1. 测试代数（不支持双层大括号）

  • 式子一

对于方程形如：x3−1=0设:ω=−1+3i2x1=1,x2=ω=−1+3i2x3=ω2=−1−3i2\begin{array}{l} \text{对于方程形如：}x^{3}-1=0 \\ \text{设}\text{:}\omega =\frac{-1+\sqrt{3}i}{2} \\ x_{1}=1,x_{2}= \omega =\frac{-1+\sqrt{3}i}{2} \\ x_{3}= \omega ^{2}=\frac{-1-\sqrt{3}i}{2} \end{array}

  • 式子二

ax2+bx+c=0Δ=b2−4acΔ=b2−4acx1,2=−b±b2−4ac2ax1+x2=−bax1x2=ca\begin{array}{l} a\mathop{x}\nolimits^{2}+bx+c=0 \\ \Delta =\mathop{b}\nolimits^{2}-4ac \\ \Delta =\mathop{b}\nolimits^{2}-4ac \\ \mathop{x}\nolimits_{1,2}=\frac{-b\pm \sqrt{\mathop{b}\nolimits^{2}-4ac}}{2a} \\ \mathop{x}\nolimits_{1}+\mathop{x}\nolimits_{2}=-\frac{b}{a} \\ \mathop{x}\nolimits_{1}\mathop{x}\nolimits_{2}=\frac{c}{a} \end{array}

  • 注：使用latex(katex)时应使用a\mathop{x}\nolimits^{2}+bx+c=0，而不是a\mathop{{x}}\nolimits^{{2}}+bx+c=0
  • 即使用单层大括号{x}包裹参数，而不是双层大括号{{x}}包裹参数。

2. 测试几何

m⊂α,n⊂α,m∩n=Pa⊥m,a⊥n}⇒a⊥α\begin{array}{l} \left.\begin{matrix} m \subset \alpha ,n \subset \alpha ,m \cap n=P \\ a \perp m,a \perp n \end{matrix}\right\}\Rightarrow a \perp \alpha \end{array}

3. 测试不等式

(∑k=1nakbk) ⁣ ⁣2≤(∑k=1nak2)(∑k=1nbk2)\begin{array}{l} \left( \sum_{k=1}^n a_k b_k \right)^{\!\!2}\leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \end{array}

4. 测试积分

f(x)=∫−∞∞f^(x)ξ e2πiξx dξ\begin{array}{l} f(x) = \int_{-\infty}^\infty \hat f(x)\xi\,e^{2 \pi i \xi x} \,\mathrm{d}\xi \end{array}

5. 测试矩阵

  • 矩阵一

Am×n=[a11a12⋯a1na21a22⋯a2n⋮⋮⋱⋮am1am2⋯amn]=[aij]\begin{array}{l} A_{m\times n}= \begin{bmatrix} a_{11}& a_{12}& \cdots & a_{1n} \\ a_{21}& a_{22}& \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m1}& a_{m2}& \cdots & a_{mn} \end{bmatrix} =\left [ a_{ij}\right ] \end{array}

  • 矩阵二

A=[aij]m×n,B=[bij]n×scij=∑k=1naikbkjC=AB=[cij]m×s=[∑k=1naikbkj]m×s\begin{array}{c} A={\left[ a_{ij}\right]_{m \times n}},B={\left[ b_{ij}\right]_{n \times s}} \\ c_{ij}= \sum \limits_{k=1}^{n}a_{ik}b_{kj} \\ C=AB=\left[ c_{ij}\right]_{m \times s} = \left[ \sum \limits_{k=1}^{n}a_{ik}b_{kj}\right]_{m \times s} \end{array}

6. 测试三角

sin⁡α+sin⁡β=2sin⁡α+β2cos⁡α−β2\begin{array}{l} \sin \alpha + \sin \beta =2 \sin \frac{\alpha + \beta}{2}\cos \frac{\alpha - \beta}{2} \end{array}

7. 测试统计

S=(Nn),Ak=(Mk)⋅(N−Mn−k)P(Ak)=(Mk)⋅(N−Mn−k)(Nn)\begin{array}{c} S= \binom{N}{n},A_{k}=\binom{M}{k}\cdot \binom{N-M}{n-k} \\ P\left ( A_{k}\right ) = \frac{\binom{M}{k}\cdot \binom{N-M}{n-k}}{\binom{N}{n}} \end{array}

P(⋃i=1nAi)=∏i=1nP(Ai)\begin{array}{l} P \left( \bigcup \limits_{i=1}^{n}A_{i}\right) = \prod \limits_{i=1}^{n}P \left( A_{i}\right) \end{array}

8. 测试数列

n+1n(n−1)⋅2n=1(n−1)⋅2n−1−1n⋅2n\begin{array}{l} \frac{n+1}{n \left( n-1 \left) \cdot 2^{n}\right. \right.}= \frac{1}{\left( n-1 \left) \cdot 2^{n-1}\right. \right.}-\frac{1}{n \cdot 2^{n}} \end{array}

(1+x)n=1+nx1!+n(n−1)x22!+⋯\begin{array}{l} (1+x)^{n} =1 + \frac{nx}{1!} + \frac{n(n-1)x^{2}}{2!} + \cdots \end{array}

9. 测试物理(不支持unicode扩展)

∯SD⋅ds=Qf∯SB⋅ds=0∮LE⋅dl=−dΦBdt∮LH⋅dl=If+dΦDdt%此公式需要在设置中开启unicode扩展支持 \begin{array}{l} {\huge \oiint}_\mathbb{S} \mathbf{D} \cdot\mathrm{d}s= Q_f \\ {\huge \oiint}_\mathbb{S} \mathbf{B} \cdot\mathrm{d}s= 0 \\ {\huge \oint}_{\mathbb{L}}^{} \mathbf{E} \cdot \mathrm{d}l=-\cfrac{\mathrm{d}\Phi _{\mathbf{B}}}{\mathrm{d}t } \\ {\huge \oint}_{\mathbb{L}}^{} \mathbf{H} \cdot \mathrm{d}l=I_f+\cfrac{\mathrm{d}\Phi _{\mathbf{D}}}{\mathrm{d}t } \end{array}

10. 测试化学(不支持mhchem扩展)

  • 源latex代码如下:

\begin{array}{l} \ce{Zn^2+ <=>[+ 2OH-][+ 2H+] $\underset{\text{amphoteres Hydroxid}}{\ce{Zn(OH)2 v}}$ <=>[+ 2OH-][+ 2H+] $\underset{\text{Hydroxozikat}}{\ce{[Zn(OH)4]^2-}}$} \end{array}