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Wikipedia:Formulalar

Wikipedia, erkin enciklopediya

TeX hám HTML kodları ayırmashılıǵı

[derekti redaktorlaw]
TeX sintaksisi TeX kórinisi HTML sintaksisi HTML kórinisi
\alpha {{math|''α''}} α
f(x) = x^2 {{math|''f''(''x'') {{=}} ''x''<sup>2</sup>}} f(x) = x2
<math>\{1,e,\pi\}</math> {{math|{{mset|1, ''e'', ''&pi;''}}}} {1, e, π}
<math>|z + 1| \leq 2</math> {{math|{{abs|''z'' + 1}} &le; 2}} |z + 1| ≤ 2

Shep táreptegi kodlardı jazıw oń táreptegi simvollardı beredi, biraq oń táreptegi simvollardı tuwrıdan-tuwrı da wikitextke qoyıw múmkin.

HTML sintaksisi HTML kórinisi
&alpha; &beta; &gamma; &delta; &epsilon; &zeta;
&eta; &theta; &iota; &kappa; &lambda; &mu; &nu;
&xi; &omicron; &pi; &rho; &sigma; &sigmaf;
&tau; &upsilon; &phi; &chi; &psi; &omega;

α β γ δ ε ζ
η θ ι κ λ μ ν
ξ ο π ρ σ ς
τ υ φ χ ψ ω

&Gamma; &Delta; &Theta; &Lambda; &Xi; &Pi;
&Sigma; &Phi; &Psi; &Omega;

Γ Δ Θ Λ Ξ Π
Σ Φ Ψ Ω

&int; &sum; &prod; &radic; &minus; &plusmn; &infin;
&asymp; &prop; = &equiv; &ne; &le; &ge;
&times; &middot; &sdot; &divide; &part; &prime; &Prime;
&nabla; &permil; &deg; &there4; &empty;

∫ ∑ ∏ √ − ± ∞
≈ ∝ = ≡ ≠ ≤ ≥
× · ⋅ ÷ ∂ ′ ″
∇ ‰ ° ∴ ∅

&isin; &notin; &cap; &cup; &sub; &sup; &sube; &supe;
&not; &and; &or; &exist; &forall;
&rArr; &hArr; &rarr; &harr; &uarr; &darr;
&alefsym; - &ndash; &mdash;

∈ ∉ ∩ ∪ ⊂ ⊃ ⊆ ⊇
¬ ∧ ∨ ∃ ∀
⇒ ⇔ → ↔ ↑ ↓
ℵ - – —

TeX járdeminde formatlaw

[derekti redaktorlaw]

Tómendegi kestelerde shep baǵanalarda arnawlı TeX sintaksisi, oń táreptegi baǵanalarda kórinetuǵın mánisi kórsetilgen. Onıń islewi ushın shep táreptegi arnawlı TeX sintaksisinen aldın <math>, al sintaksisten keyin </math> qoyılıwı kerek. Mısalı: <math> \dot{a} </math> ===>

Funkciyalar, simvollar, arnawlı tańbalar

[derekti redaktorlaw]

Accents and diacritics

[derekti redaktorlaw]
\dot{a}, \ddot{a}, \acute{a}, \grave{a}
\check{a}, \breve{a}, \tilde{a}, \bar{a}
\hat{a}, \widehat{a}, \vec{a}

Standard numerical functions

[derekti redaktorlaw]
\exp_a b = a^b, \exp b = e^b, 10^m
\ln c = \log c, \lg d = \log_{10} d
\sin a, \cos b, \tan c, \cot d, \sec f, \csc g
\arcsin h, \arccos i, \arctan j
\sinh k, \cosh l, \tanh m, \coth n
\operatorname{sh}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n
\operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q
\sgn r, \left\vert s \right\vert
\min(x,y), \max(x,y)
\min x, \max y, \inf s, \sup t
\lim u, \liminf v, \limsup w
\dim p, \deg q, \det m, \ker\phi

Projections

[derekti redaktorlaw]
\Pr j, \hom l, \lVert z \rVert, \arg z

Differentials and derivatives

[derekti redaktorlaw]
dt, \mathrm{d}t, \partial t, \nabla\psi
dy/dx, \mathrm{d}y/\mathrm{d}x, \frac{dy}{dx}, \frac{\mathrm{d}y}{\mathrm{d}x}
\frac{\partial^2}{\partial x_1\partial x_2}y, \left.\frac{\partial^3 f}{\partial^2 x \partial y}\right\vert_{p_0}
\prime, \backprime, f^\prime, f', f'', f^{(3)}, \dot y, \ddot y

Letter-like symbols or constants

[derekti redaktorlaw]
\infty, \aleph, \complement, \backepsilon, \eth, \Finv, \hbar, \N, \R, \Z, \C, \Q
\Im, \imath, \jmath, \Bbbk, \ell, \mho, \wp, \Re, \circledS, \S, \P, \AA

Modular arithmetic

[derekti redaktorlaw]
s_k \equiv 0 \pmod{m}
a \bmod b
\gcd(m, n), \operatorname{lcm}(m, n)
\mid, \nmid, \shortmid, \nshortmid
\surd, \sqrt{2}, \sqrt[n]{2}, \sqrt[3]{\frac{x^3+y^3}{2}}
+, -, \pm, \mp, \dotplus
\times, \div, \divideontimes, /, \backslash
\cdot, * \ast, \star, \circ, \bullet
\boxplus, \boxminus, \boxtimes, \boxdot
\oplus, \ominus, \otimes, \oslash, \odot
\circleddash, \circledcirc, \circledast
\bigoplus, \bigotimes, \bigodot
\{ \}, \O \empty \emptyset, \varnothing
\in, \notin \not\in, \ni, \not\ni
\cap, \Cap, \sqcap, \bigcap
\cup, \Cup, \sqcup, \bigcup, \bigsqcup, \uplus, \biguplus
\setminus, \smallsetminus, \times
\subset, \Subset, \sqsubset
\supset, \Supset, \sqsupset
\subseteq, \nsubseteq, \subsetneq, \varsubsetneq, \sqsubseteq
\supseteq, \nsupseteq, \supsetneq, \varsupsetneq, \sqsupseteq
\subseteqq, \nsubseteqq, \subsetneqq, \varsubsetneqq
\supseteqq, \nsupseteqq, \supsetneqq, \varsupsetneqq
=, \ne, \neq, \equiv, \not\equiv
\doteq, \doteqdot, \overset{\underset{\mathrm{def}}{}}{=}, :=
\sim, \nsim, \backsim, \thicksim, \simeq, \backsimeq, \eqsim, \cong, \ncong
\approx, \thickapprox, \approxeq, \asymp, \propto, \varpropto
<, \nless, \ll, \not\ll, \lll, \not\lll, \lessdot
>, \ngtr, \gg, \not\gg, \ggg, \not\ggg, \gtrdot
\le, \leq, \lneq, \leqq, \nleq, \nleqq, \lneqq, \lvertneqq
\ge, \geq, \gneq, \geqq, \ngeq, \ngeqq, \gneqq, \gvertneqq
\lessgtr, \lesseqgtr, \lesseqqgtr, \gtrless, \gtreqless, \gtreqqless
\leqslant, \nleqslant, \eqslantless
\geqslant, \ngeqslant, \eqslantgtr
\lesssim, \lnsim, \lessapprox, \lnapprox
\gtrsim, \gnsim, \gtrapprox, \gnapprox
\prec, \nprec, \preceq, \npreceq, \precneqq
\succ, \nsucc, \succeq, \nsucceq, \succneqq
\preccurlyeq, \curlyeqprec
\succcurlyeq, \curlyeqsucc
\precsim, \precnsim, \precapprox, \precnapprox
\succsim, \succnsim, \succapprox, \succnapprox
\parallel, \nparallel, \shortparallel, \nshortparallel
\perp, \angle, \sphericalangle, \measuredangle, 45^\circ
\Box, \square, \blacksquare, \diamond, \Diamond, \lozenge, \blacklozenge, \bigstar
\bigcirc, \triangle, \bigtriangleup, \bigtriangledown
\vartriangle, \triangledown
\blacktriangle, \blacktriangledown, \blacktriangleleft, \blacktriangleright
\forall, \exists, \nexists
\therefore, \because, \And
\lor \vee, \curlyvee, \bigvee

don't use \or which is now deprecated

\land \wedge, \curlywedge, \bigwedge

don't use \and which is now deprecated

\bar{q}, \bar{abc}, \overline{q}, \overline{abc},

\lnot \neg, \not\operatorname{R}, \bot, \top


\vdash \dashv, \vDash, \Vdash, \models
\Vvdash \nvdash \nVdash \nvDash \nVDash
\ulcorner \urcorner \llcorner \lrcorner
\Rrightarrow, \Lleftarrow
\Rightarrow, \nRightarrow, \Longrightarrow, \implies
\Leftarrow, \nLeftarrow, \Longleftarrow
\Leftrightarrow, \nLeftrightarrow, \Longleftrightarrow, \iff
\Uparrow, \Downarrow, \Updownarrow
\rightarrow, \to, \nrightarrow, \longrightarrow
\leftarrow, \gets, \nleftarrow, \longleftarrow
\leftrightarrow, \nleftrightarrow, \longleftrightarrow
\uparrow, \downarrow, \updownarrow
\nearrow, \swarrow, \nwarrow, \searrow
\mapsto, \longmapsto
\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons
\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \rightarrowtail \looparrowright
\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \leftarrowtail \looparrowleft
\hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow \twoheadrightarrow \twoheadleftarrow
\amalg \P \S \% \dagger \ddagger \ldots \cdots \vdots \ddots
\smile \frown \wr \triangleleft \triangleright
\diamondsuit, \heartsuit, \clubsuit, \spadesuit, \Game, \flat, \natural, \sharp

Unsorted (new stuff)

[derekti redaktorlaw]
\diagup \diagdown \centerdot \ltimes \rtimes \leftthreetimes \rightthreetimes
\eqcirc \circeq \triangleq \bumpeq \Bumpeq \doteqdot \risingdotseq \fallingdotseq
\intercal \barwedge \veebar \doublebarwedge \between \pitchfork
\vartriangleleft \ntriangleleft \vartriangleright \ntriangleright
\trianglelefteq \ntrianglelefteq \trianglerighteq \ntrianglerighteq


Quramalı ańlatpalar

[derekti redaktorlaw]

Tómengi indeksler, joqarǵı indeksler, integrallar

[derekti redaktorlaw]
Funkciya Sintaksis Nátiyje kórinisi
Superscript a^2, a^{x+3}
Subscript a_2
Grouping 10^{30} a^{2+2}
a_{i,j} b_{f'}
Combining sub & super without and with horizontal separation x_2^3
{x_2}^3
Super super 10^{10^{8}}
Preceding and/or additional sub & super \sideset{_1^2}{_3^4}\prod_a^b
{}_1^2\!\Omega_3^4
Stacking \overset{\alpha}{\omega}
\underset{\alpha}{\omega}
\overset{\alpha}{\underset{\gamma}{\omega}}
\stackrel{\alpha}{\omega}
Derivatives x', y'', f', f''
x^\prime, y^{\prime\prime}
Derivative dots \dot{x}, \ddot{x}
Underlines, overlines, vectors \hat a \ \bar b \ \vec c
\overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}
\overline{g h i} \ \underline{j k l}
Arc (workaround) \overset{\frown} {AB}
Arrows A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C
Overbraces \overbrace{ 1+2+\cdots+100 }^{5050}
Underbraces \underbrace{ a+b+\cdots+z }_{26}
Sum \sum_{k=1}^N k^2
Sum (force \textstyle) \textstyle \sum_{k=1}^N k^2
Sum in a fraction (default \textstyle) \frac{\sum_{k=1}^N k^2}{a}
Sum in a fraction (force \displaystyle) \frac{\displaystyle \sum_{k=1}^N k^2}{a}
Sum in a fraction (alternative limits style) \frac{\sum\limits^{^N}_{k=1} k^2}{a}
Product \prod_{i=1}^N x_i
Product (force \textstyle) \textstyle \prod_{i=1}^N x_i
Coproduct \coprod_{i=1}^N x_i
Coproduct (force \textstyle) \textstyle \coprod_{i=1}^N x_i
Limit \lim_{n \to \infty}x_n
Limit (force \textstyle) \textstyle \lim_{n \to \infty}x_n
Integral \int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx
Integral (alternative limits style) \int_{1}^{3}\frac{e^3/x}{x^2}\, dx
Integral (force \textstyle) \textstyle \int\limits_{-N}^{N} e^x dx
Integral (force \textstyle, alternative limits style) \textstyle \int_{-N}^{N} e^x dx
Double integral \iint\limits_D dx\,dy
Triple integral \iiint\limits_E dx\,dy\,dz
Quadruple integral \iiiint\limits_F dx\,dy\,dz\,dt
Line or path integral \int_{(x,y)\in C} x^3\, dx + 4y^2\, dy
Closed line or path integral \oint_{(x,y)\in C} x^3\, dx + 4y^2\, dy
Intersections \bigcap_{i=1}^n E_i
Unions \bigcup_{i=1}^n E_i

Bólshekler, matricalar, multiliniyalar

[derekti redaktorlaw]
Funkciya Sintaksis Nátiyje kórinisi
Fractions \frac{2}{4}=0.5 or {2 \over 4}=0.5
Small fractions (force \textstyle) \tfrac{2}{4} = 0.5
Large (normal) fractions (force \displaystyle) \dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a
Large (nested) fractions \cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a
Cancellations in fractions \cfrac{x}{1 + \cfrac{\cancel{y}}{\cancel{y}}} = \cfrac{x}{2}
Binomial coefficients \binom{n}{k}
Small binomial coefficients (force \textstyle) \tbinom{n}{k}
Large (normal) binomial coefficients (force \displaystyle) \dbinom{n}{k}
Matrices
\begin{matrix}
x & y \\
z & v
\end{matrix}
\begin{vmatrix}
x & y \\
z & v
\end{vmatrix}
\begin{Vmatrix}
x & y \\
z & v
\end{Vmatrix}
\begin{bmatrix}
0 & \cdots & 0 \\
\vdots & \ddots & \vdots \\
0 & \cdots & 0
\end{bmatrix}
\begin{Bmatrix}
x & y \\
z & v
\end{Bmatrix}
\begin{pmatrix}
x & y \\
z & v
\end{pmatrix}
\bigl( \begin{smallmatrix}
a&b\\ c&d
\end{smallmatrix} \bigr)
Case distinctions
f(n) =
\begin{cases}
n/2, & \text{if }n\text{ is even} \\
3n+1, & \text{if }n\text{ is odd}
\end{cases}
Simultaneous equations
\begin{cases}
3x + 5y + z \\
7x - 2y + 4z \\
-6x + 3y + 2z
\end{cases}
Multiline equations
\begin{align}
f(x) & = (a+b)^2 \\
& = a^2+2ab+b^2 \\
\end{align}
\begin{alignat}{2}
f(x) & = (a-b)^2 \\
& = a^2-2ab+b^2 \\
\end{alignat}
Multiline equations with multiple alignments per row
\begin{align}
f(a,b) & = (a+b)^2 && = (a+b)(a+b) \\
& = a^2+ab+ba+b^2  && = a^2+2ab+b^2 \\
\end{align}
\begin{alignat}{3}
f(a,b) & = (a+b)^2 && = (a+b)(a+b) \\
& = a^2+ab+ba+b^2  && = a^2+2ab+b^2 \\
\end{alignat}
Multiline equations (must define number of columns used ({lcl})) (should not be used unless needed)
\begin{array}{lcl}
z & = & a \\
f(x,y,z) & = & x + y + z
\end{array}
Multiline equations (more)
\begin{array}{lcr}
z & = & a \\
f(x,y,z) & = & x + y + z
\end{array}
Multiline alignment using & to left align (top example) versus && to right align (bottom example) the last column
\begin{alignat}{4}
F:\; && C(X) && \;\to\;     & C(X) \\
     && g    && \;\mapsto\; & g^2
\end{alignat}
\begin{alignat}{4}
F:\; && C(X) && \;\to\;     && C(X) \\
     && g    && \;\mapsto\; && g^2
\end{alignat}


Breaking up a long expression so that it wraps when necessary, at the expense of destroying correct spacing
<math>f(x) \,\!</math>
<math>= \sum_{n=0}^\infty a_n x^n </math>
<math>= a_0+a_1x+a_2x^2+\cdots</math>
Arrays
\begin{array}{|c|c|c|} a & b & S \\
\hline
0 & 0 & 1 \\
0 & 1 & 1 \\
1 & 0 & 1 \\
1 & 1 & 0 \\
\end{array}

Úlken ańlatpalar, qawıslar, barlardı qawısqa alıw

[derekti redaktorlaw]
Funkciya Sintaksis Nátiyje kórinisi
☒NBad ( \frac{1}{2} )^n
GoodcheckY \left ( \frac{1}{2} \right )^n

Siz \left hám \right buyrıqları kómeginde hár qıylı bóliwshilerden paydalanıwıńız múmkin:

Funkciya Sintaksis Nátiyje kórinisi
Parentheses \left ( \frac{a}{b} \right )
Brackets \left [ \frac{a}{b} \right ] \quad
\left \lbrack \frac{a}{b} \right \rbrack
Braces \left \{ \frac{a}{b} \right \} \quad
\left \lbrace \frac{a}{b} \right \rbrace
Angle brackets \left \langle \frac{a}{b} \right \rangle
Bars and double bars \left | \frac{a}{b} \right \vert \quad
\left \Vert \frac{c}{d} \right \|
Floor and ceiling functions: \left \lfloor \frac{a}{b} \right \rfloor \quad
\left \lceil \frac{c}{d} \right \rceil
Slashes and backslashes \left / \frac{a}{b} \right \backslash
Up, down, and up-down arrows \left \uparrow \frac{a}{b} \right \downarrow \quad
\left \Uparrow \frac{a}{b} \right \Downarrow \quad
\left \updownarrow \frac{a}{b} \right \Updownarrow
Delimiters can be mixed,
as long as \left and \right match
\left [ 0,1 \right )
\left \langle \psi \right |

Use \left. and \right. if you
do not want a delimiter to appear
\left . \frac{A}{B} \right \} \to X
Size of the delimiters (add "l" or "r" to indicate the side for proper spacing) ( \bigl( \Bigl( \biggl( \Biggl( \dots \Biggr] \biggr] \Bigr] \bigr] ]
\{ \bigl\{ \Bigl\{ \biggl\{ \Biggl\{ \dots
\Biggr\rangle \biggr\rangle \Bigr\rangle \bigr\rangle \rangle
\| \big\| \Big\| \bigg\| \Bigg\| \dots \Bigg| \bigg| \Big| \big| |
\lfloor \bigl\lfloor \Bigl\lfloor \biggl\lfloor \Biggl\lfloor \dots
\Biggr\rceil \biggr\rceil \Bigr\rceil \bigr\rceil \ceil
\uparrow \big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots
\Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow \Downarrow
\updownarrow \big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots
\Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow \Updownarrow
/ \big/ \Big/ \bigg/ \Bigg/ \dots
\Bigg\backslash \bigg\backslash \Big\backslash \big\backslash \backslash