Cat::GcdDomain
-- the category
of integral domains with gcdCat::GcdDomain
represents the category of integral
domains with a gcd.
Cat::GcdDomain()
Cat::IntegralDomain
Cat::GcdDomain
is an integral domain where the
greatest common divisor of two elements can be computed by the method
"gcd"
.gcd(dom x...)
x
and y
must divide
dom::gcd(x,y)
,z
divides both x
and y
,
then z
must divide dom::gcd(x,y)
,Ax::canonicalUnitNormal
then
dom::gcd(x,y)
must be equal to
dom::unitNormal(dom::gcd(x,y))
.x
divides y
if
_divide(x,y)
does not return FAIL
.lcm(dom x...)
"gcd"
to
compute the result.