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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 = | 7 1 5 1 2 |
     | 3 7 1 2 2 |
     | 6 6 6 1 6 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

       2                                                            2       
o3 = {z  - 7z + 6, y*z - 6y - 2z + 12, x*z - 6x - z + 6, 53x*y + 47y  - 131x
     ------------------------------------------------------------------------
                           2      2                               3       2
     - 481y + 5z + 794, 53x  + 27y  - 444x - 300y + 57z + 826, 53y  - 558y  +
     ------------------------------------------------------------------------
     60x + 1483y - 12z - 1206}

o3 : List

See also

Ways to use pointsByIntersection :