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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 = | 1 3 8 8 0 |
     | 1 3 1 7 7 |
     | 7 0 2 4 9 |

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

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

                   2                                              2          
o3 = {238y*z - 405z  - 960x - 909y + 2063z + 5607, 2380x*z + 2621z  - 2320x -
     ------------------------------------------------------------------------
                                 2     2                                     
     4071y - 22553z + 19173, 119y  - 6z  - 120x - 902y - 114z + 1995, 1190x*y
     ------------------------------------------------------------------------
            2                                       2       2                
     + 3069z  + 3070x - 8439y - 21657z + 5397, 1190x  - 599z  - 13170x + 549y
     ------------------------------------------------------------------------
                         3       2
     + 1947z + 27153, 34z  - 585z  - 480x + 81y + 2315z + 1197}

o3 : List

See also

Ways to use pointsByIntersection :