262 lines
9.7 KiB
TeX
262 lines
9.7 KiB
TeX
%Side sets test
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\sideset{^\backprime}{'}
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\sum_{x=1}^{\infty} x
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\sideset{a_1^2}{}\sum_{x=1}^\infty x_0
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\\
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\sideset{_\text{left bottom}'''}{_{\text{right bottom}}'''}
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\sum_{\text{quite long text}}^\infty x
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\\
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\sideset{}{'}
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\sum_{n<k,\;\text{$n$ odd}} nE_n
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\\
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\sideset{}{'}
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\sum^{n<k,\;\text{$n$ odd}} nE_n
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\\
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M_x''' M'''_x M^{'''}_x M_x{'''} M^{\prime\backprime}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%Cyrillic and Greek alphabet
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\begin{array}{lr}
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\mbox{\textcolor{Blue}{Russian}}&\mbox{\textcolor{Melon}{Greek}}\\
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\mbox{привет мир}&\mbox{γειά κόσμο}\\
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\mbox{привет мир}&\mbox{γειά κόσμο}\\
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\mathbf{\mbox{привет мир}}&\mathbf{\mbox{γειά κόσμο}}\\
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\mathit{\mbox{привет мир}}&\mathit{\mbox{γειά κόσμο}}\\
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\mathsf{\mbox{привет мир}}&\mathsf{\mbox{γειά κόσμο}}\\
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\mathtt{\mbox{привет мир}}&\mathtt{\mbox{γειά κόσμο}}\\
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\mathbf{\mathit{\mbox{привет мир}}}&\mathbf{\mathit{\mbox{γειά κόσμο}}}\\
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\mathbf{\mathsf{\mbox{привет мир}}}&\mathbf{\mathsf{\mbox{γειά κόσμο}}}\\
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\mathsf{\mathit{\mbox{привет мир}}}&\mathsf{\mathit{\mbox{γειά κόσμο}}}\\
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&\\
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\mbox{\textcolor{Salmon}{Bulgarian}}&\mbox{\textcolor{Tan}{Serbian}}\\
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\mbox{здравей свят}&\mbox{Хелло уорлд}\\
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&\\
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\mbox{\textcolor{Turquoise}{Bielorussian}}&\mbox{\textcolor{LimeGreen}{Ukrainian}}\\
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\mbox{прывітаньне Свет}&\mbox{привіт світ}\\
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\end{array}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%Complex formula test
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\begin{array}{l}
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\forall\varepsilon\in\mathbb{R}_+^*\ \exists\eta>0\ |x-x_0|\leq\eta\Longrightarrow|f(x)-f(x_0)|\leq\varepsilon\\
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\det
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\begin{bmatrix}
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a_{11}&a_{12}&\cdots&a_{1n}\\
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a_{21}&\ddots&&\vdots\\
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\vdots&&\ddots&\vdots\\
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a_{n1}&\cdots&\cdots&a_{nn}
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\end{bmatrix}
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\overset{\mathrm{def}}{=}\sum_{\sigma\in\mathfrak{S}_n}\varepsilon(\sigma)\prod_{k=1}^n a_{k\sigma(k)}\\
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\sideset{_\alpha^\beta}{_\gamma^\delta}{\begin{pmatrix}a&b\\c&d\end{pmatrix}}\\
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\int_0^\infty{x^{2n} e^{-a x^2}\,dx} = \frac{2n-1}{2a}
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\int_0^\infty{x^{2(n-1)} e^{-a x^2}\,dx} = \frac{(2n-1)!!}{2^{n+1}} \sqrt{\frac{\pi}{a^{2n+1}}}\\
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\int_a^b{f(x)\,dx} = (b - a) \sum\limits_{n = 1}^\infty
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{\sum\limits_{m = 1}^{2^n - 1} {\left( { - 1} \right)^{m + 1} } } 2^{ - n} f(a + m\left( {b - a} \right)2^{-n} )\\
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\int_{-\pi}^{\pi} \sin(\alpha x) \sin^n(\beta x) dx = \textstyle{\left \{
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\begin{array}{cc}
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(-1)^{(n+1)/2} (-1)^m \frac{2 \pi}{2^n} \binom{n}{m} & n \mbox{ odd},\ \alpha = \beta (2m-n) \\
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0 & \mbox{otherwise} \\ \end{array} \right .}\\
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L = \int_a^b \sqrt{ \left|\sum_{i,j=1}^ng_{ij}(\gamma(t))\left(\frac{d}{dt}x^i\circ\gamma(t)\right)
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\left(\frac{d}{dt}x^j\circ\gamma(t)\right)\right|}\,dt\\
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\begin{array}{rl}
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s &= \int_a^b\left\|\frac{d}{dt}\vec{r}\,(u(t),v(t))\right\|\,dt \\
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&= \int_a^b \sqrt{u'(t)^2\,\vec{r}_u\cdot\vec{r}_u + 2u'(t)v'(t)\, \vec{r}_u\cdot
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\vec{r}_v+ v'(t)^2\,\vec{r}_v\cdot\vec{r}_v}\,\,\, dt.
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\end{array}\\
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\end{array}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\definecolor{gris}{gray}{0.9}
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\definecolor{noir}{rgb}{0,0,0}
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\definecolor{bleu}{rgb}{0,0,1}
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\fatalIfCmdConflict{false}
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\newcommand{\pa}{\left|}
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\begin{array}{c}
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\LaTeX\\
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\begin{split}
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&Тепловой\ поток\ \mathrm{Тепловой\ поток}\ \mathtt{Тепловой\ поток}\\
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&\boldsymbol{\mathrm{Тепловой\ поток}}\ \mathsf{Тепловой\ поток}\\
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|I_2| &= \pa\int_0^T\psi(t)\left\{ u(a,t)-\int_{\gamma(t)}^a \frac{d\theta}{k} (\theta,t) \int_a^\theta c(\xi)
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u_t (\xi,t)\,d\xi\right\}dt\right|\\
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&\le C_6 \Bigg|\pa f \int_\Omega \pa\widetilde{S}^{-1,0}_{a,-}
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W_2(\Omega, \Gamma_1)\right|\ \right|\left| |u|\overset{\circ}{\to} W_2^{\widetilde{A}}(\Omega\Gamma_r,T)\right|\Bigg|\\
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&\\
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&\begin{pmatrix}
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\alpha&\beta&\gamma&\delta\\
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\aleph&\beth&\gimel&\daleth\\
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\mathfrak{A}&\mathfrak{B}&\mathfrak{C}&\mathfrak{D}\\
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\boldsymbol{\mathfrak{a}}&\boldsymbol{\mathfrak{b}}&\boldsymbol{\mathfrak{c}}&\boldsymbol{\mathfrak{d}}
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\end{pmatrix}
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\quad{(a+b)}^{\frac{n}{2}}=\sqrt{\sum_{k=0}^n\tbinom{n}{k}a^kb^{n-k}}\quad
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\Biggl(\biggl(\Bigl(\bigl(()\bigr)\Bigr)\biggr)\Biggr)\\
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&\forall\varepsilon\in\mathbb{R}_+^*\ \exists\eta>0\ |x-x_0|\leq\eta\Longrightarrow|f(x)-f(x_0)|\leq\varepsilon\\
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&\det
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\begin{bmatrix}
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a_{11}&a_{12}&\cdots&a_{1n}\\
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a_{21}&\ddots&&\vdots\\
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\vdots&&\ddots&\vdots\\
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a_{n1}&\cdots&\cdots&a_{nn}
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\end{bmatrix}
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\overset{\mathrm{def}}{=}\sum_{\sigma\in\mathfrak{S}_n}\varepsilon(\sigma)\prod_{k=1}^n a_{k\sigma(k)}\\
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&\Delta f(x,y)=\frac{\partial^2f}{\partial x^2}+\frac{\partial^2f}{\partial y^2}\qquad\qquad \fcolorbox{noir}{gris}
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{n!\underset{n\rightarrow+\infty}{\sim} {\left(\frac{n}{e}\right)}^n\sqrt{2\pi n}}\\
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&\sideset{_\alpha^\beta}{_\gamma^\delta}{
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\begin{pmatrix}
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a&b\\
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c&d
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\end{pmatrix}}
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\xrightarrow[T]{n\pm i-j}\sideset{^t}{}A\xleftarrow{\overrightarrow{u}\wedge\overrightarrow{v}}
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\underleftrightarrow{\iint_{\mathds{R}^2}e^{-\left(x^2+y^2\right)}\,\mathrm{d}x\mathrm{d}y}
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\end{split}\\
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\rotatebox{30}{\sum_{n=1}^{+\infty}}\quad\mbox{Mirror rorriM}\reflectbox{\mbox{Mirror rorriM}}
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\end{array}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{array}{|c|l|||r|c|}
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\hline
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\text{Matrix}&\multicolumn{2}{|c|}{\text{Multicolumns}}&\text{Font sizes commands}\cr
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\hline
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\begin{pmatrix}
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\alpha_{11}&\cdots&\alpha_{1n}\cr
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\hdotsfor{3}\cr
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\alpha_{n1}&\cdots&\alpha_{nn}
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\end{pmatrix}
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&\Large \text{Large Right}&\small \text{small Left}&\tiny \text{tiny Tiny}\cr
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\hline
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\multicolumn{4}{|c|}{\Huge \text{Huge Multicolumns}}\cr
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\hline
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\end{array}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\cornersize{0.2}
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\begin{array}{cc}
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\fbox{\text{A framed box with \textdbend}}&\shadowbox{\text{A shadowed box}}\cr
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\doublebox{\text{A double framed box}}&\ovalbox{\text{An oval framed box}}\cr
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\end{array}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%ASCII character
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\text{!"#'()*+,-./0123456789:<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]
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^_`abcdefghijklmnopqrstuvwxyz{|}~
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¡¢£¤¥¦§¨©ª«¬
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®¯°±²³´µ¶·¸¹º»¼½¾¿ÀÁÂÃÄÅÆÇÈÉÊËÌÍÎÏÐÑÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿ}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%Table test
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\newcolumntype{s}{>{\color{#1234B6}}c}
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\begin{array}{|c|c|c|s|}
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\hline
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\rowcolor{Tan}\multicolumn{4}{|c|}{\textcolor{white}{\bold{\text{Table Head}}}}\\
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\hline
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\text{Matrix}&\multicolumn{2}{|c|}{\text{Multicolumns}}&\text{Font size commands}\\
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\hline
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\begin{pmatrix}
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\alpha_{11}&\cdots&\alpha_{1n}\\
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\hdotsfor{3}\\
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\alpha_{n1}&\cdots&\alpha_{nn}
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\end{pmatrix}
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&\large \text{Left}&\cellcolor{#00bde5}\small \textcolor{white}{\text{\bold{Right}}}
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&\small \text{small Small}\\
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\hline
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\multicolumn{4}{|c|}{\text{Table Foot}}\\
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\hline
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\end{array}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\rlap{\overbrace{\phantom{1 + a + b + \cdots + z}}^{\text{total + 1}}}
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1 + \underbrace{a + b + \cdots + z}_{\text{total}}
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\\
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\frac{a\cancel{b}}{\cancel{b}} = a;
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\frac{a\bcancel{b}}{\bcancel{b}} = a;
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\frac{a\xcancel{b}}{\xcancel{b}} = a;
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\\
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\text{A long division: }\longdiv{12345}{13}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\left\{
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\begin{array}{l}
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2a < -1,\\
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a + 8 \ge 5,
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\end{array}
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\right.
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\\
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P_{r-j}=\begin{cases}
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0& \text{if $r-j$ is odd},\\
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r!\,(-1)^{(r-j)/2}& \text{if $r-j$ is even}.
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\end{cases}\text{Cases}
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\\
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P_{r-j}=\left\{\begin{array}{@{}ll@{\,}}
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0& \text{if $r-j$ is odd},\\
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r!\,(-1)^{(r-j)/2}& \text{if $r-j$ is even}.
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\end{array}\right.\text{Cases}
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\\
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P_{r-j}=\begin{cases}
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4-x\geq 0 \\
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3-x\geq 1
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\end{cases}\text{Cases}
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\\
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\left\{\begin{array}{@{}ll}
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1 & 2\\
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3 & 4
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\end{array}\right.\text{Equation}
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\\
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\left\{\begin{array}{l@{}l}
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1 & 2\\
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3 & 4
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\end{array}\right.\text{Equation}
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\\
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\left\{\begin{array}{ll@{}}
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1 & 2\\
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3 & 4
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\end{array}\right.\text{Equation}
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\\
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\begin{split}
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H_c&=\frac{1}{2n} \sum^n_{l=0}(-1)^{l}(n-{l})^{p-2}
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\sum_{l _1+\dots+ l _p=l}\prod^p_{i=1} \binom{n_i}{l _i}\\
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&\quad\cdot[(n-l )-(n_i-l _i)]^{n_i-l _i}\cdot
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\Bigl[(n-l )^2-\sum^p_{j=1}(n_i-l _i)^2\Bigr].
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\end{split}
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\\
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\begin{align}
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A_1&=N_0(\lambda;\Omega’)-\phi(\lambda;\Omega’),\\
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A_2&=\phi(\lambda;\Omega’)-\phi(\lambda;\Omega),\\
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\intertext{and}
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A_3&=\mathcal{N}(\lambda;\omega).
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\end{align}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\frac{\sum_{n > 0} z^n}
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{\prod_{1\leq k\leq n} (1-q^k)}
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\\
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\frac{{\displaystyle\sum_{n > 0} z^n}}
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{{\displaystyle\prod_{1\leq k\leq n} (1-q^k)}}
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\\
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\frac{{\displaystyle\sum\nolimits_{n> 0} z^n}}
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{{\displaystyle\prod\nolimits_{1\leq k\leq n} (1-q^k)}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\cfrac{1}{\sqrt{2}+
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\cfrac{1}{\sqrt{2}+
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\cfrac{1}{\sqrt{2}+\dotsb
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}}}
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\\
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\biggl[
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\sum_i a_i\biggl\lvert\sum_j x_{ij}
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\biggr\rvert^p\biggr]^{1/p}
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\\
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\biggl[
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\sum_i a_i\Bigl\lvert\sum_j x_{ij}
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\Bigr\rvert^p\biggr]^{1/p}
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