i1 : R = ZZ/101[x_0..x_2,y_0,y_1,Degrees=>{3:{1,0},2:{0,1}}];
|
i2 : S = ZZ/101[x_0,x_1,y_0..y_2,z_0,z_1,Degrees=>{2:{1,0,0},3:{0,1,0},2:{0,0,1}}];
|
i3 : X = projectiveVariety ideal(random({2,1},R),random({1,1},R));
o3 : ProjectiveVariety, curve in PP^2 x PP^1
|
i4 : Y = projectiveVariety ideal random({1,1,1},S);
o4 : ProjectiveVariety, hypersurface in PP^1 x PP^2 x PP^1
|
i5 : XxY = X ** Y;
o5 : ProjectiveVariety, 4-dimensional subvariety of PP^2 x PP^1 x PP^1 x PP^2 x PP^1
|
i6 : describe X
o6 = ambient:.............. PP^2 x PP^1
dim:.................. 1
codim:................ 2
degree:............... 5
multidegree:.......... 2*T_0^2+3*T_0*T_1
generators:........... (1,1)^1 (3,0)^1 (2,1)^1
purity:............... true
dim sing. l.:......... -1
Segre embedding:...... map to PP^4 ⊂ PP^5
|
i7 : describe Y
o7 = ambient:.............. PP^1 x PP^2 x PP^1
dim:.................. 3
codim:................ 1
degree:............... 12
multidegree:.......... T_0+T_1+T_2
generators:........... (1,1,1)^1
purity:............... true
dim sing. l.:......... -1
Segre embedding:...... map to PP^10 ⊂ PP^11
|
i8 : describe XxY
o8 = ambient:.............. PP^2 x PP^1 x PP^1 x PP^2 x PP^1
dim:.................. 4
codim:................ 3
degree:............... 240
multidegree:.......... 2*T_0^2*T_2+2*T_0^2*T_3+2*T_0^2*T_4+3*T_0*T_1*T_2+3*T_0*T_1*T_3+3*T_0*T_1*T_4
generators:........... (1,1,0,0,0)^1 (3,0,0,0,0)^1 (0,0,1,1,1)^1 (2,1,0,0,0)^1
purity:............... true
dim sing. l.:......... -1
Segre embedding:...... map to PP^54 ⊂ PP^71
|