Wikipedia:Formulalar
TeX hám HTML kodları ayırmashılıǵı
[derekti redaktorlaw]TeX sintaksisi | TeX kórinisi | HTML sintaksisi | HTML kórinisi |
---|---|---|---|
\alpha
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{{math|''α''}}
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α | |
f(x) = x^2
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{{math|''f''(''x'') {{=}} ''x''<sup>2</sup>}}
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f(x) = x2 | |
<math>\{1,e,\pi\}</math>
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{{math|{{mset|1, ''e'', ''π''}}}}
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{1, e, π} | |
<math>|z + 1| \leq 2</math>
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{{math|{{abs|''z'' + 1}} ≤ 2}}
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|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 |
---|---|
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 |
α β γ δ ε ζ |
Γ Δ Θ Λ Ξ Π Σ Φ Ψ Ω |
Γ Δ Θ Λ Ξ Π |
∫ ∑ ∏ √ − ± ∞ ≈ ∝ = ≡ ≠ ≤ ≥ × · ⋅ ÷ ∂ ′ ″ ∇ ‰ ° ∴ ∅ |
∫ ∑ ∏ √ − ± ∞ |
∈ ∉ ∩ ∪ ⊂ ⊃ ⊆ ⊇ ¬ ∧ ∨ ∃ ∀ ⇒ ⇔ → ↔ ↑ ↓ 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}
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\check{a}, \breve{a}, \tilde{a}, \bar{a}
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\hat{a}, \widehat{a}, \vec{a}
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Standard numerical functions[derekti redaktorlaw] | |
\exp_a b = a^b, \exp b = e^b, 10^m
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\ln c = \log c, \lg d = \log_{10} d
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\sin a, \cos b, \tan c, \cot d, \sec f, \csc g
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\arcsin h, \arccos i, \arctan j
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\sinh k, \cosh l, \tanh m, \coth n
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\operatorname{sh}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n
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\operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q
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\sgn r, \left\vert s \right\vert
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\min(x,y), \max(x,y)
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Bounds[derekti redaktorlaw] | |
\min x, \max y, \inf s, \sup t
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\lim u, \liminf v, \limsup w
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\dim p, \deg q, \det m, \ker\phi
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Projections[derekti redaktorlaw] | |
\Pr j, \hom l, \lVert z \rVert, \arg z
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Differentials and derivatives[derekti redaktorlaw] | |
dt, \mathrm{d}t, \partial t, \nabla\psi
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dy/dx, \mathrm{d}y/\mathrm{d}x, \frac{dy}{dx}, \frac{\mathrm{d}y}{\mathrm{d}x}
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\frac{\partial^2}{\partial x_1\partial x_2}y, \left.\frac{\partial^3 f}{\partial^2 x \partial y}\right\vert_{p_0}
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\prime, \backprime, f^\prime, f', f'', f^{(3)}, \dot y, \ddot y
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Letter-like symbols or constants[derekti redaktorlaw] | |
\infty, \aleph, \complement, \backepsilon, \eth, \Finv, \hbar, \N, \R, \Z, \C, \Q
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\Im, \imath, \jmath, \Bbbk, \ell, \mho, \wp, \Re, \circledS, \S, \P, \AA
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Modular arithmetic[derekti redaktorlaw] | |
s_k \equiv 0 \pmod{m}
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a \bmod b
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\gcd(m, n), \operatorname{lcm}(m, n)
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\mid, \nmid, \shortmid, \nshortmid
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Radicals[derekti redaktorlaw] | |
\surd, \sqrt{2}, \sqrt[n]{2}, \sqrt[3]{\frac{x^3+y^3}{2}}
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Operators[derekti redaktorlaw] | |
+, -, \pm, \mp, \dotplus
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\times, \div, \divideontimes, /, \backslash
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\cdot, * \ast, \star, \circ, \bullet
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\boxplus, \boxminus, \boxtimes, \boxdot
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\oplus, \ominus, \otimes, \oslash, \odot
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\circleddash, \circledcirc, \circledast
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\bigoplus, \bigotimes, \bigodot
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Sets[derekti redaktorlaw] | |
\{ \}, \O \empty \emptyset, \varnothing
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\in, \notin \not\in, \ni, \not\ni
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\cap, \Cap, \sqcap, \bigcap
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\cup, \Cup, \sqcup, \bigcup, \bigsqcup, \uplus, \biguplus
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\setminus, \smallsetminus, \times
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\subset, \Subset, \sqsubset
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\supset, \Supset, \sqsupset
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\subseteq, \nsubseteq, \subsetneq, \varsubsetneq, \sqsubseteq
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\supseteq, \nsupseteq, \supsetneq, \varsupsetneq, \sqsupseteq
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\subseteqq, \nsubseteqq, \subsetneqq, \varsubsetneqq
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\supseteqq, \nsupseteqq, \supsetneqq, \varsupsetneqq
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Relations[derekti redaktorlaw] | |
=, \ne, \neq, \equiv, \not\equiv
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\doteq, \doteqdot, \overset{\underset{\mathrm{def}}{}}{=}, :=
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\sim, \nsim, \backsim, \thicksim, \simeq, \backsimeq, \eqsim, \cong, \ncong
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\approx, \thickapprox, \approxeq, \asymp, \propto, \varpropto
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<, \nless, \ll, \not\ll, \lll, \not\lll, \lessdot
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>, \ngtr, \gg, \not\gg, \ggg, \not\ggg, \gtrdot
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\le, \leq, \lneq, \leqq, \nleq, \nleqq, \lneqq, \lvertneqq
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\ge, \geq, \gneq, \geqq, \ngeq, \ngeqq, \gneqq, \gvertneqq
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\lessgtr, \lesseqgtr, \lesseqqgtr, \gtrless, \gtreqless, \gtreqqless
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\leqslant, \nleqslant, \eqslantless
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\geqslant, \ngeqslant, \eqslantgtr
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\lesssim, \lnsim, \lessapprox, \lnapprox
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\gtrsim, \gnsim, \gtrapprox, \gnapprox
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\prec, \nprec, \preceq, \npreceq, \precneqq
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\succ, \nsucc, \succeq, \nsucceq, \succneqq
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\preccurlyeq, \curlyeqprec
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\succcurlyeq, \curlyeqsucc
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\precsim, \precnsim, \precapprox, \precnapprox
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\succsim, \succnsim, \succapprox, \succnapprox
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Geometric[derekti redaktorlaw] | |
\parallel, \nparallel, \shortparallel, \nshortparallel
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\perp, \angle, \sphericalangle, \measuredangle, 45^\circ
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\Box, \square, \blacksquare, \diamond, \Diamond, \lozenge, \blacklozenge, \bigstar
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\bigcirc, \triangle, \bigtriangleup, \bigtriangledown
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\vartriangle, \triangledown
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\blacktriangle, \blacktriangledown, \blacktriangleleft, \blacktriangleright
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Logic[derekti redaktorlaw] | |
\forall, \exists, \nexists
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\therefore, \because, \And
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\lor \vee, \curlyvee, \bigvee
don't use |
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\land \wedge, \curlywedge, \bigwedge
don't use |
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\bar{q}, \bar{abc}, \overline{q}, \overline{abc},
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\vdash \dashv, \vDash, \Vdash, \models
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\Vvdash \nvdash \nVdash \nvDash \nVDash
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\ulcorner \urcorner \llcorner \lrcorner
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Arrows[derekti redaktorlaw] | |
\Rrightarrow, \Lleftarrow
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\Rightarrow, \nRightarrow, \Longrightarrow, \implies
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\Leftarrow, \nLeftarrow, \Longleftarrow
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\Leftrightarrow, \nLeftrightarrow, \Longleftrightarrow, \iff
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\Uparrow, \Downarrow, \Updownarrow
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\rightarrow, \to, \nrightarrow, \longrightarrow
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\leftarrow, \gets, \nleftarrow, \longleftarrow
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\leftrightarrow, \nleftrightarrow, \longleftrightarrow
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\uparrow, \downarrow, \updownarrow
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\nearrow, \swarrow, \nwarrow, \searrow
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\mapsto, \longmapsto
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\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons
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\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \rightarrowtail \looparrowright
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\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \leftarrowtail \looparrowleft
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\hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow \twoheadrightarrow \twoheadleftarrow
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Special[derekti redaktorlaw] | |
\amalg \P \S \% \dagger \ddagger \ldots \cdots \vdots \ddots
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\smile \frown \wr \triangleleft \triangleright
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\diamondsuit, \heartsuit, \clubsuit, \spadesuit, \Game, \flat, \natural, \sharp
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Unsorted (new stuff)[derekti redaktorlaw] | |
\diagup \diagdown \centerdot \ltimes \rtimes \leftthreetimes \rightthreetimes
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\eqcirc \circeq \triangleq \bumpeq \Bumpeq \doteqdot \risingdotseq \fallingdotseq
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\intercal \barwedge \veebar \doublebarwedge \between \pitchfork
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\vartriangleleft \ntriangleleft \vartriangleright \ntriangleright
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\trianglelefteq \ntrianglelefteq \trianglerighteq \ntrianglerighteq
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Quramalı ańlatpalar
[derekti redaktorlaw]Tómengi indeksler, joqarǵı indeksler, integrallar
[derekti redaktorlaw]Funkciya | Sintaksis | Nátiyje kórinisi |
---|---|---|
Superscript | a^2, a^{x+3} |
|
Subscript | a_2 |
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Grouping | 10^{30} a^{2+2} |
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a_{i,j} b_{f'} |
||
Combining sub & super without and with horizontal separation | x_2^3 |
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{x_2}^3 |
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Super super | 10^{10^{8}} |
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Preceding and/or additional sub & super | \sideset{_1^2}{_3^4}\prod_a^b |
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{}_1^2\!\Omega_3^4 |
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Stacking | \overset{\alpha}{\omega} |
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\underset{\alpha}{\omega} |
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\overset{\alpha}{\underset{\gamma}{\omega}} |
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\stackrel{\alpha}{\omega} |
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Derivatives | x', y'', f', f'' |
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x^\prime, y^{\prime\prime} |
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Derivative dots | \dot{x}, \ddot{x} |
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Underlines, overlines, vectors | \hat a \ \bar b \ \vec c |
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\overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f} |
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\overline{g h i} \ \underline{j k l} |
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Arc (workaround) | \overset{\frown} {AB} |
|
Arrows | A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C |
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Overbraces | \overbrace{ 1+2+\cdots+100 }^{5050} |
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Underbraces | \underbrace{ a+b+\cdots+z }_{26} |
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Sum | \sum_{k=1}^N k^2 |
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Sum (force \textstyle )
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\textstyle \sum_{k=1}^N k^2 |
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Sum in a fraction (default \textstyle )
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\frac{\sum_{k=1}^N k^2}{a} |
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Sum in a fraction (force \displaystyle )
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\frac{\displaystyle \sum_{k=1}^N k^2}{a} |
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Sum in a fraction (alternative limits style) | \frac{\sum\limits^{^N}_{k=1} k^2}{a} |
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Product | \prod_{i=1}^N x_i |
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Product (force \textstyle )
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\textstyle \prod_{i=1}^N x_i |
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Coproduct | \coprod_{i=1}^N x_i |
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Coproduct (force \textstyle )
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\textstyle \coprod_{i=1}^N x_i |
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Limit | \lim_{n \to \infty}x_n |
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Limit (force \textstyle )
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\textstyle \lim_{n \to \infty}x_n |
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Integral | \int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx |
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Integral (alternative limits style) | \int_{1}^{3}\frac{e^3/x}{x^2}\, dx |
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Integral (force \textstyle )
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\textstyle \int\limits_{-N}^{N} e^x dx |
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Integral (force \textstyle , alternative limits style)
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\textstyle \int_{-N}^{N} e^x dx |
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Double integral | \iint\limits_D dx\,dy |
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Triple integral | \iiint\limits_E dx\,dy\,dz |
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Quadruple integral | \iiiint\limits_F dx\,dy\,dz\,dt |
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Line or path integral | \int_{(x,y)\in C} x^3\, dx + 4y^2\, dy |
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Closed line or path integral | \oint_{(x,y)\in C} x^3\, dx + 4y^2\, dy |
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Intersections | \bigcap_{i=1}^n E_i |
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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
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Small fractions (force \textstyle )
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\tfrac{2}{4} = 0.5
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Large (normal) fractions (force \displaystyle )
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\dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a
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Large (nested) fractions | \cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a
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Cancellations in fractions | \cfrac{x}{1 + \cfrac{\cancel{y}}{\cancel{y}}} = \cfrac{x}{2}
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Binomial coefficients | \binom{n}{k}
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Small binomial coefficients (force \textstyle )
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\tbinom{n}{k}
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Large (normal) binomial coefficients (force \displaystyle )
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\dbinom{n}{k}
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Matrices | \begin{matrix}
x & y \\
z & v
\end{matrix}
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\begin{vmatrix}
x & y \\
z & v
\end{vmatrix}
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\begin{Vmatrix}
x & y \\
z & v
\end{Vmatrix}
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\begin{bmatrix}
0 & \cdots & 0 \\
\vdots & \ddots & \vdots \\
0 & \cdots & 0
\end{bmatrix}
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\begin{Bmatrix}
x & y \\
z & v
\end{Bmatrix}
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\begin{pmatrix}
x & y \\
z & v
\end{pmatrix}
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\bigl( \begin{smallmatrix}
a&b\\ c&d
\end{smallmatrix} \bigr)
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Case distinctions | f(n) =
\begin{cases}
n/2, & \text{if }n\text{ is even} \\
3n+1, & \text{if }n\text{ is odd}
\end{cases}
|
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Simultaneous equations | \begin{cases}
3x + 5y + z \\
7x - 2y + 4z \\
-6x + 3y + 2z
\end{cases}
|
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Multiline equations | \begin{align}
f(x) & = (a+b)^2 \\
& = a^2+2ab+b^2 \\
\end{align}
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\begin{alignat}{2}
f(x) & = (a-b)^2 \\
& = a^2-2ab+b^2 \\
\end{alignat}
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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}
|
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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}
|
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Multiline equations (more) | \begin{array}{lcr}
z & = & a \\
f(x,y,z) & = & x + y + z
\end{array}
|
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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}
|
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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>
|
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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 |
---|---|---|
Bad | ( \frac{1}{2} )^n
|
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Good | \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 )
|
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Brackets | \left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack
|
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Braces | \left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace
|
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Angle brackets | \left \langle \frac{a}{b} \right \rangle
|
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Bars and double bars | \left | \frac{a}{b} \right \vert \quad \left \Vert \frac{c}{d} \right \|
|
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Floor and ceiling functions: | \left \lfloor \frac{a}{b} \right \rfloor \quad \left \lceil \frac{c}{d} \right \rceil
|
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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
|
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Delimiters can be mixed, as long as \left and \right match |
\left [ 0,1 \right ) \left \langle \psi \right |
|
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Use \left. and \right. if you do not want a delimiter to appear |
\left . \frac{A}{B} \right \} \to X
|
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Size of the delimiters (add "l" or "r" to indicate the side for proper spacing) | ( \bigl( \Bigl( \biggl( \Biggl( \dots \Biggr] \biggr] \Bigr] \bigr] ]
|
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\{ \bigl\{ \Bigl\{ \biggl\{ \Biggl\{ \dots \Biggr\rangle \biggr\rangle \Bigr\rangle \bigr\rangle \rangle
|
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\| \big\| \Big\| \bigg\| \Bigg\| \dots \Bigg| \bigg| \Big| \big| |
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\lfloor \bigl\lfloor \Bigl\lfloor \biggl\lfloor \Biggl\lfloor \dots \Biggr\rceil \biggr\rceil \Bigr\rceil \bigr\rceil \ceil
|
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\uparrow \big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow \Downarrow
|
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\updownarrow \big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow \Updownarrow
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/ \big/ \Big/ \bigg/ \Bigg/ \dots \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash \backslash
|