Cat::QuotientField -- the
category of quotient fields
Introduction represents the
category of quotient fields over Cat::QuotientField(R)R.
Generating
the categoryCat::QuotientField(R)
ParametersR |
- | A domain which must be from the category Cat::IntegralDomain. |
Cat::Field
, Cat::Algebra(R),
DetailsCat::QuotientField is the field of fractions over
the integral domain R.The characteristic of this domain, which is is the same as that of
R.
denom(dom x)x, which is an element
of R.numer(dom x)x, which is an element of
R.equal(dom x, dom
y)R.iszero(dom x)R._less(dom x, dom
y)R has the axiom
Cat::OrderedSet: If
R is ordered then this method implements an ordering which
is given by the ordering of the cross-product of numerators and
denominators in R.retract(dom x)x may be ``retracted'' to an element of
R (i.e. if the factor x may be regarded as an
element of R) this element is returned, otherwise FAIL is returned."_divide"
to divide numerator and denominator.