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 4 4 7 1 |
     | 3 3 1 7 0 |
     | 2 5 8 1 3 |

              3        5
o1 : Matrix ZZ  <--- ZZ

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

o2 = R

o2 : PolynomialRing

i3 : pointsByIntersection(M,R)

                   2                                              2          
o3 = {907y*z + 725z  - 636x - 2003y - 8644z + 20043, 907x*z + 156z  - 2435x +
     ------------------------------------------------------------------------
                               2       2                                 
     162y - 5548z + 14954, 907y  - 891z  + 2448x - 6751y + 9501z - 22932,
     ------------------------------------------------------------------------
                  2                                     2       2          
     907x*y - 573z  - 597x - 4537y + 6843z - 14775, 907x  - 252z  - 8625x +
     ------------------------------------------------------------------------
                               3         2
     2250y + 4776z - 4342, 907z  - 12795z  - 1236x + 4818y + 52544z - 65730}

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` :