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

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                    2                                              2        
o3 = {867y*z - 1138z  + 3872x - 4338y - 252z + 19216, 289x*z - 355z  - 1096x
     ------------------------------------------------------------------------
                               2      2                                     
     + 300y + 924z + 1984, 289y  - 28z  + 656x - 2789y - 186z + 1192, 867x*y
     ------------------------------------------------------------------------
            2                                       2       2               
     - 3590z  + 4840x - 2388y + 21360z - 28000, 289x  - 525z  - 1861x + 810y
     ------------------------------------------------------------------------
                         3        2
     + 3015z - 3660, 289z  - 4683z  + 2208x + 636y + 17588z - 13920}

o3 : List

See also

Ways to use pointsByIntersection :