1, Greek letters
| Syntax | Display | Syntax | Display |
|---|---|---|---|
| \alpha | \(\alpha\) | \beta | \(\beta\) |
| \gamma | \(\gamma\) | \delta | \(\delta\) |
| \epsilon | \(\epsilon\) | \zeta | \(\zeta\) |
| \eta | \(\eta\) | \theta | \(\theta\) |
| \iota | \(\iota\) | \kappa | \(\kappa\) |
| \lambda | \(\lambda\) | \mu | \(\mu\) |
| \nu | \(\nu\) | \xi | \(\xi\) |
| \pi | \(\pi\) | \rho | \(\rho\) |
| \sigma | \(\sigma\) | \tau | \(\tau\) |
| \upsilon | \(\upsilon\) | \phi | \(\phi\) |
| \chi | \(\chi\) | \psi | \(\psi\) |
| \omega | \(\omega\) |
In addition, each Greek letter has lowercase, uppercase and italic three display formats. Take π as an example:
| syntax | display | syntax | display | syntax | display |
|---|---|---|---|---|---|
| \pi | \(\pi\) | \Pi | \(\Pi\) | \varPi | \(\varPi\) |
2, operator
| Syntax | Display |
|---|---|
| x + y | \(x + y\) |
| x \oplus y | \(x \oplus y\) |
| x - y | \(x -y\) |
| x \ominus y | \(x \ominus y\) |
| x \times y | \( x \times y\) |
| x \otimes y | \(x \otimes y\) |
| x \bigotimes y | \(x \bigotimes y\) |
| x \cdot y | \( x \cdot y\) |
| x \odot y | \(x \odot y\) |
| x \bigodot y | \(x \bigodot y\) |
| x \ast y x * y | \( x * y\) |
| x \star y | \(x \star y\) |
| x \div y | \( x \div y\) |
| x \pm y x \mp y | \(x \pm y\) \(x \mp y\) |
| x = y | \(x = y\) |
| x \neq y | \( x \neq y\) |
| x < y | \(x < y\) |
| x \nless y | \(x \nless y\) |
| x > y | \(x > y\) |
| x \ngtr y | \(x \ngtr y\) |
| x \leq y | \(x \leq y\) |
| x \nleqslant y | \(x \nleqslant y\) |
| x \geq y | \(x \geq y\) |
| x \ngeqslant y | \(x \ngeqslant y\) |
| x \ll y | \(x \ll y\) |
| x \gg y | \(x \gg y\) |
| x \doteq y | \(x \doteq y\) |
| x \sim y | \(x \sim y\) |
| x \not\sim y | \(x \not\sim y\) |
| x \simeq y | \(x \simeq y\) |
| x \not\simeq y | \(x \not\simeq y\) |
| x \approx y | \(x \approx y\) |
| x \not\approx y | \(x \not\approx y\) |
| x \asymp y | \(x \asymp y\) |
| x \not\asymp y | \(x \not\asymp y\) |
| x \cong y | \(x \cong y\) |
| x \not\cong y | \(x \not\cong y\) |
| x \equiv y | \(x \equiv y\) |
| x \not\equiv y | \(x \not\equiv y\) |
Set operators:
| Syntax | Display |
|---|---|
| x \in y | \(x \in y\) |
| x \notin y | \(x \notin y\) |
| x \ni y | \(x \ni y\) |
| x \not\ni y | \(x \not\ni y\) |
| x \subset y | \(x \subset y\) |
| x \subseteq y | \(x \subseteq y\) |
| x \sqsubset y | \(x \sqsubset y\) |
| x \sqsubseteq y | \(x \sqsubseteq y\) |
| x \not\sqsubset y | \(x \not\sqsubset y\) |
| x \not\sqsubseteq y | \(x \not\sqsubseteq y\) |
| x \not\subset y | \(x \not\subset y\) |
| x \not\subseteq y | \(x \not\subseteq y\) |
| x \subsetneqq y | \(x \subsetneqq y\) |
| x \supset y | \(x \supset y\) |
| x \supseteq | \(x \supseteq y\) |
| x \sqsupset y | \(x \sqsupset y\) |
| x \sqsupseteq y | \(x \sqsupseteq y\) |
| x \not\sqsupseteq y | \(x \not\sqsupseteq y\) |
| x \not\sqsupset y | \(x \not\sqsupset y\) |
| x \not\supseteq y | \(x \not\supseteq y\) |
| x \not\supseteq y | \(x \not\supseteq y\) |
| x \supsetneqq y | \(x \supsetneqq y\) |
| x \cup y | \(x \cup y\) |
| x \cap y | \(x \cap y\) |
| \emptyset | \(\emptyset\) |
| \varnothing | \(\varnothing\) |
3, superscript and subscript
| Syntax | Display |
|---|---|
| _ and ^ | \({a_n}^2\) |
| \vec | \(\vec a\) \(\vec {ab}\) |
| \overrightarrow | \(\overrightarrow a\) \(\overrightarrow {ab}\) |
| \hat | \(\hat a\) |
| \overline | \(\overline a\) |
| \underline | \(\underline a\) |
| \overbrace | \(\overbrace{a+b}^{2.0}\) |
| \underbrace | \(\underbrace{a+b}_{2.0}\) |
4. Arrow
One-way arrow:
| Syntax | Display |
|---|---|
| \uparrow | \(\uparrow\) |
| \Uparrow | \(\Uparrow\) |
| \upharpoonleft | \(\upharpoonleft\) |
| \upharpoonright | \(\upharpoonright\) |
| \upuparrows | \(\upuparrows\) |
| \downarrow | \(\downarrow\) |
| \Downarrow | \(\Downarrow\) |
| \downharpoonleft | \(\downharpoonleft\) |
| \downharpoonright | \(\downharpoonright\) |
| \downdownarrows | \(\downdownarrows\) |
| \leftarrow | \(\leftarrow\) |
| \Leftarrow | \(\Leftarrow\) |
| \longleftarrow | \(\longleftarrow\) |
| \Longleftarrow | \(\Longleftarrow\) |
| \leftharpoonup | \(\leftharpoonup\) |
| \leftharpoondown | \(\leftharpoondown\) |
| \leftleftarrows | \(\leftleftarrows\) |
| \rightarrow | \(\rightarrow\) |
| \Rightarrow | \(\Rightarrow\) |
| \longrightarrow | \(\longrightarrow\) |
| \Longrightarrow | \(\Longrightarrow\) |
| \rightharpoonup | \(\rightharpoonup\) |
| \rightharpoondown | \(\rightharpoondown\) |
| \rightrightarrows | \(\rightrightarrows\) |
Double arrow:
| Syntax | Display |
|---|---|
| \leftrightarrow | \(\leftrightarrow\) |
| \Leftrightarrow | \(\Leftrightarrow\) |
| \longleftrightarrow | \(\longleftrightarrow\) |
| \Longleftrightarrow | \(\Longleftrightarrow\) |
| \updownarrow | \(\updownarrow\) |
| \Updownarrow | \(\Updownarrow\) |
| \rightleftharpoons | \(\rightleftharpoons\) |
| \leftrightharpoons | \(\leftrightharpoons\) |
Other arrows:
| Syntax | Display |
|---|---|
| \swarrow | \(\swarrow\) |
| \nearrow | \(\nearrow\) |
| \nwarrow | \(\nwarrow\) |
| \searrow | \(\searrow\) |
5, font
| font | syntax | display |
|---|---|---|
| default | {A} | \({ABCDEFG}\) |
| Isoline | \sf{A} | \(\sf{ABCDEFG}\) |
| Printer Body | \tt {A} | \(\tt {ABCDEFG}\) |
| Roman | \rm {A} | \(\rm {ABCDEFG}\) |
| Arial | \bf {A} | \(\bf {ABCDEFG}\) |
| Blackboard Bold | \Bbb{A} | \(\Bbb{ABCDEFG}\) |
| Italian | \it{A} | \(\it{ABCDEFG}\) |
| German font | \frak{A} | \(\frak{ABCDEFG}\) |
6, blank and omitted
| Description | Syntax | Display |
|---|---|---|
| None | ab | \(ab\) |
| Space | a\ b | \(a\ b\) |
| 4 spaces (Tab) | a\quad b | \(a\quad b\) |
| ellipsis (down) | 1,2,\ldots,n | \(1,2,\ldots,n\) |
| ellipsis (middle) | x_1^2 + x_2^2 + \cdots + x_n^2 | \(x_1^2 + x_2^2 + \cdots + x_n^2\) |
7, Matrix
| Description | Syntax | Display |
|---|---|---|
| Basic | \begin{matrix}1&0&0\\0&1&0\\0&0&1\\\end{matrix} | \(\begin{matrix}1&0&0\\0&1&0\\0&0&1\\\end {matrix}\) |
| Bracket border | \begin{pmatrix}1&0&0\\0&1&0\\0&0&1\\\end{pmatrix} | \(\begin{pmatrix}1&0&0\\0&1&0\\0&0&1\\ \end{pmatrix}\) |
| Bracket border | \begin{bmatrix}1&0&0\\0&1&0\\0&0&1\\\end{bmatrix} | \(\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\\ \end{bmatrix}\) |
| Brace border | \begin{Bmatrix}1&0&0\\0&1&0\\0&0&1\\\end{Bmatrix} | \(\begin{Bmatrix}1&0&0\\0&1&0\\0&0&1\\ \end{Bmatrix}\) |
| Single vertical line border | \begin{vmatrix}1&0&0\\0&1&0\\0&0&1\\\end{vmatrix} | \(\begin{vmatrix}1&0&0\\0&1&0\\0&0&1\\ \end{vmatrix}\) |
| Double vertical bar border | \begin{Vmatrix}1&0&0\\0&1&0\\0&0&1\\\end{Vmatrix} | \(\begin{Vmatrix}1&0&0\\0&1&0\\0&0&1\\ \end{Vmatrix}\) |
Additionally, ellipses can be used in matrices.
- Horizontal ellipsis: \cdots ( \(\cdots\))
- Vertical ellipsis: \vdots ( \(\vdots\))
- Slash ellipsis: \ddots ( \(\ddots\))
example:
1 | $$\begin{bmatrix}
{a_{11}}&{a_{12}}&{\cdots}&{a_{1n}}\\
{a_{21}}&{a_{22}}&{\cdots}&{a_{2n}}\\
{\vdots}&{\vdots}&{\ddots}&{\vdots}\\
{a_{m1}}&{a_{m2}}&{\cdots}&{a_{mn}}\\
\end{bmatrix}$$ |
The effect is as follows:
$$\begin{bmatrix}
{a_{11}}&{a_{12}}&{\cdots}&{a_{1n}}\\
{a_{21}}&{a_{22}}&{\cdots}&{a_{2n}}\\
{\vdots}&{\vdots}&{\ddots}&{\vdots}\\
{a_{m1}}&{a_{m2}}&{\cdots}&{a_{mn}}\\\end{bmatrix}$$
8, array
Basic syntax:
- start end:
{array} alignment statement
- Align left: l
- center: c
- right alignment: r
- Horizontal line: \hline
example:
1 | $$\begin{array}{c|lll}
{↓}&{a}&{b}&{c}\\
\hline
{R_1}&{c}&{b}&{a}\\
{R_2}&{b}&{c}&{c}\\
\end{array}$$ |
The effect is as follows:
$$\begin{array}{c|lll}
{↓}&{a}&{b}&{c}\\
\hline
{R_1}&{c}&{b}&{a}\\
{R_2}&{b}&{c}&{c}\\
\end{array}$$
9, equation system
Declaration: {cases}
example:
1 | $$\begin{cases}
a_1x+b_1y+c_1z=d_1\\
a_2x+b_2y+c_2z=d_2\\
a_3x+b_3y+c_3z=d_3\\
\end{cases}
$$ |
The effect is as follows:
$$\begin{cases}
a_1x+b_1y+c_1z=d_1\\
a_2x+b_2y+c_2z=d_2\\
a_3x+b_3y+c_3z=d_3\\
\end{cases}$$
10, function
| Syntax | Display | Syntax | Display |
|---|---|---|---|
| \sin\theta | \(\sin \theta\) | \cos\theta | \(\cos \theta\) |
| \arcsin\frac{L}{r} | \(\arcsin\frac{L}{r}\) | \arccos\frac{T}{r} | \(\arccos\frac{T} {r}\) |
| \sinh g | \(\sinh g\) | \cosh h | \(\cosh h\) |
| \operatorname{sh}j | \(\operatorname{sh}j\) | \operatorname{argsh}k | \(\operatorname{argsh}k\) |
| \operatorname{argch}l | \(\operatorname{argch}l\) | \operatorname{th}i | \(\operatorname{th}i\) |
| k'(x)=\lim_{\Delta x\to 0}\frac{k(x)-k(x-\Delta x)}{\Deltax} | \(k'(x)=\lim_ {\Delta x\to0} \frac{k(x)-k(x-\Delta x)}{\Delta x}\) | \limsup S | \(\limsup S\) |
| \max H | \(\max H\) | \min L | \(\min L\) |
| \sup t | \(\sup t\) | \exp t | \(\exp t\) |
| \lg X | \(\lg X\) | \log X | \(\log X\) |
| \ker x | \(\ker x\) | \deg x | \(\deg x\) |
| \Pr x | \(\Pr x\) | \det x | \(\det x\) |
| \arg x | \(\arg x\) | \dim x | \(\dim x\) |
| \tan\theta | \(\tan \theta\) | \arctan\frac{L}{T} | \(\arctan\frac{L}{T}\) |
| \tanh i | \(\tanh i\) | \operatorname{ch}h | \(\operatorname{ch}h\) |
| \operatorname{argth}m | \(\operatorname{argth}m\) | \liminf I | \(\liminf I\) |
| \inf s | \(\inf s\) | \ln X | \(\ln X\) |
| \log_\alpha X | \(\log_\alpha X\) | \gcd(T,U,V,W,X) | \(\gcd(T,U,V,W,X)\ ) |
| \hom x | \(\hom x\) | \lim_{t\to n}T | \(\lim_{t\to n}T\) |
Differentiation and Derivatives:
| Syntax | Display |
|---|---|
| dt | \(dt\) |
| \mathrm{d}t | \( \mathrm{d}t\) |
| \partial t | \( \partial t\) |
| \nabla\psi | \( \nabla\psi\) |
| dy/dx | \(dy/dx\) |
| \mathrm{d}y/\mathrm{d}x | \( \mathrm{d}y/\mathrm{d}x\) |
| \frac{dy}{dx} | \( \frac{dy}{dx}\) |
| \frac{\mathrm{d}y}{\mathrm{d}x} | \( \frac{\mathrm{d}y}{\mathrm{d}x}\) |
| \frac{\partial^2}{\partial x_1\partial x_2}y | \( \frac{\partial^2}{\partial x_1\partial x_2}y\) |
| \prime | \(\prime\) |
| \backprime | \( \backprime\) |
| f^\prime | \( f^\prime\) |
| f' | \( f'\) |
| f'' | \( f''\) |
| f^{(3)} | \( f^{(3)}\) |
| \dot y | \( \dot y\) |
| \ddot y | \( \ddot y\) |
Sum product, integral:
| Syntax | Display |
|---|---|
\sum_{k=1}^N k^2 | \(\sum_{k=1}^N k^2\) |
\begin{matrix} \sum_{k=1}^N k^2 \end{matrix} | \(\begin{matrix} \sum_{k=1}^N k^2 \end{matrix }\) |
\prod_{i=1}^N x_i | \(\prod_{i=1}^N x_i\) |
\begin{matrix} \prod_{i=1}^N x_i \end{matrix} | \(\begin{matrix} \prod_{i=1}^N x_i \end{matrix}\) |
\coprod_{i=1}^N x_i | \(\coprod_{i=1}^N x_i\) |
\begin{matrix} \coprod_{i=1}^N x_i \end{matrix} | \(\begin{matrix} \coprod_{i=1}^N x_i \end{matrix}\) |
\int_{-N}^{N} e^x\, {\rm d}x | \(\int_{-N}^{N} e^x\, {\rm d}x\ ) |
\begin{matrix} \int_{-N}^{N} e^x\, \mathrm{d}x \end{matrix} | \(\begin{matrix} \int_{-N}^ {N} e^x\, \mathrm{d}x \end{matrix}\) |
\iint_{D}^{W} \, \mathrm{d}x\,\mathrm{d}y | \(\iint_{D}^{W} \, \mathrm{d}x\ ,\mathrm{d}y\) |
\iiint_{E}^{V} \, \mathrm{d}x\,\mathrm{d}y\,\mathrm{d}z | \(\iiint_{E}^{V} \ , \mathrm{d}x\,\mathrm{d}y\,\mathrm{d}z\) |
\oint_{C} x^3\, \mathrm{d}x + 4y^2\, \mathrm{d}y | \(\oint_{C} x^3\, \mathrm{d} x + 4y^2\, \mathrm{d}y\) |
11. Reference
LaTeX formula manual
https://www.cnblogs.com/1024th/p/11623258.html
LaTex (2) Basic Math Symbols
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