# idealOfProjectivePoints -- computes the ideal of set of points

## 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{1, 4, 1}, Point{0, 2, -1}, Point{0, 1, 0}, Point{0, 1, 1}, ------------------------------------------------------------------------ Point{1, 1, 0}, Point{1, 2, 0}} o5 : List i6 : I2 == idealOfProjectivePoints(X2,S) o6 = true

## Ways to use idealOfProjectivePoints :

• "idealOfProjectivePoints(List,Ring)"

## For the programmer

The object idealOfProjectivePoints is .