# SAMPLES ```tex %Side sets test \sideset{^\backprime}{'} \sum_{x=1}^{\infty} x \sideset{a_1^2}{}\sum_{x=1}^\infty x_0 \\ \sideset{_\text{left bottom}'''}{_{\text{right bottom}}'''} \sum_{\text{quite long text}}^\infty x \\ \sideset{}{'} \sum_{n0\ |x-x_0|\leq\eta\Longrightarrow|f(x)-f(x_0)|\leq\varepsilon\\ \det \begin{bmatrix} a_{11}&a_{12}&\cdots&a_{1n}\\ a_{21}&\ddots&&\vdots\\ \vdots&&\ddots&\vdots\\ a_{n1}&\cdots&\cdots&a_{nn} \end{bmatrix} \overset{\mathrm{def}}{=}\sum_{\sigma\in\mathfrak{S}_n}\varepsilon(\sigma)\prod_{k=1}^n a_{k\sigma(k)}\\ \sideset{_\alpha^\beta}{_\gamma^\delta}{\begin{pmatrix}a&b\\c&d\end{pmatrix}}\\ \int_0^\infty{x^{2n} e^{-a x^2}\,dx} = \frac{2n-1}{2a} \int_0^\infty{x^{2(n-1)} e^{-a x^2}\,dx} = \frac{(2n-1)!!}{2^{n+1}} \sqrt{\frac{\pi}{a^{2n+1}}}\\ \int_a^b{f(x)\,dx} = (b - a) \sum\limits_{n = 1}^\infty {\sum\limits_{m = 1}^{2^n - 1} {\left( { - 1} \right)^{m + 1} } } 2^{ - n} f(a + m\left( {b - a} \right)2^{-n} )\\ \int_{-\pi}^{\pi} \sin(\alpha x) \sin^n(\beta x) dx = \textstyle{\left \{ \begin{array}{cc} (-1)^{(n+1)/2} (-1)^m \frac{2 \pi}{2^n} \binom{n}{m} & n \mbox{ odd},\ \alpha = \beta (2m-n) \\ 0 & \mbox{otherwise} \\ \end{array} \right .}\\ L = \int_a^b \sqrt{ \left|\sum_{i,j=1}^ng_{ij}(\gamma(t))\left(\frac{d}{dt}x^i\circ\gamma(t)\right) \left(\frac{d}{dt}x^j\circ\gamma(t)\right)\right|}\,dt\\ \begin{array}{rl} s &= \int_a^b\left\|\frac{d}{dt}\vec{r}\,(u(t),v(t))\right\|\,dt \\ &= \int_a^b \sqrt{u'(t)^2\,\vec{r}_u\cdot\vec{r}_u + 2u'(t)v'(t)\, \vec{r}_u\cdot \vec{r}_v+ v'(t)^2\,\vec{r}_v\cdot\vec{r}_v}\,\,\, dt. \end{array}\\ \end{array} ``` ![sample_2](samples/sample_2.svg) ```tex \definecolor{gris}{gray}{0.9} \definecolor{noir}{rgb}{0,0,0} \definecolor{bleu}{rgb}{0,0,1} \fatalIfCmdConflict{false} \newcommand{\pa}{\left|} \begin{array}{c} \LaTeX\\ \begin{split} &Тепловой\ поток\ \mathrm{Тепловой\ поток}\ \mathtt{Тепловой\ поток}\\ &\boldsymbol{\mathrm{Тепловой\ поток}}\ \mathsf{Тепловой\ поток}\\ |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) u_t (\xi,t)\,d\xi\right\}dt\right|\\ &\le C_6 \Bigg|\pa f \int_\Omega \pa\widetilde{S}^{-1,0}_{a,-} W_2(\Omega, \Gamma_1)\right|\ \right|\left| |u|\overset{\circ}{\to} W_2^{\widetilde{A}}(\Omega\Gamma_r,T)\right|\Bigg|\\ &\\ &\begin{pmatrix} \alpha&\beta&\gamma&\delta\\ \aleph&\beth&\gimel&\daleth\\ \mathfrak{A}&\mathfrak{B}&\mathfrak{C}&\mathfrak{D}\\ \boldsymbol{\mathfrak{a}}&\boldsymbol{\mathfrak{b}}&\boldsymbol{\mathfrak{c}}&\boldsymbol{\mathfrak{d}} \end{pmatrix} \quad{(a+b)}^{\frac{n}{2}}=\sqrt{\sum_{k=0}^n\tbinom{n}{k}a^kb^{n-k}}\quad \Biggl(\biggl(\Bigl(\bigl(()\bigr)\Bigr)\biggr)\Biggr)\\ &\forall\varepsilon\in\mathbb{R}_+^*\ \exists\eta>0\ |x-x_0|\leq\eta\Longrightarrow|f(x)-f(x_0)|\leq\varepsilon\\ &\det \begin{bmatrix} a_{11}&a_{12}&\cdots&a_{1n}\\ a_{21}&\ddots&&\vdots\\ \vdots&&\ddots&\vdots\\ a_{n1}&\cdots&\cdots&a_{nn} \end{bmatrix} \overset{\mathrm{def}}{=}\sum_{\sigma\in\mathfrak{S}_n}\varepsilon(\sigma)\prod_{k=1}^n a_{k\sigma(k)}\\ &\Delta f(x,y)=\frac{\partial^2f}{\partial x^2}+\frac{\partial^2f}{\partial y^2}\qquad\qquad \fcolorbox{noir}{gris} {n!\underset{n\rightarrow+\infty}{\sim} {\left(\frac{n}{e}\right)}^n\sqrt{2\pi n}}\\ &\sideset{_\alpha^\beta}{_\gamma^\delta}{ \begin{pmatrix} a&b\\ c&d \end{pmatrix}} \xrightarrow[T]{n\pm i-j}\sideset{^t}{}A\xleftarrow{\overrightarrow{u}\wedge\overrightarrow{v}} \underleftrightarrow{\iint_{\mathds{R}^2}e^{-\left(x^2+y^2\right)}\,\mathrm{d}x\mathrm{d}y} \end{split}\\ \rotatebox{30}{\sum_{n=1}^{+\infty}}\quad\mbox{Mirror rorriM}\reflectbox{\mbox{Mirror rorriM}} \end{array} ``` ![sample_3](samples/sample_3.svg) ```tex \begin{array}{|c|l|||r|c|} \hline \text{Matrix}&\multicolumn{2}{|c|}{\text{Multicolumns}}&\text{Font sizes commands}\cr \hline \begin{pmatrix} \alpha_{11}&\cdots&\alpha_{1n}\cr \hdotsfor{3}\cr \alpha_{n1}&\cdots&\alpha_{nn} \end{pmatrix} &\Large \text{Large Right}&\small \text{small Left}&\tiny \text{tiny Tiny}\cr \hline \multicolumn{4}{|c|}{\Huge \text{Huge Multicolumns}}\cr \hline \end{array} ``` ![sample_4](samples/sample_4.svg) ```tex \cornersize{0.2} \begin{array}{cc} \fbox{\text{A framed box with \textdbend}}&\shadowbox{\text{A shadowed box}}\cr \doublebox{\text{A double framed box}}&\ovalbox{\text{An oval framed box}}\cr \end{array} ``` ![sample_5](samples/sample_5.svg) ```tex %ASCII character \text{!"#'()*+,-./0123456789:<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\] ^_`abcdefghijklmnopqrstuvwxyz{|}~€‚ƒ † ŽžŸ ¡¢£¤¥¦§¨©ª«¬­ ®¯°±²³´µ¶·¸¹º»¼½¾¿ÀÁÂÃÄÅÆÇÈÉÊËÌÍÎÏÐÑÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿ} ``` ![sample_6](samples/sample_6.svg) ```tex %Table test \newcolumntype{s}{>{\color{#1234B6}}c} \begin{array}{|c|c|c|s|} \hline \rowcolor{Tan}\multicolumn{4}{|c|}{\textcolor{white}{\bold{\text{Table Head}}}}\\ \hline \text{Matrix}&\multicolumn{2}{|c|}{\text{Multicolumns}}&\text{Font size commands}\\ \hline \begin{pmatrix} \alpha_{11}&\cdots&\alpha_{1n}\\ \hdotsfor{3}\\ \alpha_{n1}&\cdots&\alpha_{nn} \end{pmatrix} &\large \text{Left}&\cellcolor{#00bde5}\small \textcolor{white}{\text{\bold{Right}}} &\small \text{small Small}\\ \hline \multicolumn{4}{|c|}{\text{Table Foot}}\\ \hline \end{array} ``` ![sample_7](samples/sample_7.svg) ```tex \rlap{\overbrace{\phantom{1 + a + b + \cdots + z}}^{\text{total + 1}}} 1 + \underbrace{a + b + \cdots + z}_{\text{total}} \\ \frac{a\cancel{b}}{\cancel{b}} = a; \frac{a\bcancel{b}}{\bcancel{b}} = a; \frac{a\xcancel{b}}{\xcancel{b}} = a; \\ \text{A long division: }\longdiv{12345}{13} ``` ![sample_8](samples/sample_8.svg) ```tex \left\{ \begin{array}{l} 2a < -1,\\ a + 8 \ge 5, \end{array} \right. \\ P_{r-j}=\begin{cases} 0& \text{if $r-j$ is odd},\\ r!\,(-1)^{(r-j)/2}& \text{if $r-j$ is even}. \end{cases}\text{Cases} \\ P_{r-j}=\left\{\begin{array}{@{}ll@{\,}} 0& \text{if $r-j$ is odd},\\ r!\,(-1)^{(r-j)/2}& \text{if $r-j$ is even}. \end{array}\right.\text{Cases} \\ P_{r-j}=\begin{cases} 4-x\geq 0 \\ 3-x\geq 1 \end{cases}\text{Cases} \\ \left\{\begin{array}{@{}ll} 1 & 2\\ 3 & 4 \end{array}\right.\text{Equation} \\ \left\{\begin{array}{l@{}l} 1 & 2\\ 3 & 4 \end{array}\right.\text{Equation} \\ \left\{\begin{array}{ll@{}} 1 & 2\\ 3 & 4 \end{array}\right.\text{Equation} \\ \begin{split} H_c&=\frac{1}{2n} \sum^n_{l=0}(-1)^{l}(n-{l})^{p-2} \sum_{l _1+\dots+ l _p=l}\prod^p_{i=1} \binom{n_i}{l _i}\\ &\quad\cdot[(n-l )-(n_i-l _i)]^{n_i-l _i}\cdot \Bigl[(n-l )^2-\sum^p_{j=1}(n_i-l _i)^2\Bigr]. \end{split} \\ \begin{align} A_1&=N_0(\lambda;\Omega’)-\phi(\lambda;\Omega’),\\ A_2&=\phi(\lambda;\Omega’)-\phi(\lambda;\Omega),\\ \intertext{and} A_3&=\mathcal{N}(\lambda;\omega). \end{align} ``` ![sample_9](samples/sample_9.svg) ```tex \frac{\sum_{n > 0} z^n} {\prod_{1\leq k\leq n} (1-q^k)} \\ \frac{{\displaystyle\sum_{n > 0} z^n}} {{\displaystyle\prod_{1\leq k\leq n} (1-q^k)}} \\ \frac{{\displaystyle\sum\nolimits_{n> 0} z^n}} {{\displaystyle\prod\nolimits_{1\leq k\leq n} (1-q^k)}} ``` ![sample_10](samples/sample_10.svg) ```tex \cfrac{1}{\sqrt{2}+ \cfrac{1}{\sqrt{2}+ \cfrac{1}{\sqrt{2}+\dotsb }}} \\ \biggl[ \sum_i a_i\biggl\lvert\sum_j x_{ij} \biggr\rvert^p\biggr]^{1/p} \\ \biggl[ \sum_i a_i\Bigl\lvert\sum_j x_{ij} \Bigr\rvert^p\biggr]^{1/p} ``` ![sample_11](samples/sample_11.svg)