distinctPlanePoints -- Generates the ideal of k random points in the coordinate ring $R$ of $\\P^{ 2}$

Synopsis

Usage:

(random distinctPlanePoints)(k,R)
Inputs:
- k, an integer, the number of points
- R, a polynomial ring, the homogeneous coordinate ring of $\mathbb{P}^2$
Outputs:
- an ideal, the vanishing ideal of the points

Creates the ideal of the points via a random choice of their Hilbert-Burch matrix, which is taken to be of generic shape.

i1 : setRandomSeed("alpha");

i2 : R=ZZ/32003[x_0..x_2];

i3 : Ipts=(random distinctPlanePoints)(10,R);

o3 : Ideal of R

i4 : betti res Ipts

            0 1 2
o4 = total: 1 5 4
         0: 1 . .
         1: . . .
         2: . . .
         3: . 5 4

o4 : BettiTally

The object distinctPlanePoints is an instance of the type RandomObject.