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

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                 2                                         2               
o3 = {43y*z + 11z  - 132x - 78y - 439z + 1470, 129x*z + 89z  - 939x + 96y -
     ------------------------------------------------------------------------
                       2       2                                          
     1570z + 5901, 387y  + 137z  - 1128x - 4044y - 1750z + 17241, 387x*y -
     ------------------------------------------------------------------------
        2                                    2      2                      
     59z  - 1356x - 2103y + 1135z + 5250, 43x  - 23z  - 111x - 48y + 355z -
     ------------------------------------------------------------------------
             3       2
     994, 43z  - 469z  - 1338x + 300y + 28z + 7266}

o3 : List

See also

Ways to use pointsByIntersection :