next | previous | forward | backward | up | top | index | toc | Macaulay2 website

Hadamard :: idealOfProjectivePoints

idealOfProjectivePoints -- computes the ideal of set of points

Synopsis

Usage:

idealOfProjectivePoints(L,S)
Inputs:
- L, a list, of (projective) points
- S, a ring,
Outputs:
- I, an ideal,

Description

Given a set points $X$, it returns the defining ideal of $I(X)$

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

o1 = S

o1 : PolynomialRing

i2 : X = {point{1,1,0},point{0,1,1},point{1,2,-1}}

o2 = {Point{1, 1, 0}, Point{0, 1, 1}, Point{1, 2, -1}}

o2 : List

i3 : I = idealOfProjectivePoints(X,S)

                          2           2           2    2     2            2 
o3 = ideal (3x*z - y*z + z , 3x*y - 3y  - y*z + 4z , 3x  - 3y  - 2y*z + 5z ,
     ------------------------------------------------------------------------
      2       2     3
     y z + y*z  - 2z )

o3 : Ideal of S

i4 : I2 = hadamardPower(I,2)

             2         2      2     3              2   2       2    3     2 
o4 = ideal (y z - 18x*z  + y*z  - 2z , x*y*z - 4x*z , x z - x*z , 2x  - 3x y
     ------------------------------------------------------------------------
          2       2
     + x*y  - 6x*z )

o4 : Ideal of S

i5 : X2 = hadamardPower(X,2)

o5 = {Point{0, 1, 0}, Point{0, 2, -1}, Point{0, 1, 1}, Point{1, 1, 0},
     ------------------------------------------------------------------------
     Point{1, 2, 0}, Point{1, 4, 1}}

o5 : List

i6 : I2 == idealOfProjectivePoints(X2,S)

o6 = true

Ways to use `idealOfProjectivePoints` :

"idealOfProjectivePoints(List,Ring)"

For the programmer

The object idealOfProjectivePoints is a method function.