# mathjax-experiment
Please refer to the [Github repository](https://github.com/tonghuikang/mathjax-experiment) for the [source](https://raw.githubusercontent.com/tonghuikang/mathjax-experiment/master/README.md) of this [example](https://tonghuikang.github.io/mathjax-experiment/).
This uses [MathJax](https://github.com/mathjax/MathJax).
I followed these [instructions](http://csega.github.io/mypost/2017/03/28/how-to-set-up-mathjax-on-jekyll-and-github-properly.html) instructions to make it work.
You just need to append these three lines of [javascript](https://docs.mathjax.org/en/latest/web/start.html) [code](https://docs.mathjax.org/en/latest/input/tex/delimiters.html) to your markdown file.
```
```
You can append it to the Jekyll templates if you know how to do it.
There was also a [KaTeX](https://katex.org/) parser, but I was not able to use it render [inline](https://tonghuikang.github.io/mathjax-experiment/) equations while making use of `\textcolor`.
# Basic Example
Following is an example of inline and displayed $\LaTeX$ typesetting.
When $a \neq 0$, there are two solutions to $ax^2 + bx + c = 0$ and they are
$$
x = {-b \pm \sqrt{b^2-4ac} \over 2a}
$$
# Stress Testing
The parsing is different from how I see it on Typora, for reasons intended or otherwise.
### Displayed math immediately after text
If there is displayed math is not spaced out between two blocks of text, it will be rendered inline. You need an empty line before your double dollar sign symbol.
$f(x)$ is the objective function
$$
f(x) = a + b + c + d
$$
### Vertical symbol
In markdown, vertical symbols were used to delimit the tables. It is recommended to use `\vert` in math expression.
You observe a subset $S$ with $|S|$ elements such that its weights is larger than the limit. The **knapsack cover inequality** prevents you from choosing all of these elements, you can choose at most $|S| - 1$ elements from $S$.
$$
\sum_{j \in S} x_j \leq |S| - 1 = |S| - 1
$$
### Curly braces
In TeX, curly braces are used as parenthesis and needs to be escaped. However, even after escaping, some math parses still ignore it. The workaround is to use `\lbrace` and `\rbrace`
The **recursion** for the dynamic programming is $f(k) = 1-\min\{ 1, f_{k-1}, f_{k-2}, f_{k-6} \}$
$$
f(k) = 1-\min\{ 1, f_{k-1}, f_{k-2}, f_{k-6} \}
$$
### Textcolor
Some parsers does not have certain packages.
The task is to minimise $\dfrac{\textcolor{red}{\lambda}}{2} \vert \vert \theta \vert \vert ^2 + \textcolor{red}{\dfrac{1}{n}\Sigma_{(x,y)} \xi_{x,y}}$
$$
f(\theta) = \dfrac{\textcolor{red}{\lambda}}{2} || \theta || ^2 + \textcolor{red}{\dfrac{1}{n}\Sigma_{(x,y)} \xi_{x,y}}
$$
### Double underscores
In markdown, underscores were used mark emphasis. There are still issues parsing underscores from separate math expressions. The workaround is to use double dollar signs for inline math expressions.
The objective function is $f(x) = x_1 + x_2 + x_3 + x_4$
$x_1$ is the number of oranges, $x_2$ is the number of apples, $x_3$ is the number of pears and $x_4$ is the number of bananas
$$
f(x) = x_1 + x_2 + x_3 + x_4
$$
Data $\mathcal{S}$ is made up of training data $\mathcal{S}_n,$ validation data $\mathcal{S}_{val}$ or test data $\mathcal{S}_*$
Data $$\mathcal{S}$$ is made up of training data $$\mathcal{S}_n,$$ validation data $$\mathcal{S}_{val}$$ or test data $$\mathcal{S}_*$$
There are issues with the double dollar signs. If the expression is the only content on a line or after a bullet point, it will appear as displayed even though you want to render it inline. The workaround is to break the equation into two.
$$v_{*}(s) = \max_\pi v_\pi (s) = \max_a q_*(s,a)$$
$$v_{*}(s) $$$$= \max_\pi v_\pi (s) = \max_a q_*(s,a)$$
- $$\tilde{C}_t = \tanh(W_C \cdot [h_{t-1}, x_t] + b_C)$$
- $$\tilde{C}_t$$$$= \tanh(W_C \cdot [h_{t-1}, x_t] + b_C)$$