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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 = | 4 1 6 5 5 |
     | 3 3 5 5 7 |
     | 8 9 6 4 0 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                 2                                      2                
o3 = {35y*z + 18z  + 16x - 232y - 363z + 1544, 35x*z - z  - 312x + 114y -
     ------------------------------------------------------------------------
                    2     2                                    2         
     114z + 762, 15y  - 4z  - 8x - 124y + 44z + 173, 105x*y - z  - 347x -
     ------------------------------------------------------------------------
                            2      2                                 3  
     691y - 79z + 2897, 105x  + 11z  - 593x - 694y - 391z + 5198, 35z  -
     ------------------------------------------------------------------------
         2
     401z  + 608x + 4y + 1046z - 3068}

o3 : List

See also

Ways to use pointsByIntersection :