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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 = | 8 0 1 7 5 |
     | 0 7 5 4 5 |
     | 8 9 5 5 8 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                   2                                          2             
o3 = {108y*z - 131z  - 60x - 900y + 1243z - 1080, 36x*z + 163z  - 168x + 72y
     ------------------------------------------------------------------------
                         2       2                                        
     - 2315z + 7128, 162y  - 413z  + 120x - 738y + 5209z - 16200, 324x*y +
     ------------------------------------------------------------------------
          2                                      2       2                
     1219z  - 1680x - 2628y - 15767z + 61560, 54x  - 281z  - 402x + 180y +
     ------------------------------------------------------------------------
                     3      2
     3757z - 12312, z  - 22z  + 157z - 360}

o3 : List

See also

Ways to use pointsByIntersection :