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 = | 7 4 6 9 9 |
     | 4 4 2 4 8 |
     | 6 6 1 8 6 |

              3        5
o1 : Matrix ZZ  <--- ZZ

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

o2 = R

o2 : PolynomialRing

i3 : pointsByIntersection(M,R)

               2                      2                       2      2       
o3 = {7y*z - 2z  - 42y + 72, 7x*z - 3z  - 42x - 21z + 234, 35y  - 12z  - 420y
     ------------------------------------------------------------------------
                             2                               2     2         
     + 168z + 544, 35x*y - 6z  - 140x - 315y + 84z + 972, 10x  - 8z  - 110x -
     ------------------------------------------------------------------------
                       3      2
     25y + 62z + 296, z  - 15z  + 62z - 48}

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` :