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

Synopsis

• 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

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