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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 = | 2 3 3 5 5 |
     | 4 1 6 0 2 |
     | 7 9 5 2 9 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                 2                                         2               
o3 = {22y*z + 85z  - 126x + 54y - 1007z + 2304, 44x*z + 15z  - 382x - 28y -
     ------------------------------------------------------------------------
                     2      2                                        2      
     377z + 2164, 11y  - 38z  + 54x - 141y + 452z - 1022, 44x*y - 51z  - 30x
     ------------------------------------------------------------------------
                             2       2                                  3  
     - 248y + 569z - 784, 88x  + 129z  - 830x + 252y - 1491z + 4416, 22z  -
     ------------------------------------------------------------------------
         2
     567z  + 210x - 420y + 4091z - 7140}

o3 : List

See also

Ways to use pointsByIntersection :