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

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                 2                                          2                
o3 = {71y*z - 57z  + 153x - 639y + 144z + 1944, 71x*z - 160z  - 288x + 961z +
     ------------------------------------------------------------------------
               2       2                                          2         
     1152, 284y  + 393z  - 528x - 284y - 2865z - 1296, 71x*y + 20z  - 248x -
     ------------------------------------------------------------------------
                            2      2                          3       2
     639y - 200z + 2412, 71x  - 20z  - 959x + 200z + 2700, 71z  - 990z  -
     ------------------------------------------------------------------------
     504x + 3439z + 2016}

o3 : List

See also

Ways to use pointsByIntersection :