baseLocus -- the base locus of a multi-rational map

i1 : t = gens ring PP_(ZZ/33331)^5;

i2 : Phi = rationalMap {rationalMap {t_0,t_1,t_2},rationalMap {t_3,t_4,t_5}};

o2 : MultirationalMap (rational map from PP^5 to PP^2 x PP^2)

i3 : X = baseLocus Phi;

o3 : ProjectiveVariety, surface in PP^5

i4 : describe X

o4 = ambient:.............. PP^5
     dim:.................. 2
     codim:................ 3
     degree:............... 2
     generators:........... 2^9 
     purity:............... true
     dim sing. l.:......... -1

i5 : Psi = inverse(Phi|random(3,baseLocus Phi));

o5 : MultirationalMap (birational map from PP^2 x PP^2 to hypersurface in PP^5)

i6 : Y = baseLocus Psi;

o6 : ProjectiveVariety, surface in PP^2 x PP^2

i7 : describe Y

o7 = ambient:.............. PP^2 x PP^2
     dim:.................. 2
     codim:................ 2
     degree:............... 14
     multidegree:.......... 2*T_0^2+5*T_0*T_1+2*T_1^2
     generators:........... (1,2)^1 (2,1)^1 
     purity:............... true
     dim sing. l.:......... -1
     Segre embedding:...... map to PP^8