specialCubicTransformation -- special cubic transformations whose base locus has dimension at most three

Synopsis

Usage:

specialCubicTransformation i

specialCubicTransformation(i,K)
Inputs:
- i, an integer, an integer between 1 and 9
- K, a ring, the ground field (optional, the default value is QQ)
Outputs:
- a rational map, an example of special cubic birational transformation over K, according to the classification given in Table 2 of Special cubic birational transformations of projective spaces.

Description

The field K is required to be large enough.

i1 : time specialCubicTransformation 9
     -- used 0.105553 seconds

o1 = -- rational map --
     source: Proj(QQ[x , x , x , x , x , x , x ])
                      0   1   2   3   4   5   6
     target: subvariety of Proj(QQ[t , t , t , t , t , t , t , t , t , t ]) defined by
                                    0   1   2   3   4   5   6   7   8   9
             {
                                                                             2                                                2                                                      2
              3t t  + 10t t  + 10t t  - 3t t  - 10t t  + 6t t  + 13t t  + 13t  - 10t t  - 10t t  + t t  + 10t t  - 2t t  + 10t  + 4t t  - 7t t  + 4t t  - 2t t  - 8t t  + 29t t  - 4t  + 10t t  - 4t t  - 13t t  + 13t t  + 18t t  - 4t t  + 4t t  - 7t t  + 4t t  - 2t t  - 21t t  + 19t t  - 4t t  - 4t t ,
                2 4      3 4      0 5     1 5      2 5     3 5      4 5      5      0 6      1 6    2 6      4 6     5 6      6     0 7     1 7     2 7     4 7     5 7      6 7     7      1 8     3 8      4 8      5 8      6 8     7 8     0 9     1 9     2 9     4 9      5 9      6 9     7 9     8 9
              
                                                        2                                           2                                                            2
              3t t  - 8t t  - 5t t  + 8t t  - 8t t  - 8t  + 8t t  + 8t t  + t t  - 8t t  + t t  - 8t  - 2t t  - t t  - 2t t  + 3t t  - 2t t  - 5t t  - 13t t  - t  - 3t t  - 8t t  + 2t t  + 8t t  - 8t t  - 3t t  - t t  - 2t t  - t t  - 2t t  + 3t t  - 2t t  + 3t t  - 5t t  - t t  - t t ,
                0 2     3 4     0 5     2 5     4 5     5     0 6     1 6    2 6     4 6    5 6     6     0 7    1 7     2 7     3 7     4 7     5 7      6 7    7     0 8     1 8     3 8     4 8     5 8     6 8    7 8     0 9    1 9     2 9     3 9     4 9     5 9     6 9    7 9    8 9
              
                                                              2                                    2                                 2
              t t  - t t  - 2t t  - 2t t  + 2t t  - 2t t  - 2t  + 2t t  + 2t t  + t t  - 3t t  - 3t  - t t  - t t  + t t  - 4t t  + t  - 2t t  + t t  + 2t t  - 2t t  - 3t t  + t t  - t t  - t t  + t t  + 2t t  - t t  + t t  + t t
               0 1    0 4     3 4     0 5     2 5     4 5     5     0 6     1 6    3 6     4 6     6    0 7    2 7    4 7     6 7    7     1 8    3 8     4 8     5 8     6 8    7 8    0 9    2 9    4 9     5 9    6 9    7 9    8 9
             }
     defining forms: {
                          2                 2         2       2    3                          2         2                         2                  2     2                 2                          2                                     2                         2        2       2       2       2      2     3               2                            2                                     2                                                                                      2         2       2       2       2      2       2     3
                      - 6x x  - 2x x x  + 8x x  + 5x x  - 6x x  + x  + 2x x x  - 16x x x  + 7x x  + 8x x  - 5x x x  - 2x x x  + 3x x  + 2x x x  - x x  + 6x x  - 2x x x  - 4x x  - x x x  + 8x x x  - 3x x  + 2x x x  + 8x x x  - 9x x x  - 4x x  + 5x x x  - x x x  + x x  + x x  - 6x x  + 2x x  + 6x x  + x x  - 2x  + 4x x x  - 4x x  - 11x x x  - 2x x x  + 6x x  - 4x x x  + 8x x x  + 2x x x  - 4x x  + 2x x x  - 5x x x  - 2x x x  + 4x x x  + 4x x x  - 2x x x  - 4x x x  + x x x  + 5x x  + 2x x  + 2x x  - 6x x  - 2x x  + x x  - 3x x  + 2x ,
                          0 2     0 1 2     1 2     0 2     1 2    2     0 2 3      1 2 3     2 3     2 3     0 2 4     1 2 4     2 4     2 3 4    2 4     0 5     0 1 5     1 5    0 2 5     1 2 5     2 5     0 3 5     1 3 5     2 3 5     3 5     0 4 5    2 4 5    4 5    0 5     1 5     2 5     3 5    4 5     5     0 1 6     1 6      0 2 6     1 2 6     2 6     0 3 6     1 3 6     2 3 6     3 6     1 4 6     2 4 6     3 4 6     0 5 6     1 5 6     2 5 6     3 5 6    4 5 6     5 6     0 6     1 6     2 6     3 6    4 6     5 6     6
                      
                          3     2         2     2                 2         2      2      2                 2                           2         2        2       2     3    2                                                                  2      2      2      2                                     2                                     2                                      2       2       2     2                2                                      2                                             2                                               2         2       2       2       2       2
                      - 6x  - 8x x  - 6x x  + 4x x  + 7x x x  + 6x x  + 2x x  + x x  + 12x x  + 6x x x  - 6x x  - 6x x x  - 9x x x  - 2x x  - 2x x  + 10x x  + 2x x  - 4x  - x x  - 3x x x  + x x x  + 3x x x  + 7x x x  - x x x  - 4x x x  + x x  - x x  + x x  - 10x x  - 9x x x  + 8x x x  + 9x x x  + 2x x  + 8x x x  - 8x x x  - 6x x x  + 6x x  - 3x x x  + 3x x x  + x x x  - 4x x  + 4x x  - 2x x  + 4x x  - x x x  - 6x x  - 2x x x  + 4x x x  + 14x x x  - 8x x  + 5x x x  - x x x  - 2x x x  + 2x x x  + x x  + 2x x x  - 8x x x  + 10x x x  + x x x  - 2x x  + 4x x  + 4x x  - 4x x  + 2x x  + 4x x ,
                          0     0 1     0 1     0 2     0 1 2     1 2     0 2    1 2      0 3     0 1 3     1 3     0 2 3     1 2 3     2 3     0 3      1 3     2 3     3    0 4     0 1 4    0 2 4     1 2 4     0 3 4    1 3 4     2 3 4    0 4    2 4    3 4      0 5     0 1 5     0 2 5     1 2 5     2 5     0 3 5     1 3 5     2 3 5     3 5     0 4 5     2 4 5    3 4 5     0 5     2 5     3 5     0 6    0 1 6     1 6     1 2 6     0 3 6      1 3 6     3 6     0 4 6    1 4 6     2 4 6     3 4 6    4 6     0 5 6     1 5 6      3 5 6    4 5 6     5 6     0 6     1 6     3 6     4 6     5 6
                      
                        3     2          2      2                  2        2                                         2       2      2                2                                                         2         2      2      2    3     2                   2                                                             2                                      2         2        2       2       2      2     3      2                   2                                                  2                                               2                                                              2         2       2
                      6x  + 4x x  - 10x x  - 14x x  - 12x x x  - 6x x  - 10x x  + 6x x x  + 18x x x  + 10x x x  + 4x x  - 4x x  + 11x x  + x x x  - 2x x  - 5x x x  - 5x x x  - 6x x x  - 2x x x  + 8x x x  + 4x x  + 6x x  - x x  + x x  + x  + 4x x  - 13x x x  - 14x x  - 22x x x  - 11x x x  + 2x x x  + 18x x x  + 12x x x  - 4x x  + 10x x x  - 4x x x  - 7x x x  + 4x x  - 6x x  - 15x x  - 8x x  + 8x x  - x x  - 4x  + 18x x  + 28x x x  + 10x x  - 4x x x  - 30x x x  - 22x x x  + 4x x x  + 12x x  + 11x x x  + 7x x x  + 2x x x  - 8x x x  + x x  + 30x x x  + 27x x x  - 4x x x  - 24x x x  + 13x x x  + 12x x  - 2x x  - 2x x ,
                        0     0 1      0 1      0 2      0 1 2     1 2      0 3     0 1 3      0 2 3      1 2 3     0 3     2 3      0 4    0 1 4     1 4     0 2 4     1 2 4     0 3 4     1 3 4     2 3 4     3 4     0 4    1 4    2 4    4     0 5      0 1 5      1 5      0 2 5      1 2 5     0 3 5      1 3 5      2 3 5     3 5      0 4 5     1 4 5     2 4 5     4 5     0 5      1 5     2 5     3 5    4 5     5      0 6      0 1 6      1 6     0 2 6      0 3 6      1 3 6     2 3 6      3 6      0 4 6     1 4 6     2 4 6     3 4 6    4 6      0 5 6      1 5 6     2 5 6      3 5 6      4 5 6      5 6     1 6     4 6
                      
                           3     2       2                 2         2       2     3     2                                      2         2       2      2                                     2                                     2         2      2     2                 2                             2                                                                2         2       2       2       2      2     3     2                 2                           2                                                                                                       2         2       2       2      2       2
                      - 12x  - 8x x  + 7x x  + 6x x x  + 8x x  + 3x x  - 6x x  + 2x  + 8x x  - 8x x x  + 5x x x  - 16x x x  + 8x x  + 8x x  + 8x x  - 10x x  - 4x x x  + 6x x x  + 2x x x  + 2x x  + 4x x x  - 4x x x  + 3x x x  + 4x x  - 2x x  + x x  - 8x x  - 6x x x  - 4x x  + 12x x x  + 12x x x  - 2x x  + 7x x x  + 4x x x  - 7x x x  - x x x  + 5x x x  + x x x  + x x  - 3x x  - 6x x  + 6x x  + 5x x  + x x  - 2x  - 3x x  - 8x x x  - 4x x  + 7x x x  + 2x x x  + 3x x  + 4x x x  + 4x x x  + x x x  - x x x  - 2x x x  + x x x  + 4x x x  + 5x x x  + x x x  + 2x x x  + 4x x  - 3x x  - 2x x  - 2x x  - x x  - 2x x ,
                           0     0 1     0 2     0 1 2     1 2     0 2     1 2     2     0 3     0 1 3     0 2 3      1 2 3     2 3     0 3     2 3      0 4     0 1 4     0 2 4     1 2 4     2 4     0 3 4     1 3 4     2 3 4     3 4     0 4    2 4     0 5     0 1 5     1 5      0 2 5      1 2 5     2 5     0 3 5     1 3 5     2 3 5    0 4 5     2 4 5    3 4 5    4 5     0 5     1 5     2 5     3 5    4 5     5     0 6     0 1 6     1 6     0 2 6     1 2 6     2 6     0 3 6     1 3 6    2 3 6    0 4 6     1 4 6    2 4 6     0 5 6     2 5 6    3 5 6     4 5 6     5 6     0 6     1 6     2 6    4 6     5 6
                      
                         3      2          2      3               2         2       2    3      2                   2                            2          2        2       2      3      2                  2                 2                                       2          2       2       2     3     2                   2                           2                                        2                                               2         2        2      2        2       2     3      2                  2                            2                                        2                                                2                                                           2         2        2       2        2       2        2     3
                      12x  - 12x x  - 12x x  + 12x  + 6x x x  - 6x x  - 3x x  + 4x x  - x  + 14x x  + 24x x x  - 38x x  - 7x x x  + 14x x x  - 5x x  - 10x x  + 38x x  - 8x x  - 12x  + 24x x  - 16x x x  - 8x x  + 3x x x  - 2x x  + 17x x x  + 17x x x  - 5x x x  - 8x x  + 15x x  - 5x x  + 5x x  + 3x  - 4x x  - 16x x x  + 20x x  + 2x x x  - 5x x x  + 2x x  + 15x x x  - 41x x x  + 6x x x  + 20x x  - 4x x x  - 12x x x  + x x x  + 12x x x  - x x  - 5x x  + 11x x  - x x  - 11x x  - 4x x  + 2x  + 20x x  + 8x x x  - 28x x  - 6x x x  + 12x x x  - 4x x  - 6x x x  + 58x x x  - 14x x x  - 28x x  + 26x x x  + 6x x x  - 4x x x  - 6x x x  + 8x x  + 8x x x  - 32x x x  + 5x x x  + 32x x x  + 7x x x  - 9x x  + 4x x  + 20x x  - 6x x  - 20x x  + 2x x  + 12x x  - 4x ,
                         0      0 1      0 1      1     0 1 2     1 2     0 2     1 2    2      0 3      0 1 3      1 3     0 2 3      1 2 3     2 3      0 3      1 3     2 3      3      0 4      0 1 4     1 4     1 2 4     2 4      0 3 4      1 3 4     2 3 4     3 4      0 4     1 4     3 4     4     0 5      0 1 5      1 5     0 2 5     1 2 5     2 5      0 3 5      1 3 5     2 3 5      3 5     0 4 5      1 4 5    2 4 5      3 4 5    4 5     0 5      1 5    2 5      3 5     4 5     5      0 6     0 1 6      1 6     0 2 6      1 2 6     2 6     0 3 6      1 3 6      2 3 6      3 6      0 4 6     1 4 6     2 4 6     3 4 6     4 6     0 5 6      1 5 6     2 5 6      3 5 6     4 5 6     5 6     0 6      1 6     2 6      3 6     4 6      5 6     6
                      
                          3      2         2      3    2                 2        2       2      2                  2                            2          2       2     3      2                  2                2                                      2         2       2      2       2    3     2                  2                            2                                        2                                                 2        2       2        2       2     3      2                   2                  2                                         2                                      2                                                 2          2       2       2       2       2       2
                      - 6x  + 20x x  - 2x x  - 12x  - x x  - 2x x x  + 8x x  - x x  - 4x x  - 14x x  + 2x x x  + 32x x  + 2x x x  - 16x x x  + 4x x  - 28x x  + 8x x  + 8x  - 11x x  + 17x x x  + 4x x  - 6x x x  + x x  - 12x x x  - 8x x x  + 6x x x  + 4x x  - 6x x  + 3x x  + x x  - 2x x  - x  + 5x x  + 7x x x  - 22x x  - 2x x x  + 10x x x  - 3x x  - 6x x x  + 38x x x  - 10x x x  - 16x x  + 3x x x  + 9x x x  - 4x x x  - 8x x x  + 3x x  - 12x x  + 3x x  + 10x x  + 3x x  - 2x  - 18x x  + 18x x x  + 20x x  - 12x x x  + 2x x  - 12x x x  - 36x x x  + 12x x x  + 16x x  - 18x x x  + 2x x x  + 4x x x  - 4x x  + 28x x x  - 8x x x  - 24x x x  - 4x x x  + 8x x  - 12x x  - 8x x  + 4x x  + 8x x  - 4x x  - 8x x ,
                          0      0 1     0 1      1    0 2     0 1 2     1 2    0 2     1 2      0 3     0 1 3      1 3     0 2 3      1 2 3     2 3      1 3     2 3     3      0 4      0 1 4     1 4     1 2 4    2 4      0 3 4     1 3 4     2 3 4     3 4     0 4     1 4    2 4     3 4    4     0 5     0 1 5      1 5     0 2 5      1 2 5     2 5     0 3 5      1 3 5      2 3 5      3 5     0 4 5     1 4 5     2 4 5     3 4 5     0 5      1 5     2 5      3 5     4 5     5      0 6      0 1 6      1 6      1 2 6     2 6      0 3 6      1 3 6      2 3 6      3 6      0 4 6     1 4 6     2 4 6     4 6      1 5 6     2 5 6      3 5 6     4 5 6     5 6      0 6     1 6     2 6     3 6     4 6     5 6
                      
                           3     2          2     2                 2         2       2    3     2                                       2          2       2      2                 2                           2                                      2          2     3      2                  2                            2                                      2                                                  2         2       2       2       2       2     3      2                  2                            2                                       2                                                2                                                           2         2       2       2       2       2       2
                      - 24x  + 8x x  + 16x x  - 4x x  - 4x x x  + 8x x  + 3x x  - 4x x  + x  - 8x x  - 32x x x  + 8x x x  - 16x x x  + 5x x  + 16x x  + 8x x  - 32x x  + 4x x x  + 8x x  - 2x x x  - 4x x x  + 2x x  - 4x x x  - 16x x x  + 6x x x  + 8x x  - 14x x  - 2x  - 10x x  + 26x x x  + 4x x  - 4x x x  + 10x x x  - 2x x  - 26x x x  - 8x x x  - 9x x x  + 4x x  - 11x x x  + 12x x x  - 3x x x  - 12x x x  - 3x x  + 7x x  + 6x x  + 3x x  - 6x x  + 3x x  + 2x  - 30x x  - 14x x x  + 4x x  + 3x x x  - 10x x x  + 4x x  + 14x x x  - 8x x x  + 12x x x  + 4x x  - 25x x x  - 8x x x  + 3x x x  + 8x x x  - 5x x  - 23x x x  + 2x x x  - 6x x x  - 2x x x  - 11x x x  - 2x x  - 6x x  - 4x x  + 4x x  + 4x x  - 2x x  - 4x x ,
                           0     0 1      0 1     0 2     0 1 2     1 2     0 2     1 2    2     0 3      0 1 3     0 2 3      1 2 3     2 3      0 3     2 3      0 4     0 1 4     1 4     0 2 4     1 2 4     2 4     0 3 4      1 3 4     2 3 4     3 4      0 4     4      0 5      0 1 5     1 5     0 2 5      1 2 5     2 5      0 3 5     1 3 5     2 3 5     3 5      0 4 5      1 4 5     2 4 5      3 4 5     4 5     0 5     1 5     2 5     3 5     4 5     5      0 6      0 1 6     1 6     0 2 6      1 2 6     2 6      0 3 6     1 3 6      2 3 6     3 6      0 4 6     1 4 6     2 4 6     3 4 6     4 6      0 5 6     1 5 6     2 5 6     3 5 6      4 5 6     5 6     0 6     1 6     2 6     3 6     4 6     5 6
                      
                        2         2      3     2                  2         2       2     3      2                  2                            2         2        2        2      3     2                  2                           2                                     2         2       2       2       2    3     2                   2                            2                                         2                            2         2        2       2        2      2     3      2                  2                             2                                         2                                              2                                                              2          2       2       2       2       2     3
                      8x x  - 4x x  - 24x  - 7x x  + 5x x x  + 24x x  + 4x x  - 9x x  + 3x  - 10x x  + 4x x x  + 70x x  - x x x  - 47x x x  + 11x x  - 2x x  - 66x x  + 22x x  + 20x  - 2x x  + 18x x x  + 2x x  - 8x x x  + 2x x x  + 2x x  - 19x x x  - 7x x x  + x x x  + 4x x  - 3x x  + 7x x  - 3x x  - 7x x  - x  + 9x x  - 12x x x  - 42x x  + 7x x x  + 28x x x  - 4x x  + 13x x x  + 82x x x  - 24x x x  - 38x x  + 16x x x  + 4x x x  + 6x x  - 3x x  - 27x x  + 9x x  + 27x x  + x x  - 6x  + 16x x  + 9x x x  + 24x x  - 13x x x  - 22x x x  + 5x x  - 16x x x  - 54x x x  + 21x x x  + 28x x  + 7x x x  + 4x x x  - 6x x x  - 6x x x  - x x  + 17x x x  + 29x x x  - 13x x x  - 33x x x  + 9x x x  + 12x x  + 14x x  - 6x x  + 6x x  + 3x x  - 2x x  + 4x ,
                        0 1     0 1      1     0 2     0 1 2      1 2     0 2     1 2     2      0 3     0 1 3      1 3    0 2 3      1 2 3      2 3     0 3      1 3      2 3      3     0 4      0 1 4     1 4     0 2 4     1 2 4     2 4      0 3 4     1 3 4    2 3 4     3 4     0 4     1 4     2 4     3 4    4     0 5      0 1 5      1 5     0 2 5      1 2 5     2 5      0 3 5      1 3 5      2 3 5      3 5      0 4 5     2 4 5     4 5     0 5      1 5     2 5      3 5    4 5     5      0 6     0 1 6      1 6      0 2 6      1 2 6     2 6      0 3 6      1 3 6      2 3 6      3 6     0 4 6     1 4 6     2 4 6     3 4 6    4 6      0 5 6      1 5 6      2 5 6      3 5 6     4 5 6      5 6      0 6     1 6     3 6     4 6     5 6     6
                      
                           2        3      2                  2         2       2      2                  2                             2         2        2        2     3                2                           2                              2       2       2      2                            2                                        2                                      2       2       2     2                  2                                                            2                                              2                                                      2         2       2       2       2       2
                      - 12x x  + 12x  + 12x x  - 4x x x  - 14x x  + 8x x  + 6x x  + 12x x  - 4x x x  - 32x x  + 10x x x  + 26x x x  - 6x x  + 4x x  + 28x x  - 12x x  - 8x  - 10x x x  - 2x x  + 10x x x  + 3x x x  + x x  + 10x x x  + 2x x x  - 2x x  + 2x x  + 2x x  + 12x x  + 4x x x  - 17x x x  + 7x x  + 2x x x  - 24x x x  + 18x x x  + 12x x  - x x x  + 3x x x  + 2x x x  + 3x x  - 5x x  - 4x x  - 6x x  - 12x x x  - 6x x  + 9x x x  + 10x x x  + 10x x x  + 10x x x  - 6x x x  - 4x x  - 5x x x  - 5x x x  + 4x x x  + 4x x x  - x x  - x x x  + x x x  + 8x x x  + 2x x x  - x x x  + 2x x  - 6x x  - 6x x  + 4x x  - 2x x  - 4x x ,
                           0 1      1      0 2     0 1 2      1 2     0 2     1 2      0 3     0 1 3      1 3      0 2 3      1 2 3     2 3     0 3      1 3      2 3     3      0 1 4     1 4      0 2 4     1 2 4    2 4      0 3 4     1 3 4     1 4     2 4     3 4      1 5     0 2 5      1 2 5     2 5     0 3 5      1 3 5      2 3 5      3 5    1 4 5     2 4 5     3 4 5     1 5     2 5     3 5     0 6      0 1 6     1 6     0 2 6      1 2 6      0 3 6      1 3 6     2 3 6     3 6     0 4 6     1 4 6     2 4 6     3 4 6    4 6    0 5 6    1 5 6     2 5 6     3 5 6    4 5 6     5 6     0 6     1 6     3 6     4 6     5 6
                      
                        2          2      3      2                   2          2        2     3     2                   2                              2          2        2        2      3     2                  2                            2                                        2         2       2       2       2    3      2                   2                            2                                         2                                                2         2        2       2        2      2     3     2                  2                             2                              2                                              2                                                             2         2        2       2        2       2       2
                      8x x  - 12x x  + 24x  - 11x x  + 17x x x  - 24x x  - 10x x  + 11x x  - 3x  - 6x x  + 28x x x  - 70x x  - 21x x x  + 47x x x  - 13x x  - 14x x  + 66x x  - 22x x  - 20x  + 2x x  - 2x x x  - 10x x  - 11x x x  + 8x x x  - 5x x  + 3x x x  + 23x x x  - 11x x x  - 12x x  + 3x x  - 3x x  - 2x x  + 3x x  + x  - 11x x  + 14x x x  + 34x x  - 6x x x  - 16x x x  + 3x x  - 15x x x  - 66x x x  + 12x x x  + 30x x  - 19x x x  + 2x x x  - 5x x x  - 2x x x  - 7x x  + 6x x  + 21x x  - 3x x  - 21x x  + x x  + 5x  - 8x x  + 7x x x  - 32x x  - 13x x x  + 28x x x  - 9x x  + 70x x x  - 27x x x  - 36x x  + x x x  + 4x x x  - 7x x x  - 2x x x  + 3x x  - 25x x x  - 23x x x  + 4x x x  + 27x x x  - 14x x x  - 9x x  - 2x x  + 10x x  - 6x x  - 10x x  + 3x x  - 2x x
                        0 1      0 1      1      0 2      0 1 2      1 2      0 2      1 2     2     0 3      0 1 3      1 3      0 2 3      1 2 3      2 3      0 3      1 3      2 3      3     0 4     0 1 4      1 4      0 2 4     1 2 4     2 4     0 3 4      1 3 4      2 3 4      3 4     0 4     1 4     2 4     3 4    4      0 5      0 1 5      1 5     0 2 5      1 2 5     2 5      0 3 5      1 3 5      2 3 5      3 5      0 4 5     1 4 5     2 4 5     3 4 5     4 5     0 5      1 5     2 5      3 5    4 5     5     0 6     0 1 6      1 6      0 2 6      1 2 6     2 6      1 3 6      2 3 6      3 6    0 4 6     1 4 6     2 4 6     3 4 6     4 6      0 5 6      1 5 6     2 5 6      3 5 6      4 5 6     5 6     0 6      1 6     2 6      3 6     4 6     5 6
                     }

o1 : RationalMap (cubic birational map from PP^6 to 6-dimensional subvariety of PP^9)

i2 : time describe oo
     -- used 0.0256002 seconds

o2 = rational map defined by forms of degree 3
     source variety: PP^6
     target variety: complete intersection of type (2,2,2) in PP^9
     dominance: true
     birationality: true
     projective degrees: {1, 3, 9, 17, 21, 16, 8}
     number of minimal representatives: 1
     dimension base locus: 3
     degree base locus: 10
     coefficient ring: QQ

Ways to use specialCubicTransformation :

specialCubicTransformation(Ring,ZZ)
specialCubicTransformation(ZZ)
specialCubicTransformation(ZZ,Ring)

For the programmer

The object specialCubicTransformation is a method function.

specialCubicTransformation -- special cubic transformations whose base locus has dimension at most three

Synopsis

Description

See also

Ways to use specialCubicTransformation :

For the programmer