next | previous | forward | backward | up | top | index | toc | Macaulay2 web site

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 7 7 4 5 |
     | 1 6 1 3 7 |
     | 7 1 6 1 5 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                 2                                       2               
o3 = {31y*z + 60z  + 72x - 103y - 523z + 391, 31x*z + 64z  - 103x + 72y -
     ------------------------------------------------------------------------
                    2     2                                      2         
     593z + 601, 31y  - 3z  - 16x - 263y - 25z + 602, 31x*y - 48z  - 101x -
     ------------------------------------------------------------------------
                           2      2                              3       2
     209y + 344z + 363, 31x  - 19z  - 339x - 2y + 131z + 754, 31z  - 414z  +
     ------------------------------------------------------------------------
     24x - 24y + 1541z - 1182}

o3 : List

See also

Ways to use pointsByIntersection :