I'll advice you to read Bruno Buchberger's (inventor of Groebner Basis) introduction:

http://www.risc.jku.at/people/buchberg/papers/2001-02-19-A.pdf

It's rather short, but signifact and useful for understanding general idea and perspectives.

Well, the actual problem A0, A1, A2 are unknown functions of (x,y).

I just need to declare them as functions, not as numbers. Hmm...

By the way, I'd like to use this variables A0, A1, A2, A3 as functions of (x,y).

Is there any efficient way how to declare them as functions?

Kitonium: Thank you!

Thanks. That's a point!