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

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

             2                          2                     2    2        
o3 = {y*z + z  - 5y - 21z + 80, x*z + 3z  - 5x - 45z + 150, 4y  - z  - 68y +
     ------------------------------------------------------------------------
                         2                           2     2                 
     12z + 253, 8x*y + 3z  - 64x - 48y - 48z + 549, x  + 7z  - 9x + 10y - 93z
     ------------------------------------------------------------------------
             3      2
     + 218, z  - 21z  + 143z - 315}

o3 : List

See also

Ways to use pointsByIntersection :