i1 : K = ZZ/33331; C = PP_K^(1,4);  rational normal quartic curve
o2 : ProjectiveVariety, curve in PP^4

i3 : Phi = rationalMap C;  map defined by the quadrics through C
o3 : MultirationalMap (rational map from PP^4 to PP^5)

i4 : Q = random(2,C);  random quadric hypersurface through C
o4 : ProjectiveVariety, hypersurface in PP^4

i5 : Phi = PhiQ;
o5 : MultirationalMap (rational map from Q to PP^5)

i6 : image Phi
o6 = threefold in PP^5 cut out by 2 hypersurfaces of degrees 1^1 2^1
o6 : ProjectiveVariety, threefold in PP^5

i7 : Psi = trim Phi;
o7 : MultirationalMap (rational map from Q to PP^4)

i8 : image Psi
o8 = hypersurface in PP^4 defined by a form of degree 2
o8 : ProjectiveVariety, hypersurface in PP^4

i9 : Phi  Phi  Psi;
o9 : MultirationalMap (rational map from Q x Q x Q to PP^5 x PP^5 x PP^4)

i10 : image oo
o10 = 9dimensional subvariety of PP^5 x PP^5 x PP^4 cut out by 5 hypersurfaces of multidegrees (0,0,2)^1 (0,1,0)^1 (0,2,0)^1 (1,0,0)^1 (2,0,0)^1
o10 : ProjectiveVariety, 9dimensional subvariety of PP^5 x PP^5 x PP^4

i11 : trim (Phi  Phi  Psi);
o11 : MultirationalMap (rational map from Q x Q x Q to PP^4 x PP^4 x PP^4)

i12 : image oo
o12 = 9dimensional subvariety of PP^4 x PP^4 x PP^4 cut out by 3 hypersurfaces of multidegrees (0,0,2)^1 (0,2,0)^1 (2,0,0)^1
o12 : ProjectiveVariety, 9dimensional subvariety of PP^4 x PP^4 x PP^4
