Arbitrary equations systems

Here we define a list of equations separated by a newline character. Each equation defines a recursive expression that this variable has to fulfill eg. x = cos(y) + x defines an equation for the variable $x$ and its dependence on the variables $y$ and $x$. A formal grammar in short could look like this:

$$\langle{Equation}\rangle \textrm{ ::= } \langle{Variable}\rangle \textrm{\textbf{=}} \langle{Expression}\rangle$$

I am not going to go in details how expressions in our grammar looks like, see http://www.singsurf.org/djep/html/grammar.html for more details what expressions are allowed. List of supported functions is available here: http://www.singsurf.org/djep/html/grammar.html. On top of that we added functions $\max$ and $\min$ with arbitrary number of arguments. Obviously if such function occurs in our equation system, Newton method won't work as it won't be able to differentiate them.