Tex:Syntax

lastmod 2024-03-07created 2021-11-0513 edits

Explanation and list of Tex syntax.

Operations

Name	Syntax	Result
Multiplication	`\times`	\(\times\)
Division	`\div`	\(\div\)
Addition	`+`	\(+\)
Subtraction	`-`	\(-\)
Dot product (dot)	`\cdot`	\(\cdot\)

Special symbols

Name	Syntax	Result
Root (square root; Root)	`\sqrt{2}`	\(\sqrt{2}\)
Radical with index	`\sqrt[3]{5}`	\(\sqrt[3]{5}\)
Integral sign	`\int_{-\infty}^{\infty}{x}`	\(\int_{-\infty}^{\infty}{x}\)
Fraction	`\frac{1}{2}`	\(\frac{1}{2}\)
Inline (horizontal) fraction	`{1}/{2}`	\({1}/{2}\)
Subscript/superscript	`2_{5}^{10}`	\(2_{5}^{10}\)
Sum (SIGMA)	`\sum_{n=0}^{10}`	\(\sum_{n=0}^{10}\)
Product	`\prod{x}`	\(\prod{x}\)
Coproduct	`\coprod{x}`	\(\coprod{x}\)
Union	`\bigcup{x}`	\(\bigcup{x}\)
Intersection	`\bigcap{x}`	\(\bigcap{x}\)
V	`\bigvee{x}`	\(\bigvee{x}\)
Wedge	`\bigwedge{x}`	\(\bigwedge{x}\)

Brackets

You can just write brackets as (), but then they won't scale to the size of the content inside them. To have them sized automatically, use \left( and \right). Example:

Name	Syntax	Result
Plain	`(\frac{x}{y})`	\((\frac{x}{y})\)
Fitted	`\left(\frac{x}{y}\right)`	\(\left(\frac{x}{y}\right)\)

Bracket types:

Name	Syntax	Result
Parentheses	`\left( x \right)`	\(\left( x \right)\)
Braces	`\left\{ x \right\}`	\(\left\{ x \right\}\)
Square brackets	`\left[ x \right]`	\(\left[ x \right]\)
Angle brackets (chevrons)	`\left< x \right>`	\(\left< x \right>\)
Absolute value	`\left\| x \right\|`	\(\left\| x \right\|\)

Accents

Name	Syntax	Result
Dot	`\dot{x}`	\(\dot{x}\)
Double dot	`\ddot{x}`	\(\ddot{x}\)
Triple dot	`\dddot{x}`	\(\dddot{x}\)
Quadruple dot	`\ddddot{x}`	\(\ddddot{x}\)
Hat (hat)	`\hat{x}`	\(\hat{x}\)
Check (check)	`\check{x}`	\(\check{x}\)

Spacing

Name	Syntax	Result
Double quad space	`a \qquad b`	\(a \qquad b\)
Quad space	`a \quad b`	\(a \quad b\)
Space	`a\ b`	\(a\ b\)
Space	`a\;b`	\(a\;b\)
Space	`a\>b`	\(a\>b\)
Small space	`a\,b`	\(a\,b\)
Small space	`a\ b`	\(a\ b\)
No space	`ab`	\(ab\)
Negative space	`a\!b`	\(a\!b\)

Shapes

Name	Syntax	Result
Angle	`\angle`	\(\angle\)
Triangle	`\triangle`	\(\triangle\)
Inverted triangle	`\nabla`	\(\nabla\)
Triangle left	`\triangleleft`	\(\triangleleft\)
Triangle right	`\triangleright`	\(\triangleright\)
Square	`\square`	\(\square\)
Black square	`\blacksquare`	\(\blacksquare\)
Circle	`\circ`	\(\circ\)
Degree	`^{\circ}`	\(^{\circ}\)
Big circle	`\bigcirc`	\(\bigcirc\)
Asterisk	`\ast`	\(\ast\)
Star	`\star`	\(\star\)
Diamond	`\diamond`	\(\diamond\)
Spade	`\spadesuit`	\(\spadesuit\)
Club	`\clubsuit`	\(\clubsuit\)
Diamond	`\Diamond`	\(\Diamond\)
Heart	`\heartsuit`	\(\heartsuit\)

Greek letters

Category	Uppercase	Lowercase
Name	Command	Output
Alpha	`A`	\(A\)
Beta	`B`	\(B\)
Gamma	`\Gamma`	\(\Gamma\)
Delta	`\Delta`	\(\Delta\)
Epsilon	`E`	\(E\)
Zeta	`Z`	\(Z\)
Eta	`H`	\(H\)
Theta	`\Theta`	\(\Theta\)
Iota	`I`	\(I\)
Kappa	`K`	\(K\)
Lambda	`\Lambda`	\(\Lambda\)
Mu	`M`	\(M\)
Nu	`N`	\(N\)
Xi	`\Xi`	\(\Xi\)
Omicron	`O`	\(O\)
Pi	`\Pi`	\(\Pi\)
Rho	`P`	\(P\)
Sigma	`\Sigma`	\(\Sigma\)
Tau	`T`	\(T\)
Upsilon	`\Upsilon`	\(\Upsilon\)
Phi	`\Phi`	\(\Phi\)
Chi	`X`	\(X\)
Psi	`\Psi`	\(\Psi\)
Omega	`\Omega`	\(\Omega\)

Relational operators

Name	Command	Output
Congruence symbol	`\equiv`	\(\equiv\)
Approximately equal	`\approx`	\(\approx\)
Proportional to	`\propto`	\(\propto\)
simeq	`\simeq`	\(\simeq\)
Similar	`\sim`	\(\sim\)
Not equal	`\neq`	\(\neq\)
Less than or equal	`\leq`	\(\leq\)
Greater than or equal	`\geq`	\(\geq\)
Much greater than	`\gg`	\(\gg\)
Much less than	`\ll`	\(\ll\)

Logic symbols

Name	Command	Output
Bullet	`\bullet`	\(\bullet\)
Negation	`\neg`	\(\neg\)
wedge	`\wedge`	\(\wedge\)
vee	`\vee`	\(\vee\)
Logical OR	`\oplus`	\(\oplus\)
Left arrow	`\leftarrow`	\(\leftarrow\)
Right arrow	`\rightarrow`	\(\rightarrow\)
Left-right arrow	`\leftrightarrow`	\(\leftrightarrow\)
Left arrow	`\Leftarrow`	\(\Leftarrow\)
Right arrow	`\Rightarrow`	\(\Rightarrow\)
Left-right arrow	`\Leftrightarrow`	\(\Leftrightarrow\)
There exists	`\exists`	\(\exists\)
For all	`\forall`	\(\forall\)

Hats

Name	Command	Output
Hat	`\hat{x} \hat{xyz}`	\(\hat{xyz}\)
Wide hat	`\widehat{x} \widehat{xyz}`	\(\widehat{x}\ \widehat{xyz}\)
Tilde hat	`\tilde{x} \tilde{xyz}`	\(\tilde{x}\ \tilde{xyz}\)
Wide tilde hat	`\widetilde{x} \widetilde{xyz}`	\(\widetilde{x}\ \widetilde{xyz}\)
acute	`\acute{x}`	\(\acute{x}\)
grave	`\grave{x}`	\(\grave{x}\)
Dot hat	`\dot{x}`	\(\dot{x}\)
Double dot hat	`\ddot{x}`	\(\ddot{x}\)
Check hat	`\check{x}`	\(\check{x}\)
breve	`\breve{x}`	\(\breve{x}\)
bar	`\bar{x} \bar{xyz}`	\(\bar{x}\ \bar{xyz}\)
overline	`\overline{x} \overline{xyz}`	\(\overline{x}\ \overline{xyz}\)
Arrow hat	`\vec{x} \vec{xyz}`	\(\vec{x} \vec{xyz}\)

Set symbols

Name	Command	Output
Intersection	`\cap`	\(\cap\)
Union	`\cup`	\(\cup\)
Superset	`\supset`	\(\supset\)
Superset	`\subseteq`	\(\subseteq\)
Proper superset	`\subsetneq`	\(\subsetneq\)
Subset	`\subset`	\(\subset\)
Subset	`\subseteq`	\(\subseteq\)
Proper subset	`\subsetneq`	\(\subsetneq\)
Not a subset	`\not\subset`	\(\not\subset\)
Not a subset	`\nsubseteq`	\(\nsubseteq\)
Empty set	`\emptyset`	\(\emptyset\)
Set Z	`\mathbb{Z}`	\(\mathbb{Z}\)
Element of	`\in`	\(\in\)
Not an element of	`\notin`	\(\notin\)
Join	`\Join`	\(\Join\)

Vectors

Name	Command	Output
vector	`\vec{a}`	\(\vec{a}\)

Matrices

There are the following 5 ways to write matrices in TeX.

Name	Command	Output
array	`\begin{array} a & b \\ c & d \end{array}`	\(\begin{array} a & b \\ c & d \end{array}\)
matrix	`\begin{matrix} a & b \\ c & d \end{matrix}`	\(\begin{matrix} a & b \\ c & d \end{matrix}\)
bmatrix	`\begin{bmatrix} a & b \\ c & d \end{bmatrix}`	\(\begin{bmatrix} a & b \\ c & d \end{bmatrix}\)
pmatrix	`\begin{pmatrix} a & b \\ c & d \end{pmatrix}`	\(\begin{pmatrix} a & b \\ c & d \end{pmatrix}\)
vmatrix	`\begin{vmatrix} a & b \\ c & d \end{vmatrix}`	\(\begin{vmatrix} a & b \\ c & d \end{vmatrix}\)
Vmatrix	`\begin{Vmatrix} a & b \\ c & d \end{Vmatrix}`	\(\begin{Vmatrix} a & b \\ c & d \end{Vmatrix}\)

Alignment

Mainly used when writing proofs of equations.

\begin{align}
f(x) &= (x + a)^2 \\
&= (x + a) (x + a) \\
&= x^2 + 2ax + a^2
\end{align}

The result is as follows.

\[ \begin{align} f(x) &= (x + a)^2 \\ &= (x + a) (x + a) \\ &= x^2 + 2ax + a^2 \end{align} \]

Other

Name	Command	Output
Center dot	`\cdot`	\(\cdot\)
Ellipsis	`\dots`	\(\dots\)
Ellipsis	`\cdots`	\(\cdots\)
Ellipsis	`\ldots`	\(\ldots\)
Vertical ellipsis	`\vdots`	\(\vdots\)
Diagonal ellipsis	`\ddots`	\(\ddots\)
Division	`\div`	\(\div\)
Tilde	`\sim`	\(\sim\)
Double tilde	`\approx`	\(\approx\)
Plus-minus	`\pm`	\(\pm\)
Minus-plus	`\mp`	\(\mp\)
Prime	`\prime`	\(\prime\)
Infinity	`\infty`	\(\infty\)
Integral (integral sign)	`\int`	\(\int\)
Partial derivative	`\partial`	\(\partial\)

displaystyle

As shown below, the fraction looks small, as if squeezed to fit on one line...

\(y=y_{0}+(y_{1}-y_{0}){\frac {x-x_{0}}{x_{1}-x_{0}}}\)

If you use {\displaystyle ... },

\({\displaystyle y=y_{0}+(y_{1}-y_{0}){\frac {x-x_{0}}{x_{1}-x_{0}}}}\)

it adjusts to the line size and looks nicer.

Document begin and end

\begin{document}
\end{document}

If you want a bracket on only one side

For the right side that pairs with the left \left\{, put a dot: \right..

\(\alpha(x) = \left\{ \begin{matrix} A & B \\ C & D \end{matrix} \right.\)

If you want alignment inside a matrix

Put it between \begin{matrix} \begin{align} and \end{align} \end{matrix}.

Alignment is based on &, so place it at the appropriate positions.

\(L \leftarrow \left\{ \begin{matrix} \begin{align} & 116*Y^{1/3}-16 & \textrm{for} Y>0.008856 \\ & 903.3*Y & \textrm{for} Y \le 0.008856 \end{align} \end{matrix} \right.\)

Inserting non-italic text

Use it like \textrm{for}.

\(\textrm{for} vs for\)

Adding tags

Use it like \tag{1}.

\(\begin{align} x^2 +y^2=r^2 \tag{1} \\ x\sin \theta +y\cos\theta =r^2 \tag{2} \end{align}\)

Line breaks

\\ (backslash twice)
\newline
\break

Favorite site

Extension:Math/Help:Formula - MediaWiki

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