Definition: Euclidean Function
A Euclidean function on an integral domain is a function such that for each , where , there exist with and either or .
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Definition: Euclidean Function
A Euclidean function on an integral domain R is a function f:R∖{0}→N0 such that for each a,b∈R, where b=0, there exist q,r∈R with a=bq+r and either r=0 or f(r)<f(b).