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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 = | 3 5 2 5 2 |
     | 0 1 7 5 4 |
     | 7 0 1 2 6 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                  2                                           2              
o3 = {22y*z + 331z  + 735x + 623y - 2018z - 4298, 22x*z - 109z  - 299x - 235y
     ------------------------------------------------------------------------
                       2       2                                         2  
     + 578z + 1730, 11y  - 113z  - 225x - 296y + 686z + 1410, 22x*y - 23z  -
     ------------------------------------------------------------------------
                                  2      2                            3  
     185x - 139y + 104z + 954, 11x  + 13z  - 48x + 25y - 76z - 60, 11z  -
     ------------------------------------------------------------------------
         2
     338z  - 545x - 485y + 1602z + 3210}

o3 : List

See also

Ways to use pointsByIntersection :