LaTeX mathematic cheat sheet

09/01/2022 15:55

Practically, LaTeX is the standard typesetting system for scientific writing. Most of the well-written equations that appeared in books and around the web are written using LaTeX.

Accents/diacritics

`\acute{a} \grave{a} \hat{a} \tilde{a} \breve{a}`	${\acute {a}}{\grave {a}}{\hat {a}}{\tilde {a}}{\breve {a}}\,$
`\check{a} \bar{a} \ddot{a} \dot{a}`	${\check {a}}{\bar {a}}{\ddot {a}}{\dot {a}}$

Standard functions

`\sin a \cos b \tan c`	$\sin a\cos b\tan c$
`\sec d \csc e \cot f`	$\sec d\csc e\cot f\,$
`\arcsin h \arccos i \arctan j`	$\arcsin h\arccos i\arctan j\,$
`\sinh k \cosh l \tanh m \coth n`	$\sinh k\cosh l\tanh m\coth n$
`\operatorname{sh}o\, \operatorname{ch}p\, \operatorname{th}q`	$\operatorname {sh} o\,\operatorname {ch} p\,\operatorname {th} q$
`\operatorname{arsinh}r\, \operatorname{arcosh}s\, \operatorname{artanh}t`	$\operatorname {arsinh} r\,\operatorname {arcosh} s\,\operatorname {artanh} t$
`\lim u \limsup v \liminf w \min x \max y`	$\lim u\limsup v\liminf w\min x\max y$
`\inf z \sup a \exp b \ln c \lg d \log e \log_{10} f \ker g`	$\inf z\sup a\exp b\ln c\lg d\log e\log _{10}f\ker g$
`\deg h \gcd i \Pr j \det k \hom l \arg m \dim n`	$\deg h\gcd i\Pr j\det k\hom l\arg m\dim n$

Modular arithmetic

`s_k \equiv 0 \pmod{m}`	$s_{k}\equiv 0{\pmod {m}}\,$
`a\, \bmod\, b`	$a\,{\bmod {\,}}b\,$

Derivatives

\nabla\, \partial x\, dx\, \dot x\, \ddot y\, dy/dx\, \frac{dy}{dx}\, \frac{\partial^2 y}, {\partial x_1\,\partial x_2}

$\nabla \,\partial x\,dx\,{\dot {x}}\,{\ddot {y}}\,dy/dx\,{\frac {dy}{dx}}\,{\frac {\partial ^{2}y}{\partial x_{1}\,\partial x_{2}}}$

Sets

`\forall \exists \empty \emptyset \varnothing`	$\forall \exists \emptyset \emptyset \varnothing \,$
`\in \ni \not\in \notin \not\ni \subset \subseteq \supset \supseteq`	$\in \ni \not \in \notin \not \ni \subset \subseteq \supset \supseteq \,$
`\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus`	$\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus \,$
`\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup`	$\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup \,$

Operators

`+ \oplus \bigoplus \pm \mp -`	$+\oplus \bigoplus \pm \mp -\,$
`\times \otimes \bigotimes \cdot \circ \bullet \bigodot`	$\times \otimes \bigotimes \cdot \circ \bullet \bigodot \,$
`\star */ \div \frac{1}{2}`	$\star */\div {\frac {1}{2}}\,$

Logic

`\land (or \and) \wedge \bigwedge \bar{q} \to p`	$\land \wedge \bigwedge {\bar {q}}\to p\,$
`\lor \vee \bigvee \lnot \neg q \And`	$\lor \vee \bigvee \lnot \neg q\And \,$

Root

\sqrt{2} \sqrt[n]{x}

${\sqrt {2}}{\sqrt[{n}]{x}}\,$

Relations

`\sim \approx \simeq \cong \dot= \overset{\underset{\mathrm{def}}{}}{=}`	$\sim \approx \simeq \cong {\dot {=}}{\overset {\underset {\mathrm {def} }{}}{=}}\,$
`< \le \ll \gg \ge > \equiv \not\equiv \ne \mbox{or} \neq \propto`	$<\leq \ll \gg \geq >\equiv \not \equiv \neq {\mbox{or}}\neq \propto \,$
`\lessapprox \lesssim \eqslantless \leqslant \leqq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox`	$\lessapprox \lesssim \eqslantless \leqslant \leqq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox$

Geometric

\Diamond \Box \triangle \angle \perp \mid \nmid \| 45^\circ

$\Diamond \,\Box \,\triangle \,\angle \perp \,\mid \;\nmid \,\|45^{\circ }\,$

Arrows

`\leftarrow (or \gets) \rightarrow (or \to) \nleftarrow \nrightarrow \leftrightarrow \nleftrightarrow \longleftarrow \longrightarrow \longleftrightarrow`	$\leftarrow \rightarrow \nleftarrow \nrightarrow \leftrightarrow \nleftrightarrow \longleftarrow \longrightarrow \longleftrightarrow \,$
`\Leftarrow \Rightarrow \nLeftarrow \nRightarrow \Leftrightarrow \nLeftrightarrow \Longleftarrow` `(or \impliedby) \Longrightarrow (or \implies) \Longleftrightarrow (or \iff)`	$\Leftarrow \Rightarrow \nLeftarrow \nRightarrow \Leftrightarrow \nLeftrightarrow \Longleftarrow \Longrightarrow \Longleftrightarrow$
`\uparrow \downarrow \updownarrow \Uparrow \Downarrow \Updownarrow \nearrow \searrow \swarrow \nwarrow`	$\uparrow \downarrow \updownarrow \Uparrow \Downarrow \Updownarrow \nearrow \searrow \swarrow \nwarrow$
`\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons`	$\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons \,$
`\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \Rrightarrow` `\rightarrowtail \looparrowright`	$\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \Rrightarrow \rightarrowtail \looparrowright \,$
`\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \Lleftarrow` `\leftarrowtail \looparrowleft`	$\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \Lleftarrow \leftarrowtail \looparrowleft \,$
`\mapsto \longmapsto \hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow`	$\mapsto \longmapsto \hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow \,$

Special

`\And \eth \S \P \% \dagger \ddagger \ldots \cdots \colon`	$\And \eth \S \P \%\dagger \ddagger \ldots \cdots \colon \,$
`\smile \frown \wr \triangleleft \triangleright \infty \bot \top`	$\smile \frown \wr \triangleleft \triangleright \infty \bot \top \,$
`\vdash \vDash \Vdash \models \lVert \rVert \imath \hbar`	$\vdash \vDash \Vdash \models \lVert \rVert \imath \hbar \,$
`\ell \mho \Finv \Re \Im \wp \complement`	$\ell \mho \Finv \Re \Im \wp \complement \,$
`\diamondsuit \heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp`	$\diamondsuit \heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp \,$

USubscripts, superscripts, integrals

Feature	Syntax	How it looks rendered
Superscript	`a^2`	$a^{2}$
Subscript	`a_2`	$a_{2}$
Grouping	`a^{2+2}`	$a^{2+2}$
Grouping	`a_{i,j}`	$a_{i,j}$
Combining sub & super without and with horizontal separation	`x_2^3`	$x_{2}^{3}$
	`{x_2}^3`	${x_{2}}^{3}$
Super super	`10^{10^{8}}`	$10^{10^{8}}$
Preceding and/or Additional sub & super	`_nP_k`	$_{n}P_{k}$
	`\sideset{_1^2}{_3^4}\prod_a^b`	$\sideset {_{1}^{2}}{_{3}^{4}}\prod _{a}^{b}$
	`{}_1^2\!\Omega_3^4`	${}_{1}^{2}\!\Omega _{3}^{4}$
Stacking	`\overset{\alpha}{\omega}`	${\overset {\alpha }{\omega }}$
	`\underset{\alpha}{\omega}`	${\underset {\alpha }{\omega }}$
	`\overset{\alpha}{\underset{\gamma}{\omega}}`	${\overset {\alpha }{\underset {\gamma }{\omega }}}$
	`\stackrel{\alpha}{\omega}`	${\stackrel {\alpha }{\omega }}$
Derivatives	`x', y'', f', f''`
Derivatives	`x^\prime, y^{\prime\prime}`	$x^{\prime },y^{\prime \prime }$
Derivative dots	`\dot{x}, \ddot{x}`	${\dot {x}},{\ddot {x}}$
Underlines, overlines, vectors	`\hat a\ \bar b\ \vec c`	${\hat {a}}\ {\bar {b}}\ {\vec {c}}$
	`\overrightarrow{a b}\ \overleftarrow{c d}\ \widehat{d e f}`	${\overrightarrow {ab}}\ {\overleftarrow {cd}}\ {\widehat {def}}$
	`\overline{g h i}\ \underline{j k l}`	${\overline {ghi}}\ {\underline {jkl}}$
	`\not 1\ \cancel{123}`	$\not 1\ {\cancel {123}}$
Arrows	`A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C`	$A{\xleftarrow {n+\mu -1}}B{\xrightarrow[{T}]{n\pm i-1}}C$
Overbraces	`\overbrace{ 1+2+\cdots+100 }^{\text{sum}\,=\,5050}`	$\overbrace {1+2+\cdots +100} ^{{\text{sum}}\,=\,5050}$
Underbraces	`\underbrace{ a+b+\cdots+z }_{26\text{ terms}}`	$\underbrace {a+b+\cdots +z} _{26{\text{ terms}}}$
Sum	`\sum_{k=1}^N k^2`	$\sum _{k=1}^{N}k^{2}$
Sum (force `\textstyle`)	`\textstyle \sum_{k=1}^N k^2`	$\textstyle \sum _{k=1}^{N}k^{2}$
Product	`\prod_{i=1}^N x_i`	$\prod _{i=1}^{N}x_{i}$
Product (force `\textstyle`)	`\textstyle \prod_{i=1}^N x_i`	$\textstyle \prod _{i=1}^{N}x_{i}$
Coproduct	`\coprod_{i=1}^N x_i`	$\coprod _{i=1}^{N}x_{i}$
Coproduct (force `\textstyle`)	`\textstyle \coprod_{i=1}^N x_i`	$\textstyle \coprod _{i=1}^{N}x_{i}$
Limit	`\lim_{n \to \infty}x_n`	$\lim _{n\to \infty }x_{n}$
Limit (force `\textstyle`)	`\textstyle \lim_{n \to \infty}x_n`	$\textstyle \lim _{n\to \infty }x_{n}$
Integral	`\int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx`	$\int \limits _{1}^{3}{\frac {e^{3}/x}{x^{2}}}\,dx$
Integral (alternate limits style)	`\int_{1}^{3}\frac{e^3/x}{x^2}\, dx`	$\int _{1}^{3}{\frac {e^{3}/x}{x^{2}}}\,dx$
Integral (force `\textstyle`)	`\textstyle \int\limits_{-N}^{N} e^x\, dx`	$\textstyle \int \limits _{-N}^{N}e^{x}\,dx$
Integral (force `\textstyle`, alternate limits style)	`\textstyle \int_{-N}^{N} e^x\, dx`	$\textstyle \int _{-N}^{N}e^{x}\,dx$
Double integral	`\iint\limits_D \, dx\,dy`	$\iint \limits _{D}\,dx\,dy$
Triple integral	`\iiint\limits_E \, dx\,dy\,dz`	$\iiint \limits _{E}\,dx\,dy\,dz$
Quadruple integral	`\iiiint\limits_F \, dx\,dy\,dz\,dt`	$\iiiint \limits _{F}\,dx\,dy\,dz\,dt$
Line or path integral	`\int_C x^3\, dx + 4y^2\, dy`	$\int _{C}x^{3}\,dx+4y^{2}\,dy$
Closed line or path integral	`\oint_C x^3\, dx + 4y^2\, dy`	$\oint _{C}x^{3}\,dx+4y^{2}\,dy$
Intersections	`\bigcap_1^n p`	$\bigcap _{1}^{n}p$
Unions	`\bigcup_1^k p`	$\bigcup _{1}^{k}p$

Fractions, matrices, multi-lines

Feature	Syntax	How it looks rendered
Fractions	`\frac{1}{2}=0.5`	${\frac {1}{2}}=0.5$
Small ("text style") fractions	`\tfrac{1}{2} = 0.5`	${\tfrac {1}{2}}=0.5$
Large ("display style") fractions	`\dfrac{k}{k-1} = 0.5`	${\dfrac {k}{k-1}}=0.5$
Mixture of large and small fractions	`\dfrac{ \tfrac{1}{2}[1-(\tfrac{1}{2})^n] }{ 1-\tfrac{1}{2} } = s_n`	${\dfrac {{\tfrac {1}{2}}[1-({\tfrac {1}{2}})^{n}]}{1-{\tfrac {1}{2}}}}=s_{n}$
Continued fractions (note the difference in formatting)	\cfrac{2}{ c + \cfrac{2}{ d + \cfrac{1}{2} } } = a \qquad \dfrac{2}{ c + \dfrac{2}{ d + \dfrac{1}{2} } } = a	${\cfrac {2}{c+{\cfrac {2}{d+{\cfrac {1}{2}}}}}}=a\qquad {\dfrac {2}{c+{\dfrac {2}{d+{\dfrac {1}{2}}}}}}=a$
Binomial coefficients	`\binom{n}{k}`	${\binom {n}{k}}$
Small ("text style") binomial coefficients	`\tbinom{n}{k}`	${\tbinom {n}{k}}$
Large ("display style") binomial coefficients	`\dbinom{n}{k}`	${\dbinom {n}{k}}$
Matrices	\begin{matrix} x & y \\ z & v \end{matrix}	${\begin{matrix}x&y\\z&v\end{matrix}}$
	\begin{vmatrix} x & y \\ z & v \end{vmatrix}	${\begin{vmatrix}x&y\\z&v\end{vmatrix}}$
	\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}	${\begin{Vmatrix}x&y\\z&v\end{Vmatrix}}$
	\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0 \end{bmatrix}	${\begin{bmatrix}0&\cdots &0\\\vdots &\ddots &\vdots \\0&\cdots &0\end{bmatrix}}$
	\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}	${\begin{Bmatrix}x&y\\z&v\end{Bmatrix}}$
	\begin{pmatrix} x & y \\ z & v \end{pmatrix}	${\begin{pmatrix}x&y\\z&v\end{pmatrix}}$
	\bigl( \begin{smallmatrix} a&b\\ c&d \end{smallmatrix} \bigr)	${\bigl (}{\begin{smallmatrix}a&b\\c&d\end{smallmatrix}}{\bigr )}$
Arrays	\begin{array}{\|c\|c\|\|c\|} a & b & S \\ \hline 0&0&1\\ 0&1&1\\ 1&0&1\\ 1&1&0 \end{array}	${\begin{array}{\|c\|c\|\|c\|}a&b&S\\\hline 0&0&1\\0&1&1\\1&0&1\\1&1&0\end{array}}$
Cases	f(n) = \begin{cases} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{cases}	$f(n)={\begin{cases}n/2,&{\mbox{if }}n{\mbox{ is even}}\\3n+1,&{\mbox{if }}n{\mbox{ is odd}}\end{cases}}$
System of equations	\begin{cases} 3x + 5y + z &= 1 \\ 7x - 2y + 4z &= 2 \\ -6x + 3y + 2z &= 3 \end{cases}	${\begin{cases}3x+5y+z&=1\\7x-2y+4z&=2\\-6x+3y+2z&=3\end{cases}}$
Breaking up a long expression so it wraps when necessary	<math>f(x) = \sum_{n=0}^\infty a_n x^n</math> <math>= a_0 + a_1x + a_2x^2 + \cdots</math>	$f(x)=\sum _{n=0}^{\infty }a_{n}x^{n}$ $=a_{0}+a_{1}x+a_{2}x^{2}+\cdots$
Multiline equations	\begin{align} f(x) & = (a+b)^2 \\ & = a^2+2ab+b^2 \end{align}	${\begin{aligned}f(x)&=(a+b)^{2}\\&=a^{2}+2ab+b^{2}\end{aligned}}$
Multiline equations	\begin{alignat}{2} f(x) & = (a-b)^2 \\ & = a^2-2ab+b^2 \end{alignat}	${\begin{alignedat}{2}f(x)&=(a-b)^{2}\\&=a^{2}-2ab+b^{2}\end{alignedat}}$
Multiline equations with alignment specified (left, center, right)	\begin{array}{lcl} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}	${\begin{array}{lcl}z&=&a\\f(x,y,z)&=&x+y+z\end{array}}$
	\begin{array}{lcr} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}	${\begin{array}{lcr}z&=&a\\f(x,y,z)&=&x+y+z\end{array}}$

Parenthesizing big expressions, brackets, bars

Feature	Syntax	How it looks rendered
Bad	`( \frac{1}{2} )`	$({\frac {1}{2}})$
Good	`\left ( \frac{1}{2} \right )`	$\left({\frac {1}{2}}\right)$

You can use various delimiters with \left and \right:

Feature	Syntax	How it looks rendered
Parentheses	`\left ( \frac{a}{b} \right )`	$\left({\frac {a}{b}}\right)$
Brackets	`\left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack`	$\left[{\frac {a}{b}}\right]\quad \left\lbrack {\frac {a}{b}}\right\rbrack$
Braces (note the backslash before the braces in the code)	`\left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace`	$\left\{{\frac {a}{b}}\right\}\quad \left\lbrace {\frac {a}{b}}\right\rbrace$
Angle brackets	`\left \langle \frac{a}{b} \right \rangle`	$\left\langle {\frac {a}{b}}\right\rangle$
Bars and double bars (note: "bars" provide the absolute value function)	`\left \| \frac{a}{b} \right \vert \left \Vert \frac{c}{d} \right \\|`	$\left\|{\frac {a}{b}}\right\vert \left\Vert {\frac {c}{d}}\right\\|$
Floor and ceiling functions:	`\left \lfloor \frac{a}{b} \right \rfloor \left \lceil \frac{c}{d} \right \rceil`	$\left\lfloor {\frac {a}{b}}\right\rfloor \left\lceil {\frac {c}{d}}\right\rceil$
Slashes and backslashes	`\left / \frac{a}{b} \right \backslash`	$\left/{\frac {a}{b}}\right\backslash$
Up, down and up-down arrows	`\left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow`	$\left\uparrow {\frac {a}{b}}\right\downarrow \quad \left\Uparrow {\frac {a}{b}}\right\Downarrow \quad \left\updownarrow {\frac {a}{b}}\right\Updownarrow$
Delimiters can be mixed, as long as `\left` and `\right` are both used	`\left [ 0,1 \right ) \left \langle \psi \right \|`	$\left[0,1\right)$ $\left\langle \psi \right\|$
Use `\left.` or `\right.` if you don't want a delimiter to appear:	`\left . \frac{A}{B} \right \} \to X`	$\left.{\frac {A}{B}}\right\}\to X$
Size of the delimiters	`\big( \Big( \bigg( \Bigg( \dots \Bigg] \bigg] \Big] \big]`	${\big (}{\Big (}{\bigg (}{\Bigg (}\dots {\Bigg ]}{\bigg ]}{\Big ]}{\big ]}$
	`\big\{ \Big\{ \bigg\{ \Bigg\{ \dots \Bigg\rangle \bigg\rangle` `\Big\rangle \big\rangle`	${\big \{}{\Big \{}{\bigg \{}{\Bigg \{}\dots {\Bigg \rangle }{\bigg \rangle }{\Big \rangle }{\big \rangle }$
	`\big\| \Big\| \bigg\| \Bigg\| \dots \Bigg\\| \bigg\\| \Big\\| \big\\|`	${\big \|}{\Big \|}{\bigg \|}{\Bigg \|}\dots {\Bigg \\|}{\bigg \\|}{\Big \\|}{\big \\|}$
	`\big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor \dots \Bigg\rceil` `\bigg\rceil \Big\rceil \big\rceil`	${\big \lfloor }{\Big \lfloor }{\bigg \lfloor }{\Bigg \lfloor }\dots {\Bigg \rceil }{\bigg \rceil }{\Big \rceil }{\big \rceil }$
	`\big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots \Bigg\Downarrow` `\bigg\Downarrow \Big\Downarrow \big\Downarrow`	${\big \uparrow }{\Big \uparrow }{\bigg \uparrow }{\Bigg \uparrow }\dots {\Bigg \Downarrow }{\bigg \Downarrow }{\Big \Downarrow }{\big \Downarrow }$
	`\big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots` `\Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow`	${\big \updownarrow }{\Big \updownarrow }{\bigg \updownarrow }{\Bigg \updownarrow }\dots {\Bigg \Updownarrow }{\bigg \Updownarrow }{\Big \Updownarrow }{\big \Updownarrow }$
	`\big / \Big / \bigg / \Bigg / \dots \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash`	${\big /}{\Big /}{\bigg /}{\Bigg /}\dots {\Bigg \backslash }{\bigg \backslash }{\Big \backslash }{\big \backslash }$

Alphabets

Greek alphabet
Boldface (greek)
`\Alpha \Beta \Gamma \Delta \Epsilon \Zeta`	$\mathrm {A} \mathrm {B} \Gamma \Delta \mathrm {E} \mathrm {Z} \,$
`\Eta \Theta \Iota \Kappa \Lambda \Mu`	$\mathrm {H} \Theta \mathrm {I} \mathrm {K} \Lambda \mathrm {M} \,$
`\Nu \Xi \Omicron \Pi \Rho \Sigma \Tau`	$\mathrm {N} \Xi \mathrm {O} \Pi \mathrm {P} \Sigma \mathrm {T} \,$
`\Upsilon \Phi \Chi \Psi \Omega`	$\Upsilon \Phi \mathrm {X} \Psi \Omega \,$
`\alpha \beta \gamma \delta \epsilon \zeta`	$\alpha \beta \gamma \delta \epsilon \zeta \,$
`\eta \theta \iota \kappa \lambda \mu`	$\eta \theta \iota \kappa \lambda \mu \,$
`\nu \xi \omicron \pi \rho \sigma \tau`	$\nu \xi \mathrm {o} \pi \rho \sigma \tau \,$
`\upsilon \phi \chi \psi \omega`	$\upsilon \phi \chi \psi \omega \,$
`\varepsilon \digamma \vartheta \varkappa`	$\varepsilon \digamma \vartheta \varkappa \,$
`\varpi \varrho \varsigma \varphi`	$\varpi \varrho \varsigma \varphi \,$
`\boldsymbol{\Alpha} \boldsymbol{\Beta} \boldsymbol{\Gamma} \boldsymbol{\Delta} \boldsymbol{\Epsilon} \boldsymbol{\Zeta}`	${\boldsymbol {\mathrm {A} }}{\boldsymbol {\mathrm {B} }}{\boldsymbol {\Gamma }}{\boldsymbol {\Delta }}{\boldsymbol {\mathrm {E} }}{\boldsymbol {\mathrm {Z} }}\,$
`\boldsymbol{\Eta} \boldsymbol{\Theta} \boldsymbol{\Iota} \boldsymbol{\Kappa} \boldsymbol{\Lambda}` `\boldsymbol{\Mu}`	${\boldsymbol {\mathrm {H} }}{\boldsymbol {\Theta }}{\boldsymbol {\mathrm {I} }}{\boldsymbol {\mathrm {K} }}{\boldsymbol {\Lambda }}{\boldsymbol {\mathrm {M} }}\,$
`\boldsymbol{\Nu} \boldsymbol{\Xi} \boldsymbol{\Pi} \boldsymbol{\Rho} \boldsymbol{\Sigma}` `\boldsymbol{\Tau}`	${\boldsymbol {\mathrm {N} }}{\boldsymbol {\Xi }}{\boldsymbol {\Pi }}{\boldsymbol {\mathrm {P} }}{\boldsymbol {\Sigma }}{\boldsymbol {\mathrm {T} }}\,$
`\boldsymbol{\Upsilon} \boldsymbol{\Phi} \boldsymbol{\Chi} \boldsymbol{\Psi} \boldsymbol{\Omega}`	${\boldsymbol {\Upsilon }}{\boldsymbol {\Phi }}{\boldsymbol {\mathrm {X} }}{\boldsymbol {\Psi }}{\boldsymbol {\Omega }}\,$
`\boldsymbol{\alpha} \boldsymbol{\beta} \boldsymbol{\gamma} \boldsymbol{\delta} \boldsymbol{\epsilon}` `\boldsymbol{\zeta}`	${\boldsymbol {\alpha }}{\boldsymbol {\beta }}{\boldsymbol {\gamma }}{\boldsymbol {\delta }}{\boldsymbol {\epsilon }}{\boldsymbol {\zeta }}\,$
`\boldsymbol{\eta} \boldsymbol{\theta} \boldsymbol{\iota} \boldsymbol{\kappa} \boldsymbol{\lambda}` `\boldsymbol{\mu}`	${\boldsymbol {\eta }}{\boldsymbol {\theta }}{\boldsymbol {\iota }}{\boldsymbol {\kappa }}{\boldsymbol {\lambda }}{\boldsymbol {\mu }}\,$
`\boldsymbol{\nu} \boldsymbol{\xi} \boldsymbol{\pi} \boldsymbol{\rho} \boldsymbol{\sigma}` `\boldsymbol{\tau}`	${\boldsymbol {\nu }}{\boldsymbol {\xi }}{\boldsymbol {\pi }}{\boldsymbol {\rho }}{\boldsymbol {\sigma }}{\boldsymbol {\tau }}\,$
`\boldsymbol{\upsilon} \boldsymbol{\phi} \boldsymbol{\chi} \boldsymbol{\psi} \boldsymbol{\omega}`	${\boldsymbol {\upsilon }}{\boldsymbol {\phi }}{\boldsymbol {\chi }}{\boldsymbol {\psi }}{\boldsymbol {\omega }}\,$
`\boldsymbol{\varepsilon} \boldsymbol{\digamma} \boldsymbol{\vartheta} \boldsymbol{\varkappa}`	${\boldsymbol {\varepsilon }}{\boldsymbol {\digamma }}{\boldsymbol {\vartheta }}{\boldsymbol {\varkappa }}\,$
`\boldsymbol{\varpi} \boldsymbol{\varrho} \boldsymbol{\varsigma} \boldsymbol{\varphi}`	${\boldsymbol {\varpi }}{\boldsymbol {\varrho }}{\boldsymbol {\varsigma }}{\boldsymbol {\varphi }}\,$