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

              3        5
o1 : Matrix ZZ  <--- ZZ

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

o2 = R

o2 : PolynomialRing

i3 : pointsByIntersection(M,R)

                 2                                  2                      
o3 = {61y*z - 53z  - 261y - 37z + 1290, 61x*z - 118z  - 61x - 100y + 622z +
     ------------------------------------------------------------------------
            2      2                                    2                
     96, 61y  + 36z  - 839y - 258z + 3060, 122x*y - 123z  - 732x - 158y +
     ------------------------------------------------------------------------
                     2       2                                  3       2
     729z + 342, 122x  + 447z  - 1220x - 12y - 3051z + 5238, 61z  - 654z  -
     ------------------------------------------------------------------------
     120y + 2003z - 690}

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` :