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

## Synopsis

• Function: point
• Usage:
point X
• Inputs:
• X, , defined over a finite field
• Outputs:
• , a random rational point on $X$

## Description

 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 0.163771 seconds 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 6.31137 seconds o5 = q o5 : ProjectiveVariety, a point in PP^3 x PP^2 x PP^9 i6 : assert(isSubset(p,X) and isSubset(q,Y))

The list of homogeneous coordinates can be obtained with the operator |-.

 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