graph(RingMap) -- closure of the graph of a rational map

Synopsis

Function: graph
Usage:

graph phi
Inputs:
- phi, a ring map, representing a rational map $\Phi:X \dashrightarrow Y$
Optional inputs:
- BlowUpStrategy => ..., default value "Eliminate",
Outputs:
- a ring map, representing the projection on the first factor $\mathbf{Graph}(\Phi) \to X$
- a ring map, representing the projection on the second factor $\mathbf{Graph}(\Phi) \to Y$

Description

i1 : phi = map(QQ[x_0..x_3],QQ[y_0..y_2],{-x_1^2+x_0*x_2,-x_1*x_2+x_0*x_3,-x_2^2+x_1*x_3})

                                      2                           2
o1 = map (QQ[x ..x ], QQ[y ..y ], {- x  + x x , - x x  + x x , - x  + x x })
              0   3       0   2       1    0 2     1 2    0 3     2    1 3

o1 : RingMap QQ[x ..x ] <-- QQ[y ..y ]
                 0   3          0   2

i2 : graph phi

                      QQ[x ..x , y ..y ]                                     
                          0   3   0   2                                      
o2 = (map (----------------------------------------, QQ[x ..x ], {x , x , x ,
           (x y  - x y  + x y , x y  - x y  + x y )      0   3     0   1   2 
             3 0    2 1    1 2   2 0    1 1    0 2                           
     ------------------------------------------------------------------------
                           QQ[x ..x , y ..y ]
                               0   3   0   2
     x }), map (----------------------------------------, QQ[y ..y ], {y ,
      3         (x y  - x y  + x y , x y  - x y  + x y )      0   2     0 
                  3 0    2 1    1 2   2 0    1 1    0 2
     ------------------------------------------------------------------------
     y , y }))
      1   2

o2 : Sequence

Ways to use this method: