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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 = | 5 1 9 0 1 |
     | 9 3 9 1 7 |
     | 3 4 8 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 = {85y*z + 381z  + 270x - 810y - 5172z + 15732, 425x*z + 1184z  - 2745x -
     ------------------------------------------------------------------------
                                2        2                                  
     180y - 15673z + 45333, 425y  - 1068z  - 1560x - 3140y + 12996z - 27741,
     ------------------------------------------------------------------------
                  2                                     2       2          
     425x*y - 432z  - 4265x + 215y + 5104z - 11159, 425x  + 418z  - 4265x +
     ------------------------------------------------------------------------
                              3        2
     640y - 5946z + 19016, 85z  - 1446z  + 180x - 30y + 7517z - 12462}

o3 : List

See also

Ways to use pointsByIntersection :