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 3 2 2 2 |
     | 0 7 8 4 9 |
     | 7 8 7 4 5 |

              3        5
o1 : Matrix ZZ  <--- ZZ

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

o2 = R

o2 : PolynomialRing

i3 : pointsByIntersection(M,R)

                  2                                          2              
o3 = {78y*z - 203z  + 816x - 444y + 1785z - 4996, 78x*z - 11z  - 594x - 6y -
     ------------------------------------------------------------------------
                   2       2                                          2  
     27z + 872, 39y  + 235z  - 648x - 393y - 2685z + 9224, 78x*y - 77z  -
     ------------------------------------------------------------------------
                                 2              3       2
     336x - 198y + 903z - 1540, x  - 5x + 6, 13z  - 230z  - 96x - 12y + 1337z
     ------------------------------------------------------------------------
     - 2260}

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` :