# points -- make the ideal of a set of points

## Synopsis

• Usage:
i = points pointsMat
• Inputs:
• pointsMat, , matrix whose columns are the homogeneous cooredinates of the points
• Outputs:

## Description

 i1 : R = ZZ/101[vars(0..4)] o1 = R o1 : PolynomialRing i2 : pointsMat = randomPointsMat(R,11) o2 = | 1 0 0 0 0 1 24 19 -29 21 -18 | | 0 1 0 0 0 1 -36 -10 -24 34 -13 | | 0 0 1 0 0 1 -30 -29 -38 19 -43 | | 0 0 0 1 0 1 -29 -8 -16 -47 -15 | | 0 0 0 0 1 1 19 -22 39 -39 -28 | 5 11 o2 : Matrix R <--- R i3 : points pointsMat o3 = ideal (a*d - 2b*d + 26c*d - 15a*e + 37b*e + 8c*e + 46d*e, b*c - 36b*d + ------------------------------------------------------------------------ 23c*d + 48a*e + 48b*e - 50c*e - 34d*e, a*c + 50b*d + 41c*d + 28a*e + ------------------------------------------------------------------------ 50b*e - 42c*e - 27d*e, a*b - 10b*d - 44c*d + 37a*e + 20b*e - 8c*e + ------------------------------------------------------------------------ 2 2 2 2 2 2 4d*e, b*d*e + 20c*d*e + 23d e - 26a*e - b*e + 12c*e - 29d*e , c e + ------------------------------------------------------------------------ 2 2 2 2 2 2 2 19c*d*e + 14d e + 17a*e - 29b*e + 7c*e - 29d*e , b e - 2c*d*e - 3d e ------------------------------------------------------------------------ 2 2 2 2 2 2 2 - 11a*e + 25b*e + 33c*e - 43d*e , a e - c*d*e - 30d e - 27a*e + ------------------------------------------------------------------------ 2 2 2 11b*e + 5c*e + 41d*e ) o3 : Ideal of R