An object of the class RationalMap can be basically replaced by a homogeneous ring map of quotients of polynomial rings by homogeneous ideals. One main advantage to using this class is that things computed using non-probabilistic algorithms are stored internally (or partially stored).
The constructor for the class is rationalMap, which works quite similar to toMap. See in particular the methods: rationalMap(RingMap), rationalMap(Ideal,ZZ,ZZ), rationalMap(Tally), and rationalMap(PolynomialRing,List).
In the package MultiprojectiveVarieties, this class has been extended to provide support to rational maps between multi-projective varieties, see MultirationalMap.
The object RationalMap is a type, with ancestor classes MutableHashTable < HashTable < Thing.