# affineFatPointsByIntersection -- computes ideal of fat points by intersecting powers of maximal ideals

## Synopsis

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

## Description

This function computes the ideal of a finite set of fat points by intersecting powers of the maximal ideals of each point.

 i1 : R = QQ[x,y] o1 = R o1 : PolynomialRing i2 : M = transpose matrix{{0,0},{1,1}} o2 = | 0 1 | | 0 1 | 2 2 o2 : Matrix ZZ <--- ZZ i3 : mults = {3,2} o3 = {3, 2} o3 : List i4 : affineFatPointsByIntersection(M,mults,R) 2 2 3 3 2 3 3 4 2 3 5 4 o4 = {x y - 2x*y + y , x - 3x*y + 2y , x*y - y - x*y + y , y - 2y + ------------------------------------------------------------------------ 3 y } o4 : List