User blog comment:Wythagoras/Finite Promise Games/@comment-1605058-20140829184949

I don't really know what you mean by "smoother" function. I believe the only difference will be that values will be shifted by 1.

Multivariable polynomials allow multiplication of different variables, so xy is allowed. Constant polynomials are polynomials of degree 0, so they are allowed as well.