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

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                 2                                           2              
o3 = {6y*z + 143z  - 114x - 320y - 1161z + 3244, 12x*z + 385z  - 330x - 832y
     ------------------------------------------------------------------------
                       2      2                                        2  
     - 3075z + 8636, 3y  - 80z  + 60x + 143y + 630z - 1696, 4x*y - 153z  +
     ------------------------------------------------------------------------
                                   2      2                               3  
     102x + 312y + 1203z - 3300, 2x  - 83z  + 52x + 180y + 653z - 1824, 6z  +
     ------------------------------------------------------------------------
         2
     401z  - 366x - 992y - 3489z + 10132}

o3 : List

See also

Ways to use pointsByIntersection :