pointsByIntersection -- computes ideal of point set by intersecting maximal ideals

Synopsis

Usage:
pointsByIntersection(M,R)
Inputs:
- M, a matrix, in which each column consists of the coordinates of a point
- R, a polynomial ring, coordinate ring of the affine space containing the points
Outputs:
- a list, grobner basis for ideal of a finite set of points

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 = | 0 0 9 0 2 |
     | 8 0 3 2 5 |
     | 0 6 1 8 3 |

              3        5
o1 : Matrix ZZ  <--- ZZ

i2 : R = QQ[x,y,z]

o2 = R

o2 : PolynomialRing

i3 : pointsByIntersection(M,R)

                   2                                               2        
o3 = {889y*z + 511z  - 1968x - 4800y - 9466z + 38400, 889x*z + 252z  - 1101x
     ------------------------------------------------------------------------
                                2       2                                 
     - 864y - 2664z + 6912, 889y  - 441z  + 2784x - 3314y + 7710z - 30384,
     ------------------------------------------------------------------------
                  2                                    2       2          
     889x*y + 252z  - 2879x - 864y - 2664z + 6912, 127x  - 126z  - 1037x +
     ------------------------------------------------------------------------
                              3         2
     432y + 1332z - 3456, 889z  - 10101z  - 5430x - 8040y + 17882z + 64320}

o3 : List

Ways to use `pointsByIntersection` :

pointsByIntersection(Matrix,Ring)

pointsByIntersection -- computes ideal of point set by intersecting maximal ideals

Synopsis

Description

See also

Ways to use pointsByIntersection :

Ways to use `pointsByIntersection` :