phi = rationalMapping(f)
phi = rationalMapping(targetRing, sourceRing, l)
phi = rationalMapping(targetRing, sourceRing, m)
phi = rationalMapping(targetVariety, sourceVariety, l)
phi = rationalMapping(targetVariety, sourceVariety, m)
A RationalMapping is a Type that is used to treat maps between projective varieties geometrically. It stores essentially equivalent data to the corresponding map between the homogeneous coordinate rings. The way to construct the object is to use the function rationalMapping.
For example, the following is a Cremona transformation on $P^2$ constructed in multiple ways (in this case, the entries describing the map all have degree 2).





The source and target can also be different. For example, consider the following map from $P^1$ to a nodal cubic in $P^2$.








Notice that when defining a map between projective varieties, we keep the target then source input convention.
Warning, the list or matrix describing the map needs every entry to have the same degree.
The object RationalMapping is a type, with ancestor classes HashTable < Thing.