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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 = | 3 5 6 3 8 |
     | 6 6 4 3 7 |
     | 7 2 7 1 9 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                   2                                          2          
o3 = {117y*z - 121z  + 200x - 519y + 467z + 260, 234x*z - 215z  - 1418x +
     ------------------------------------------------------------------------
                             2      2                                      
     330y + 853z + 1924, 234y  - 71z  + 40x - 2280y + 655z + 4030, 468x*y -
     ------------------------------------------------------------------------
         2                                    2      2                     
     265z  - 2428x - 2238y + 2537z + 7514, 26x  - 15z  - 238x - 6y + 123z +
     ------------------------------------------------------------------------
              3        2
     390, 117z  - 1814z  - 560x - 840y + 8263z - 2366}

o3 : List

See also

Ways to use pointsByIntersection :