Category of integral domains with gcd


Cat::GcdDomain represents the category of integral domains with a gcd.

A Cat::GcdDomain is an integral domain where the greatest common divisor of two elements can be computed by the method "gcd".


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Basic Methods

gcd — Greatest common divisor

gcd(x, …)

The method must satisfy the following conditions:

  1. x and y must divide dom::gcd(x,y),

  2. if z divides both x and y, then z must divide dom::gcd(x,y),

  3. if a domain has the axiom Ax::canonicalUnitNormal then dom::gcd(x,y) must be equal to dom::unitNormal(dom::gcd(x,y)).

Remember that x divides y if _divide(x,y) does not return FAIL.

Mathematical Methods

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