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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 8 9 3 |
     | 7 6 2 0 9 |
     | 4 8 5 0 3 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                   2                                             2          
o3 = {762y*z - 835z  + 904x - 2068y + 3659z - 8136, 762x*z + 109z  - 3688x -
     ------------------------------------------------------------------------
                                2      2                                     
     1004y - 6977z + 33192, 381y  + 79z  - 733x - 4286y + 868z + 6597, 762x*y
     ------------------------------------------------------------------------
          2                                      2       2                  
     - 71z  - 4246x - 4694y - 1055z + 38214, 381x  - 433z  - 2117x + 1220y +
     ------------------------------------------------------------------------
                        3        2
     2549z - 11808, 381z  - 4742z  - 400x - 1580y + 14737z + 3600}

o3 : List

See also

Ways to use pointsByIntersection :