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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 = | 6 2 4 6 4 |
     | 1 2 3 2 7 |
     | 1 6 3 8 4 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                  2                                           2          
o3 = {113y*z - 89z  + 192x - 540y + 636z - 1272, 113x*z + 184z  - 1127x +
     ------------------------------------------------------------------------
                              2       2                                      
     154y - 2356z + 8102, 113y  - 254z  + 567x - 1291y + 2422z - 4392, 113x*y
     ------------------------------------------------------------------------
          2                                  2       2                      
     + 34z  - 293x - 426y - 342z + 1814, 113x  - 108z  - 638x - 56y + 980z -
     ------------------------------------------------------------------------
               3       2
     1056, 113z  - 819z  - 2145x + 630y - 968z + 13914}

o3 : List

See also

Ways to use pointsByIntersection :