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Cremona :: isBirational

isBirational -- whether a rational map is birational

Synopsis

Description

The testing passes through the methods projectiveDegrees, degreeMap and isDominant.

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 0.0154286 seconds

o3 = true
i4 : time isBirational(phi,MathMode=>true)
MathMode: output certified!
     -- used 0.0162886 seconds

o4 = true

See also

Ways to use isBirational :

For the programmer

The object isBirational is a method function with options.