## Math

- inline formulas

`$x^2=-1$`

- displayed formulas

```
$$\frac{-b+\sqrt{b^2-4ac}}{2a}$$
\begin{equation*}
f(x)=\sum_{i=0}^{\infty} a_i x^i
\end{equation*}
```

- numbered equations and references

```
\begin{align}
& a^2+b^2=c^2\\
& e^{\pi i} + 1 = 0\label{Euler}
\end{align}
The equation \eqref{Euler} is known as the Euler identity.
```

- LaTeX macros

```
\newcommand{\tuple}[1]{\langle #1 \rangle}
$\tuple{a, b, c}$
```

## Headings

```
# A level-one heading
## A level-two heading
### A heading with an identifier {#custom-id}
Heading references: As [Section](#custom-id) illustrates, ...
```

## Paragraphs

```
This is the first paragraph. To start a new paragraph, leave one or more blank lines.
This is the second paragraph.
:::{#paragraphs-with-identifiers}
**Theorem (Hahn-Banach)**. Let $X$ be locally convex topological vector space over $K$ (either $\mathbb{R}$ or $\mathbb{C}$), $M$ a vector subspace of $X$, and $f$ a continuous linear functional on $M$. There $f$ has a continuous linear extension to all of $X$.
:::
By the above [Theorem](#paragraphs-with-identifiers), ...
```

## Line breaks

```
For line breaks, end a line with two or more spaces.
This is a new line.
```

## Horizontal rules

```
contents above the horizontal rule
---------------
contents below the horizontal rule
```

## Inline formatting

```
This text is _emphasized with underscores_, and this
is *emphasized with asterisks*.
This is **strong emphasis** and __with underscores__.
This ~~is deleted text.~~
```

## Blocks

- quotations

```
> This is a block quote.
>
> > A block quote within a block quote.
```

- code blocks

```
```
Your codes go here...
```
```

- line blocks

`| This is a line block `

## Lists

- bulleted lists

```
- here is my first bulleted list item.
+ child item
+ child item
- and my second.
```

- ordered lists

```
#. here is my first ordered list item.
#. and my second.
(@example1) This is the first numbered example.
(@example2) and the second.
As @example1 illustrates, ...
```

## Links

- inline links

```
This is an [inline link](https://functors.net)
Email addresses in inline links are not autodetected, so they have to be prefixed with "mailto": [Write me!](mailto:[email protected])
```

- reference links

```
See [the website][my label].
[my label]: https://functors.net
```

## Images

- inline images

```
![This is the caption](https://example.com/image1.png)
![an image with some attributes](https://example.com/image2.png){#identifier1 width=50 hight=50}
The [image](#identifier1)'s dimension is 50px $\times$ 50px.
```

- reference images

```
![image][ref1]
![an image with some attributes][ref2]
The width of [the above image][#identifier2] is half of that of the article.
[ref1]: https://example.com/image3.png
[ref2]: https://example.com/image4.png {#identifier2 width=50%}
```

## Footnotes

```
Here is an inline note.^[Inlines notes are easier to write, since
you don't have to pick an identifier and move down to type the
note.]
Here is a footnote reference,[^1] and another.[^longnote]
[^1]: Here is the footnote.
[^longnote]: Here's one with multiple blocks.
Subsequent paragraphs are indented to show that they
belong to the previous footnote.
The whole paragraph can be indented, or just the first
line. In this way, multi-paragraph footnotes work like
multi-paragraph list items.
This paragraph won't be part of the note, because it
isn't indented.
```

## Citations

- First, you have to upload your bibliographic data in the format of BibLaTeX, BibTeX or JSON. For example, the following are two bibliographic items in BibLaTeX:

```
@book{dirac,
title={The Principles of Quantum Mechanics},
author={Paul Adrien Maurice Dirac},
isbn={9780198520115},
series={International series of monographs on physics},
year={1981},
publisher={Clarendon Press},
keywords = {physics}
}
@article{einstein,
author = "Albert Einstein",
title = "{Zur Elektrodynamik bewegter K{\"o}rper}. ({German})
[{On} the electrodynamics of moving bodies]",
journal = "Annalen der Physik",
volume = "322",
number = "10",
pages = "891--921",
year = "1905",
DOI = "http://dx.doi.org/10.1002/andp.19053221004"
}
```

- Then you can cite the items like this:

```
[@einstein; @dirac]
[@einstein, section 1; @dirac, p. 1-2]
```

# Tables

```
| Right | Left | Default | Center |
|------:|:-----|---------|:------:|
| 12 | 12 | 12 | 12 |
| 123 | 123 | 123 | 123 |
```