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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 6 5 |
     | 1 0 8 4 9 |
     | 6 8 4 3 8 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                   2                                              2          
o3 = {149y*z + 559z  - 900x - 1092y - 7025z + 24024, 447x*z - 306z  - 1596x -
     ------------------------------------------------------------------------
                              2       2                                      
     220y + 1300z + 1264, 149y  - 164z  + 360x - 1381y + 1320z - 1504, 894x*y
     ------------------------------------------------------------------------
            2                                        2      2               
     + 3267z  - 8676x - 3506y - 37921z + 128984, 447x  - 39z  - 3087x - 104y
     ------------------------------------------------------------------------
                       3        2
     + 899z + 500, 149z  - 2697z  + 360x - 40y + 15326z - 27728}

o3 : List

See also

Ways to use pointsByIntersection :