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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 = | 5 1 9 8 0 |
     | 2 0 2 5 4 |
     | 1 0 8 8 0 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                 2                                         2               
o3 = {7y*z + 330z  + 672x + 168y - 3368z - 672, 7x*z - 114z  - 224x - 56y +
     ------------------------------------------------------------------------
                     2       2                                             2
     1087z + 224, 28y  + 481z  + 1008x + 140y - 4905z - 1008, 28x*y + 1241z 
     ------------------------------------------------------------------------
                                       2       2                             
     + 2464x + 616y - 12609z - 2464, 7x  - 209z  - 455x - 112y + 2085z + 448,
     ------------------------------------------------------------------------
      3     2
     z  - 9z  + 8z}

o3 : List

See also

Ways to use pointsByIntersection :