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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 4 4 9 2 |
     | 9 4 1 4 5 |
     | 9 3 1 3 2 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                 2                              2                          
o3 = {29y*z - 26z  - 51y + 21z + 27, 29x*z + 13z  - 87x - 18y - 141z + 378,
     ------------------------------------------------------------------------
      2    2                    2                         2      2         
     y  - z  - 7y + 7z, 2x*y + z  - 8x - 6y - 7z + 36, 58x  - 73z  - 754x -
     ------------------------------------------------------------------------
                            3       2
     354y + 823z + 1692, 29z  - 384z  - 84y + 1285z - 846}

o3 : List

See also

Ways to use pointsByIntersection :