Polynomial

A polynomial is any function which obtains its result solely by some combination of: multiplying its inputs together, adding them together, or rescaling them.

Examples

The volume of a cube is a polynomial in its side length.

Every linear transformation is uniquely associated to a polynomial called its characteristic polynomial.

A computer program consisting of some number of for loops (and no recursion or gotos or other loops), where each for loop runs exactly Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} times, will take a number of steps to run which is given by some polynomial in Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} . In fact, any polynomial at all can be realized in this way.

Generating functions in combinatorics.