i1 : X = projectiveVariety ideal(random({2,1},ring PP_(ZZ/101)^{2,1}),random({1,1},ring PP^{2,1}));
o1 : ProjectiveVariety, curve in PP^2 x PP^1
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i2 : Y = projectiveVariety ideal random({1,1,1},ring PP^{1,2,1});
o2 : ProjectiveVariety, hypersurface in PP^1 x PP^2 x PP^1
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i3 : X ** Y
o3 = 4-dimensional subvariety of PP^2 x PP^1 x PP^1 x PP^2 x PP^1 cut out by 4 hypersurfaces of multi-degrees (0,0,1,1,1)^1 (1,1,0,0,0)^1 (2,1,0,0,0)^1 (3,0,0,0,0)^1
o3 : ProjectiveVariety, X x Y
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