Polynomial

In mathematics, polynomial functions, or polynomials, are an important class of simple and smooth functions. Here, simple means they are constructed using only multiplication and addition. Smooth means they are infinitely differentiable, i.e., they have derivatives of all finite orders.

Several variables

In multivariate calculus, polynomials in several variables play an important role. These are the simplest multivariate functions and can be defined using addition and multiplication alone. An example of a polynomial in the variables x, y, and z is

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: f(x, y, z) = 2 x^2 y z^3 - 3 y^2 + 5 y z - 2. ,

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The total degree of such a multivariate polynomial can be gotten by adding the exponents of the variables in every term, and taking the maximum. The above polynomial f(x, y, z) has total degree 6.

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