valaxy/docs/pages/examples/katex.md

title	date	updated	toc	categories
KaTeX	2020-03-23 02:02:15	2020-03-23 02:02:15	true	examples

\KaTeX

• https://katex.org/docs/autorender.html
• KaTeX Supported Functions
• KaTeX Support Table

行内公式

\{x | Ax = b\}

$\{x | Ax = b\}$

\mathcal{X}_{c^*}<1, \mathcal{X}_{q^*}<1

E = mc^2

\frac{\partial}{\partial t}

$E = mc^2$
$\frac{\partial}{\partial t}$

行间公式

 E = mc^2 

$$ E = mc^2 $$

---

 \vec a=\frac{d\vec v}{dt}=\frac{d(\frac{dr}{dt}\vec e*{i}+r\frac{d\theta}{dt}\vec e*{j})}{dt}=\frac{d^2r}{dt^2}\vec e*{i}+\frac{dr}{dt}\frac{d\vec e*{i}}{dt}+\frac{dr}{dt}\frac{d\theta}{dt}\vec e*{j}+r\frac{d^2\theta}{dt^2}\vec e*{j}+r\frac{d\theta}{dt}\frac{d\vec e\_{j}}{dt} 

$$ \vec a=\frac{d\vec v}{dt}=\frac{d(\frac{dr}{dt}\vec e_{i}+r\frac{d\theta}{dt}\vec e_{j})}{dt}=\frac{d^2r}{dt^2}\vec e_{i}+\frac{dr}{dt}\frac{d\vec e_{i}}{dt}+\frac{dr}{dt}\frac{d\theta}{dt}\vec e_{j}+r\frac{d^2\theta}{dt^2}\vec e_{j}+r\frac{d\theta}{dt}\frac{d\vec e_{j}}{dt} $$

 m_t=g_t 

 V_t=1 

$$ m_t=g_t $$
$$ V_t=1 $$

 \eta_t=lr*{\frac {m_t}{\sqrt V_t}}=lr*g_t 

 w\_{t+1}=w_t-\eta_t=w_t-lr*{\frac {m_t}{\sqrt V_t}}=w_t-lr*g_t 

q''_s = -k \left.\frac{\partial }{\partial x} (T_1+T_2) \right|_{x=0} = \underbrace{-k \left.\frac{\partial T_1}{\partial x} \right|_{x=0}}_{q''_s}  -k \left.\frac{\partial T_2}{\partial x} \right|_{x=0} \rightarrow \boxed{0 = -k \left.\frac{\partial T_2}{\partial x} \right|_{x=0}}

$$ \eta_t=lr*{\frac {m_t}{\sqrt V_t}}=lr*g_t $$
$$ w_{t+1}=w_t-\eta_t=w_t-lr*{\frac {m_t}{\sqrt V_t}}=w_t-lr*g_t $$

<div text="red">

$$
q''_s = -k \left.\frac{\partial }{\partial x} (T_1+T_2) \right|_{x=0} = \underbrace{-k \left.\frac{\partial T_1}{\partial x} \right|_{x=0}}_{q''_s}  -k \left.\frac{\partial T_2}{\partial x} \right|_{x=0} \rightarrow \boxed{0 = -k \left.\frac{\partial T_2}{\partial x} \right|_{x=0}}
$$

</div>

\begin{bmatrix}
  a & b \\
  c & d
\end{bmatrix}

$$
\begin{bmatrix}
  a & b \\
  c & d
\end{bmatrix}
$$

\begin{equation}
  \left\{
    \begin{aligned}
      x=a\cos\theta\\
      y=b\sin\theta\\
    \end{aligned}
  \right.
\end{equation}

$$
\begin{equation}
  \left\{
    \begin{aligned}
      x=a\cos\theta\\
      y=b\sin\theta\\
    end{aligned}
  \right.
\end{equation}
$$