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 Wikisource. 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 Wikisource.

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

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

angoli

$15^\circ 12' 38''$   15^\circ 12' 38''       $A\hat BC$   A\hat BC       $\widehat{HJK}$   \widehat{HJK}       $\angle A\hat BC$   \angle A\hat BC      $\widehat{\mathbf{vw}}$   \widehat{\mathbf{vw}}       $\angle\vec{OA}\vec{OB}$   \angle \vec{OA}\vec{OB}

B

binomiali, coefficienti

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

${n \choose k} = {n-1 \choose k-1} + {n-1 \choose k}$       {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}       $\Re(x+iy) = x$   \Re(x+iy) = x       $\Im(x+iy) = y$   \Im(x+iy) = y      

D

derivate

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

determinanti

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

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

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

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

disponibili / segni

$\heartsuit$   \heartsuit	$\spadesuit$   \spadesuit	$\clubsuit$   \clubsuit	$\diamondsuit$   \diamondsuit
$\imath$   \imath	$\ell$   \ell	$\wp$   \wp	$\mho$   \mho
$\flat$   \flat	$\natural$   \natural	$\sharp$   \sharp	$\mathcal{x}$   \mathcal{x}
$\top$   \top	$\bot$   \bot	$\Box$   \Box	$\Diamond$   \Diamond

E

ebraiche / lettere       \aleph   $\aleph$       \beth $\beth$       \gimel $\gimel$       \daleth$\daleth$

entità particolari

$\empty$   \empty	$\infty$   \infty	$\hbar$   \hbar
$\N$   \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

$\mathcal{CALLIGRAFICA}$   \mathcal{CALLIGRAFICA}

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

$\mathfrak{fraktur\ minuscolo}$   \mathfrak{fraktur\ minuscolo

$\mathfrak{FRAKTUR\ MAIUSCOLO}$   \mathfrak{FRAKTUR\ MAIUSCOLO}

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

$\mathrm{Normale\ (Roman)}$   \mathrm{Normale\ (Roman)

$\mathsf{Sans\ Serif}$   \mathsf{Sans\ Serif}

$\mathbb{STILE\ LAVAGNA}$   \mathbb{STILE\ LAVAGNA}

fraktur / fonte

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

$\mathfrak{ABCDEFGHIJKLM} \mathfrak{NOPQRSTUVWXYZ}$   \mathfrak{ABCDEFGHIJKLM} \mathfrak{NOPQRSTUVWXYZ}

frazioni

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

frecce

\leftarrow   $\leftarrow$	\rightarrow   $\rightarrow$	\uparrow   $\uparrow$
\longleftarrow   $\longleftarrow$	\longrightarrow   $\longrightarrow$	\downarrow   $\downarrow$
\Leftarrow   $\Leftarrow$	\Rightarrow   $\Rightarrow$	\Uparrow   $\Uparrow$
\Longleftarrow   $\Longleftarrow$	\Longrightarrow   $\Longrightarrow$	\Downarrow   $\Downarrow$
\leftrightarrow   $\leftrightarrow$	\updownarrow   $\updownarrow$
\Leftrightarrow   $\Leftrightarrow$	\Longleftrightarrow   $\Longleftrightarrow$	\Updownarrow   $\Updownarrow$
\to   $\to$	\mapsto   $\mapsto$	\longmapsto   $\longmapsto$
\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

$\triangle$   \triangle             $\angle$   \angle      

grassetto / caratteri in

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

greche / lettere

\alpha , $\alpha$	\vartheta , $\vartheta$	\varpi , $\varpi$	\chi , $\chi$	\Eta , $\Eta$	\Pi , $\Pi$
\beta , $\beta$	\iota , $\iota$	\rho , $\rho$	\psi , $\psi$	\Theta , $\Theta$	\Rho , $\Rho$
\gamma , $\gamma$	\kappa , $\kappa$	\varrho , $\varrho$	\omega , $\omega$	\Iota , $\Iota$	\Sigma , $\Sigma$
\delta , $\delta$	\lambda , $\lambda$	\sigma , $\sigma$	\Alpha , $\Alpha$	\Kappa , $\Kappa$	\Tau , $\Tau$
\epsilon , $\epsilon$	\mu , $\mu$	\varsigma , $\varsigma$	\Beta , $\Beta$	\Lambda , $\Lambda$	\Upsilon , $\Upsilon$
\varepsilon , $\varepsilon$	\nu , $\nu$	\tau , $\tau$	\Gamma , $\Gamma$	\Mu , $\Mu$	\Phi , $\Phi$
\zeta , $\zeta$	\xi , $\xi$	\upsilon , $\upsilon$	\Delta , $\Delta$	\Nu , $\Nu$	\Chi , $\Chi$
\eta , $\eta$	o (gewoon o) , $o$	\phi , $\phi$	\Epsilon , $\Epsilon$	\Xi , $\Xi$	\Psi , $\Psi$
\theta , $\theta$	\pi , $\pi$	\varphi , $\varphi$	\Zeta , $\Zeta$	O (gewoon O), $O$	\Omega , $\Omega$

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

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

$\int_{-\infty}^\infty dx\;e^{-(x-m)^2\over 2\sigma^2} g(x)$     \int_{-\infty}^\infty dx\;e^{-(x-m)^2\over 2\sigma^2} g(x)

L

limiti

$\lim_{n \to \infty}x_n$   \lim_{n \to \infty}x_n

logica

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

$lor \vee \; \bigvee \; \lnot \; \neg q \; \setminus \; \smallsetminus$   lor \vee \; \bigvee \; \lnot \; \neg q \; \setminus \; \smallsetminus

M

matrici

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

$\begin{pmatrix} A+B & {B-C\over 2} \\ {C-B\over 2} & D \end{pmatrix}$     \begin{pmatrix} A+B & {B+C\over 2} \\ {B+c\over 2} & D \end{pmatrix}

$\begin{vmatrix} 1 & 1 & 1 & 1 & 1 \\ 1 & 2 & 3 & 4 & 5 \\ 1 & 3 & 6 & 10 & 15 \\ 1 & 4 & 10 & 20 & 35 \\ 1 & 5 & 15 & 35 & 70 \end{vmatrix}$     \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}

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

$\begin{bmatrix} M_{1,1}&M_{1,2}&M_{1,3}\\M_{2,1}&M_{2,2}&M_{2,3} \end{bmatrix}$     \begin{bmatrix} M_{1,1}&M_{1,2}&M_{1,3}\\M_{2,1}&M_{2,2}&M_{2,3} \end{bmatrix}

$\begin{Bmatrix}\cos\theta&\sin\theta\\-\sin\theta&\cos\theta\end{Bmatrix}$     \begin{Bmatrix}\cos\theta&\sin\theta\\-\sin\theta&\cos\theta\end{Bmatrix}

$\begin{vmatrix} \begin{bmatrix} x & y \\ v & w \end{bmatrix} & \begin{bmatrix} a \\ b \end{bmatrix} \\ \begin{bmatrix} a & b \end{bmatrix} & [1] \end{vmatrix}$     \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}

$\begin{bmatrix} x_{11}&x_{12}&\cdots&x_{1n} \\ x_{21}&x_{22}&\cdots&x_{2n} \\ \vdots&\vdots&\ddots&\vdots \\ x_{m1}&x_{m2}&\cdots& x_{mn} \end{bmatrix}$     \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

$s_k \equiv 0 \pmod{m}$ s_k \equiv 0 \pmod{m}

$a \bmod b$ a \bmod b

N

negazione di relazioni si ottiene premettendo la macro \not

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

neretto / caratteri in v. grassetto / caratteri in

O

operatori binari

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

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

$\sum$   \sum	$\prod$   \prod	$\coprod$   \coprod
$\bigcap$   \bigcap	$\bigcup$   \bigcup	$\biguplus$   \biguplus
$\bigodot$   \bigodot	$\bigoplus$   \bigoplus	$\bigotimes$   \bigotimes
$\bigsqcup$   \bigsqcup	$\bigvee$   \bigvee	$\bigwedge$   \bigwedge

operatori unari

$\nabla$   \nabla       $\partial$   \partial       $\neg$   \neg       $\sim$   \sim

P

parentesi

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

parentesi adattabili

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

$\cos\left(\int_0^\pi dx\;e^{-x} P_{2k}(x)\right)$   \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   $\ldots$       \cdots   $\cdots$       \vdots   $\vdots$       \ddots   $\ddots$ (v.a. matrici)

Q

quantificatori       $\forall$   \forall       $\exists$   \exists

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

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

\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}

$x_{1,2} = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$   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}	$\underline{\mbox{esatto}}$   \underline{\mbox{esatto}}
$\overleftarrow{HK}$   \overleftarrow{HK}	$\overrightarrow{PQ}$   \overrightarrow{PQ}
$\overbrace{x_1x_2\cdots x_n}$   \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}	$\sqrt[3]{p^3-{qr\over3}}$   \sqrt[n]{p^3-{qr\over3}}
$\widehat{ABC}$   \widehat{ABC}

$\overbrace{\overline{F\circ G}}$   \overbrace{\overline{F\circ G}}

$\widehat{\overline{\overline{F\circ G}}}$   \widehat{\overline{\overline{F\circ G}}}

relazioni

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

S

sans serif / fonte

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

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

sistemi di equazioni

$\left\{\begin{matrix}ax+by=h \\ cx+dy=k\end{matrix}\right.$     \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}       $S_{r_1r_2}^{\ \ \ \ r_3r_4}$   S_{r_1r_2}^{\ \ \ \ r_3r_4}       $T_{\ j\ k}^{i\ h}$   T_{\ j\ k}^{i\ h}

${}_1^2\!X_3^4$   {}_1^2\!X_3^4

V

vettori

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

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

VARIE

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

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

Voci correlate

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