Vikipeedia:Matemaatiliste valemite kirjutamine

Allikas: Vikipeedia

Matemaatiliste valemid, mis on kirjutatud lÃ¤htudes LaTeX sÃ¼ntaksist, tÃ¶Ã¶tavad vaid siis, kui nende Ã¼mber asuvad <math> ja </math> kÃ¤sud. NÃ¤iteks: <math>ax^2+bx=c</math>.

KÃµik kÃ¤sud LaTeX sÃ¼ntaksis algavad sÃ¼mboliga \. ÃœlejÃ¤Ã¤nud artikkel tutvustab enimkasutatavaid kÃ¤ske LaTeX'i sÃ¼ntaksis.

Sisukord

[peida]

1 Matemaatilised sÃ¼mbolid
2 Lihtsaimad konstruktsioonid
3 Binoomkordajad, maatriksid ja mitmerealised valemid
4 PiirvÃ¤Ã¤rtus, summa, korrutismÃ¤rk, integraal
5 Trigonomeetria
6 Fondid
7 Sulud
8 Nooled
9 TÃ¼hikud
10 Funktsioonid
11 RÃµhumÃ¤rgid
12 Teisi konstruktsioone
13 Vektorid
14 Vaata ka:

[redigeeri] Matemaatilised sÃ¼mbolid

SÃ¼ntaks:	Tulemus:
\cdot \times : \pm \mp	$\cdot \times : \pm \mp$
\cap \cup \vee \wedge \setminus \wr \forall \not \in \ni \neg \empty \exists	$\cap \cup \vee \wedge \setminus \wr \forall \not \in \ni \neg \empty \exists$
\subseteq \supseteq \cong \subset \supset \subseteq \supseteq \cong \approx	$\subseteq \supseteq \cong \subset \supset \subseteq \supseteq \cong \approx$
= \sim \simeq \cong \le \leqslant \geqslant \ge \equiv \approx \ne \models	$= \sim \simeq \cong \le \leqslant \geqslant \ge \equiv \approx \ne \models$
\angle \perp \\| \mid	$\angle \perp \\| \mid$
\star \circ \bullet \nabla \partial \triangleleft \triangleright \oplus \otimes \dagger \ddagger \frown \smile \ldots	$\star \circ \bullet \nabla \partial \triangleleft \triangleright \oplus \otimes \dagger \ddagger \frown \smile \ldots$

[redigeeri] Lihtsaimad konstruktsioonid

	SÃ¼ntaks:	Tulemus:
Harilikud murrud	\frac{2}{4} = {2 \over 4} (vÃµrdvÃ¤Ã¤rsed)	$\frac{2}{4} = {2 \over 4}$
Juured	\sqrt{abc} + \sqrt[3]{abc} + \sqrt[n+1]{abc}	$\sqrt{abc} + \sqrt[3]{abc} + \sqrt[n+1]{abc}$
Astmed ja indeksid	a^2 = a^{b+9}	$a 2 = a b + 9$
	a_2 + a_{i,j}	$a 2 + a i, j$
	a_2^3 a_{2+3}^{4-5}	$a_2^3 + a_{2+3}^{4-5}$
Logaritmid	\log_39=2	$log 3 9 = 2$
Logaritmid	\ln e=1	$ln e = 1$
Funktsioonid	f(x) = g'(x) \cdot h''(x)	$f(x) = g'(x) \cdot h''(x)$
Nurgad	\alpha = \angle CAB = 45^\circ12'32''	$\alpha = \angle CAB = 45^\circ 12'32''$

[redigeeri] Binoomkordajad, maatriksid ja mitmerealised valemid

SÃ¼ntaks:	Tulemus:
\binom{n}{k} vÃµi {n \choose k}	${n \choose k}$
\begin{pmatrix} x & y \\ z & v \end{pmatrix}	$\begin{pmatrix} x & y \\ z & v \end{pmatrix}$
\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0\end{bmatrix}	$\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0\end{bmatrix}$
\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}	$\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}$
\begin{vmatrix} x & y \\ z & v \end{vmatrix}	$\begin{vmatrix} x & y \\ z & v \end{vmatrix}$
\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}	$\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}$
\begin{matrix} x & y \\ z & v \end{matrix}	$\begin{matrix} x & y \\ z & v \end{matrix}$
f(n)=\left\{\begin{matrix} n/2, & \mbox{kui }n\mbox{ on paarisarv} \\ 3n+1, & \mbox{kui }n\mbox{ on paaritu arv} \end{matrix}\right.	$f(n)=\left\{\begin{matrix} n/2, & \mbox{kui }n\mbox{ on paarisarv} \\ 3n+1, & \mbox{kui }n\mbox{ on paaritu arv} \end{matrix}\right.$
\begin{matrix}f(n+1)&=& (n+1)^2 \\ \ & =& n^2 + 2n + 1\end{matrix}	$\begin{matrix}f(n+1)&=& (n+1)^2 \\ \ & =& n^2 + 2n + 1\end{matrix}$

[redigeeri] PiirvÃ¤Ã¤rtus, summa, korrutismÃ¤rk, integraal

SÃ¼ntaks:	Tulemus:
\lim_{n \to \infty}x_n	$\lim_{n \to \infty}x_n$
\sum_{k=1}^N k^2	$\sum_{k=1}^N k^2$
\prod_{i=1}^N x_i	$\prod_{i=1}^N x_i$
\int_{-N}^{N} e^x\, dx	$\int_{-N}^{N} e^x\, dx$
\oint_{C} x^3\, dx + 4y^2\, dy	$\oint_{C} x^3\, dx + 4y^2\, dy$

[redigeeri] Trigonomeetria

Et trigonomeetrilised funktsioonid oleks muudest muutujatest eristatavad, kasutage jÃ¤rgnevaid kÃ¤ske:

\cos \sin \tan \cot \arccos \arcsin \arctan \arccot \cosh \sinh \tanh \coth \sec \cosec

[redigeeri] Fondid

	SÃ¼ntaks:	Tulemus:
Kreeka tÃ¤hed	\alpha \beta \gamma \delta \epsilon \varepsilon \zeta \eta \theta \vartheta \iota \kappa \lambda \mu \nu \xi o \pi \varpi \rho \varrho \sigma \varsigma \tau \upsilon \phi \varphi \chi \psi \omega	$\alpha \beta \gamma \delta \epsilon \varepsilon \zeta \eta \theta \vartheta \iota \kappa \lambda \mu \nu \xi o \pi \varpi \rho \varrho \sigma \varsigma \tau \upsilon \phi \varphi \chi \psi \omega$
Kreeka tÃ¤hed	\Gamma \Delta \Theta \Lambda \Xi \Pi \Sigma \Upsilon \Phi \Psi \Omega	$\Gamma \Delta \Theta \Lambda \Xi \Pi \Sigma \Upsilon \Phi \Psi \Omega \,\!$
Hulgad	x\in\mathbb{N}\mathbb{Z}\sub\mathbb{R}\sub\mathbb{C}	$x\in\mathbb{N}\sub\mathbb{Z}\sub\mathbb{R}\sub\mathbb{C}$
Rasvane kiri	\mathbf{x}\cdot\mathbf{y}=0	$\mathbf{x}\cdot\mathbf{y}=0$
Rasvased kreeka tÃ¤hed	\boldsymbol{\alpha}+\boldsymbol{\beta}+\boldsymbol{\gamma}	$\boldsymbol{\alpha}+\boldsymbol{\beta}+\boldsymbol{\gamma}$
Fraktuur	\mathfrak{AaBbCc}	$\mathfrak{Aa Bb Cc}$
KÃ¤sikiri	\mathcal{AaBbCc}	$\mathcal{ABC}$
Heebrea tÃ¤hed	\aleph \beth \gimel \daleth	$\aleph \beth \gimel \daleth$
Sirge kiri	\mbox{Aa Bb Cc}	$Aa Bb Cc$

[redigeeri] Sulud

	SÃ¼ntaks:	Tulemus:
()	(\frac{a}{b})	$(\frac{a}{b})$
()	\left(\frac{a}{b}\right)	$\left(\frac{a}{b}\right)$
[]	\left[A\right]	$\left[A\right]$
{}	\left\{A\right\}	$\left\{A\right\}$
<>	\left\langle A\right\rangle	$\left\langle A\right\rangle$
\|\|	\left\|A\right\|	$\left\|A\right\|$
	\left\lfloor A\right\rfloor, \left\lceil A\right\rceil, \left\\|A\right\\|	$\left\lfloor A\right\rfloor, \left\lceil A\right\rceil, \left\\|A\right\\|$
\left. ja \right. peidavad sulu	\left.\frac{a}{b}\right\}\to X	$\left.\frac{a}{b}\right\}\to X$

[redigeeri] Nooled

SÃ¼ntaks:	Tulemus:
\leftarrow\longleftarrow\uparrow	$\leftarrow\longleftarrow\uparrow$
\Leftarrow\Longleftarrow\Uparrow	$\Leftarrow\Longleftarrow\Uparrow$
\rightarrow\longrightarrow\downarrow	$\rightarrow\longrightarrow\downarrow$
\Rightarrow\Longrightarrow\Downarrow	$\Rightarrow\Longrightarrow\Downarrow$
\leftrightarrow\updownarrow\Leftrightarrow\Updownarrow	$\leftrightarrow\updownarrow\Leftrightarrow\Updownarrow$
\mapsto\longmapsto\hookleftarrow\hookrightarrow	$\mapsto\longmapsto\hookleftarrow\hookrightarrow$
\swarrow\nwarrow\nearrow\searrow	$\swarrow\nwarrow\nearrow\searrow$

[redigeeri] TÃ¼hikud

LaTeX paneb tÃ¼hikuid automaatselt, kuid mÃµnikord on vaja neid ka kÃ¤sitsi panna:

SÃ¼ntaks:	Tulemus:
a \qquad b	$a \qquad b$
a \quad b	$a \quad b$
a\ b	$a\ b$
a\;b	$a\;b$
a\,b	$a\,b$
ab (tÃ¼hikuta)	$ab\,$
a\!b (kokkusurutult}	$a\!b$

[redigeeri] Funktsioonid

Et deklareerida mingit uut funktsiooni, mis nÃ¤eks vÃ¤lja nÃ¤iteks nagu \sin ja \cos, kasutage kÃ¤sku \operatorname:

Vale	sgn z	$s g n z$
Ã•ige	\operatorname{sgn} z	$\operatorname{sgn} z$

[redigeeri] RÃµhumÃ¤rgid

SÃ¼ntaks:	Tulemus:
\hat{a}	$\hat{a}$
\acute{a}	$\acute{a}$
\bar{a}	$\bar{a}$
\dot{a}	$\dot{a}$
\breve{a}	$\breve{a}$
\check{a}	$\check{a}$
\grave{a}	$\grave{a}$
\vec{a}	$\vec{a}$
\ddot{a}	$\ddot{a}$
\tilde{a}	$\tilde{a}$

[redigeeri] Teisi konstruktsioone

SÃ¼ntaks:	Tulemus:
\widehat{abc}	$\widehat{abc}$
\overleftarrow{abc}	$\overleftarrow{abc}$
\overrightarrow{abc}	$\overrightarrow{abc}$
\overline{abc}	$\overline{abc}$
\underline{abc}	$\underline{abc}$
\overbrace{abc}	$\overbrace{abc}$
\underbrace{abc}	$\underbrace{abc}$