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

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                 2                                       2                   
o3 = {26y*z - 59z  - 120x - 36y + 409z + 390, 26x*z + 41z  - 66x - 90y - 479z
     ------------------------------------------------------------------------
               2      2                                     2                
     + 858, 26y  - 55z  - 96x + 18y + 413z + 78, 26x*y + 87z  + 132x - 366y -
     ------------------------------------------------------------------------
                    2     2                               3       2
     693z + 234, 26x  - 7z  - 380x - 10y + 45z + 1326, 13z  - 300z  - 240x +
     ------------------------------------------------------------------------
     240y + 1637z - 390}

o3 : List

See also

Ways to use pointsByIntersection :