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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 = | 0 0 3 4 0 |
     | 9 5 5 3 0 |
     | 0 4 2 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 = {57y*z + 85z  - 10x - 185y - 810z + 1665, 19x*z - 24z  - 62x + 12y +
     ------------------------------------------------------------------------
                    2      2                                      2        
     108z - 108, 19y  - 49z  + 46x - 99y + 363z - 648, 19x*y + 16z  - 79x -
     ------------------------------------------------------------------------
                       2     2                           3       2
     8y - 72z + 72, 19x  - 8z  - 65x + 4y + 36z - 36, 57z  - 427z  - 104x +
     ------------------------------------------------------------------------
     14y + 810z - 126}

o3 : List

See also

Ways to use pointsByIntersection :