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

              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 - 5z  - 6x - 9y - 37z + 66, 44x*z + 9z  - 42x - 360y - 325z +
     ------------------------------------------------------------------------
              2     2                                    2                   
     2244, 22y  - 5z  - 6x - 218y + 29z + 528, 22x*y - 5z  - 138x - 86y + 29z
     ------------------------------------------------------------------------
               2      2                                 3       2
     + 528, 44x  - 19z  - 586x - 120y + 295z + 1716, 22z  - 379z  - 270x +
     ------------------------------------------------------------------------
     1080y + 1569z - 5940}

o3 : List

See also

Ways to use pointsByIntersection :