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

• Usage:

  affineFatPointsByIntersection(M,mults,R)

• Inputs:
  • M, a matrix, 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

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