\documentclass[final]{article}
\input{definitions}

\usepackage{amsfonts}
\begin{document}

$$\Max{a}{a>\SProduct{\pmatrix{\frac{\sin{(a^{1/(x-y)})}N!}{\root1/3\of{\exp{a}}}&\F{\beta}{x^{(a+b^2)}}{1/2}\check N!\cr 
\frac{\Quotient{\tan^2{a}}{\frac{a}{b}}+\hat a}{3.513}&\Ceil{(a+b)}\geq \sqrt{(q+a)}}}{\pmatrix{\Int{x+3}{\sqrt{\infty}}{\frac{\tan{(x^2+\sqrt{y})}}{N!}}{x}& \F{f}{x}{1/3} \cr \Suml{x=a}{b^2-c/y}{\frac{c}{\Suml{x=a}{b^2-c/y}{\frac{\root{2/7}\of{(c+b)!}}{x}}}} & \Limit{x\to0}{x^y}}}x}=b$$

$$\Vector{\tan{(a^b)}, \frac{\beta+\hat{\omega}}{c}}\Vector{u^v\cr \root{N!}\of{w}}$$
$\Selector{\beta}{i}{}{}-a_j=x \in\In{(a,c]}$
$(\hat a + \check b)(\tilde a-\acute a)^3=\grave a\dot a /(\ddot a\breve a-\bar a!)$
$$\Quotient{\tan^2{a}}{\frac{x}{b}}+\hat a\Min{x}{x+0.5<1}=0$$
$$\F{f}{x^2,y}{3}=\Max{a,b}{}$$
$$ax^z-(b^2+cx)+d=a\mod b$$
$$\root{(x+a)y^2}\of{(x+y)N!}=a\gcd(a,v,t)$$
$$\Abs{x}{\frac{\Conjugate{x+\ImI y}}{\Re{(x+\ImI y)}}}=\lcm{(a,b,c)}$$
$$\Floor{a}+\Ceil{(a+b)}\neq r \sqrt{(q+a)}$$

$$\Int{x \in D}{}{\Int{x}{y}{\F{f}{x,y}{}}{x}}{y}=0$$
$$\Diff{x}{3}{\Diff{z}{}{\Intl{x}{y}{\F{f}{x,y,z}{}}{x}}}$$
$$\Suml{x=a}{b^2-c/y}{\frac{\Curl{\F{f}{b}{c}}{2}}{\Suml{x=a}{b^2-c/y}{u}}}$$

$$\partial_{x}\F{f}{x}{}\equiv{\partial f \over \partial x}\equiv\partial \F{f}{x}{} \over \partial x$$
$${\partial^k \over \partial x^k} \F{f}{z}{} +{\partial \over \partial x}{\partial^5 \over \partial y^5} \F{f}{x}{}+w=19$$
%${\partial^3 \over {\partial x \partial y^2}} \F{f}{x}{}$ not implemented
%$\frac{\partial^k f(x)}{\partial x^n \partial y^m \partial z^o}$ not implemented


$$\Grad{\Laplacian{x\Div{\F{f}{b}{c}}{2}+a\Div{\F{f}{b}{c}}{}}}{1}=\Curl{\F{f}{b}{}}{}$$

$$\frac{\exp x}{\ln y/\log_{17.3} y}=\Limit{x\to B}{x+y}$$

A set specified by listing $\Setl{x,y,z}$ a set specified by condition$\Setc{x}{x>0\Land y=0}$ a list specified by listing $\Listl{x,y,z}$ a list specified by condition$\Listc{x}{x>0\Land y=0}$
$$A \cup B\Rightarrow \Card{A}=\Card{B}\neq \emptyset$$
$$a\Land(b \Lor c)\Xor d \Land g\Rightarrow\False$$
$$\PiCst \ln{\ExpE+\ImI \NaN}=x^{17.3}\EulerGamma$$

$$a\in \Rationals{} \Land z \in \Integers{3} \Land 17 \in \Primes{} \Land \PiCst \in \Reals{} \Land (n+\ImI m) \in\Complexes{}$$
$$\pmatrix{ax&a\frac{x}{N!}\cr y&1}$$
$$\left(\matrix{x&0\cr y&1}\right)$$
$$\Vector{\tan{(a^b)}, \frac{b}{c}}\Vector{u^v\cr \root{N!}\of{w}}$$
$$\Vector{a\cr b\cr c}$$
$$\Moment{X}{}{}$$
$$\Moment{X}{a}{2}$$
$$\Moment{X}{x}{}$$
$$x\searrow 0$$
$$\Limit{x\to0}{x^y}$$
$$\Card{x}$$
$$\lnot(c \Lor b)$$

$$\Image{\sin}=\Reals{}$$
$$f\circ\Inv{f}{}=\Ident$$
$$f\circ\Inv{f}{x}=\Ident$$

$$\Suml{x=a}{b^2}{c}$$
$$\Int{x+3}{\infty}{\frac{\tan{(x^2)}}{N!}}{x}$$
$$a\SProduct{\Vector{xy, y}}{\Vector{a\cr b}}x=b$$
$$\Vector{xz\cr y}b=0$$
$$a\pmatrix{\tan{(a^2)}N!&N!\cr b&d}=b$$

$$\frac{((a+n)(x+y))!}{d/c}=0$$

$$x=(a+b)(c-d\F{f}{x}{})$$
$$x=\cases{pq+x^2&if $ \frac{\tan{(x^2+\sqrt{y})}}{N!}=0$;\cr \F{f}{x}{}&if $ x^2>1$}$$
$$\lbrace a \rbrace$$
$$\Image{\sin}=\Reals{}$$
$$\Domain{f}=\Codomain{g}=\Reals{}$$
$$f\circ\Inv{f}{}=\Ident$$
$$f\circ g$$
$$f\circ\Inv{f}{x}=\Ident$$
$$\In{(b,\infty)}$$


\begin{eqnarray}
a=0
\end{eqnarray}

$(\Listl{t,x})\in\Reals{2}$
$\Selector{\hat{\beta}}{i}{}{}=0$
$x\in\In{(a,c]}$
$$x^2=0$$
$$\F{f\beta}{x,y}{}=0$$
$$\F{f}{x^2,y}{3}=0$$


%${\partial^3 \over {\partial x \partial y^2}} \F{f}{x}{}$ not implemented
%$\frac{\partial^k f(x)}{\partial x^n \partial y^m \partial z^o}$ not implemented

$$\Suml{x=a}{b^2-c/y}{\frac{c}{x}}$$
$$\frac{c}{x/y}$$
$$\exp x$$
$$\log_{17.3} y$$
$$\ln y$$
$$\Limit{x\to B}{x+y}$$
$$\Setl{x,y,z}$$
$$\Setc{x}{x>0\Land y=0}$$
$$\Listl{x,y,z}$$
$$\Listc{x}{x>0\Land y=0}$$
$$A \cup B$$
$$\Card{A}=\Card{B}$$
$$x\Rightarrow a$$
$$\False\Rightarrow a$$
$$a\Rightarrow \False$$
$$a\Land(b \Lor c)\Xor d \Land g\Rightarrow\False$$
$$\ExpE$$
$$\ImI$$
$$\NaN$$
$$\True$$
$$\False$$
$$\emptyset$$
$$\PiCst$$
$$\EulerGamma$$
$$\infty$$

$$\Rationals{}$$
$$\Integers{3}$$
$$\Primes{}$$
$$\Reals{}$$
$$\Integers{}$$
$$\Complexes{}$$
$$\pmatrix{ax&a\frac{x}{N!}\cr y&1}$$
$$\VProduct{\pmatrix{a&y\cr b&d}}{\pmatrix{a&y\cr b&d}}$$
$$\SProduct{\pmatrix{a&y\cr b&d}}{\pmatrix{a&y\cr b&d}}$$
$$\OProduct{\pmatrix{a&y\cr b&d}}{\pmatrix{a&y\cr b&d}}$$
$$\Selector{\pmatrix{a&y\cr b&d}}{1}{2}{m}$$


%%%%%limits%%%%%%%
%arbitrary functions like f(x) should be rewritten \F{name}{argument}{power}, e.g. f(x) becomes \F{f}{x}{}
%TeX functions' arguments must be delimited explicitely
%unary operatos arguments are either a function, a simple symbol or a delimited expression

\end{document}

