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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 = | 7 2 9 2 7 |
     | 7 6 0 6 9 |
     | 8 8 4 5 3 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                 2                                          2                
o3 = {82y*z + 63z  - 60x - 356y - 1311z + 4776, 82x*z + 241z  - 620x - 180y -
     ------------------------------------------------------------------------
                        2       2                                           2
     3297z + 11960, 205y  - 321z  - 198x - 1675y + 4173z - 9774, 41x*y + 12z 
     ------------------------------------------------------------------------
                                     2      2                               3
     - 234x - 347y - 156z + 2538, 41x  - 14z  - 383x + 70y + 182z - 378, 41z 
     ------------------------------------------------------------------------
           2
     - 660z  - 4x + 20y + 3291z - 5192}

o3 : List

See also

Ways to use pointsByIntersection :