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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 = | 8 3 6 8 2 |
     | 1 4 8 3 7 |
     | 4 2 5 9 1 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                 2                                            2              
o3 = {86y*z + 89z  + 268x - 274y - 1443z + 2134, 258x*z - 193z  - 1102x - 60y
     ------------------------------------------------------------------------
                       2      2                                           2  
     + 469z + 1832, 43y  - 10z  - 234x - 477y + 252z + 1458, 258x*y + 293z  +
     ------------------------------------------------------------------------
                                      2       2                              
     518x - 1104y - 4193z + 6980, 258x  - 193z  - 3424x - 60y + 2533z + 3896,
     ------------------------------------------------------------------------
         3        2
     129z  - 1747z  + 1028x + 660y + 5290z - 10348}

o3 : List

See also

Ways to use pointsByIntersection :