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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 = | 7 4 6 2 5 |
     | 3 2 0 9 7 |
     | 7 8 9 5 0 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                    2                                               2        
o3 = {982y*z + 1347z  + 1178x - 2218y - 13979z + 9636, 982x*z - 589z  - 8140x
     ------------------------------------------------------------------------
                                  2        2                           
     - 3580y - 2471z + 65760, 491y  - 1263z  - 1636x - 10215y + 6277z +
     ------------------------------------------------------------------------
                         2                                     2      2  
     55626, 491x*y + 585z  - 419x + 1530y - 2119z - 25800, 491x  - 56z  -
     ------------------------------------------------------------------------
                                       3        2
     5423x - 1204y - 430z + 23268, 491z  - 9060z  - 2928x - 9192y + 34945z +
     ------------------------------------------------------------------------
     78984}

o3 : List

See also

Ways to use pointsByIntersection :