Hi, I'm new here, and not a mathematician at all :(
I am looking for an algorithm to find the roots (in the complex domain) of a polynom of several variables.
Thanks for any light you could bring to me.
Hi, I'm new here, and not a mathematician at all :( I am looking for an algorithm to find the roots (in the complex domain) of a polynom of several variables. Thanks for any light you could bring to me. 


To add a little to the previous answer, the zeros of a polynomial in more than one variable will not typically form a discrete set: consider the example of $f(x,y)=yx^2$. The points in the plane which satisfy the equation $f(x,y)=0$ describe a parabola. Your request for an 'algorithm' is too broad to answer here, but many mathematical software packages will plot the zeros for you. In Mathematica, try ContourPlot[f[x,y]==0., ... 


There will be infinitely many. You need as many polynomials as variables to have a finite number. (There is much, much more to say.) 

