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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 3 3 6 3 |
     | 7 6 6 6 5 |
     | 9 3 1 9 3 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                2                                                 2    2  
o3 = {16y*z - 3z  + 48x - 48y - 84z + 135, x*z - 9x - 3z + 27, 16y  - z  +
     ------------------------------------------------------------------------
                                     2                             2    2  
     16x - 176y + 4z + 429, 32x*y - z  - 176x - 96y + 4z + 525, 16x  + z  -
     ------------------------------------------------------------------------
                       3      2
     160x - 4z + 339, z  - 13z  + 39z - 27}

o3 : List

See also

Ways to use pointsByIntersection :