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 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''       $A{\hat {B}}C$   A\hat BC       ${\widehat {HJK}}$   \widehat{HJK}       $\angle A{\hat {B}}C$   \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

$\emptyset$   \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)

${\mathsf {Sans\ Serif}}$   \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 , $\mathrm {H}$	\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}

$x_{1,2}={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}$   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}
$\overbrace {x_{1}x_{2}\cdots x_{n}}$   \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	$\propto$   \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}       $S_{r_{1}r_{2}}^{\ \ \ \ r_{3}r_{4}}$   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