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 = | 2 2 6 3 3 |
     | 6 5 1 2 0 |
     | 1 4 1 5 5 |

              3        5
o1 : Matrix ZZ  <--- ZZ

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

o2 = R

o2 : PolynomialRing

i3 : pointsByIntersection(M,R)

                 2                                  2                  2  
o3 = {12y*z + 19z  - 60x - 60y - 171z + 560, x*z - z  - x + 3z - 2, 16y  +
     ------------------------------------------------------------------------
        2                                      2                            
     23z  + 100x - 32y - 67z - 540, 48x*y - 29z  - 108x - 144y + 129z + 404,
     ------------------------------------------------------------------------
       2     2                    3      2
     4x  + 3z  - 32x - 15z + 60, z  - 10z  + 29z - 20}

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` :