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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 = | 1 6 6 2 3 |
     | 5 0 6 3 3 |
     | 8 4 8 5 4 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

               2                                 2                          
o3 = {9y*z - 4z  - 6x - 42y + 3z + 88, 9x*z + 13z  - 66x - 30y - 165z + 632,
     ------------------------------------------------------------------------
        2     2                                     2                      
     18y  - 7z  - 24x - 78y + 39z + 100, 18x*y + 25z  - 84x - 138y - 255z +
     ------------------------------------------------------------------------
              2    2                            3      2
     1124, 18x  - z  - 132x + 30y - 33z + 292, z  - 17z  + 92z - 160}

o3 : List

See also

Ways to use pointsByIntersection :