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Cremona :: isBirational

isBirational -- whether a rational map is birational

Synopsis

Description

The testing passes through the methods degreeOfRationalMap and projectiveDegrees.

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

o1 = GF 109561[t , t , t , t , t ]
                0   1   2   3   4

o1 : PolynomialRing
i2 : phi=toMap(minors(2,matrix{{t_0..t_3},{t_1..t_4}}),Dominant=>infinity)

                                       GF 109561[x , x , x , x , x , x ]
                                                  0   1   2   3   4   5      2                           2                                          2
o2 = map(GF 109561[t , t , t , t , t ],---------------------------------,{- t  + t t , - t t  + t t , - t  + t t , - t t  + t t , - t t  + t t , - t  + t t , a})
                    0   1   2   3   4          x x  - x x  + x x             1    0 2     1 2    0 3     2    1 3     1 3    0 4     2 3    1 4     3    2 4
                                                2 3    1 4    0 5

                                                GF 109561[x , x , x , x , x , x ]
                                                           0   1   2   3   4   5
o2 : RingMap GF 109561[t , t , t , t , t ] <--- ---------------------------------
                        0   1   2   3   4               x x  - x x  + x x
                                                         2 3    1 4    0 5
i3 : time isBirational phi
     -- used 0.0498287 seconds

o3 = true
i4 : time isBirational(phi,MathMode=>true)
MathMode: output certified!
     -- used 0.688891 seconds

o4 = true

Ways to use isBirational :