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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 = | 1 5 4 5 6 |
     | 3 7 8 6 7 |
     | 1 0 7 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 = {1179y*z + 321z  + 3260x - 4923y - 10510z + 18161, 131x*z + 17z  - 515x
     ------------------------------------------------------------------------
                              2       2                                  
     + 360y - 768z + 55, 1179y  + 141z  + 2240x - 14283y - 1153z + 31010,
     ------------------------------------------------------------------------
                   2                                       2      2          
     2358x*y + 321z  - 13246x - 6102y - 2257z + 26414, 131x  + 25z  - 1081x +
     ------------------------------------------------------------------------
                            3        2
     252y - 197z + 366, 393z  - 5460z  - 2120x + 5328y + 17899z - 26696}

o3 : List

See also

Ways to use pointsByIntersection :