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

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

              2                                    2                     
o3 = {4y*z + z  - 2x - 36y - 33z + 224, 16x*z + 25z  - 90x + 36y - 445z +
     ------------------------------------------------------------------------
             2    2                                   2                      
     1584, 4y  - z  + 2x - 24y + 13z - 24, 16x*y - 37z  - 78x - 100y + 553z -
     ------------------------------------------------------------------------
             2      2                               3       2
     1488, 8x  + 91z  - 70x - 36y - 1335z + 4976, 8z  - 171z  - 2x - 12y +
     ------------------------------------------------------------------------
     1199z - 2704}

o3 : List

See also

Ways to use pointsByIntersection :