i1 : QQ[x_0..x_5]; phi = rationalMap {x_4^2x_3*x_5,x_2*x_4x_1*x_5,x_2*x_3x_1*x_4,x_2^2x_0*x_5,x_1*x_2x_0*x_4,x_1^2x_0*x_3};
o2 : RationalMap (quadratic rational map from PP^5 to PP^5)

i3 : describe phi
o3 = rational map defined by forms of degree 2
source variety: PP^5
target variety: PP^5
coefficient ring: QQ

i4 : time phi! ;
 used 0.0994591 seconds
o4 : RationalMap (Cremona transformation of PP^5 of type (2,2))

i5 : describe phi
o5 = rational map defined by forms of degree 2
source variety: PP^5
target variety: PP^5
dominance: true
birationality: true (the inverse map is already calculated)
projective degrees: {1, 2, 4, 4, 2, 1}
number of minimal representatives: 1
dimension base locus: 2
degree base locus: 4
coefficient ring: QQ

i6 : QQ[x_0..x_4]; phi = rationalMap {x_1^2+x_0*x_2,x_1*x_2+x_0*x_3,x_2^2+x_1*x_3,x_1*x_3+x_0*x_4,x_2*x_3+x_1*x_4,x_3^2+x_2*x_4};
o7 : RationalMap (quadratic rational map from PP^4 to PP^5)

i8 : describe phi
o8 = rational map defined by forms of degree 2
source variety: PP^4
target variety: PP^5
coefficient ring: QQ

i9 : time phi! ;
 used 0.0581217 seconds
o9 : RationalMap (quadratic rational map from PP^4 to PP^5)

i10 : describe phi
o10 = rational map defined by forms of degree 2
source variety: PP^4
target variety: PP^5
image: smooth quadric hypersurface in PP^5
dominance: false
birationality: false
degree of map: 1
projective degrees: {1, 2, 4, 4, 2}
number of minimal representatives: 1
dimension base locus: 1
degree base locus: 4
coefficient ring: QQ
