# Singular

#### D.10.2.16 vanishId

Procedure from library `decodegb.lib` (see decodegb_lib).

Usage:
vanishId (points); point is a list of matrices
'points' is a list of points for which the vanishing ideal is to be constructed

Return:
Vanishing ideal corresponding to the given set of points

Example:
 ```LIB "decodegb.lib"; ring r=3,(x(1..3)),dp; //generate all 3-vectors over GF(3) list points=pointsGen(3,1); list points2=convPoints(points); //grasps the first 11 points list p=graspList(points2,1,11); print(p); ==> [1]: ==> _[1,1]=0 ==> _[2,1]=0 ==> _[3,1]=0 ==> [2]: ==> _[1,1]=0 ==> _[2,1]=0 ==> _[3,1]=1 ==> [3]: ==> _[1,1]=0 ==> _[2,1]=0 ==> _[3,1]=-1 ==> [4]: ==> _[1,1]=0 ==> _[2,1]=1 ==> _[3,1]=0 ==> [5]: ==> _[1,1]=0 ==> _[2,1]=1 ==> _[3,1]=1 ==> [6]: ==> _[1,1]=0 ==> _[2,1]=1 ==> _[3,1]=-1 ==> [7]: ==> _[1,1]=0 ==> _[2,1]=-1 ==> _[3,1]=0 ==> [8]: ==> _[1,1]=0 ==> _[2,1]=-1 ==> _[3,1]=1 ==> [9]: ==> _[1,1]=0 ==> _[2,1]=-1 ==> _[3,1]=-1 ==> [10]: ==> _[1,1]=1 ==> _[2,1]=0 ==> _[3,1]=0 ==> [11]: ==> _[1,1]=1 ==> _[2,1]=0 ==> _[3,1]=1 //construct the vanishing ideal ideal id=vanishId(p); print(id); ==> x(1)*x(2), ==> x(1)^2-x(1), ==> x(3)^3-x(3), ==> x(1)*x(3)^2-x(1)*x(3), ==> x(2)^3-x(2) ```