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Points :: pointsByIntersection

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 5 2 6 7 |
     | 0 0 8 5 2 |
     | 8 9 4 7 9 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                 2                                      2                   
o3 = {11y*z + 10z  - 15x - 84y - 185z + 930, 11x*z - 15z  - 104x + 5y + 184z
     ------------------------------------------------------------------------
               2      2                                       2              
     - 416, 22y  - 12z  + 51x - 95y + 255z - 1578, 22x*y + 40z  - 5x - 149y -
     ------------------------------------------------------------------------
                     2      2                              3       2
     685z + 2950, 22x  - 26z  - 269x + 5y + 415z - 834, 11z  - 219z  + 15x -
     ------------------------------------------------------------------------
     15y + 1351z - 2514}

o3 : List

See also

Ways to use pointsByIntersection :