Euclidean function
= Euclidean function
{wiki}
A Euclidean function on an integral domain $R$ assigns a nonnegative integer to every nonzero element so that, for $a,b\in R$ with $b\ne0$, there are $q,r\in R$ satisfying $a=bq+r$ and either $r=0$ or $d(r)<d(b)$.