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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 3 6 0 7 |
     | 7 6 8 6 0 |
     | 3 2 4 4 7 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                  2                                         2               
o3 = {46y*z + 185z  - 66x + 14y - 1485z + 1792, 23x*z - 101z  - 50x - 126y +
     ------------------------------------------------------------------------
                   2       2                                         2       
     600z - 28, 46y  - 277z  + 66x - 842y + 1761z + 784, 46x*y + 337z  - 438x
     ------------------------------------------------------------------------
                               2      2                                3  
     + 210y - 2265z + 2408, 46x  + 75z  - 304x + 84y - 699z + 1092, 23z  -
     ------------------------------------------------------------------------
         2
     417z  + 60x - 180y + 1948z - 1512}

o3 : List

See also

Ways to use pointsByIntersection :