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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 3 8 1 1 |
     | 9 2 2 5 1 |
     | 0 7 0 8 3 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                  2                                           2              
o3 = {52y*z - 321z  + 616x + 704y + 2583z - 6336, 26x*z + 127z  - 280x - 320y
     ------------------------------------------------------------------------
                        2      2                                           2
     - 1167z + 2880, 39y  + 96z  - 140x - 589y - 772z + 2142, 156x*y - 111z 
     ------------------------------------------------------------------------
                                      2        2                           
     - 116x + 224y + 917z - 2016, 546x  - 1461z  - 1498x + 3280y + 13447z -
     ------------------------------------------------------------------------
               3       2
     29520, 13z  - 270z  + 280x + 320y + 1453z - 2880}

o3 : List

See also

Ways to use pointsByIntersection :