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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 = | 8 4 8 3 8 |
     | 9 0 4 8 5 |
     | 6 2 2 5 7 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                  2                                          2              
o3 = {14y*z + 161z  - 100x + 72y - 1539z + 2834, 14x*z + 105z  - 128x + 100y
     ------------------------------------------------------------------------
                        2        2                                        
     - 1077z + 2134, 42y  + 1113z  - 650x + 482y - 10189z + 18526, 21x*y +
     ------------------------------------------------------------------------
         2                                  2       2                       
     420z  - 400x + 232y - 3860z + 7640, 42x  - 105z  - 404x - 100y + 965z -
     ------------------------------------------------------------------------
            3       2
     566, 7z  - 126z  + 20x - 20y + 669z - 970}

o3 : List

See also

Ways to use pointsByIntersection :