Definition:Polynomial Function

Definition
Let $K$ be a commutative ring with unity.

Let the mapping $p: K \to K$ be defined such that there exists a sequence:
 * $\left \langle {\alpha_k} \right \rangle_{k \in \left[{0 \,.\,.\, n}\right]}$

of elements of $K$ such that:
 * $\displaystyle p = \sum_{k \mathop = 0}^n \alpha_k {I_K}^k$

where $I_K$ is the identity mapping on $K$.

Then $p$ is known as a polynomial function on $K$.

In most contexts, $K$ is one of the standard number fields $\R$ or $\C$.

Also see

 * Polynomial Form
 * Polynomial Equation
 * Polynomial Coefficient


 * Ring of Polynomial Forms
 * Ring of Polynomial Functions
 * Equality of Polynomials


 * Polynomial Functions form Submodule of All Functions