test

$$a+b=c$$
$$ X mathop{rightarrow}^{ P} Y$$
$ X mathop{rightarrow}^{ P} Y$
$$E_1 times E_2 equiv E_2 times E_1
E_1 bowtie E_2 equiv E_2 bowtie E_1
E_1 mathop{bowtie}_{F} E_2 equiv E_2 mathop{bowtie}_{F}E_1 $$
$$cos 2theta = cos^2 theta - sin^2 theta = 2 cos^2 theta$$
$$ sum_{i=0}^n i^2 = frac{(n^2+n)(2n+1)}{6} $$
$$ x = dfrac{-b pm sqrt{b^2 - 4ac}}{2a} $$
$$
f(n) =
begin{cases}
n/2, & text{if $n$ is even} \
3n+1, & text{if $n$ is odd}
end{cases}
$$

$$ R cup S={t|t in R wedge t in S }$$
$$ bowtie _{a+b}^{} 23333$$
$$ {begin{matrix}R bowtie S a theta b end{matrix}} $$
$$ sum _{k=1}^{n} $$

$${begin{matrix}R bowtie S\a theta bend{matrix}} $$
$$ {begin{matrix}R bowtie S\a theta bend{matrix}} $$
$$mathop{ R bowtie S}_{a theta b} = { mathop{t_rt_s}^{ frown} | t_r in R wedge t in S wedge t_r[A] theta t_s[B]}$$
⋉ ▷ ⋊
$$
usepackage{wasysym}
R bowtie S
Bowtie
$$

$$R under{bowtie}_{233} S$$

在Unicode中，左外连接符号 : ⟕ ⟕
在Unicode中，右外连接符号是 ⟖ ⟖
在Unicode中，全外连接符号是 ⟗ ⟗

$$R times S ={r cup s| r in R, s in S }$$
$${displaystyle Xtimes Y=left{left(x,yright)mid xin Xland yin Yright}}。$$
$$R times S ={ usepackage{t_r, t_s} t_r frown t_s | t_r in R, t_s in S }$$
$$overline{a+b+c+d} $$
$$ usepackage{a,b}$$
$$ frown{a,b}$$
$$ t_r^frown t_s $$
设关系模式$R(A_1,A_2…A_n)$,它的一个关系为R。t $in$ R 表示 t 是R的一个元组。$t[A_i]$则表示元组 t 中相应于属性$A_i$的一个分量。

$$sigma_F(R)$$

$$
begin{equation}
begin{split}
frac{partial^2 f}{partial{x^2}} &= frac{partial(Delta_x f(i,j))}{partial x} = frac{partial(f(i+1,j)-f(i,j))}{partial x} \
&= frac{partial f(i+1,j)}{partial x} - frac{partial f(i,j)}{partial x} \
&= f(i+2,j) -2f(f+1,j) + f(i,j)
end{split}
nonumber
end{equation}
$$

$$
begin{equation}
sum_{i=0}^n F_i cdot phi (H, p_i) - sum_{i=1}^n a_i cdot ( tilde{x_i}, tilde{y_i}) + b_i cdot ( tilde{x_i}^2 , tilde{y_i}^2 )
end{equation}
$$
$$
begin{equation}
beta^*(D) = mathop{argmin} limits_{beta} lambda {||beta||}^2 + sum_{i=1}^n max(0, 1 - y_i f_{beta}(x_i))
end{equation}
$$

$$
begin{equation}
sum_{i=0}^n F_i cdot phi (H, p_i) - sum_{i=1}^n a_i cdot ( tilde{x_i}, tilde{y_i}) + b_i cdot ( tilde{x_i}^2 , tilde{y_i}^2 )
nonumber
end{equation}
$$
$$
begin{equation}
beta^*(D) = mathop{argmin} limits_{beta} lambda {||beta||}^2 + sum_{i=1}^n max(0, 1 - y_i f_{beta}(x_i))
end{equation}
$$

$$
begin{equation}
sum_{i=0}^n F_i cdot phi (H, p_i) - sum_{i=1}^n a_i cdot ( tilde{x_i}, tilde{y_i}) + b_i cdot ( tilde{x_i}^2 , tilde{y_i}^2 ) tag{1.2.3}
end{equation}
$$

$$
left(
begin{array}{c}
s \
t
end{array}
right)
=
left(
begin{array}{cc}
cos(b) & -sin(b) \
sin(b) & cos(b)
end{array}
right)
left(
begin{array}{c}
x \
y
end{array}
right)
$$

$$
left[
begin{array}{cc|c}
1&2&3\
4&5&6
end{array}
right]
$$