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.

More variables

One also speaks of polynomials in several variables, obtained by taking the ring of polynomials of a ring of polynomials: R = (R) = (R). These are of fundamental importance in algebraic geometry which studies the simultaneous zero sets of several such multivariate polynomials.

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Polynomials are frequently used to encode information about some other object. The characteristic polynomial of a matrix or linear operator contains information about the operator's eigenvalues. The minimal polynomial of an algebraic element records the simplest algebraic relation satisfied by that element.

Related Topics:
Characteristic polynomial - Eigenvalues - Minimal polynomial - Algebraic element

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Other related objects studied in abstract algebra are formal power series, which are like polynomials but may have infinite degree, and the rational functions, which are ratios of polynomials.

Related Topics:
Formal power series - Rational function

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