# Thread: Terminology for Equation with mixed Variables

1. ## Terminology for Equation with mixed Variables

I am familiar with polynomials, for example, f1(x) = a0 x0 + a1 x1 + a2 x2 + a3 x3 + ...

where the ai are constant coefficients.

But now I am wondering what the correct terminology is for an equation with mixed terms.
For example, say you have a function of two variables f(x, y), three variables f(x, y, z), or more. Something like the following:

f2(x,y) = a0 x0 + a1 xy + a2 x2y + a3 x3y + a4 xy4 + a5 x2 y2

Basically, the equation is comprised of a bunch of mixed terms, but no transcendentals.

Does this sort of equation have a name when it is being discussed?

2. ## Re: Terminology for Equation with mixed Variables

a polynomial in 2 variables is called a bivariate polynomial

3. ## Re: Terminology for Equation with mixed Variables

By the way, a "polynomial" is of the form $f_1(x) = a_0 x^0 + a_1 x^1 + a_2 x^2 + a_3 x^3 + ...+ a_nx^n$ for some positive integer, n. What you wrote, $f_1(x) = a_0 x^0 + a_1 x^1 + a_2 x^2 + a_3 x^3 + ...$, implies an infinite "power series" which is not a "polynomial".

4. ## Re: Terminology for Equation with mixed Variables

Thank you both for the feedback; you pointed me in the right direction.

The right term (from Wikipedia) seems to be "multivariate polynomial."

I am writing my latest blog post and want to be as meticulous as possible. Hopefully, I'll have time to edit it later today.