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 7 6 1 4 |
     | 1 1 7 4 2 |
     | 7 6 5 9 6 |

              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 - 12z  + 3x - 3y + 169z - 612, 2x*z - 2z  - 11x + 3y + 27z - 100,
     ------------------------------------------------------------------------
       2      2                                      2                    
     3y  + 39z  - 14x - 51y - 577z + 2204, 2x*y + 18z  - 7x - 23y - 259z +
     ------------------------------------------------------------------------
           2     2                            3      2
     964, x  + 8z  - 13x - 6y - 124z + 504, 3z  - 78z  + 4x + 12y + 653z -
     ------------------------------------------------------------------------
     1798}

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` :