Aiuto:Prontuario TeX

In questa pagina presentiamo i segni e i costrutti facenti parte del sottolinguaggio TeX/LaTeX che consente l'inserimento di formule matematiche nelle pagine di Wikibooks. Le possibilità sono presentate in ordine alfabetico al fine di facilitare il ritrovamento da parte di chi possegga già qualche conoscenza di TeX, di LaTeX o delle formule per le pagine di Wikibooks.

In questa pagina si intendono anche fornire esempi tendenzialmente significativi, anche al fine di stimolare la omogeneità delle notazioni.

A - B- C - D - E - F - G - I - L - M - N - O - P - Q - R - S - T - V- VARIE

A

accenti e segni diacritici

$\stackrel{`}{a}$   \grave{a}	$\acute{e}$   \acute{e}
$\hat{H}$   \hat{H}	$\check{c}$   \check{c}
$\overline{𝐯}$   \bar{\mathbf{v}}	$\overrightarrow{ℳ}$   \vec{\mathcal{M}}
$\dot{\rho }$   \dot{\rho}	$\ddot{𝖷}$   \ddot{\mathsf{X}}
$\breve{o}$   \breve{o}	$\tilde{N}$   \tilde{N}

angoli

$15^{\circ }12^{\prime }38^{″}$   15^\circ 12' 38''       $A\hat{B}C$   A\hat BC       $\widehat{HJK}$   \widehat{HJK}       $\mathrm{\angle }A\hat{B}C$   \angle A\hat BC      $\widehat{𝐯𝐰}$   \widehat{\mathbf{vw}}       $\mathrm{\angle }\overrightarrow{OA}\overrightarrow{OB}$   \angle \vec{OA}\vec{OB}

B

binomiali, coefficienti

$(\genfrac{}{}{0ex}{}{n}{k}):=\frac{n!}{k!(n-k)!}$     {n \choose k} := \frac{n!}{k!(n-k)!}

$(\genfrac{}{}{0ex}{}{n}{k})=(\genfrac{}{}{0ex}{}{n-1}{k-1})+(\genfrac{}{}{0ex}{}{n-1}{k})$       {n \choose k} = (n-1 \choose k-1} + (n-1 \choose k}

C

calligrafica / fonte : v. fonti speciali

complessi / espressioni per numeri

$z=x+iy=\rho e^{i\theta }=|z|e^{i\arg z}$   z = x+iy = \rho e^{i\theta} = |z| e^{i \arg z}       $\mathrm{\Re }(x+iy)=x$   \Re(x+iy) = x       $\mathrm{\Im }(x+iy)=y$   \Im(x+iy) = y      

D

derivate

$\frac{d}{dx}f(x)$   {d\over dx} f(x)       $\mathrm{\nabla }\partial xdx\dot{x}\ddot{y}\psi (x)$   \nabla \; \partial x \; dx \; \dot x \; \ddot y \psi(x)       $\frac{\partial }{\partial y}F(x,y)$   {\partial \over \partial y} F(x,y)

determinanti

$\det [\frac{\partial }{\partial x_i}\frac{\partial }{\partial x_j}|1\le i,j\le n]$

\det\left[ \frac{\partial}{\partial x_i}\frac{\partial}{\partial x_j} \,|\, 1\leq i,j\leq n \right]

$\left|\begin{array}{cccc}1& 1& 1& 1\\ 1& 2& 3& 4\\ 1& 3& 6& 10\\ 1& 4& 10& 20\end{array}\right|=1$

\begin{vmatrix} 1 & 1 & 1 & 1 \\ 1 & 2 & 3 & 4 \\ 1 & 3 & 6 & 10 \\ 1 & 4 & 10 & 20 \end{vmatrix} = 1

disponibili / segni

$\mathrm{♡}$   \heartsuit	$\mathrm{♠}$   \spadesuit	$\mathrm{♣}$   \clubsuit	$\mathrm{♢}$   \diamondsuit
$ı$   \imath	$\ell$   \ell	$\mathrm{\wp }$   \wp	$\mho$   \mho
$\mathrm{♭}$   \flat	$\mathrm{♮}$   \natural	$\mathrm{♯}$   \sharp	$𝓍$   \mathcal{x}
$\mathrm{\top }$   \top	$\mathrm{\perp }$   \bot	$◻$   \Box	$◊$   \Diamond

E

ebraiche / lettere       \aleph   $\mathrm{\aleph }$       \beth $\beth$       \gimel $\gimel$       \daleth$\daleth$

entità particolari

$\mathrm{\varnothing }$   \empty	$\mathrm{\infty }$   \infty	$\hslash$   \hbar
$\mathbb{N}$   \N	$ℝ$   \R

esponenziali

10^{a+b}   $10^{a+b}$       \,10^{a+b}\,   $10^{a+b}$       e^{-x^2}   $e^{-x^2}$       ${{4^4}^4}^4$   {{4^4}^4}^4       ${{{5^5}^5}^5}^5$   {{{5^5}^5}^5}^5

F

fonti / confronto

$𝒞𝒜ℒℒℐ𝒢ℛ𝒜ℱℐ𝒞𝒜$   \mathcal{CALLIGRAFICA}

$Corsivo\mathit{(}𝐼𝑡𝑎𝑙𝑖𝑐\mathit{)}$   Corsivo\ \mathrm{(Italic)

$𝔣𝔯𝔞𝔨𝔱𝔲𝔯𝔪𝔦𝔫𝔲𝔰𝔠𝔬𝔩𝔬$   \mathfrak{fraktur\ minuscolo

$𝔉\Re 𝔄𝔎𝔗𝔘\Re 𝔐𝔄\Im 𝔘𝔖ℭ𝔒𝔏𝔒$   \mathfrak{FRAKTUR\ MAIUSCOLO}

$𝐆𝐫𝐚𝐬𝐬𝐞𝐭𝐭𝐨\mathbf{(}𝐛𝐨𝐥𝐝𝐟𝐚𝐜𝐞\mathbf{)}$   \mathbf{Grassetto (boldface)}

$\mathrm{N}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{(}\mathrm{R}\mathrm{o}\mathrm{m}\mathrm{a}\mathrm{n}\mathrm{)}$   \mathrm{Normale\ (Roman)

$𝖲𝖺𝗇𝗌𝖲𝖾𝗋𝗂𝖿$   \mathsf{Sans\ Serif}

$𝕊𝕋𝕀𝕃𝔼𝕃𝔸𝕍𝔸𝔾\mathbb{N}𝔸$   \mathbb{STILE\ LAVAGNA}

fraktur / fonte

$𝔞𝔟𝔠𝔡𝔢𝔣𝔤𝔥𝔦𝔧𝔨𝔩𝔪𝔫𝔬𝔭𝔮𝔯𝔰𝔱𝔲𝔳𝔴𝔵𝔶𝔷$   \mathfrak{abcdefghijklm} \mathfrak{nopqrstuvwxyz}

$𝔄𝔅ℭ𝔇𝔈𝔉𝔊ℌ\Im 𝔍𝔎𝔏𝔐𝔑𝔒𝔓𝔔\Re 𝔖𝔗𝔘𝔙𝔚𝔛𝔜ℨ$   \mathfrak{ABCDEFGHIJKLM} \mathfrak{NOPQRSTUVWXYZ}

frazioni

{a\over b}   $\frac{a}{b}$       \frac{x+a}{x^2-2x+5}   $\frac{x+a}{x^2-2x+5}$

frecce

\leftarrow   $\leftarrow$	\rightarrow   $\to$	\uparrow   $\uparrow$
\longleftarrow   $⟵$	\longrightarrow   $⟶$	\downarrow   $\downarrow$
\Leftarrow   $\Leftarrow$	\Rightarrow   $\Rightarrow$	\Uparrow   $\Uparrow$
\Longleftarrow   $⟸$	\Longrightarrow   $⟹$	\Downarrow   $\Downarrow$
\leftrightarrow   $\leftrightarrow$	\updownarrow   $\updownarrow$
\Leftrightarrow   $\iff$	\Longleftrightarrow   $⟺$	\Updownarrow   $\Updownarrow$
\to   $\to$	\mapsto   $\mapsto$	\longmapsto   $⟼$
\hookleftarrow   $\hookleftarrow$	\hookrightarrow   $\hookrightarrow$	\nearrow   $\nearrow$
\searrow   $\searrow$	\swarrow   $\swarrow$	\nwarrow   $\nwarrow$

funzioni standard / simboli per le

\arccos	\cos	\csc	\exp	\ker	\limsup	\min	\sinh
\arcsin	\cosh	\deg	\gcd	\lg	\ln	\Pr	\sup
\arctan	\cot	\det	\hom	\lim	\log	\sec	\tan
\arg	\coth	\dim	\inf	\liminf	\max	\sin	\tanh

G

geometria / simboli per la

$\mathrm{△}$   \triangle             $\mathrm{\angle }$   \angle      

grassetto / caratteri in

lettere normali	\mathbf{x}, \mathbf{y}, \mathbf{Z}	$𝐱,𝐲,𝐙$
lettere greche	\boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma}	$\mathit{\alpha },\mathit{\beta },\mathit{\gamma }$

greche / lettere

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

I

insiemi / espressioni concernenti

$f\left(\bigcap _{i=1}^n{S}_i\right)\subseteq \bigcap _{i=1}^{n}f\left(S_i\right)$   f\left(\bigcap_{i=1}^n S_i\right) \subseteq \bigcap_{i=1}^n f\left(S_i\right)

integrali

$\int$   \int       $\iint$   \iint       $\iiint$   \iiint       $\oint$   \oint

$\underset{-2\pi }{\overset{2\pi }{\int }}f(x)dx$     \int_{-2\pi}^{2\pi} f(x) dx      

$\underset{-\mathrm{\infty }}{\overset{\mathrm{\infty }}{\int }}dx{e}^{\frac{-(x-m{)}^2}{2{\sigma }^2}}g(x)$     \int_{-\infty}^\infty dx\;e^{-(x-m)^2\over 2\sigma^2} g(x)

L

limiti

$\underset{n\to \mathrm{\infty }}{\lim }{x}_n$   \lim_{n \to \infty}x_n

logica

$p\wedge \wedge \bigwedge \overline{q}\to p$   p \land \wedge \; \bigwedge \; \bar{q} \to p\

$lor\vee \bigvee \mathrm{\neg }\mathrm{\neg }q\setminus \setminus$   lor \vee \; \bigvee \; \lnot \; \neg q \; \setminus \; \smallsetminus

M

matrici

$\begin{array}{cc}x& y\\ v& w\end{array}$     \begin{matrix} x & y \\ v & w \end{matrix}

$\left(\begin{array}{cc}A+B& \frac{B-C}{2}\\ \frac{C-B}{2}& D\end{array}\right)$     \begin{pmatrix} A+B & {B+C\over 2} \\ {B+c\over 2} & D \end{pmatrix}

$\left|\begin{array}{ccccc}1& 1& 1& 1& 1\\ 1& 2& 3& 4& 5\\ 1& 3& 6& 10& 15\\ 1& 4& 10& 20& 35\\ 1& 5& 15& 35& 70\end{array}\right|$     \begin{vmatrix} 1 & 1 & 1 & 1 & 1 \\ 1 & 2 & 3 & 4 & 5 \\ 1 & 3 & 6 & 10 & 15 \\ 1 & 4 & 10 & 20 & 35 \\ 1 & 5 & 15 & 35 & 70 \end{vmatrix}

$\Vert \begin{array}{cc}x& y\\ v& w\end{array}\Vert$     \begin{Vmatrix} x & y \\ v & w \end{Vmatrix}

$\left[\begin{array}{ccc}{M}_{1,1}& M_{1,2}& M_{1,3}\\ M_{2,1}& M_{2,2}& M_{2,3}\end{array}\right]$     \begin{bmatrix} M_{1,1}&M_{1,2}&M_{1,3}\\M_{2,1}&M_{2,2}&M_{2,3} \end{bmatrix}

$\left\{\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right\}$     \begin{Bmatrix}\cos\theta&\sin\theta\\-\sin\theta&\cos\theta\end{Bmatrix}

$\left|\begin{array}{cc}\left[\begin{array}{cc}x& y\\ v& w\end{array}\right]& \left[\begin{array}{c}a\\ b\end{array}\right]\\ \left[\begin{array}{cc}a& b\end{array}\right]& [1]\end{array}\right|$     \begin{vmatrix} \begin{bmatrix} x & y \\ v & w \end{bmatrix} & \begin{bmatrix} a \\ b \end{bmatrix} \\ \begin{bmatrix} a & b \end{bmatrix} & [1] \end{vmatrix}

$\left[\begin{array}{cccc}{x}_{11}& x_{12}& \cdots & x_{1n}\\ x_{21}& x_{22}& \cdots & x_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ x_{m1}& x_{m2}& \cdots & x_{mn}\end{array}\right]$     \begin{bmatrix} x_{11}&x_{12}&\cdots&x_{1n} \\ x_{21}&x_{22}&\cdots&x_{2n} \\ \vdots&\vdots&\ddots&\vdots \\ x_{m1}&x_{m2}&\cdots& x_{mn} \end{bmatrix}

moduli

$s_k\equiv 0(\mathrm{mod}m)$ s_k \equiv 0 \pmod{m}

$amodb$ a \bmod b

N

negazione di relazioni si ottiene premettendo la macro \not

\not\leq   $\le ̸$)       \not\sim $\sim ̸$       \not\models   $\models ̸$       \not=   $=$       \not<   $<$ . . . .

neretto / caratteri in v. grassetto / caratteri in

O

operatori binari

$\pm$   \pm	$▹$   \triangleright	$\setminus$   \setminus	$\circ$   \circ
$\mp$   \mp	$\times$   \times	$\bullet$   \bullet	$\star$   \star
$\vee$   \vee	$\wr$   \wr	$‡$   \ddagger	$\cap$   \cap
$†$   \dagger	$\oplus$   \oplus	$\setminus$   \smallsetminus	$\cdot$   \cdot
$\wedge$   \wedge	$\otimes$   \otimes	$\cup$   \cup	$◃$   \triangleleft
$𝓉$   \mathcal{t}	$𝓊$   \mathcal{u}

operatori n-ari (v.a. produttoria, sommatoria)

$\sum$   \sum	$\prod$   \prod	$\coprod$   \coprod
$\bigcap$   \bigcap	$\bigcup$   \bigcup	$⨄$   \biguplus
$⨀$   \bigodot	$⨁$   \bigoplus	$⨂$   \bigotimes
$⨆$   \bigsqcup	$\bigvee$   \bigvee	$\bigwedge$   \bigwedge

operatori unari

$\mathrm{\nabla }$   \nabla       $\partial$   \partial       $\mathrm{\neg }$   \neg       $\sim$   \sim

P

parentesi

$(...)$   (...)	$[...]$   [...]	$\{...\}$   \{...\}
$|...|$   |...|	$\Vert ...\Vert$   \|...\|	$⟨$   \langle	$⟩$   \rangle
$\lfloor$   \lfloor	$\rfloor$   \rfloor	$\lceil$   \lceil	$\rceil$   \rceil

parentesi adattabili

$(x^2+2bx+c)$   \left(x^2+2bx+c\right)

$\cos (\underset{0}{\overset{\pi }{\int }}dx{e}^{-x}{P}_{2k}(x))$   \cos\left(\int_0^\pi dx\;e^{-x} P_{2k}(x)\right)

produttoria

$\prod _{k=1}^3{K}_{k+4}=K_5\cdot K_6\cdot K_7$   \prod_{k=1}^3 K_{k+4} = K_5\cdot K_6\cdot K_7

puntini       \ldots   $\dots$       \cdots   $\cdots$       \vdots   $⋮$       \ddots   $\ddots$ (v.a. matrici)

Q

quantificatori       $\mathrm{\forall }$   \forall       $\mathrm{\exists }$   \exists

${\mathrm{\forall }}_{i\in \mathbb{N},j\in \mathbb{N}\setminus \{0\}}(i/j\in \mathbb{Q})$     \forall_{i \in \N, j \in \N \setminus \{0\}} (i/j \in \mathbb{Q})

$\mathrm{\exists }𝐱\in {𝕂}^n\text{tale che}ℳ𝐱=𝐯$

\mathbf{x} \in \mathbb{K}^n \ \mbox{tale che}\ \mathcal{M} \mathbf{x} = \mathbf{v}

R

radici

$\sqrt{7}$       \sqrt 7             $\sqrt{2\pi \rho }$       \sqrt{2\pi\rho}

$\sqrt{A^2+B^2+C^2}$   \sqrt{A^2+B^2+C^2}

$x_{1,2}=\frac{-b\pm \sqrt{b^{-}4ac}}{2a}$   x_{1,2} = \frac{-b\pm\sqrt{b^-4ac}}{2a}

$\sqrt[3]{3}$       \sqrt[3]3             $\sqrt[h+k]{a\pm \sin (2k\pi )}$             \sqrt[h+k]{ a\pm\sin(2k\pi)} }

raggruppamenti di simboli

$\overline{f\circ g\circ h}$   \overline{f\circ g\circ h}	$\underset{\_}{\text{esatto}}$   \underline{\mbox{esatto}}
$\overleftarrow{HK}$   \overleftarrow{HK}	$\overrightarrow{PQ}$   \overrightarrow{PQ}
$\overbrace{x_1{x}_2\cdots x_n}$   \overbrace{x_1x_2\cdots x_n}	$\underbrace{\alpha \beta \gamma \delta }$   \underbrace{\alpha\beta\gamma\delta}
$\sqrt{A^2+B^2}$   \sqrt{A^2+B^2}	$\sqrt[3]{p^3-\frac{qr}{3}}$   \sqrt[n]{p^3-{qr\over3}}
$\widehat{ABC}$   \widehat{ABC}	$\overbrace{\overline{F\circ G}}$   \overbrace{\overline{F\circ G}}
$\widehat{\bar{\stackrel{‾}{F\circ G}}}$   \widehat{\overline{\overline{F\circ G}}}

relazioni

$<$   \,<\,	$\le$   \leq	$>$   \,>\,	$\ge$   \geq
$\subset$   \subset	$\subseteq$   \subseteq	$\supset$   \supset	$\supseteq$   \supseteq
$\in$   \in	$\ni$   \ni	$⊢$   \vdash	$𝒶$   \mathcal{a}
$\cong$   \cong	$\simeq$   \simeq	$\approx$   \approx	$\sim$   \sim
$\perp$   \perp	$\Vert$   \|	$\mid$   \mid	$\equiv$   \equiv
$⌢$   \frown	$⌣$   \smile	$◃$   \triangleleft	$▹$   \triangleright
$𝓋$   \mathcal{v}	$𝓌$   \mathcal{w}	$\models$   \models	$\propto$   \propto

S

sans serif / fonte

$𝖺𝖻𝖼𝖽𝖾𝖿𝗀𝗁𝗂𝗃𝗄𝗅𝗆𝗇𝗈𝗉𝗊𝗋𝗌𝗍𝗎𝗏𝗐𝗑𝗒𝗓$   \mathsf{abcdefghijklm} \mathsf{nopqrstuvwxyz}

$𝖠𝖡𝖢𝖣𝖤𝖥𝖦𝖧𝖨𝖩𝖪𝖫𝖬𝖭𝖮𝖯𝖰𝖱𝖲𝖳𝖴𝖵𝖶𝖷𝖸𝖹$   \mathsf{ABCDEFGHIJKLM} \mathsf{NOPQRSTUVWXYZ}

sistemi di equazioni

$\{\begin{array}{c}ax+by=h\\ cx+dy=k\end{array}$     \left\{\begin{matrix}ax+by=h \\ cx+dy=k\end{matrix}\right.

sommatoria

$\sum _{k=1}^n{k}^2$       \sum_{k=1}^n k^2

T

tensori e simili

$g_i^j$   g_i^{\ j}       $S_{r_1{r}_2}^{r_3{r}_4}$   S_{r_1r_2}^{\ \ \ \ r_3r_4}       $T_{jk}^{ih}$   T_{\ j\ k}^{i\ h}

${}_1^2{X}_3^4$   {}_1^2\!X_3^4

V

vettori

$𝐫=⟨x_1,x_2,x_3⟩$       \mathbf{r}=\langle x_1,x_2,x_3\rangle

${𝐞}_i:=⟨j=1,...,n:|{\delta }_{i,j}⟩$   \mathbf{e}_i :\!= \langle j=1,...,n :| \delta_{i,j} \rangle

VARIE

$100{}^{\circ }\mathrm{C}$   100\,^{\circ}\mathrm{C}

$\frac{A}{B}\}\to X$   \left. {A \over B} \right\} \to X

Voci correlate

• Aiuto:Formule matematiche TeX
• sito ufficiale Wikimedia per le Tex