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Cremona :: RationalMap == RationalMap

RationalMap == RationalMap -- equality of rational maps

Synopsis

Description

i1 : QQ[x_0..x_5]

o1 = QQ[x ..x ]
         0   5

o1 : PolynomialRing
i2 : phi = rationalMap {x_0*x_4^2-x_0*x_3*x_5,x_0*x_2*x_4-x_0*x_1*x_5,x_0*x_2*x_3-x_0*x_1*x_4,x_0*x_2^2-x_0^2*x_5,x_0*x_1*x_2-x_0^2*x_4,x_0*x_1^2-x_0^2*x_3}

o2 = -- rational map --
     source: Proj(QQ[x , x , x , x , x , x ])
                      0   1   2   3   4   5
     target: Proj(QQ[x , x , x , x , x , x ])
                      0   1   2   3   4   5
     defining forms: {
                         2
                      x x  - x x x ,
                       0 4    0 3 5
                      
                      x x x  - x x x ,
                       0 2 4    0 1 5
                      
                      x x x  - x x x ,
                       0 2 3    0 1 4
                      
                         2    2
                      x x  - x x ,
                       0 2    0 5
                      
                                2
                      x x x  - x x ,
                       0 1 2    0 4
                      
                         2    2
                      x x  - x x
                       0 1    0 3
                     }

o2 : RationalMap (cubic rational map from PP^5 to PP^5)
i3 : psi = rationalMap {x_4^2-x_3*x_5,x_2*x_4-x_1*x_5,x_2*x_3-x_1*x_4,x_2^2-x_0*x_5,x_1*x_2-x_0*x_4,x_1^2-x_0*x_3}

o3 = -- rational map --
     source: Proj(QQ[x , x , x , x , x , x ])
                      0   1   2   3   4   5
     target: Proj(QQ[x , x , x , x , x , x ])
                      0   1   2   3   4   5
     defining forms: {
                       2
                      x  - x x ,
                       4    3 5
                      
                      x x  - x x ,
                       2 4    1 5
                      
                      x x  - x x ,
                       2 3    1 4
                      
                       2
                      x  - x x ,
                       2    0 5
                      
                      x x  - x x ,
                       1 2    0 4
                      
                       2
                      x  - x x
                       1    0 3
                     }

o3 : RationalMap (quadratic rational map from PP^5 to PP^5)
i4 : phi == psi

o4 = true