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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 = | 1 2 8 5 8 |
     | 1 2 5 4 8 |
     | 3 8 2 7 4 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

               2                                   2                        
o3 = {2y*z + 3z  - 4x - 2y - 37z + 84, 47x*z + 113z  - 308x + 192y - 1342z +
     ------------------------------------------------------------------------
              2      2                                        2         
     2984, 47y  - 25z  + 289x - 735y + 336z - 384, 94x*y - 67z  + 156x -
     ------------------------------------------------------------------------
                             2      2                                 3  
     1058y + 861z - 1172, 47x  - 59z  - 226x - 240y + 714z - 1192, 47z  -
     ------------------------------------------------------------------------
         2
     773z  + 380x - 420y + 3952z - 6128}

o3 : List

See also

Ways to use pointsByIntersection :