Aiuto:Prontuario TeX

Da WikiDsy.

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

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

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