# affinePointsByIntersection -- computes ideal of point set by intersecting maximal ideals

## Synopsis

• Usage:
affinePointsByIntersection(M,R)
• Inputs:
• M, , in which each column consists of the coordinates of a point
• R, , coordinate ring of the affine space containing the points
• Outputs:
• a list, grobner basis for ideal of a finite set of points

## Description

This function computes the ideal of a finite set of points by intersecting the ideals for each point. The coordinates of the points are the columns in the input matrix M.
 i1 : M = random(ZZ^3, ZZ^5) o1 = | 8 7 3 8 8 | | 1 8 7 5 5 | | 3 3 8 7 2 | 3 5 o1 : Matrix ZZ <--- ZZ i2 : R = QQ[x,y,z] o2 = R o2 : PolynomialRing i3 : affinePointsByIntersection(M,R) 2 2 o3 = {39y*z - 10z + 70x - 107y - 105z - 165, 39x*z + 25z - 292x - 25y - ------------------------------------------------------------------------ 2 2 2 537z + 2811, 13y + 31z + 56x - 109y - 279z + 206, 39x*y - 5z - 277x - ------------------------------------------------------------------------ 2 2 3 2 307y + 45z + 2121, 39x - 20z - 445x + 20y + 180z + 684, 13z - 166z + ------------------------------------------------------------------------ 70x + 10y + 623z - 1296} o3 : List