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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 = | 2 0 9 3 7 |
     | 7 6 4 9 4 |
     | 2 6 4 3 3 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                 2                                   2                      
o3 = {32y*z + 63z  + 50x - 56y - 669z + 930, x*z - 5z  - 8x - 4y + 36z - 12,
     ------------------------------------------------------------------------
       2      2                                      2                      
     8y  + 27z  + 10x - 96y - 209z + 570, 32x*y + 51z  - 118x - 88y - 377z +
     ------------------------------------------------------------------------
             2       2                               3      2
     954, 16x  - 169z  - 270x - 88y + 1211z - 654, 4z  - 33z  + 10x + 8y +
     ------------------------------------------------------------------------
     63z - 102}

o3 : List

See also

Ways to use pointsByIntersection :