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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 1 7 8 9 |
     | 9 2 9 3 5 |
     | 5 0 0 5 0 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

       2                             2                                      
o3 = {z  - 5z, 3x*z + 2y*z - 30z, 95y  + 45y*z + 210x - 1225y - 279z + 1860,
     ------------------------------------------------------------------------
                                                     2
     285x*y + 113y*z - 885x - 1725y - 9z + 3765, 285x  - 104y*z - 3120x +
     ------------------------------------------------------------------------
     720y + 945z + 1395}

o3 : List

See also

Ways to use pointsByIntersection :