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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 5 1 9 6 |
     | 6 6 2 5 0 |
     | 5 1 5 5 0 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

              2                    2                      2       2        
o3 = {y*z - 6z  - 5y + 30z, x*z + z  - 5x - 11z + 30, 175y  - 399z  + 60x -
     ------------------------------------------------------------------------
                                        2                                   2
     1385y + 2469z - 360, 175x*y + 1106z  - 890x - 135y - 6436z + 5340, 175x 
     ------------------------------------------------------------------------
           2                                 3     2
     - 679z  - 1615x - 360y + 3149z + 3390, z  - 6z  + 5z}

o3 : List

See also

Ways to use pointsByIntersection :