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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 = | 8 9 2 4 2 |
     | 1 8 2 3 2 |
     | 5 1 3 8 1 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                    2                                               2        
o3 = {1465y*z - 321z  + 1176x - 2837y - 1646z + 2359, 1465x*z - 482z  - 5833x
     ------------------------------------------------------------------------
                               2      2                                     
     + 5096y - 1002z + 28, 293y  + 50z  - 342x - 2531y - 200z + 4724, 293x*y
     ------------------------------------------------------------------------
          2                                   2      2                      
     + 44z  - 676x - 2532y - 176z + 5376, 293x  + 80z  - 3067x - 182y - 320z
     ------------------------------------------------------------------------
                 3        2
     + 5566, 293z  - 3540z  + 1008x - 1176y + 10351z - 6768}

o3 : List

See also

Ways to use pointsByIntersection :