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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 = | 3 1 1 7 0 |
     | 7 7 7 6 5 |
     | 1 8 2 4 4 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                                      2                                  2  
o3 = {y*z - 4y - 7z + 28, 107x*z + 78z  - 380x - 336y - 887z + 3980, 107y  -
     ------------------------------------------------------------------------
       2                                         2                           
     4z  + 14x - 1275y + 40z + 3604, 107x*y - 28z  - 651x + 63y + 280z - 987,
     ------------------------------------------------------------------------
         2      2                                 3        2
     107x  + 90z  - 743x - 42y - 900z + 2370, 107z  - 1225z  + 168x - 1176y +
     ------------------------------------------------------------------------
     3262z + 5584}

o3 : List

See also

Ways to use pointsByIntersection :