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Thread: Terminology for Equation with mixed Variables

  1. #1
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    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?
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  2. #2
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    Re: Terminology for Equation with mixed Variables

    a polynomial in 2 variables is called a bivariate polynomial
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    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".
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    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.
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