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

              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 + 271z  + 223x - 36y - 1202z - 597, x*z - 74z  - 63x + 6y + 325z +
     ------------------------------------------------------------------------
           2       2                                      2              
     177, y  + 398z  + 324x - 53y - 1744z - 870, x*y + 41z  + 28x - 15y -
     ------------------------------------------------------------------------
                 2       2                             3      2
     169z - 60, x  - 227z  - 195x + 24y + 991z + 528, z  + 64z  + 58x - 6y -
     ------------------------------------------------------------------------
     303z - 162}

o3 : List

See also

Ways to use pointsByIntersection :