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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 = | 1 6 9 9 9 |
     | 3 3 4 3 6 |
     | 1 4 7 8 4 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                 2                                     2                    
o3 = {18y*z + 11z  + 84x - 156y - 249z + 568, 9x*z - 4z  + 12x - 48y - 69z +
     ------------------------------------------------------------------------
             2      2                                                   2  
     196, 27y  - 11z  - 84x - 159y + 195z + 134, x*y - 3x - 9y + 27, 27x  -
     ------------------------------------------------------------------------
        2                              3      2
     20z  - 165x - 240y + 60z + 818, 3z  - 50z  - 84x + 84y + 327z - 448}

o3 : List

See also

Ways to use pointsByIntersection :