pointsByIntersection -- computes ideal of point set by intersecting maximal ideals

Synopsis

Usage:
pointsByIntersection(M,R)
Inputs:
- M, a matrix, in which each column consists of the coordinates of a point
- R, a polynomial ring, coordinate ring of the affine space containing the points
Outputs:
- a list, grobner basis for ideal of a finite set of points

Description

This function computes the ideal of a finite set of points by intersecting the ideals for each point. The coordinates of the points are the columns in the input matrix M.

i1 : M = random(ZZ^3, ZZ^5)

o1 = | 3 0 3 2 8 |
     | 9 6 9 7 1 |
     | 1 5 9 8 8 |

              3        5
o1 : Matrix ZZ  <--- ZZ

i2 : R = QQ[x,y,z]

o2 = R

o2 : PolynomialRing

i3 : pointsByIntersection(M,R)

               2                                    2                    
o3 = {2y*z + 9z  - 21x - 37y - 108z + 477, 2x*z + 9z  - 37x - 21y - 96z +
     ------------------------------------------------------------------------
            2      2                                       2                
     381, 6y  + 33z  - 109x - 157y - 330z + 1551, 3x*y - 3z  - 4x - 7y + 30z
     ------------------------------------------------------------------------
             2      2                              3     2
     - 33, 6x  + 33z  - 127x - 67y - 330z + 1227, z  + 6z  - 56x - 56y - 151z
     ------------------------------------------------------------------------
     + 816}

o3 : List

Ways to use `pointsByIntersection` :

pointsByIntersection(Matrix,Ring)

pointsByIntersection -- computes ideal of point set by intersecting maximal ideals

Synopsis

Description

See also

Ways to use pointsByIntersection :

Ways to use `pointsByIntersection` :