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 6 5 4 7 |
     | 2 2 6 5 6 |
     | 6 7 3 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 = {61y*z + 56z  + 12x - 324y - 826z + 2760, 61x*z + 11z  - 307x + 54y -
     ------------------------------------------------------------------------
                     2      2                                       2       
     391z + 1370, 61y  - 36z  - 60x - 515y + 348z + 474, 61x*y - 16z  - 230x
     ------------------------------------------------------------------------
                            2      2                                3       2
     - 500y - 8z + 2488, 61x  + 59z  - 715x + 90y - 489z + 2446, 61z  - 894z 
     ------------------------------------------------------------------------
     + 96x - 30y + 4067z - 6102}

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` :