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affinePointsByIntersection -- computes ideal of point set by intersecting maximal ideals

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 7 3 8 8 |
     | 1 8 7 5 5 |
     | 3 3 8 7 2 |

              3       5
o1 : Matrix ZZ  <-- ZZ
 
i2 : R = QQ[x,y,z]

o2 = R

o2 : PolynomialRing
 
i3 : affinePointsByIntersection(M,R)

                 2                                       2               
o3 = {39y*z - 10z  + 70x - 107y - 105z - 165, 39x*z + 25z  - 292x - 25y -
     ------------------------------------------------------------------------
                     2      2                                      2         
     537z + 2811, 13y  + 31z  + 56x - 109y - 279z + 206, 39x*y - 5z  - 277x -
     ------------------------------------------------------------------------
                           2      2                               3       2
     307y + 45z + 2121, 39x  - 20z  - 445x + 20y + 180z + 684, 13z  - 166z  +
     ------------------------------------------------------------------------
     70x + 10y + 623z - 1296}

o3 : List

See also

Ways to use affinePointsByIntersection:

  • affinePointsByIntersection(Matrix,Ring)

For the programmer

The object affinePointsByIntersection is a method function.

The source of this document is in Points.m2:1017:0.