# Homotopy Type Theory polynomial function > history (Rev #2)

## Definition

In a commutative ring $A$, given a natural number $n:\mathbb{N}$ and a function $a:[0,n] \to A$ called the coefficient, a degree $n$ polynomial is an endofunction $f:A \to A$ defined as

$f(x) \coloneqq \sum_{i:[0,n]} a(i) \cdot x^i$