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

Synopsis

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 = | 6 1 2 1 9 |
     | 7 8 8 8 8 |
     | 7 7 2 3 3 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                                  2                            2            
o3 = {y*z - 7y - 8z + 56, 5x*z + z  - 15x + 100y - 15z - 764, y  - 15y + 56,
     ------------------------------------------------------------------------
                           2     2                           3      2
     x*y - 8x - 6y + 48, 5x  + 7z  - 50x - 75y - 70z + 792, z  - 12z  + 41z -
     ------------------------------------------------------------------------
     42}

o3 : List

See also

Ways to use pointsByIntersection :