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 = | 8 2 6 4 9 |
     | 5 0 0 3 2 |
     | 8 4 6 4 6 |

              3        5
o1 : Matrix ZZ  <--- ZZ

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

o2 = R

o2 : PolynomialRing

i3 : pointsByIntersection(M,R)

                 2                                      2                   
o3 = {10y*z - 41z  - 24x - 24y + 458z - 1128, 5x*z - 17z  - 38x + 12y + 176z
     ------------------------------------------------------------------------
               2     2                                   2               
     - 396, 20y  - 9z  + 24x - 76y + 42z - 72, 2x*y - 13z  - 12x + 154z -
     ------------------------------------------------------------------------
            2      2                              3      2
     384, 5x  - 59z  - 111x + 54y + 732z - 1782, z  - 18z  + 104z - 192}

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` :