isBirational -- whether a rational map is birational

i1 : GF(331^2)[t_0..t_4]

o1 = GF 109561[t ..t ]
                0   4

o1 : PolynomialRing

i2 : phi = rationalMap(minors(2,matrix{{t_0..t_3},{t_1..t_4}}),Dominant=>infinity)

o2 = -- rational map --
     source: Proj(GF 109561[t , t , t , t , t ])
                             0   1   2   3   4
     target: subvariety of Proj(GF 109561[x , x , x , x , x , x ]) defined by
                                           0   1   2   3   4   5
             {
              x x  - x x  + x x
               2 3    1 4    0 5
             }
     defining forms: {
                         2
                      - t  + t t ,
                         1    0 2
                      
                      - t t  + t t ,
                         1 2    0 3
                      
                         2
                      - t  + t t ,
                         2    1 3
                      
                      - t t  + t t ,
                         1 3    0 4
                      
                      - t t  + t t ,
                         2 3    1 4
                      
                         2
                      - t  + t t
                         3    2 4
                     }

o2 : RationalMap (quadratic dominant rational map from PP^4 to hypersurface in PP^5)

i3 : time isBirational phi
 -- used 0.070776s (cpu); 0.0332999s (thread); 0s (gc)

o3 = true

i4 : time isBirational(phi,Certify=>true)
 -- used 0.0121245s (cpu); 0.0118955s (thread); 0s (gc)
Certify: output certified!

o4 = true