format mathematical expressions. MathJax is a tool that lets us display LaTeX expressions on a browser.

To use MathJax, enclose your mathematical expressions within single($...$) or double($$...$$) dollar signs. Single dollar signs make the expression inline, for example, Let $x$ be a variable gives:

Let $$x$$ be a variable.

On the other hand, double dollar signs make the expression a block element. It gets its own line, and is slightly larger. For example, The equation of motion is as follows: $$v=u+at$$ It is a SUVAT equation gives:

The equation of motion is as follows: $$v=u+at$$ It is a SUVAT equation

Note that the extra spaces in LaTeX do not render, use \: or ~ for a space.

## Basic MathJax

### Superscripts and subscripts

You can denote superscripts via the ^ character, and subscripts via _. For example, x^2 renders as $$x^2$$, x_1 renders as $$x_1$$, and x_1^3 renders as $$x_1^3$$.

If you want to include more than one character in the super/sub script, enclose it in curly braces ({...}).

For example, x^10 renders as $$x^10$$, but x^{10} renders as $$x^{10}$$

To put superscripts before the symbol, do this: {^{a}R_{b}} which renders as: $${^{a}R_{b}}$$

### Fractions and square roots

Fractions can be easily displayed using \frac{..}{..}. For example, \frac{a+b^c}{de+f} renders as $$\frac{a+b^c}{de+f}$$

Protip: You can exclude the braces for single-character numerators/denominators (if the first character is a letter, you need to use a space after \frac, though). For example \frac12 renders as $$\frac12$$, and \frac ab renders as $$\frac ab$$

Square roots can be added in a similar manner, via \sqrt{....}. For example, \sqrt{x+y} renders as $$\sqrt{x+y}$$.

### Embellishments

\dot{x} \hat{y} \bar{h} \overrightarrow{v} J^\dagger J^{+} T^\top z' a^{\circ} render as:

$$\dot{x}$$ $$\hat{y}$$ $$\bar{h}$$ $$\overrightarrow{v}$$ $$J^\dagger$$ $$J^{+}$$ $$T^\top$$ $$z'$$ $$a^{\circ}$$

### Matrices and vectors

Row vectors are easy enough. $[xyz]$ $(xyz)$ render as: $$[xyz]$$ $$(xyz)$$ But you might want to use a space separator. $[1,2,3]$ $[x~y~z]$ $(x~y~z)$ render as: $$[1,2,3]$$ $$[x~y~z]$$ $$(x~y~z)$$

Column vectors are done like this. \begin{pmatrix} x \\ y \\ z \end{pmatrix} \begin{bmatrix} a \\ b \\ c \end{bmatrix} render as:

$$\begin{pmatrix} x \\ y \\ z \end{pmatrix}~~\begin{bmatrix} a \\ b \\ c \end{bmatrix}$$

2D matrices can also have parentheses or brackets by using pmatrix or bmatrix accordingly. Here is the structure:

\begin{bmatrix}
r_{11} & r_{12} & r_{13}\\
r_{21} & r_{22} & r_{23}\\
r_{31} & r_{32} & r_{33}
\end{bmatrix}


$$\begin{bmatrix} r_{11} & r_{12} & r_{13}\\ r_{21} & r_{22} & r_{23}\\ r_{31} & r_{32} & r_{33} \end{bmatrix}$$

### Operations

\otimes \cdot \in \circ \bullet render as: $$\otimes$$ $$\cdot$$ $$\in$$ $$\circ$$ $$\bullet$$

### Greek letters

Greek letters can be added usung a backslash (\), followed by the name of the letter. Captialise the first letter of the name for greek capital letters.

Eg \alpha \beta \gamma \delta \Omega \Delta renders as $$\alpha$$ $$\beta$$ $$\gamma$$ $$\delta$$ $$\Omega$$ $$\Delta$$.

Make sure that you put spaces after these if you are typing normal alphabet characters. Eg e^{\pii} gives an error, you need to use e^{\pi i} for $$e^{\pi i}$$.

Note that there are special commands \varepsilon \varsigma \varrho \varpi to distinguish between the lunate Greek letters ($$\varepsilon$$ $$\varsigma$$ $$\varrho$$ $$\varpi$$ rather than $$\epsilon$$ $$\sigma$$ $$\rho$$ $$\pi$$).

### Misc. Symbols

\nabla \infty \partial renders as $$\nabla$$ $$\infty$$ $$\partial$$

### Font stuff

boldsymbol and mathbf have slightly different results: for example: \boldsymbol{x} \mathbf{x} render as: $$\boldsymbol{x}$$ $$\mathbf{x}$$

Another fancy font: \mathbb{R} renders as: $$\mathbb{R}$$