projectivePointsByIntersection -- computes ideal of projective points by intersecting point ideals

Synopsis

• Usage:

  projectivePointsByIntersection(M,R)

• Inputs:
  • M, a matrix, in which each column consists of the projective coordinates of a 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 projective 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 : projectivePointsByIntersection(M,R)

o3 = {y - z, x*z}

o3 : List

See also

• projectivePoints(Matrix,Ring) -- produces the ideal and initial ideal from the coordinates of a finite set of projective points