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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 = | 6 2 1 2 2 |
     | 8 3 5 3 2 |
     | 7 5 0 9 6 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                  2                                          2              
o3 = {137y*z + 43z  + 33x - 951y - 1013z + 4722, 137x*z - 28z  - 1092x + 84y
     ------------------------------------------------------------------------
                       2      2                                          2  
     + 118z + 672, 137y  - 54z  - 1284x - 523y + 756z + 474, 137x*y - 12z  -
     ------------------------------------------------------------------------
                                     2      2                            
     1153x - 238y + 168z + 1658, 137x  - 20z  - 1191x + 60y + 280z + 754,
     ------------------------------------------------------------------------
         3        2
     137z  - 1656z  + 5286x - 3252y + 2497z + 10974}

o3 : List

See also

Ways to use pointsByIntersection :