coefficients of a polynomial in two or more variables

Thanks to all for your quick and helpful answers! The functions of Eric 
work perfectly for my needs.

I am a teacher of mathematics from Austria and I use Maxima for 
constructing exercises for my students. Moreover, I recently use maxima 
in my lessons in the higher classes. I have taught myself to write some 
simple functions with Maxima, but my programming skills in Maxima are 
still limited. I can understand Barton's ideas, but it is hard for me to 
understand how Eric's functions work. Are there some recommendable 
examples that help to learn programming with Maxima?

Best regards,
Christian