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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 = | 3 2 4 2 5 |
     | 1 4 4 2 1 |
     | 5 2 4 0 9 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                 2                                         2               
o3 = {89y*z + 15z  - 294x - 234y - 152z + 1056, 89x*z - 34z  - 277x - 57y -
     ------------------------------------------------------------------------
                   2     2                                      2         
     53z + 668, 89y  + 3z  + 48x - 474y - 66z + 496, 89x*y + 12z  - 431x -
     ------------------------------------------------------------------------
                         2      2                              3        2
     205y + 3z + 916, 89x  - 11z  - 532x - 42y + 64z + 792, 89z  - 1269z  +
     ------------------------------------------------------------------------
     1590x - 1350y + 3532z - 480}

o3 : List

See also

Ways to use pointsByIntersection :