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# projectiveFatPointsByIntersection -- computes ideal of fat points by intersecting powers of point ideals

- Usage:
    `projectiveFatPointsByIntersection(M,mults,R)`
- Inputs:
  - M, a matrix, in which each column consists of the projective coordinates of a point
  - mults, a list, in which each element determines the multiplicity of the corresponding point
  - R, a ring, homogeneous coordinate ring of the projective 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 ideals of each point.

    i1 : R = QQ[x,y,z]

    o1 = R

    o1 : PolynomialRing

    i2 : M = transpose matrix{{1,0,0},{0,1,1}}

    o2 = | 1 0 |
         | 0 1 |
         | 0 1 |

                  3       2
    o2 : Matrix ZZ  <-- ZZ

    i3 : mults = {3,2}

    o3 = {3, 2}

    o3 : List

    i4 : projectiveFatPointsByIntersection(M,mults,R)

           2        2    3   3       2     3       2      3   2 3
    o4 = {y z - 2y*z  + z , y  - 3y*z  + 2z , x*y*z  - x*z , x z }

    o4 : List

## See also

- projectiveFatPoints(Matrix,List,Ring) -- produces the ideal and initial ideal from the coordinates of a finite set of fat points

## Ways to use projectiveFatPointsByIntersection:

- `projectiveFatPointsByIntersection(Matrix,List,Ring)`

## For the programmer

The object projectiveFatPointsByIntersection is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Points.m2:1250:0.