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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 = | 3 8 0 4 1 |
     | 7 4 9 3 6 |
     | 5 9 4 0 8 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                   2                                            2          
o3 = {832y*z + 359z  + 1570x - 70y - 7249z - 6070, 832x*z - 957z  - 8278x -
     ------------------------------------------------------------------------
                               2      2                                    
     7262y + 6443z + 54898, 13y  - 12z  - 15x - 220y + 129z + 603, 832x*y +
     ------------------------------------------------------------------------
          2                                      2       2                  
     1039z  - 3118x + 3626y - 10217z - 8390, 416x  - 769z  - 4078x - 4214y +
     ------------------------------------------------------------------------
                        3        2
     6983z + 22298, 208z  - 3321z  - 1470x - 3750y + 14111z + 17130}

o3 : List

See also

Ways to use pointsByIntersection :