More generally, if d is a list of multi-degrees, then the output is the intersection of the hypersurfaces random(d_i,X).
i1 : X = PP_(ZZ/65521)^(1,3); -- twisted cubic curve o1 : ProjectiveVariety, curve in PP^3 |
i2 : random({2},X);
o2 : ProjectiveVariety, surface in PP^3
|
i3 : ideal oo
2 2
o3 = ideal(t - t t - 68t t - 20741t + 68t t + 20741t t )
1 0 2 1 2 2 0 3 1 3
ZZ
o3 : Ideal of -----[t ..t ]
65521 0 3
|
i4 : random({{2},{2}},X);
o4 : ProjectiveVariety, curve in PP^3
|
i5 : ideal oo
2 2 2
o5 = ideal (t t + 21021t - t t - 21021t t , t - t t + 29086t -
1 2 2 0 3 1 3 1 0 2 2
------------------------------------------------------------------------
29086t t )
1 3
ZZ
o5 : Ideal of -----[t ..t ]
65521 0 3
|
i6 : X = X^2; o6 : ProjectiveVariety, X x X |
i7 : random({1,2},X);
o7 : ProjectiveVariety, hypersurface in PP^3 x PP^3
|
i8 : ideal oo
2 2 2 2
o8 = ideal(x0 x1 + 29294x0 x1 + 16820x0 x1 + 1316x0 x1 - x0 x1 x1 -
0 1 1 1 2 1 3 1 0 0 2
------------------------------------------------------------------------
29294x0 x1 x1 - 16820x0 x1 x1 - 1316x0 x1 x1 - 3472x0 x1 x1 -
1 0 2 2 0 2 3 0 2 0 1 2
------------------------------------------------------------------------
2
29829x0 x1 x1 + 2976x0 x1 x1 - 23867x0 x1 x1 - 32075x0 x1 +
1 1 2 2 1 2 3 1 2 0 2
------------------------------------------------------------------------
2 2 2
17896x0 x1 - 7591x0 x1 - 19385x0 x1 + 3472x0 x1 x1 + 29829x0 x1 x1
1 2 2 2 3 2 0 0 3 1 0 3
------------------------------------------------------------------------
- 2976x0 x1 x1 + 23867x0 x1 x1 + 32075x0 x1 x1 - 17896x0 x1 x1 +
2 0 3 3 0 3 0 1 3 1 1 3
------------------------------------------------------------------------
7591x0 x1 x1 + 19385x0 x1 x1 )
2 1 3 3 1 3
ZZ
o8 : Ideal of -----[x0 ..x0 , x1 ..x1 ]
65521 0 3 0 3
|
i9 : random({{1,2},{1,2},{2,0}},X);
o9 : ProjectiveVariety, threefold in PP^3 x PP^3
|
i10 : degrees oo
o10 = {({1, 2}, 2), ({2, 0}, 1)}
o10 : List
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