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 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

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

$\emptyset$ \empty	$\infty$ \infty	$\hbar$ \hbar
$\mathbb{N}$ \N	$\mathbb{R}$ \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)

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

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

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

\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}

$x_{{1,2}}={\frac {-b\pm {\sqrt {b^{-}4ac}}}{2a}}$ 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}
$\overbrace {x_{1}x_{2}\cdots x_{n}}$ \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}	${\sqrt[ {3}]{p^{3}-{qr \over 3}}}$ \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