Latex formula insert record

Insertion of Roman numerals

insert:

\RNum{2}

You can get the Roman numeral 2. The
premise is that there is this sentence at the beginning of the article:

\newcommand{\RNum}[1]{\uppercase\expandafter{\romannumeral #1\relax}}

Insertion of formulas: superscript and subscript

$$
x_k^i
$$

Subscripts and subscripts can be inserted at the same time, the
effect is as follows
$x_k^i$

Commonly used Greek letters tao, tau, t, fai, phi

write:

$\tau$

Effect:
$\tau$
writing:

$\phi$

Effect:
$\varphi$
There is a blogger who has done a good job in organizing the Greek letters, and recommends: thewriting of the Greek letters in latex

Score input

enter:

$$
a_k^i=\frac{num}{den}
$$

Effect:
$$a_k^i=\frac{num}{den}$$

Points input

enter:

$$
\int_{min}^{max}f(x)dx
$$

The effect is as follows:
$${\int }_{min}^{max}f(x)dx$$

Writing

enter:

$$
x^{\prime}
$$

Effect:
$$x^{\prime }$$

Use cases to implement multi-line formulas in braces

Method one
input:

$$f(x)=
\begin{cases}
x& \text{x>0}\\
0& \text{x=0}\\
-x& \text{x<0}
\end{cases}$$

效果：
$$f(x)=\{\begin{array}{ll}x& \text{x>0}\\ 0& \text{x=0}\\ -x& \text{x<0}\end{array}$$
Method two
input:

\begin{equation}  
\left\{  
\begin{array}{lr}  
v=v+1&  \\  
s=s+1& v_k^i\leq{v_k^{\prime}}\\    
\end{array}  
\right.  
\end{equation}

效果：
$$\{\begin{array}{lr}v=v+1& \\ s=s+1& v_k^i\le v_k^{\prime }\end{array}$$

Less than or equal to and greater than or equal to

enter:

$\geq$
$\leq$

Effect:
$\ge$
$\le$

Square root

enter:

$$
y=\sqrt{x}
$$

Effect:
$$Y=\sqrt{x}$$

multiplication

Dot multiplication
input:

$$
a\cdot b
$$

Effect:
$$a\cdot b$$
Cross product
Input:

$$
a\times b
$$

Effect:
$$a\times b$$

curly braces

enter:

$\lbrace x \rbrace$

Effect:
$\left\{x\right\}$
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