A <Euclidean domain> is an <integral domain> equipped with a function $\delta:R\setminus\{0\}\to\mathbb N$ such that for every $a\in R$ and nonzero $b\in R$ there are $q,r\in R$ with $a=qb+r$ and either $r=0$ or $\delta(r)<\delta(b)$. One may additionally require $\delta(a)\le\delta(ab)$ for nonzero $a,b$; degree on a <polynomial ring> also satisfies this convention.

Solution

Past exam of the algebra, analysis and differential equations II course of the University of Oxford / 2008 printed variant / 3 / b / Solution

 Solution (source code)