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%& --translate-file=il2-pl
\documentclass[a4paper,12pt]{article}
\usepackage{polski}
\usepackage{tgtermes}
\usepackage{qtxmath}
\pagestyle{empty}
%
\begin{document}
%
\noindent
%
Matematyka
w~tek¶cie: $\sum_{\alpha\rightarrow\infty}\frac{a+1}{a-b^4}$
i~dalej ($f_m,f_n)=(f_{r_{k-1}}, f_{r_k})$. I~jeszcze $x^{4m}+y^{4m}=z^{4m}$,
gdzie $m\xgeq 1$.
$\cal A + \cal G$. ${\varGamma}+\Phi$. Cyfry nautyczne
\oldstylenums{0123456789}.
Litery $g, v, w, y$ posiadaj± odmianê, której mo¿emy u¿yæ pisz±c
\verb+\varg+ itd.: $\varg, \varv, \varw, \vary$.
U¿ycie pakietu z~opcj± \verb+[altg]+ spowoduje, ¿e domy¶lnie zostan±
u¿yte $\varg\varv\varw\vary$ a~dodaj±c \verb+\var+ otrzymamy $gvwy$.
$$A,\dots,Z\quad a,\dots,z\quad \Gamma, \dots,\Omega\quad
\varGamma, \dots, \varOmega\quad
\alpha,\dots,\omega$$%\quad \varg \varv \varw \vary,\quad gvwy$$
\smallskip
$$\aleph_\alpha\times\aleph_\beta=\aleph_\beta\iff \alpha\le \beta$$
\smallskip
$$\forall \varepsilon >\alpha, \Gamma_\alpha\hookrightarrow
\Gamma_\varepsilon$$
$$|x-a| < \delta \Rightarrow |f(x)-l| < \varepsilon$$
\smallskip
$$\underbrace {V \times \cdots \times V}_k \times
\underbrace {V \times \cdots \times V}_l \rightarrow
\underbrace {V \times \cdots \times V}_{k+l}$$
\smallskip
$$\{x\mid x \ne x\} = \emptyset\qquad (A\cap B)^\circ\subset A^\circ
\cap B^\circ$$
%
\begin{eqnarray*}
\omega &=& \nu+v(x,y)\,dx + w(x,y)\,dy+d\varPsi\\
d\omega &=& d\nu+ \left(\frac{\partial w}{\partial x}-
\frac{\partial v}{\partial y}\right) dx\wedge dy
\end{eqnarray*}
%
$$\hat x+\widehat X+\widehat{xy}+\widehat{xyz}+\vec A$$
\smallskip
$$R_{ijkl}=-R_{jikl}=-R_{ijlk}=R_{klij}$$
\smallskip
$$f(x)=\cases{|x|&$x>a$\cr -|x|&$x\le a$\cr}$$
\smallskip
$$\int_{-\infty}^\infty e^{-x\cdot\,x}\,dx=\sqrt\pi$$
\smallskip
$$ X=\sum_i \xi^i \frac{\partial}{\partial x^i}+\sum_j
x^j\frac{\partial}{\partial \dot x^j}$$
\smallskip
$$\prod_{j\ge0}\biggl(\sum_{k\ge0}a_{jk}z^k\biggr)
=\sum_{n\ge0}z^n\,\Biggl(\sum_
{\scriptstyle k_0,k_1,\ldots\ge0\atop
\scriptstyle k_0+k_1+\cdots=n}
a_{0k_0}a_{1k_1}\ldots\,\Biggr)$$
\smallskip
$$\int_0^\infty\frac{t-ib}{t^2+b^2}e^{iat}\,dt=e^{ab}E_1(ab),\qquad a,b>0$$
\end{document}
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