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 3 1 5 4 |
     | 1 7 9 6 7 |
     | 0 3 3 8 0 |

              3        5
o1 : Matrix ZZ  <--- ZZ

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

o2 = R

o2 : PolynomialRing

i3 : pointsByIntersection(M,R)

                 2                                         2                
o3 = {40y*z - 19z  + 360x + 240y - 103z - 3120, 40x*z + 11z  - 360x - 240y -
     ------------------------------------------------------------------------
                     2      2                                       2        
     273z + 3120, 40y  - 67z  + 960x + 320y + 521z - 8040, 2x*y + 3z  - 56x -
     ------------------------------------------------------------------------
                          2       2                                   3  
     44y - 23z + 476, 120x  - 167z  + 1440x + 1920y + 1261z - 21120, z  -
     ------------------------------------------------------------------------
        2
     11z  + 24z}

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` :