next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
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 = | 8 3 9 4 3 |
     | 2 4 1 0 6 |
     | 3 6 7 8 4 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                   2                                            2          
o3 = {145y*z + 385z  + 182x - 109y - 3959z + 6304, 145x*z - 220z  - 1206x -
     ------------------------------------------------------------------------
                             2       2                                      
     903y + 862z + 7368, 145y  - 475z  - 214x - 1717y + 4483z - 4608, 145x*y
     ------------------------------------------------------------------------
          2                                2      2                      
     + 70z  - 104x - 207y - 472z - 288, 29x  + 10z  - 367x - 42y - 142z +
     ------------------------------------------------------------------------
               3        2
     1500, 145z  - 2745z  - 48x - 564y + 15866z - 25296}

o3 : List

See also

Ways to use pointsByIntersection :