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

- 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

## Description

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");
     -- setting random seed to 10206284518

    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

## For the programmer

The object distinctPlanePoints is an instance of the type RandomObject.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/RandomPlaneCurves.m2:184:0.