# Category:Real Polynomial Functions

This category contains results about **Real Polynomial Functions**.

Definitions specific to this category can be found in Definitions/Real Polynomial Functions.

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

### Definition 1

A **real polynomial function** on $S$ is a function $f: S \to \R$ for which there exist:

- a natural number $n\in \N$

- real numbers $a_0, \ldots, a_n \in \R$

such that for all $x \in S$:

- $\map f x = \ds \sum_{k \mathop = 0}^n a_k x^k$

where $\sum$ denotes indexed summation.

### Definition 2

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 $\iota$.

## Subcategories

This category has only the following subcategory.

## Pages in category "Real Polynomial Functions"

The following 4 pages are in this category, out of 4 total.