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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 8 7 5 7 |
     | 0 8 9 8 1 |
     | 6 7 9 6 5 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                   2                                          2             
o3 = {143y*z - 163z  - 72x - 813y + 1191z - 1278, 143x*z + 41z  - 882x + 15y
     ------------------------------------------------------------------------
                         2      2                                         2  
     - 1605z + 8154, 143y  - 62z  + 120x - 1219y + 446z - 444, 13x*y + 56z  -
     ------------------------------------------------------------------------
                                  2       2                                
     48x - 35y - 896z + 3360, 143x  + 508z  - 1403x + 430y - 7972z + 29544,
     ------------------------------------------------------------------------
         3        2
     143z  - 3024z  + 96x - 60y + 20863z - 47202}

o3 : List

See also

Ways to use pointsByIntersection :