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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 = | 4 0 5 6 6 |
     | 0 7 2 2 1 |
     | 7 5 7 4 7 |

              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 - 5z  - 7y + 53z - 126, x*z + 6z  - 7x - 72z + 210, 9y  + 133z  +
     ------------------------------------------------------------------------
                                         2                              2  
     6x - 21y - 1461z + 3686, 9x*y - 139z  - 6x - 42y + 1533z - 3896, 9x  +
     ------------------------------------------------------------------------
         2                             3      2
     133z  - 93x + 6y - 1461z + 3938, z  - 16z  + 83z - 140}

o3 : List

See also

Ways to use pointsByIntersection :