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Points :: points

points -- make the ideal of a set of points

Synopsis

Description

i1 : R = ZZ/101[vars(0..4)]

o1 = R

o1 : PolynomialRing
i2 : pointsMat = randomPointsMat(R,11)

o2 = | 1 0 0 0 0 1 24  19  -29 21  -18 |
     | 0 1 0 0 0 1 -36 -10 -24 34  -13 |
     | 0 0 1 0 0 1 -30 -29 -38 19  -43 |
     | 0 0 0 1 0 1 -29 -8  -16 -47 -15 |
     | 0 0 0 0 1 1 19  -22 39  -39 -28 |

             5       11
o2 : Matrix R  <--- R
i3 : points pointsMat

                                                                            
o3 = ideal (a*d - 2b*d + 26c*d - 15a*e + 37b*e + 8c*e + 46d*e, b*c - 36b*d +
     ------------------------------------------------------------------------
                                                                         
     23c*d + 48a*e + 48b*e - 50c*e - 34d*e, a*c + 50b*d + 41c*d + 28a*e +
     ------------------------------------------------------------------------
                                                                        
     50b*e - 42c*e - 27d*e, a*b - 10b*d - 44c*d + 37a*e + 20b*e - 8c*e +
     ------------------------------------------------------------------------
                                2         2      2        2        2   2   
     4d*e, b*d*e + 20c*d*e + 23d e - 26a*e  - b*e  + 12c*e  - 29d*e , c e +
     ------------------------------------------------------------------------
                  2         2        2       2        2   2               2 
     19c*d*e + 14d e + 17a*e  - 29b*e  + 7c*e  - 29d*e , b e - 2c*d*e - 3d e
     ------------------------------------------------------------------------
            2        2        2        2   2               2         2  
     - 11a*e  + 25b*e  + 33c*e  - 43d*e , a e - c*d*e - 30d e - 27a*e  +
     ------------------------------------------------------------------------
          2       2        2
     11b*e  + 5c*e  + 41d*e )

o3 : Ideal of R

See also

For the programmer

The object points is a function closure.