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

              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 - 20z  + 39x - 72y + 124z - 24, x*z + 4z  - 15x - 44z + 120, 12y 
     ------------------------------------------------------------------------
         2                                   2                     2      
     - 4z  + 9x - 156y + 44z + 360, 9x*y + 8z  - 66x - 88z + 240, x  - 8x,
     ------------------------------------------------------------------------
       3      2
     2z  - 10z  - 45x - 72z + 360}

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` :