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 WikiAppunti. Le possibilità sono presentate in ordine alfabetico al fine di facilitare il ritrovamento da parte di chi possegga già qualche conoscenza di TeX o LaTeX.
In questa pagina si intendono anche fornire esempi tendenzialmente significativi, al fine di stimolare la omogeneità delle notazioni.
A[modifica sorgente]
- accenti e segni diacritici
<math>\grave{a}</math> | \grave{a} | <math>\acute{e}</math> | \acute{e} |
<math>\hat{H}</math> | \hat{H} | <math>\check{c}</math> | \check{c} |
<math>\bar{\mathbf{v}}</math> | \bar{\mathbf{v}} | <math>\vec{\mathcal{M}}</math> | \vec{\mathcal{M}} |
<math>\dot{\rho}</math> | \dot{\rho} | <math>\ddot{\mathsf{X}}</math> | \ddot{\mathsf{X}} |
<math>\breve{o}</math> | \breve{o} | <math>\tilde{N}</math> | \tilde{N} |
- angoli
<math>15^\circ 12' 38</math> | 15^\circ 12' 38 | <math>A \hat B C</math> | A \hat B C |
<math>\widehat{HJK}</math> | \widehat{HJK} | <math>\angle A\hat B C</math> | \angle A \hat B C |
<math>\widehat{\mathbf{vw}}</math> | \widehat{\mathbf{vw}} | <math>\angle \vec{OA} \vec{OB}</math> | \angle \vec{OA} \vec{OB} |
B[modifica sorgente]
- binomiali, coefficienti
<math> {n \choose k} := \frac{n!}{k!(n-k)!} </math> | {n \choose k} := \frac{n!}{k!(n-k)!} |
<math> {n \choose k} = {n-1 \choose k-1} + {n-1 \choose k} </math> | {n \choose k} = (n-1 \choose k-1} + (n-1 \choose k} |
C[modifica sorgente]
- calligrafica, font
vedi font speciali
- complessi, espressioni per numeri
<math>\, z = x + iy = \rho e^{i \theta} = |z| e^{i \arg z} </math> | z = x + iy = \rho e^{i \theta} = |z| e^{i \arg z} | ||
<math> \Re(x + iy) = x </math> | \Re(x + iy) = x | <math> \Im(x + iy) = y </math> | \Im(x + iy) = y |
D[modifica sorgente]
- derivate
<math>{d\over dx} f(x)</math> | {d\over dx} f(x) | <math>{\partial \over \partial y} F(x,y)</math> | {\partial \over \partial y} F(x,y) |
<math>\nabla \; \partial x \; dx \; \dot x \; \ddot y \; \psi(x)</math> | \nabla, \partial x, dx, \dot x, \ddot y, \psi(x) |
- determinanti
\, 1\leq i,j\leq n\right]</math> | \det\left[\frac{\partial}{\partial x_i}\frac{\partial}{\partial x_j} \,|\, 1\leq i,j\leq n \right] |
<math>\begin{vmatrix} 1 & 1 & 1 & 1 \\ 1 & 2 & 3 & 4 \\ 1 & 3 & 6 & 10 \\ 1 & 4 & 10 & 20 \end{vmatrix} = 1 </math> | \begin{vmatrix} 1 & 1 & 1 & 1 \\ 1 & 2 & 3 & 4 \\ 1 & 3 & 6 & 10 \\ 1 & 4 & 10 & 20 \end{vmatrix} = 1 |
- disponibili, segni
<math>\heartsuit</math> | \heartsuit | <math>\spadesuit</math> | \spadesuit | <math>\clubsuit</math> | \clubsuit | <math>\diamondsuit</math> | \diamondsuit |
<math>\imath</math> | \imath | <math>\ell</math> | \ell | <math>\wp</math> | \wp | <math>\mho</math> | \mho |
<math>\flat</math> | \flat | <math>\natural</math> | \natural | <math>\sharp</math> | \sharp | <math>\mathcal{x}</math> | \mathcal{x} |
<math>\top</math> | \top | <math>\bot</math> | \bot | <math>\Box</math> | \Box | <math>\Diamond</math> | \Diamond |
E[modifica sorgente]
- ebraiche, lettere
\aleph <math>\aleph</math> \beth <math>\beth</math> \gimel <math>\gimel</math> \daleth<math>\daleth</math>
- entità particolari
<math>\empty</math> \empty | <math>\infty</math> \infty | <math>\hbar</math> \hbar |
<math>\N</math> \N | <math>\R</math> \R |
- esponenziali
10^{a+b} <math>10^{a+b}</math> \,10^{a+b}\, <math>\,10^{a+b}\,</math> e^{-x^2} <math>e^{-x^2}</math> <math>{{4^4}^4}^4</math> {{4^4}^4}^4 <math>{{{5^5}^5}^5}^5</math> {{{5^5}^5}^5}^5
F
- font, confronto
<math>\mathcal{CALLIGRAFICA}</math> \mathcal{CALLIGRAFICA}
<math>\mathit{Corsivo\ (Italic)}</math> \mathit{Corsivo\ (Italic)}
<math>\mathfrak{fraktur\ minuscolo}</math> \mathfrak{fraktur\ minuscolo}
<math>\mathfrak{FRAKTUR\ MAIUSCOLO}</math> \mathfrak{FRAKTUR\ MAIUSCOLO}
<math>\mathbf{Grassetto\ (boldface)}</math> \mathbf{Grassetto (boldface)}
<math>\mathrm{Normale\ (Roman)}</math> \mathrm{Normale\ (Roman)}
<math>\mathsf{Sans\ Serif}</math> \mathsf{Sans\ Serif}
<math>\mathbb{STILE\ LAVAGNA}</math> \mathbb{STILE\ LAVAGNA}
- fraktur, font
<math>\mathfrak{abcdefghijklm} \mathfrak{nopqrstuvwxyz} </math> \mathfrak{abcdefghijklm} \mathfrak{nopqrstuvwxyz}
<math>\mathfrak{ABCDEFGHIJKLM} \mathfrak{NOPQRSTUVWXYZ} </math> \mathfrak{ABCDEFGHIJKLM} \mathfrak{NOPQRSTUVWXYZ}
- frazioni
{a\over b} <math>{a\over b}</math> \frac{x+a}{x^2-2x+5} <math>\frac{x+a}{x^2-2x+5}</math>
- frecce
\leftarrow <math>\leftarrow</math> | \rightarrow <math>\rightarrow</math> | \uparrow <math>\uparrow</math> |
\longleftarrow <math>\longleftarrow</math> | \longrightarrow <math>\longrightarrow</math> | \downarrow <math>\downarrow</math> |
\Leftarrow <math>\Leftarrow</math> | \Rightarrow <math>\Rightarrow</math> | \Uparrow <math>\Uparrow</math> |
\Longleftarrow <math>\Longleftarrow</math> | \Longrightarrow <math>\Longrightarrow</math> | \Downarrow <math>\Downarrow</math> |
\leftrightarrow <math>\leftrightarrow</math> | \updownarrow <math>\updownarrow</math> | |
\Leftrightarrow <math>\Leftrightarrow</math> | \Longleftrightarrow <math>\Longleftrightarrow</math> | \Updownarrow <math>\Updownarrow</math> |
\to <math>\to</math> | \mapsto <math>\mapsto</math> | \longmapsto <math>\longmapsto</math> |
\hookleftarrow <math>\hookleftarrow</math> | \hookrightarrow <math>\hookrightarrow</math> | \nearrow <math>\nearrow</math> |
\searrow <math>\searrow</math> | \swarrow <math>\swarrow</math> | \nwarrow <math>\nwarrow</math> |
- 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
<math>\triangle</math> \triangle <math>\angle</math> \angle
- grassetto, caratteri in
lettere normali | \mathbf{x}, \mathbf{y}, \mathbf{Z} | <math>\mathbf{x}, \mathbf{y}, \mathbf{Z}</math> |
lettere greche | \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma} | <math>\boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma}</math> |
- greche, lettere
\alpha , <math>\alpha</math> | \vartheta , <math>\vartheta</math> | \varpi , <math>\varpi</math> | \chi , <math>\chi</math> | \Eta , <math>\Eta</math> | \Pi , <math>\Pi</math> |
\beta , <math>\beta</math> | \iota , <math>\iota</math> | \rho , <math>\rho</math> | \psi , <math>\psi</math> | \Theta , <math>\Theta</math> | \Rho , <math>\Rho</math> |
\gamma , <math>\gamma</math> | \kappa , <math>\kappa</math> | \varrho , <math>\varrho</math> | \omega , <math>\omega</math> | \Iota , <math>\Iota</math> | \Sigma , <math>\Sigma</math> |
\delta , <math>\delta</math> | \lambda , <math>\lambda</math> | \sigma , <math>\sigma</math> | \Alpha , <math>\Alpha</math> | \Kappa , <math>\Kappa</math> | \Tau , <math>\Tau</math> |
\epsilon , <math>\epsilon</math> | \mu , <math>\mu</math> | \varsigma , <math>\varsigma</math> | \Beta , <math>\Beta</math> | \Lambda , <math>\Lambda</math> | \Upsilon , <math>\Upsilon</math> |
\varepsilon , <math>\varepsilon</math> | \nu , <math>\nu</math> | \tau , <math>\tau</math> | \Gamma , <math>\Gamma</math> | \Mu , <math>\Mu</math> | \Phi , <math>\Phi</math> |
\zeta , <math>\zeta</math> | \xi , <math>\xi</math> | \upsilon , <math>\upsilon</math> | \Delta , <math>\Delta</math> | \Nu , <math>\Nu</math> | \Chi , <math>\Chi</math> |
\eta , <math>\eta</math> | o (gewoon o) , <math>o</math> | \phi , <math>\phi</math> | \Epsilon , <math>\Epsilon</math> | \Xi , <math>\Xi</math> | \Psi , <math>\Psi</math> |
\theta , <math>\theta</math> | \pi , <math>\pi</math> | \varphi , <math>\varphi</math> | \Zeta , <math>\Zeta</math> | O (gewoon O), <math>O</math> | \Omega , <math>\Omega</math> |
I
- insiemi, espressioni concernenti
<math>f\left(\bigcap_{i=1}^n S_i\right) \subseteq \bigcap_{i=1}^n f\left(S_i\right)</math> f\left(\bigcap_{i=1}^n S_i\right) \subseteq \bigcap_{i=1}^n f\left(S_i\right)
- integrali
<math>\int</math> \int <math>\iint</math> \iint <math>\iiint</math> \iiint <math>\oint</math> \oint
<math> \int_{-2\pi}^{2\pi} f(x) dx </math> \int_{-2\pi}^{2\pi} f(x) dx
<math> \int_{-\infty}^\infty dx\;e^{-(x-m)^2\over 2\sigma^2} g(x) </math> \int_{-\infty}^\infty dx\;e^{-(x-m)^2\over 2\sigma^2} g(x)
L
- limiti
<math>\lim_{n \to \infty}x_n</math> \lim_{n \to \infty}x_n
- logica
<math>p \land \wedge \; \bigwedge \; \bar{q} \to p\ </math> p \land \wedge \; \bigwedge \; \bar{q} \to p\
<math>\lor \; \vee \; \bigvee \; \lnot \; \neg q \; \setminus \; \smallsetminus</math> \lor \; \vee \; \bigvee \; \lnot \; \neg q \; \setminus \; \smallsetminus
M
- matrici
<math>\begin{matrix} x & y \\ v & w \end{matrix}</math> \begin{matrix} x & y \\ v & w \end{matrix}
<math>\begin{pmatrix} A+B & {B+C\over 2} \\ {C-B\over 2} & D \end{pmatrix}</math> \begin{pmatrix} A+B & {B+C\over 2} \\ {C-B\over 2} & D \end{pmatrix}
<math>\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}</math> \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}
<math>\begin{Vmatrix} x & y \\ v & w \end{Vmatrix}</math> \begin{Vmatrix} x & y \\ v & w \end{Vmatrix}
<math>\begin{bmatrix} M_{1,1}&M_{1,2}&M_{1,3}\\M_{2,1}&M_{2,2}&M_{2,3} \end{bmatrix}</math> \begin{bmatrix} M_{1,1}&M_{1,2}&M_{1,3}\\M_{2,1}&M_{2,2}&M_{2,3} \end{bmatrix}
<math>\begin{Bmatrix}\cos\theta&\sin\theta\\-\sin\theta&\cos\theta\end{Bmatrix}</math> \begin{Bmatrix}\cos\theta&\sin\theta\\-\sin\theta&\cos\theta\end{Bmatrix}
<math>\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}</math> \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}
<math>\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}</math> \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
<math>s_k \equiv 0 \pmod{m}</math> s_k \equiv 0 \pmod{m}
<math>a \bmod b</math> a \bmod b
N
- negazione di relazioni[1]
\not\leq <math>\not\leq</math>) \not\sim <math>\not\sim</math> \not\models <math>\not\models</math> \not= <math>\not=</math> \not< <math>\not<</math> . . . .
- neretto, caratteri in
O
- operatori binari
<math>\pm</math> \pm | <math>\triangleright</math> \triangleright | <math>\setminus</math> \setminus | <math>\circ</math> \circ |
<math>\mp</math> \mp | <math>\times</math> \times | <math>\bullet</math> \bullet | <math>\star</math> \star |
<math>\vee</math> \vee | <math>\wr</math> \wr | <math>\ddagger</math> \ddagger | <math>\cap</math> \cap |
<math>\dagger</math> \dagger | <math>\oplus</math> \oplus | <math>\smallsetminus</math> \smallsetminus | <math>\cdot</math> \cdot |
<math>\wedge</math> \wedge | <math>\otimes</math> \otimes | <math>\cup</math> \cup | <math>\triangleleft</math> \triangleleft |
<math>\mathcal{t}</math> \mathcal{t} | <math>\mathcal{u}</math> \mathcal{u} |
- operatori n-ari
vedi anche produttoria, sommatoria
<math>\sum</math> \sum | <math>\prod</math> \prod | <math>\coprod</math> \coprod |
<math>\bigcap</math> \bigcap | <math>\bigcup</math> \bigcup | <math>\biguplus</math> \biguplus |
<math>\bigodot</math> \bigodot | <math>\bigoplus</math> \bigoplus | <math>\bigotimes</math> \bigotimes |
<math>\bigsqcup</math> \bigsqcup | <math>\bigvee</math> \bigvee | <math>\bigwedge</math> \bigwedge |
- operatori unari
<math>\nabla</math> \nabla <math>\partial</math> \partial <math>\neg</math> \neg <math>\sim</math> \sim
P
- parentesi
<math>(...)</math> (...) | <math>[...]</math> [...] | <math>\{...\}</math> \{...\} | |
...|</math> |...| | ...\|</math> \|...\| | <math>\langle</math> \langle | <math>\rangle</math> \rangle |
<math>\lfloor</math> \lfloor | <math>\rfloor</math> \rfloor | <math>\lceil</math> \lceil | <math>\rceil</math> \rceil |
- parentesi adattabili
<math>\left(x^2+2bx+c\right)</math> \left(x^2+2bx+c\right)
<math>\cos\left(\int_0^\pi dx\;e^{-x} P_{2k}(x)\right)</math> \cos\left(\int_0^\pi dx\;e^{-x} P_{2k}(x)\right)
- produttoria
<math>\prod_{k=1}^3 K_{k+4} = K_5\cdot K_6\cdot K_7</math> \prod_{k=1}^3 K_{k+4} = K_5\cdot K_6\cdot K_7
- puntini \ldots <math>\ldots</math> \cdots <math>\cdots</math> \vdots <math>\vdots</math> \ddots <math>\ddots</math> (v.a. matrici)
Q
- quantificatori
<math>\forall</math> \forall <math>\exists</math> \exists
<math>\forall_{i \in \N, j \in \N \setminus \{0\}} (i/j \in \mathbb{Q})</math> \forall_{i \in \N, j \in \N \setminus \{0\}} (i/j \in \mathbb{Q})
<math>\exists \mathbf{x} \in \mathbb{K}^n ~\mbox{tale che}~ \mathcal{M} \mathbf{x} = \mathbf{v}</math>
- \mathbf{x} \in \mathbb{K}^n \ \mbox{tale che}\ \mathcal{M} \mathbf{x} = \mathbf{v}
R[modifica sorgente]
- radici
<math> \sqrt 7 </math> \sqrt 7 <math> \sqrt{2\pi\rho} </math> \sqrt{2\pi\rho}
<math>\sqrt{A^2+B^2+C^2}</math> \sqrt{A^2+B^2+C^2}
<math>x_{1,2} = \frac{-b\pm\sqrt{b^2-4ac}}{2a}</math> x_{1,2} = \frac{-b\pm\sqrt{b^-4ac}}{2a}
<math> \sqrt[3]3 </math> \sqrt[3]3 <math> \sqrt[h+k]{a\pm\sin(2k\pi)} </math> \sqrt[h+k]{ a\pm\sin(2k\pi)} }
- raggruppamenti di simboli
<math>\overline{f\circ g\circ h}</math> \overline{f\circ g\circ h} | <math>\underline{\mbox{esatto}}</math> \underline{\mbox{esatto}} |
<math>\overleftarrow{HK}</math> \overleftarrow{HK} | <math>\overrightarrow{PQ}</math> \overrightarrow{PQ} |
<math>\overbrace{x_1x_2\cdots x_n}</math> \overbrace{x_1x_2\cdots x_n} | <math>\underbrace{\alpha\beta\gamma\delta}</math> \underbrace{\alpha\beta\gamma\delta} |
<math>\sqrt{A^2+B^2}</math> \sqrt{A^2+B^2} | <math>\sqrt[n]{p^3-{qr\over3}}</math> \sqrt[n]{p^3-{qr\over3}} |
<math>\widehat{ABC}</math> \widehat{ABC} |
<math>\overbrace{\overline{F\circ G}}</math> \overbrace{\overline{F\circ G}}
<math>\widehat{\overline{\overline{F\circ G}}}</math> \widehat{\overline{\overline{F\circ G}}}
- relazioni
<math>\,<\,</math> \,<\, | <math>\leq</math> \leq | <math>\,>\,</math> \,>\, | <math>\geq</math> \geq |
<math>\subset</math> \subset | <math>\subseteq</math> \subseteq | <math>\supset</math> \supset | <math>\supseteq</math> \supseteq |
<math>\in</math> \in | <math>\ni</math> \ni | <math>\vdash</math> \vdash | <math>\mathcal{a}</math> \mathcal{a} |
<math>\cong</math> \cong | <math>\simeq</math> \simeq | <math>\approx</math> \approx | <math>\sim</math> \sim |
<math>\perp</math> \perp | </math> \| | <math>\mid</math> \mid | <math>\equiv</math> \equiv |
<math>\frown</math> \frown | <math>\smile</math> \smile | <math>\triangleleft</math> \triangleleft | <math>\triangleright</math> \triangleright |
<math>\mathcal{v}</math> \mathcal{v} | <math>\mathcal{w}</math> \mathcal{w} | <math>\models</math> \models | <math>\propto</math> \propto |
S[modifica sorgente]
- sans serif, font
<math>\mathsf{abcdefghijklm} \mathsf{nopqrstuvwxyz}</math> \mathsf{abcdefghijklm} \mathsf{nopqrstuvwxyz}
<math>\mathsf{ABCDEFGHIJKLM} \mathsf{NOPQRSTUVWXYZ}</math> \mathsf{ABCDEFGHIJKLM} \mathsf{NOPQRSTUVWXYZ}
- sistemi di equazioni
<math>\left\{\begin{matrix}ax+by=h \\ cx+dy=k\end{matrix}\right.</math> \left\{\begin{matrix}ax+by=h \\ cx+dy=k\end{matrix}\right.
- sommatoria
<math>\sum_{k=1}^n k^2 </math> \sum_{k=1}^n k^2
- spaziature
<math>a \qquad b</math> a \qquad b
<math> a \quad b</math> a \quad b
<math>a\ b</math> a\ b
<math>a\;b</math> a\;b
<math>a\,b</math> a\,b
<math>a\!b</math> a\!b
T[modifica sorgente]
- tensori e simili
<math>g_i^{\ j}</math> g_i^{\ j} <math>S_{r_1r_2}^{\ \ \ \ r_3r_4}</math> S_{r_1r_2}^{\ \ \ \ r_3r_4} <math>T_{\ j\ k}^{i\ h}</math> T_{\ j\ k}^{i\ h}
<math>{}_1^2\!X_3^4</math> {}_1^2\!X_3^4
V[modifica sorgente]
- vettori
<math>\mathbf{r}=\langle x_1,x_2,x_3\rangle</math> \mathbf{r}=\langle x_1,x_2,x_3\rangle
<math>\mathbf{e}_i := \langle j=1,...,n :| \delta_{i,j} \rangle</math> \mathbf{e}_i :\!= \langle j=1,...,n :| \delta_{i,j} \rangle
VARIE[modifica sorgente]
<math>100\,^{\circ}\mathrm{C}</math> 100\,^{\circ}\mathrm{C}
<math>\left. {A \over B} \right\} \to X</math> \left. {A \over B} \right\} \to X
Note[modifica sorgente]
- ↑ si ottengono con la macro \not