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Cat::EuclideanDomain

Category of Euclidean domains

Description

Cat::EuclideanDomain represents the category of Euclidean domains.

A Cat::EuclideanDomain is a principal ideal domain with an "Euclidean degree" function "euclideanDegree" and operations "quo" and "rem" computing the Euclidean quotient and Euclidean remainder.

The Euclidean degree returns nonnegative integers such that for each non-zero x and y there exist s and r such that x = ys + r and either the Euclidean degree of r is less than that of s or r is zero.

In addition s is equal to quo(x,y) and r is equal to rem(x,y).

Methods

expand all

Basic Methods

euclideanDegree(x)

divide(x, y)

Mathematical Methods

_divide(x, y)

gcd(x, …)

gcdex(x, y)

idealGenerator(x, …)

quo(x, y)

The default implementation provided here uses the basic method "divide".

rem(x, y)

The default implementation provided here uses the basic method "divide".

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