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Cremona :: isIsomorphism(RationalMap)

isIsomorphism(RationalMap) -- whether a birational map is an isomorphism

Synopsis

Description

This method computes the inverse rational map using inverse.

i1 : P1 := QQ[a,b]; P4 := QQ[x,y,z,w];
i3 : phi = rationalMap({a^4,a^3*b,a^2*b^2,a*b^3,b^4},Dominant=>true)

o3 = -- rational map --
     source: Proj(QQ[a, b])
     target: subvariety of Proj(QQ[t , t , t , t , t ]) defined by
                                    0   1   2   3   4
             {
               2
              t  - t t ,
               3    2 4
              
              t t  - t t ,
               2 3    1 4
              
              t t  - t t ,
               1 3    0 4
              
               2
              t  - t t ,
               2    0 4
              
              t t  - t t ,
               1 2    0 3
              
               2
              t  - t t
               1    0 2
             }
     defining forms: {
                       4
                      a ,
                      
                       3
                      a b,
                      
                       2 2
                      a b ,
                      
                         3
                      a*b ,
                      
                       4
                      b
                     }

o3 : RationalMap (dominant rational map from PP^1 to curve in PP^4)
i4 : isIsomorphism phi

o4 = true

See also

Ways to use this method: