数学公式

提示

Valaxy 支持两种数学渲染引擎：KaTeX（默认，渲染快）和 MathJax（SVG 输出，无需外部 CSS/字体）。

当前文档站使用 MathJax 渲染。

行内公式

${x | A x = b}$

md[object Promise]

$X_{c^{*}} < 1, X_{q^{*}} < 1$

$E = m c^{2}$

$\frac{\partial}{\partial t}$

latex[object Promise]

E = m c^{2}

latex[object Promise]

\vec{a} = \frac{d \vec{v}}{d t} = \frac{d (\frac{d r}{d t} \vec{e} * i + r \frac{d θ}{d t} \vec{e} * j)}{d t} = \frac{d^{2} r}{d t^{2}} \vec{e} * i + \frac{d r}{d t} \frac{d \vec{e} * i}{d t} + \frac{d r}{d t} \frac{d θ}{d t} \vec{e} * j + r \frac{d^{2} θ}{d t^{2}} \vec{e} * j + r \frac{d θ}{d t} \frac{d \vec{e}_j}{d t}

latex[object Promise]

m_{t} = g_{t}

V_{t} = 1

latex[object Promise]

η_{t} = l r * \frac{m_{t}}{{\sqrt{V}}_{t}} = l r * g_{t}

w_t + 1 = w_{t} - η_{t} = w_{t} - l r * \frac{m_{t}}{{\sqrt{V}}_{t}} = w_{t} - l r * g_{t}

q_{s}^{″} = - k {\frac{\partial}{\partial x} (T_{1} + T_{2}) |}_{x = 0} = \underset{q_{s}^{″}}{\underset{⏟}{- k {\frac{\partial T_{1}}{\partial x} |}_{x = 0}}} - k {\frac{\partial T_{2}}{\partial x} |}_{x = 0} \to 0 = - k {\frac{\partial T_{2}}{\partial x} |}_{x = 0}

latex[object Promise]

[\begin{matrix} a & b \\ c & d \end{matrix}]

latex[object Promise]

{\begin{array}{r} x = a \cos θ \\ y = b \sin θ \end{array}

latex[object Promise]

MathJax 相比 KaTeX 支持更多 LaTeX 扩展。以下是一些 MathJax 的额外功能示例：

CO_{2} + C ⟶ 2 CO

latex[object Promise]

(\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix})

latex[object Promise]