point(MultiprojectiveVariety) -- pick a random rational point on a multi-projective variety

i1 : K = ZZ/1000003;

i2 : X = PP_K^({1,1,2},{3,2,3});

o2 : ProjectiveVariety, 4-dimensional subvariety of PP^3 x PP^2 x PP^9

i3 : time p := point X
 -- used 0.0558173s (cpu); 0.020482s (thread); 0s (gc)

o3 = point of coordinates ([421369, 39917, -212481, 1],[-128795, -176966, 1],[3870, -390108, -496127, -308581, 46649, 164926, -446111, 48038, 415309, 1])

o3 : ProjectiveVariety, a point in PP^3 x PP^2 x PP^9

i4 : Y = random({2,1,2},X);

o4 : ProjectiveVariety, hypersurface in PP^3 x PP^2 x PP^9

i5 : time q = point Y
 -- used 1.8351s (cpu); 1.1939s (thread); 0s (gc)

o5 = q

o5 : ProjectiveVariety, a point in PP^3 x PP^2 x PP^9

i6 : assert(isSubset(p,X) and isSubset(q,Y))

i7 : |- p

o7 = ([421369, 39917, -212481, 1], [-128795, -176966, 1], [3870, -390108,
     ------------------------------------------------------------------------
     -496127, -308581, 46649, 164926, -446111, 48038, 415309, 1])

o7 : Sequence

i8 : |- q

o8 = ([158712, 271608, 202519, 1], [-411495, 350529, 1], [499681, 293896,
     ------------------------------------------------------------------------
     -144543, 481344, 258084, 405184, -259486, -147014, 37168, 1])

o8 : Sequence