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Aiuto:Prontuario TeX

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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 Wikipedia. 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 Wikipedia.

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

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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}

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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}

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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

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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

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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

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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

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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 , $α$	\vartheta , $\vartheta$	\varpi , $\varpi$	\chi , $χ$	\Eta , $Η$	\Pi , $Π$
\beta , $β$	\iota , $ι$	\rho , $ρ$	\psi , $ψ$	\Theta , $Θ$	\Rho , $Ρ$
\gamma , $γ$	\kappa , $κ$	\varrho , $\varrho$	\omega , $ω$	\Iota , $Ι$	\Sigma , $Σ$
\delta , $δ$	\lambda , $λ$	\sigma , $σ$	\Alpha , $Α$	\Kappa , $Κ$	\Tau , $Τ$
\epsilon , $ε$	\mu , $μ$	\varsigma , $\varsigma$	\Beta , $Β$	\Lambda , $Λ$	\Upsilon , $Υ$
\varepsilon , $\varepsilon$	\nu , $ν$	\tau , $τ$	\Gamma , $Γ$	\Mu , $Μ$	\Phi , $Φ$
\zeta , $ζ$	\xi , $ξ$	\upsilon , $υ$	\Delta , $Δ$	\Nu , $Ν$	\Chi , $Χ$
\eta , $η$	o (gewoon o) , $o$	\phi , $φ$	\Epsilon , $Ε$	\Xi , $Ξ$	\Psi , $Ψ$
\theta , $θ$	\pi , $π$	\varphi , $\varphi$	\Zeta , $Ζ$	O (gewoon O), $O$	\Omega , $Ω$

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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)

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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

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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}

$a mod b$ a \bmod b

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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

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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

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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)

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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}

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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}	$\underline{\mbox{esatto}}$ \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