A *multi-rational map* is a rational map between multi-projective varieties, $$\Phi:X\subseteq \mathbb{P}^{r_1}\times\mathbb{P}^{r_2}\times\cdots\times\mathbb{P}^{r_n}\dashrightarrow Y \subseteq \mathbb{P}^{s_1}\times\mathbb{P}^{s_2}\times\cdots\times\mathbb{P}^{s_m} .$$Thus, it can be represented by an ordered list of rational maps$$\Phi_i = (\Phi:X\dashrightarrow Y)\circ(pr_i:Y\to Y_i\subseteq\mathbb{P}^{s_i}) ,$$for $i=1,\ldots,m$. The maps $\Phi_i:X\dashrightarrow Y_i\subseteq\mathbb{P}^{s_i}$, since the target $Y_i$ is a standard projective variety, are implemented with the class RationalMap (more properly, when $n>1$ the class of such maps is called MultihomogeneousRationalMap). Recall that the main constructor for the class RationalMap (as well as for the class MultihomogeneousRationalMap) is the method rationalMap.

The constructor for the class of multi-rational maps is multirationalMap, which can often be abbreviated to rationalMap (see also shortcuts). It takes as input the list of maps $\{\Phi_1:X\dashrightarrow Y_1,\ldots,\Phi_m:X\dashrightarrow Y_m\}$, together with the variety $Y$, and returns the map $\Phi:X\dashrightarrow Y$.

- WeightedRationalMap -- the class of all weighted-rational maps

- inverse2 -- inverse of a birational map using a faster algorithm for a special class of maps
- multirationalMap -- the multi-rational map defined by a list of rational maps
- compose(MultirationalMap,MultirationalMap) -- see MultirationalMap * MultirationalMap -- composition of multi-rational maps

- baseLocus(MultirationalMap) -- see baseLocus -- the base locus of a multi-rational map
- check(MultirationalMap) -- check that a multi-rational map is well-defined
- clean(MultirationalMap) -- clean the internal information of a multi-rational map
- coefficientRing(MultirationalMap) -- the coefficient ring of a multi-rational map
- degree(MultirationalMap) -- degree of a multi-rational map
- degreeMap(MultirationalMap) -- see degree(MultirationalMap) -- degree of a multi-rational map
- degree(MultirationalMap,Option) -- degree of a multi-rational map using a probabilistic approach
- degreeSequence(MultirationalMap) -- see degreeSequence -- the (multi)-degree sequence of a (multi)-rational map
- ? MultirationalMap -- see describe(MultirationalMap) -- describe a multi-rational map
- describe(MultirationalMap) -- describe a multi-rational map
- entries(MultirationalMap) -- list the defining polynomials of a rational map
- factor(MultirationalMap) -- the list of rational maps defining a multi-rational map
- forceImage(MultirationalMap,MultiprojectiveVariety) -- declare which is the image of a multi-rational map
- forceImage(MultirationalMap,ZZ) -- see forceImage(MultirationalMap,MultiprojectiveVariety) -- declare which is the image of a multi-rational map
- GG(ZZ,MultirationalMap) -- induced automorphism of the Grassmannian
- graph(MultirationalMap) -- the graph of a multi-rational map
- image(MultirationalMap) -- image of a multi-rational map
- inverse(MultirationalMap) -- inverse of a birational map
- inverse2(MultirationalMap) -- see inverse2 -- inverse of a birational map using a faster algorithm for a special class of maps
- isIsomorphism(MultirationalMap) -- whether a birational map is an isomorphism
- isMember(MultirationalMap,RAT) -- test membership in a hom-set of rational maps
- isMorphism(MultirationalMap) -- whether a multi-rational map is a morphism
- isWellDefined(MultirationalMap) -- whether a multi-rational map is well-defined
- multidegree(MultirationalMap) -- projective degrees of a multi-rational map
- projectiveDegrees(MultirationalMap) -- see multidegree(MultirationalMap) -- projective degrees of a multi-rational map
- multidegree(ZZ,MultirationalMap) -- i-th projective degree of a multi-rational map using a probabilistic approach
- MultirationalMap * MultirationalMap -- composition of multi-rational maps
- MultirationalMap * RationalMap -- see MultirationalMap * MultirationalMap -- composition of multi-rational maps
- MultirationalMap ^ ZZ -- see MultirationalMap * MultirationalMap -- composition of multi-rational maps
- RationalMap * MultirationalMap -- see MultirationalMap * MultirationalMap -- composition of multi-rational maps
- MultirationalMap ** Ring -- change the coefficient ring of a multi-rational map
- MultirationalMap << MultiprojectiveVariety -- force the change of the target in a multi-rational map
- MultirationalMap <==> MultirationalMap -- equality of multi-rational maps with checks on internal data
- MultirationalMap == MultirationalMap -- equality of multi-rational maps
- MultirationalMap == RationalMap -- see MultirationalMap == MultirationalMap -- equality of multi-rational maps
- MultirationalMap == ZZ -- see MultirationalMap == MultirationalMap -- equality of multi-rational maps
- RationalMap == MultirationalMap -- see MultirationalMap == MultirationalMap -- equality of multi-rational maps
- ZZ == MultirationalMap -- see MultirationalMap == MultirationalMap -- equality of multi-rational maps
- MultirationalMap ^* -- see MultirationalMap ^** MultiprojectiveVariety -- inverse image via a multi-rational map
- MultirationalMap ^** MultiprojectiveVariety -- inverse image via a multi-rational map
- MultirationalMap | List -- see MultirationalMap | MultiprojectiveVariety -- restriction of a multi-rational map
- MultirationalMap | MultiprojectiveVariety -- restriction of a multi-rational map
- MultirationalMap | MultirationalMap -- product of multi-rational maps
- MultirationalMap | RationalMap -- see MultirationalMap | MultirationalMap -- product of multi-rational maps
- RationalMap | MultirationalMap -- see MultirationalMap | MultirationalMap -- product of multi-rational maps
- MultirationalMap || List -- see MultirationalMap || MultiprojectiveVariety -- restriction of a multi-rational map
- MultirationalMap || MultiprojectiveVariety -- restriction of a multi-rational map
- MultirationalMap || MultirationalMap -- product of multi-rational maps
- MultirationalMap || RationalMap -- see MultirationalMap || MultirationalMap -- product of multi-rational maps
- RationalMap || MultirationalMap -- see MultirationalMap || MultirationalMap -- product of multi-rational maps
- MultirationalMap MultiprojectiveVariety -- direct image via a multi-rational map
- multirationalMap(MultirationalMap,MultiprojectiveVariety) -- change the target of a multi-rational map
- rationalMap(MultirationalMap,MultiprojectiveVariety) -- see multirationalMap(MultirationalMap,MultiprojectiveVariety) -- change the target of a multi-rational map
- projectionMaps(MultirationalMap) -- get the compositions of the multi-rational map with the projections of the target
- rationalMap(MultirationalMap) -- see rationalMap(List,MultiprojectiveVariety) -- the multi-rational map defined by a list of rational maps
- segre(MultirationalMap) -- the composition of a multi-rational map with the Segre embedding of the target
- show(MultirationalMap) -- display a multi-rational map
- source(MultirationalMap) -- the source for a multi-rational map
- super(MultirationalMap) -- get the multi-rational map whose target is a product of projective spaces
- target(MultirationalMap) -- the target for a multi-rational map
- toRationalMap(MultirationalMap) -- see toRationalMap -- convert a multi-rational map consisting of a single rational map to a standard rational map
- trim(MultirationalMap) -- trim the target of a multi-rational map

The object MultirationalMap is a type, with ancestor classes MutableHashTable < HashTable < Thing.

- multirationalMap -- the multi-rational map defined by a list of rational maps
- rationalMap(List,MultiprojectiveVariety) -- the multi-rational map defined by a list of rational maps