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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 1 0 2 9 |
     | 9 1 2 9 3 |
     | 0 6 1 5 3 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                     2                                                 2  
o3 = {1567y*z + 5864z  + 4020x - 5607y - 44227z + 46443, 1567x*z + 616z  -
     ------------------------------------------------------------------------
                                       2        2                          
     4035x - 108y - 5407z + 5007, 1567y  - 1198z  + 750x - 16681y + 5840z +
     ------------------------------------------------------------------------
                           2                                       2       2
     22452, 1567x*y + 1018z  - 3753x - 2356y - 7160z + 10854, 1567x  + 500z 
     ------------------------------------------------------------------------
                                          3         2
     - 14641x + 1866y - 512z - 3720, 1567z  - 13863z  + 870x + 2400y + 29966z
     ------------------------------------------------------------------------
     - 22470}

o3 : List

See also

Ways to use pointsByIntersection :