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

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                  2                                             2          
o3 = {267y*z + 26z  - 396x - 1391y - 1673z + 10767, 267x*z - 32z  - 1320x -
     ------------------------------------------------------------------------
                             2      2                                     
     157y - 1453z + 8745, 89y  + 10z  + 12x - 1247y - 130z + 4326, 89x*y -
     ------------------------------------------------------------------------
        2                                 2     2                       
     10z  - 813x - 622y + 130z + 5286, 89x  + 5z  - 1151x - 134y - 65z +
     ------------------------------------------------------------------------
               3        2
     4566, 267z  - 3697z  + 1224x + 76y + 13618z - 17988}

o3 : List

See also

Ways to use pointsByIntersection :