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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 = | 5 1 6 0 8 |
     | 9 2 2 7 1 |
     | 9 9 7 9 5 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

              2                          2                       2       2  
o3 = {2y*z - z  - 18y + 12z - 27, x*z + z  - 9x - 22z + 117, 108y  - 193z  -
     ------------------------------------------------------------------------
                                             2                            
     280x - 1028y + 2388z - 3955, 54x*y - 86z  - 458x - 70y + 501z + 2947,
     ------------------------------------------------------------------------
        2      2                               3      2
     54x  - 53z  - 254x - 40y + 1158z - 5849, z  - 21z  + 143z - 315}

o3 : List

See also

Ways to use pointsByIntersection :