-- -*- M2-comint -*- hash: 11093813010086391996

i1 : Phi = inverse first graph last graph rationalMap PP_(ZZ/33331)^(1,3)

o1 = Phi

o1 : MultirationalMap (birational map from threefold in PP^3 x PP^2 to threefold in PP^3 x PP^2 x PP^2)

i2 : time describe Phi
 -- used 0.18288s (cpu); 0.137681s (thread); 0s (gc)

o2 = multi-rational map consisting of 3 rational maps
     source variety: threefold in PP^3 x PP^2 cut out by 2 hypersurfaces of multi-degree (1,1)
     target variety: threefold in PP^3 x PP^2 x PP^2 cut out by 7 hypersurfaces of multi-degrees (0,1,1)^3 (1,0,1)^2 (1,1,0)^2 
     base locus: empty subscheme of PP^3 x PP^2
     dominance: true
     multidegree: {10, 14, 19, 25}
     degree: 1
     degree sequence (map 1/3): [(1,0)]
     degree sequence (map 2/3): [(0,1), (2,0)]
     degree sequence (map 3/3): [(0,1), (2,0)]
     coefficient ring: ZZ/33331

i3 : show Phi

o3 = -- multi-rational map --
                                  ZZ                                ZZ
     source: subvariety of Proj(-----[x0 , x0 , x0 , x0 ]) x Proj(-----[x1 , x1 , x1 ]) defined by
                                33331   0    1    2    3          33331   0    1    2
             {
              x0 x1  - x0 x1  + x0 x1 ,
                1  0     2  1     3  2
              
              x0 x1  - x0 x1  + x0 x1
                0  0     1  1     2  2
             }
                                  ZZ                                ZZ                           ZZ
     target: subvariety of Proj(-----[x0 , x0 , x0 , x0 ]) x Proj(-----[x1 , x1 , x1 ]) x Proj(-----[x2 , x2 , x2 ]) defined by
                                33331   0    1    2    3          33331   0    1    2          33331   0    1    2
             {
              x1 x2  - x1 x2 ,
                2  1     1  2
              
              x1 x2  - x1 x2 ,
                2  0     0  2
              
              x1 x2  - x1 x2 ,
                1  0     0  1
              
              x0 x2  - x0 x2  + x0 x2 ,
                1  0     2  1     3  2
              
              x0 x2  - x0 x2  + x0 x2 ,
                0  0     1  1     2  2
              
              x0 x1  - x0 x1  + x0 x1 ,
                1  0     2  1     3  2
              
              x0 x1  - x0 x1  + x0 x1
                0  0     1  1     2  2
             }
     -- rational map 1/3 -- 
     map 1/3, unique representative:
     {
      x0 ,
        0
      
      x0 ,
        1
      
      x0 ,
        2
      
      x0
        3
     }
     -- rational map 2/3 -- 
     map 2/3, representative 1/2:
     {
      x1 ,
        0
      
      x1 ,
        1
      
      x1
        2
     }
     map 2/3, representative 2/2:
     {
        2
      x0  - x0 x0 ,
        2     1  3
      
      x0 x0  - x0 x0 ,
        1  2     0  3
      
        2
      x0  - x0 x0
        1     0  2
     }
     -- rational map 3/3 -- 
     map 3/3, representative 1/2:
     {
      x1 ,
        0
      
      x1 ,
        1
      
      x1
        2
     }
     map 3/3, representative 2/2:
     {
        2
      x0  - x0 x0 ,
        2     1  3
      
      x0 x0  - x0 x0 ,
        1  2     0  3
      
        2
      x0  - x0 x0
        1     0  2
     }

i4 : 
