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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 = | 2 0 2 0 4 |
     | 5 3 2 5 0 |
     | 2 0 1 0 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 + 2z  + 5x - 14z, 7x*z - 5z  - 5x + z, 7y  - 9z  - 30x - 56y + 48z
     ------------------------------------------------------------------------
                      2                2     2                3      2
     + 105, 7x*y + 13z  + 20x - 81z, 7x  - 4z  - 18x + 12z, 7z  - 51z  - 30x
     ------------------------------------------------------------------------
     + 104z}

o3 : List

See also

Ways to use pointsByIntersection :