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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 4 1 1 7 |
     | 1 9 2 4 3 |
     | 7 8 0 7 2 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                   2                                              2          
o3 = {664y*z - 461z  - 210x - 4718y + 1919z + 9646, 664x*z - 1089z  - 3178x +
     ------------------------------------------------------------------------
                              2       2                                      
     490y + 6819z + 2198, 332y  - 863z  - 1374x - 2118y + 6077z + 4282, 83x*y
     ------------------------------------------------------------------------
          2                                 2       2                       
     - 81z  - 377x - 181y + 595z + 573, 332x  + 351z  - 2046x - 350y - 2357z
     ------------------------------------------------------------------------
                3        2
     + 2414, 83z  - 1005z  - 420x - 140y + 3008z + 700}

o3 : List

See also

Ways to use pointsByIntersection :