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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 4 5 1 1 |
     | 5 7 4 4 5 |
     | 3 9 4 9 9 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

             2                          2                     2     2        
o3 = {y*z + z  - 9y - 17z + 72, x*z + 2z  - 9x - 31z + 117, 5y  + 2z  - 10x -
     ------------------------------------------------------------------------
                               2                          2      2        
     45y - 34z + 254, 5x*y - 2z  - 35x - 5y + 14z + 71, 5x  - 11z  - 25x +
     ------------------------------------------------------------------------
                  3      2
     147z - 412, z  - 16z  + 75z - 108}

o3 : List

See also

Ways to use pointsByIntersection :