Cat::QuotientField
-- the
category of quotient fields
represents the
category of quotient fields over Cat::QuotientField
(R)R
.
Cat::QuotientField(R)
R |
- | A domain which must be from the category Cat::IntegralDomain . |
Cat::Field
, Cat::Algebra(R)
,
Cat::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.