Category:Examples of Division over Euclidean Domain
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This category contains examples of Division over Euclidean Domain.
Let $\struct {D, +, \circ}$ be a Euclidean domain:
- whose zero is $0_D$
- whose Euclidean valuation is denoted $\nu$.
Let $a, b \in D$ such that $b \ne 0_D$.
By the definition of Euclidean valuation:
- $\exists q, r \in D: a = q \circ b + r$
such that either:
- $\map \nu r < \map \nu b$
or:
- $r = 0_D$
The process of finding $q$ and $r$ is known as division of $a$ by $b$, and we write:
- $a \div b = q \rem r$
Subcategories
This category has the following 2 subcategories, out of 2 total.
I
P
- Polynomial Division (empty)