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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 = | 8 7 6 6 1 |
     | 8 9 5 7 2 |
     | 6 4 9 9 5 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                   2                                             2          
o3 = {202y*z + 283z  + 780x - 1818y - 5341z + 20466, 202x*z + 81z  - 1038x -
     ------------------------------------------------------------------------
                       2     2                                            2  
     2311z + 9558, 101y  + 4z  + 147x - 1212y + 139z + 1078, 202x*y + 187z  -
     ------------------------------------------------------------------------
                                      2       2                            3
     728x - 1212y - 2213z + 9138, 101x  + 134z  - 883x - 1656z + 5712, 101z 
     ------------------------------------------------------------------------
            2
     - 1905z  + 60x + 11344z - 21780}

o3 : List

See also

Ways to use pointsByIntersection :