Cat::Field
-- the category of
fieldsCat::Field
represents the category of fields.
Cat::Field()
Cat::EuclideanDomain
, Cat::FactorialDomain
, Cat::SkewField
Ax::canonicalUnitNormal
Cat::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.