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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 = | 4 0 6 5 3 |
     | 8 7 4 5 1 |
     | 7 0 6 4 4 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                 2                                         2               
o3 = {35y*z + 31z  + 108x - 194y - 531z + 1358, 35x*z - 44z  - 212x + 36y +
     ------------------------------------------------------------------------
                    2      2                                        2       
     284z - 252, 35y  + 16z  + 198x - 309y - 256z + 448, 70x*y + 53z  - 206x
     ------------------------------------------------------------------------
                              2      2                              3      2
     - 282y - 533z + 1974, 28x  - 31z  - 276x + 26y + 307z - 182, 5z  - 47z 
     ------------------------------------------------------------------------
     + 24x - 12y + 72z + 84}

o3 : List

See also

Ways to use pointsByIntersection :