factor(MultirationalMap) -- the list of rational maps defining a multi-rational map

i1 : ZZ/33331[t_0..t_2,u_0..u_1,Degrees=>{3:{1,0},2:{0,1}}];

i2 : f0 = rationalMap {t_0,t_1,t_2}

o2 = -- rational map --
                    ZZ                        ZZ
     source: Proj(-----[t , t , t ]) x Proj(-----[u , u ])
                  33331  0   1   2          33331  0   1
                    ZZ
     target: Proj(-----[x , x , x ])
                  33331  0   1   2
     defining forms: {
                      t ,
                       0
                      
                      t ,
                       1
                      
                      t
                       2
                     }

o2 : MultihomogeneousRationalMap (rational map from PP^2 x PP^1 to PP^2)

i3 : f1 = rationalMap {u_0,u_1}

o3 = -- rational map --
                    ZZ                        ZZ
     source: Proj(-----[t , t , t ]) x Proj(-----[u , u ])
                  33331  0   1   2          33331  0   1
                    ZZ
     target: Proj(-----[x , x ])
                  33331  0   1
     defining forms: {
                      u ,
                       0
                      
                      u
                       1
                     }

o3 : MultihomogeneousRationalMap (rational map from PP^2 x PP^1 to PP^1)

i4 : f2 = rationalMap {t_0*u_1,t_1*u_0}

o4 = -- rational map --
                    ZZ                        ZZ
     source: Proj(-----[t , t , t ]) x Proj(-----[u , u ])
                  33331  0   1   2          33331  0   1
                    ZZ
     target: Proj(-----[x , x ])
                  33331  0   1
     defining forms: {
                      t u ,
                       0 1
                      
                      t u
                       1 0
                     }

o4 : MultihomogeneousRationalMap (rational map from PP^2 x PP^1 to PP^1)

i5 : Phi = rationalMap {f0,f1,f2};

o5 : MultirationalMap (rational map from PP^2 x PP^1 to PP^2 x PP^1 x PP^1)

i6 : assert(factor Phi === {f0,f1,f2})