# 测试基本数据公式
$$ x^2 + y^2 = z^2$$
${\frac{-b \pm \sqrt{b^2-4ac}}{2a}}$
$$-b \pm \sqrt{b^2-4ac} \over 2a$$ $x^{y^z}=(1+e^x)^{-2xy^w}$
$x^{y^z}=(1+e^x)^{-2xy^w}$
## 测试指数和乘除法
$$ x^{2} + 3x \cdot y^{2} \div 2 = z^{2}$$
$$ (x + y)^{2} - (x - y)^{2}$$
$$ x^{2} + y^{2} = z^{2} \sqrt{x^{2} + y^{2}}$$
## 测试对数和自然对数
$$ ln(x) + e^{y}$$
## 测试求和、求积等符号：
$f(x_1,x_2,\cdots,x_n) = x_1^2 + x_2^2 + \cdots + x_n^2$
$$\int_{a}^{b} f(x) dx$$
## 左右箭头
$\overleftarrow{xy} \quad \overleftrightarrow{xy} \quad \overrightarrow{xy}$
## 方程组
$\begin{cases} a_1x+b_1y+c_1z=d_1\\ a_2x+b_2y+c_2z=d_2\\ a_3x+b_3y+c_3z=d_3\\ \end{cases}$
$f(x,y,z) = \left {\begin{align} &3x + 5y + z \quad &, x < 0 \\ &7x - 2y + 4z\quad&, x > 0 \\ &-6x + 3y + 2z \quad &,x = 0\end{align}\right.$
$\begin{aligned}l(\theta) &= \sum\limits_{i = 1}^n\log p(y^{(i)}|x^{(i)};\theta) \\ \\&=\sum\limits_{i = 1}^n\log\prod\limits_{j = 1}^k\phi_j^{I\{{y^{(i)} = j\}}}\\\\&= \sum\limits_{i = 1}^n\log\prod\limits_{j = 1}^k(\frac{e^{\theta_j^Tx^{(i)}}}{\sum\limits_{l = 1}^ke^{\theta_l^Tx^{(i)}}})^{I\{{y^{(i)} = j\}}}\end{aligned}$
### 上下标
$x^{y^z}=(1+e^x)^{-2xy^w}$ $C_n^2$
$\int_0^1 {x^2} {\rm d}x$
$\Alpha$
$\alpha$
$\Delta$
$\delta$
$\Lambda$
$\Eta$
$\Epsilon$
$\Theta$
$\Phi$
$\Omega$
