Macaulay 2 provides for fraction fields of integral domains.
In some cases, normal forms of fractions makes sense, but in general for fraction fieldss of quotient rings, there is no notion of normal form for a fraction. In other words, fractions may be equal without displaying the same numerator and denominator.
Computations over fraction fields, or polynomial rings over fraction fields, especially Groebner basis computations, are much slower than over prime fields. Still, an attempt is made to speed up these computations as much as possible, and more is planned in the future.
For an overview, see
fraction fields and
frac.
Useful functions for use with fractions and fraction fields include:
- frac -- construct a fraction field
- numerator -- numerator of a fraction
- denominator -- denominator of a fraction
- liftable -- whether a ring element can be lifted to another ring
- lift -- lift to another ring