Definition:Polynomial Function/Complex/Definition 2

Definition

Let $S \subset \C$ be a subset of the complex numbers.

Let $\C \sqbrk X$ be the polynomial ring in one variable over $\C$.

Let $\C^S$ be the ring of mappings from $S$ to $\C$.

Let $\iota \in \C^S$ denote the inclusion $S \hookrightarrow \C$.

A complex polynomial function on $S$ is a function $f: S \to \C$ which is in the image of the evaluation homomorphism $\C \sqbrk X \to \C^S$ at $\iota$.

Also known as

A polynomial function is often simply called polynomial.

Some sources refer to it as a rational integral function.

Also see

• Equivalence of Definitions of Complex Polynomial Function

Sources

There are no source works cited for this page. Source citations are highly desirable, and mandatory for all definition pages. Definition pages whose content is wholly or partly unsourced are in danger of having such content deleted. To discuss this page in more detail, feel free to use the talk page.