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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 = | 9 0 9 9 4 |
     | 9 7 0 5 5 |
     | 3 8 7 8 2 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                   2                                            2          
o3 = {263y*z - 387z  + 150x - 1429y + 2430z + 603, 263x*z - 783z  - 1984x +
     ------------------------------------------------------------------------
                              2        2                                 
     540y + 6678z - 7092, 263y  + 1139z  + 162x - 2427y - 11525z + 23406,
     ------------------------------------------------------------------------
                  2                                     2       2          
     263x*y - 261z  - 1801x - 2187y + 3015z + 7893, 263x  + 522z  - 2447x -
     ------------------------------------------------------------------------
                               3        2
     360y - 6030z + 17352, 263z  - 3951z  - 120x - 540y + 17518z - 18156}

o3 : List

See also

Ways to use pointsByIntersection :