-- -*- M2-comint -*- hash: 7881253114260834067

i1 : phi = quadroQuadricCremonaTransformation(5,1)

o1 = -- rational map --
     source: Proj(QQ[x, y, z, t, u, v])
     target: Proj(QQ[x, y, z, t, u, v])
     defining forms: {
                             2
                      y*z - v ,
                      
                             2
                      x*z - u ,
                      
                             2
                      x*y - t ,
                      
                      - z*t + u*v,
                      
                      - y*u + t*v,
                      
                      t*u - x*v
                     }

o1 : RationalMap (Cremona transformation of PP^5 of type (2,2))

i2 : K := frac(QQ[vars(0..5)]); phi = phi ** K

o3 = -- rational map --
     source: Proj(frac(QQ[a..f])[x, y, z, t, u, v])
     target: Proj(frac(QQ[a..f])[x, y, z, t, u, v])
     defining forms: {
                             2
                      y*z - v ,
                      
                             2
                      x*z - u ,
                      
                             2
                      x*y - t ,
                      
                      - z*t + u*v,
                      
                      - y*u + t*v,
                      
                      t*u - x*v
                     }

o3 : RationalMap (quadratic rational map from PP^5 to PP^5)

i4 : p = trim minors(2,(vars K)||(vars source phi))

                e        d        c        b        a
o4 = ideal (u - -*v, t - -*v, z - -*v, y - -*v, x - -*v)
                f        f        f        f        f

o4 : Ideal of frac(QQ[a..f])[x, y, z, t, u, v]

i5 : q = phi p

                                                           2       
                b*e - d*f        c*d - e*f        - a*b + d        
o5 = ideal (u + ---------*v, t + ---------*v, z + ----------*v, y +
                d*e - a*f        d*e - a*f         d*e - a*f       
     ------------------------------------------------------------------------
              2                 2
     - a*c + e         - b*c + f
     ----------*v, x + ----------*v)
      d*e - a*f         d*e - a*f

o5 : Ideal of frac(QQ[a..f])[x, y, z, t, u, v]

i6 : time phi^** q
 -- used 0.145794s (cpu); 0.145794s (thread); 0s (gc)

                e        d        c        b        a
o6 = ideal (u - -*v, t - -*v, z - -*v, y - -*v, x - -*v)
                f        f        f        f        f

o6 : Ideal of frac(QQ[a..f])[x, y, z, t, u, v]

i7 : oo == p

o7 = true

i8 : 
