Latex Notes

Posted on | In

Latex is a great way to express mathematical expressions in a clear and readable way, just like what you see in textbooks. The setup is tedious, and the usage is even messier.

The following notes are what I usually use for writing posts. Hope it can help you master Latex without the need to go through all pains that I have experienced.

Installation

  1. npm install hexo-math --save
  2. In the folder that you need MathJex, execute the command hexo math install

  3. Add the following line in the _config.yml file

    1
    plugins: hexo-math

    If you have multiple plugins, add

    1
    2
    3
    plugins:
    - hexo-math
    - ...

Notice: if you work offline, the Latex won’t be rendered.

Usage of Latex code on Hexo

Inline

Only for very basic stuff, such as pure variables and formulas.

$a = b + c$ will be rendered as $a = b + c$.

Block

Render Latex code on a newline.

$$ velocity = \frac{distance}{time} $$ will be rendered as $$ velocity = \frac{distance}{time} $$

Rendering issue

Try this… $x_k = x_1 - [ ( a_1 + a2 + … + a{k - 1} ) - (k - 1) \times avg]$. It fails because of the markdown engine rendering priority issue.

So, instead of using $ ... $, use

1
2
3
4
5
{% math %}
\begin{aligned}
x_k = x_1 - [ ( a_1 + a_2 + ... + a_{k - 1} ) - (k - 1) \times avg]
\end{aligned}
{% endmath %}

The result will be very satisfying :)

$$\begin{aligned} x_k = x_1 - [ ( a_1 + a_2 + ... + a_{k - 1} ) - (k - 1) \times avg] \end{aligned}$$

That’s why I mentioned basic stuff in the inline section. One hour wasted on this issue…

Latex code notes

Basics

Plain Text

Use \text{…} for plain text. You can use $$ within it.

\text{Hello World! $x^2 = y^3$} is $\text{Hello World! $x^2 = y^3$}$

Escape

Special characters used for MathJax interpreting can be escaped using the \ character

  • \$ is $\$$
  • \{ is ${$
  • \_ is $_$

Spacing

This is a book becomes $This is a book$. So we need to specify the spacing by using:

  • \, for thin space
  • \; for normal space

This\, is\; a\; book becomes $This\, is\; a\; book$

Superscripts and Subscripts

Use ^ for superscripts and _ for subscripts. e.g. x_i^2 is $x_i^2$

Notice: without {}, the ^ and _ only apply to the next character only.

Group

Superscripts, subscripts, and other operations apply only to the next “group” (use {} for grouping). For example, to represent 10 to the 10th power, you shouldn’t write…

10^10 $10^10$

You should write…

10^{10} $10^{10}$

Fraction

  1. \frac ab is $\frac ab$
  2. \frac{a+1}{b+1} is $\frac{a+1}{b+1}$
  3. {a+1\over b+1} is ${a+1\over b+1}$

Special Letters and Symbols

Greek Letters

  • alpha \beta \delta \Delta \gamma \Gamma \omega \Omega is $\alpha \beta \delta \Delta \gamma \Gamma \omega \Omega$
  • \epsilon \varepsilon \phi \varphi is $\epsilon \varepsilon \phi \varphi$

Special Symbol

  • \lt \gt \le \ge \neq is $\lt \gt \le \ge \neq$
  • \times \div \pm \mp \cdot is $\times \div \pm \mp \cdot$
  • \cup \cap \setminus \subset \subseteq \subsetneq \supset \in \notin \emptyset \varnothing is $\cup \cap \setminus \subset \subseteq \subsetneq \supset \in \notin \emptyset \varnothing$
  • \to \rightarrow \leftarrow \Rightarrow \Leftarrow \mapsto is $\to \rightarrow \leftarrow \Rightarrow \Leftarrow \mapsto$
  • \land \lor \lnot \forall \exists \top \bot \vdash \vDash is $\land \lor \lnot \forall \exists \top \bot \vdash \vDash$
  • \star \ast \oplus \circ \bullet is $\star \ast \oplus \circ \bullet$
  • \approx \sim \simeq \cong \equiv \prec \lhd is $\approx \sim \simeq \cong \equiv \prec \lhd$
  • a\equiv b\pmod n is $a\equiv b\pmod n$
  • \ldots for $a1, a2, \ldots, an$, and \cdots for $a1 + a2 + \cdots + an$
  • \hat x \bar x \overline x \vec x \overrightarrow {xy} is $\hat x\; \bar x\; \overline x\; \vec x\; \overrightarrow {xy}$

Special Function: trigonometry, limit, sqrt, sum

  • Trigonometry
    • \sin x is $\sin x$
    • \cos x is $\cos x$
    • \tan x is $\tan x$
  • Limits
    • \lim_{x\to 0} is $\lim_{x \to 0}$
  • Square root
    • \sqrt{\frac xy} is $\sqrt{\frac xy}$
    • \sqrt[3]{\frac xy} is $\sqrt[3]{\frac xy}$

  • Summation

    • \sum_{i=0}^n i^2 = \frac{n(n+1)(2n+1)}{6} is $\sum_{i=0}^n i^2 = \frac{n(n+1)(2n+1)}{6}$

    • For multiline subscripts

      1
      2
      3
      4
      5
      \sum_{\substack{
          0\le i\lt n\\
          0\le j\lt m}
      }
      i^2+j^3
      $$\sum_{\substack{ 0\le i\lt n\\ 0\le j\lt m} } i^2+j^3$$

Equations and Functions

System of Equations

1
2
3
4
5
\begin{cases}
a_1x+b_1y+c_1z=d_1 \\
a_2x+b_2y+c_2z=d_2 \\
a_3x+b_3y+c_3z=d_3
\end{cases}
$$\begin{cases} a_1x+b_1y+c_1z=d_1 \\ a_2x+b_2y+c_2z=d_2 \\ a_3x+b_3y+c_3z=d_3 \end{cases}$$

Tagging Equations

1
2
3
4
5
6
7
{% math %}
\begin{align*}
   a &= p^2 - q^2 &&\text{Equation note 1} \tag 1\\
   b &= 2pq  &&\text{Equation note 2} \tag 2\\
   c &= p^2 + q^2 &&\text{Equation note 3} \tag 3\\
\end{align*}
{% endmath %}
$$\begin{align*} a &= p^2 - q^2 &&\text{Equation note 1} \tag 1\\ b &= 2pq &&\text{Equation note 2} \tag 2\\ c &= p^2 + q^2 &&\text{Equation note 3} \tag 3\\ \end{align*}$$

P.S. & is the cell separator in tabulars and similar constructions. A single & means “go to the next cell of the alignment”, so && means “the next cell is empty, go to the following one”.

Check out here for notes on aligning.

Pairwise Functions

1
2
3
4
5
f(n) =
\begin{cases}
n/2,  & \text{if $n$ is even} \\
3n+1, & \text{if $n$ is odd}
\end{cases}
$$f(n) = \begin{cases} n/2, & \text{if $n$ is even} \\ 3n+1, & \text{if $n$ is odd} \end{cases}$$

Matrix

Basic version.

1
2
3
4
5
6
7
8
{% math %}
\begin{aligned}
        \begin{matrix}
        a & b \\
        0 & 1 \\
        \end{matrix}
\end{aligned}
{% endmath %}
$$\begin{aligned} \begin{matrix} a & b \\ 0 & 1 \\ \end{matrix} \end{aligned}$$

Bracket matrix with exponent associated with it.

1
2
3
4
5
6
7
8
{% math %}
\begin{aligned}
        \begin{bmatrix}
        a & b \\
        0 & 1 \\
        \end{bmatrix}^{n}
\end{aligned}
{% endmath %}
$$\begin{aligned} \begin{bmatrix} a & b \\ 0 & 1 \\ \end{bmatrix}^{n} \end{aligned}$$

Two more kinds…

1
2
3
4
5
6
7
8
{% math %}
\begin{aligned}
        \begin{pmatrix}
        a & b \\
        0 & 1 \\
        \end{pmatrix}^{n}
\end{aligned}
{% endmath %}
$$\begin{aligned} \begin{pmatrix} a & b \\ 0 & 1 \\ \end{pmatrix}^{n} \end{aligned}$$ 
1
2
3
4
5
6
7
8
{% math %}
\begin{aligned}
        \begin{vmatrix}
        a & b \\
        0 & 1 \\
        \end{vmatrix}^{n}
\end{aligned}
{% endmath %}
$$\begin{aligned} \begin{vmatrix} a & b \\ 0 & 1 \\ \end{vmatrix}^{n} \end{aligned}$$