Definition:Polynomial Function/Real/Definition 2

Definition

Let $S \subset \R$ be a subset of the real numbers.

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

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

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

A real polynomial function on $S$ is a function $f: S \to \R$ which is in the image of the evaluation homomorphism $\R \sqbrk X \to \R^S$ 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 Real Polynomial Function

Sources

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