Cat::Field -- the category of
fields
IntroductionCat::Field represents the category of fields.
Generating
the categoryCat::Field()
Cat::EuclideanDomain
, Cat::FactorialDomain, Cat::SkewField
Ax::canonicalUnitNormal
DetailsCat::Field is a factorial domain, an Euclidean
domain and a skew field. As Euclidean domain it has a commutative
multiplication * (_mult) and as skew field the
multiplication is invertible.associates(dom x, dom
y)TRUE iff x and y are
associate elements. For a field this is true iff both arguments are
nonzero._divide(dom x, dom
y)x * y^(-1).divide(dom x, dom
y)[_divide(x,y), dom::zero].divides(dom x, dom
y)TRUE.euclideanDegree(dom x)0 if x is zero and 1
otherwise.factor(dom x)x to
the power of 1 only. The factorization is returned as an object of the
domain Factored
and represents an irreducible factorization over this domain.gcd(dom x...)dom::one if at least
one argument is nonzero and dom::zero otherwise.irreducible(dom x)FALSE.isUnit(dom x)TRUE iff
x is nonzero.quo(dom x, dom
y)_divide(x, y).rem(dom x, dom
y)dom::zero.sqrfree(dom x)x to
the power of 1 only. The factorization is returned as an object of the
domain Factored
and represents an irreducible factorization over this domain.unitNormal(dom x)dom::zero if x is zero and
dom::one otherwise.unitNormalRep(dom x)[dom::one, x^(-1), x] if
x is nonzero and [dom::zero, dom::one,
dom::one] if x is zero.