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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 = | 4 0 6 5 2 |
     | 1 8 1 9 9 |
     | 6 7 9 3 0 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                    2                                                 2  
o3 = {1121y*z + 812z  + 2328x - 6063y - 14853z + 49911, 1121x*z - 647z  -
     ------------------------------------------------------------------------
                                       2      2                           
     6477x + 942y + 2813z + 4476, 1121y  - 28z  - 1008x - 10769y + 1092z +
     ------------------------------------------------------------------------
                         2                                       2       2  
     8136, 1121x*y + 560z  - 7865x - 4336y - 3904z + 34576, 1121x  - 163z  -
     ------------------------------------------------------------------------
                                      3       2
     6989x - 1076y - 369z + 19178, 59z  - 815z  - 666x - 306y + 2580z + 4086}

o3 : List

See also

Ways to use pointsByIntersection :