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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 = | 4 4 2 8 7 |
     | 2 7 1 3 9 |
     | 4 1 7 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 = {86y*z + 15z  - 165x - 107y - 282z + 1074, 86x*z - 105z  - 737x + 405y +
     ------------------------------------------------------------------------
                     2       2                                              2
     856z - 982, 258y  + 367z  + 951x - 3885y - 4440z + 14822, 129x*y + 194z 
     ------------------------------------------------------------------------
                                      2      2                             
     - 27x - 1338y - 2340z + 8008, 86x  - 11z  - 825x - 105y - 120z + 2790,
     ------------------------------------------------------------------------
        3       2
     43z  - 481z  + 45x - 135y + 1277z - 74}

o3 : List

See also

Ways to use pointsByIntersection :