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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 = | 0 9 4 5 5 |
     | 6 9 4 2 5 |
     | 1 6 5 7 2 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                  2                                           2              
o3 = {153y*z + 87z  - 64x - 881y - 1434z + 5715, 153x*z - 129z  - 343x - 440y
     ------------------------------------------------------------------------
                        2       2                                          2
     + 132z + 2637, 153y  - 129z  - 88x - 1766y + 744z + 4473, 153x*y + 15z 
     ------------------------------------------------------------------------
                                       2       2                         
     - 922x - 1040y - 300z + 6525, 153x  - 165z  - 1027x - 800y + 1005z +
     ------------------------------------------------------------------------
             3      2
     3960, 3z  - 39z  - 10x + 10y + 156z - 180}

o3 : List

See also

Ways to use pointsByIntersection :