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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 = | 4 4 0 7 2 |
     | 5 8 6 7 1 |
     | 9 3 3 8 6 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

               2                                   2                         
o3 = {3y*z + 6z  + 10x - 29y - 97z + 357, 3x*z + 9z  + 2x - 22y - 131z + 444,
     ------------------------------------------------------------------------
        2      2                                          2                
     90y  - 63z  - 398x - 464y + 1109z - 3216, 45x*y + 27z  - 293x - 134y -
     ------------------------------------------------------------------------
                     2       2                               3      2
     301z + 1464, 45x  + 189z  + 29x - 418y - 2477z + 8238, z  - 20z  - 2x +
     ------------------------------------------------------------------------
     4y + 125z - 246}

o3 : List

See also

Ways to use pointsByIntersection :