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MultiprojectiveVarieties :: segre(MultirationalMap)

segre(MultirationalMap) -- the composition of a multi-rational map with the Segre embedding of the target

Synopsis

Description

i1 : ZZ/65521[x_0..x_4];
i2 : f = rationalMap({x_3^2-x_2*x_4,x_2*x_3-x_1*x_4,x_1*x_3-x_0*x_4,x_2^2-x_0*x_4,x_1*x_2-x_0*x_3,x_1^2-x_0*x_2},Dominant=>true);

o2 : RationalMap (quadratic dominant rational map from PP^4 to hypersurface in PP^5)
i3 : g = rationalMap {x_3^2-x_2*x_4,x_2*x_3-x_1*x_4,x_1*x_3-x_0*x_4,x_2^2-x_0*x_4,x_1*x_2-x_0*x_3};

o3 : RationalMap (quadratic rational map from PP^4 to PP^4)
i4 : h = rationalMap {-x_3^2+x_2*x_4,2*x_2*x_3-2*x_1*x_4,-3*x_2^2+2*x_1*x_3+x_0*x_4, 2*x_1*x_2-2*x_0*x_3,-x_1^2+x_0*x_2};

o4 : RationalMap (quadratic rational map from PP^4 to PP^4)
i5 : Phi = multirationalMap {f,g,h};

o5 : MultirationalMap (rational map from PP^4 to hypersurface in PP^5 x PP^4 x PP^4)
i6 : time segre Phi
     -- used 0.620599 seconds

o6 = -- rational map --
                    ZZ
     source: Proj(-----[x , x , x , x , x ])
                  65521  0   1   2   3   4
                    ZZ
     target: Proj(-----[y , y , y , y , y , y , y , y , y , y , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y  , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   , y   ])
                  65521  0   1   2   3   4   5   6   7   8   9   10   11   12   13   14   15   16   17   18   19   20   21   22   23   24   25   26   27   28   29   30   31   32   33   34   35   36   37   38   39   40   41   42   43   44   45   46   47   48   49   50   51   52   53   54   55   56   57   58   59   60   61   62   63   64   65   66   67   68   69   70   71   72   73   74   75   76   77   78   79   80   81   82   83   84   85   86   87   88   89   90   91   92   93   94   95   96   97   98   99   100   101   102   103   104   105   106   107   108   109   110   111   112   113   114   115   116   117   118   119   120   121   122   123   124   125   126   127   128   129   130   131   132   133   134   135   136   137   138   139   140   141   142   143   144   145   146   147   148   149
     defining forms: {
                         6       4       2 2 2    3 3
                      - x  + 3x x x  - 3x x x  + x x ,
                         3     2 3 4     2 3 4    2 4
                      
                          5     2 3         4       3   2         2 2       2 3
                      2x x  - 4x x x  - 2x x x  + 2x x x  + 4x x x x  - 2x x x ,
                        2 3     2 3 4     1 3 4     2 3 4     1 2 3 4     1 2 4
                      
                          2 4       5     3 2           3        4       4 2       2   2         2 2      2 3
                      - 3x x  + 2x x  + 6x x x  - 4x x x x  + x x x  - 3x x  + 2x x x x  - 2x x x x  + x x x ,
                          2 3     1 3     2 3 4     1 2 3 4    0 3 4     2 4     1 2 3 4     0 2 3 4    0 2 4
                      
                            4       5       2 2           3         3 2       2   2
                      2x x x  - 2x x  - 4x x x x  + 4x x x x  + 2x x x  - 2x x x x ,
                        1 2 3     0 3     1 2 3 4     0 2 3 4     1 2 4     0 2 3 4
                      
                         2 4        4     2   2         2 2      2 2 2      3 2
                      - x x  + x x x  + 2x x x x  - 2x x x x  - x x x  + x x x ,
                         1 3    0 2 3     1 2 3 4     0 2 3 4    1 2 4    0 2 4
                      
                           5     2 3        4      3   2         2 2      2 3
                      - x x  + 2x x x  + x x x  - x x x  - 2x x x x  + x x x ,
                         2 3     2 3 4    1 3 4    2 3 4     1 2 3 4    1 2 4
                      
                        2 4     3 2           3         2   2     2 2 2     2   3
                      2x x  - 2x x x  - 4x x x x  + 4x x x x  + 2x x x  - 2x x x ,
                        2 3     2 3 4     1 2 3 4     1 2 3 4     1 3 4     1 2 4
                      
                          3 3         4     4          2 2       2 3          3         3 2     2     2      2   2        2 2          3
                      - 3x x  + 2x x x  + 3x x x  + x x x x  - 2x x x  + x x x x  - 3x x x  + 2x x x x  - x x x x  - x x x x  + x x x x ,
                          2 3     1 2 3     2 3 4    1 2 3 4     1 3 4    0 2 3 4     1 2 4     1 2 3 4    0 2 3 4    0 1 3 4    0 1 2 4
                      
                          2 3         4       3         2   2         2 2           3       2 2 2             2
                      2x x x  - 2x x x  - 2x x x x  - 2x x x x  + 2x x x x  + 2x x x x  + 2x x x  - 2x x x x x ,
                        1 2 3     0 2 3     1 2 3 4     1 2 3 4     0 2 3 4     0 1 3 4     1 2 4     0 1 2 3 4
                      
                         2   3      2 3    2 2          3        3 2            2      3   2        2 2
                      - x x x  + x x x  + x x x x  - x x x x  + x x x  - x x x x x  - x x x  + x x x x ,
                         1 2 3    0 2 3    1 2 3 4    0 2 3 4    1 3 4    0 1 2 3 4    1 2 4    0 1 2 4
                      
                           5         3        4        2   2         2 2      2 3
                      - x x  + 2x x x x  + x x x  - x x x x  - 2x x x x  + x x x ,
                         1 3     1 2 3 4    0 3 4    1 2 3 4     0 2 3 4    0 2 4
                      
                            4       2 2       2 3           3       2     2       2   2         2 2           3
                      2x x x  - 2x x x x  - 2x x x  - 2x x x x  + 2x x x x  + 2x x x x  + 2x x x x  - 2x x x x ,
                        1 2 3     1 2 3 4     1 3 4     0 2 3 4     1 2 3 4     0 2 3 4     0 1 3 4     0 1 2 4
                      
                            2 3     2 4       3         2   2         2 2          3         3 2            2    2 2 2    2   3
                      - 3x x x  + 2x x  + 3x x x x  - 2x x x x  + 3x x x x  - x x x x  - 3x x x  + x x x x x  - x x x  + x x x ,
                          1 2 3     1 3     1 2 3 4     1 2 3 4     0 2 3 4    0 1 3 4     0 2 4    0 1 2 3 4    0 3 4    0 2 4
                      
                        2   3         4     2 2         2 3           2 2     2     2
                      2x x x  - 2x x x  - 2x x x x  + 2x x x  + 2x x x x  - 2x x x x ,
                        1 2 3     0 1 3     1 2 3 4     0 3 4     0 1 2 4     0 2 3 4
                      
                         3 3          3    3              2          2 2      2   2        2   2    2 2 2
                      - x x  + x x x x  + x x x x  - x x x x x  + x x x x  - x x x x  - x x x x  + x x x ,
                         1 3    0 1 2 3    1 2 3 4    0 1 2 3 4    0 1 3 4    0 2 3 4    0 1 2 4    0 2 4
                      
                         2 4     3 2        4      4 2         2 2      2 3
                      - x x  + 2x x x  + x x x  - x x  - 2x x x x  + x x x ,
                         2 3     2 3 4    0 3 4    2 4     0 2 3 4    0 2 4
                      
                        3 3     4           2 2           3         3 2       2   2         2 2           3
                      2x x  - 2x x x  - 2x x x x  - 2x x x x  + 2x x x  + 2x x x x  + 2x x x x  - 2x x x x ,
                        2 3     2 3 4     1 2 3 4     0 2 3 4     1 2 4     0 2 3 4     0 1 3 4     0 1 2 4
                      
                          4 2       2 3     5         3           2 2           3         3 2             2    2 2 2    2   3
                      - 3x x  + 2x x x  + 3x x  - 2x x x x  + 4x x x x  - 2x x x x  - 4x x x  + 2x x x x x  - x x x  + x x x ,
                          2 3     1 2 3     2 4     1 2 3 4     0 2 3 4     0 1 3 4     0 2 4     0 1 2 3 4    0 3 4    0 2 4
                      
                          3 2       2 3       4         3               2       2 3           2 2     2     2
                      2x x x  - 2x x x  - 2x x x  + 2x x x x  - 2x x x x x  + 2x x x  + 2x x x x  - 2x x x x ,
                        1 2 3     0 2 3     1 2 4     0 2 3 4     0 1 2 3 4     0 3 4     0 1 2 4     0 2 3 4
                      
                         2 2 2      3 2    2 3        4        2 2      2   2        2   2    2 2 2
                      - x x x  + x x x  + x x x  - x x x  + x x x x  - x x x x  - x x x x  + x x x ,
                         1 2 3    0 2 3    1 2 4    0 2 4    0 1 3 4    0 2 3 4    0 1 2 4    0 2 4
                      
                             4      5       2 2           3        3 2      2   2
                      - x x x  + x x  + 2x x x x  - 2x x x x  - x x x  + x x x x ,
                         1 2 3    0 3     1 2 3 4     0 2 3 4    1 2 4    0 2 3 4
                      
                          2 3         4       3         2   2         2 2           3       2 2 2             2
                      2x x x  - 2x x x  - 2x x x x  - 2x x x x  + 2x x x x  + 2x x x x  + 2x x x  - 2x x x x x ,
                        1 2 3     0 2 3     1 2 3 4     1 2 3 4     0 2 3 4     0 1 3 4     1 2 4     0 1 2 3 4
                      
                            3 2     2   3       2 3         4       4       2 2           3               2      2 3          2 2    2     2
                      - 3x x x  + 2x x x  + 3x x x  - 2x x x  + 3x x x  - 2x x x x  - 3x x x x  + 3x x x x x  - x x x  - x x x x  + x x x x ,
                          1 2 3     1 2 3     0 2 3     0 1 3     1 2 4     1 2 3 4     0 2 3 4     0 1 2 3 4    0 3 4    0 1 2 4    0 2 3 4
                      
                        2 2 2           3     2 4     2 3           2         2   2
                      2x x x  - 4x x x x  + 2x x  - 2x x x  + 4x x x x x  - 2x x x x ,
                        1 2 3     0 1 2 3     0 3     1 2 4     0 1 2 3 4     0 2 3 4
                      
                         3   2        2 2      2 3    2   3    3 2          3        2          2 2
                      - x x x  + x x x x  + x x x  - x x x  + x x x  - x x x x  - x x x x x  + x x x x ,
                         1 2 3    0 1 2 3    0 1 3    0 2 3    1 2 4    0 1 2 4    0 1 2 3 4    0 2 3 4
                      
                           5     2 3        4      3   2         2 2      2 3
                      - x x  + 2x x x  + x x x  - x x x  - 2x x x x  + x x x ,
                         2 3     2 3 4    1 3 4    2 3 4     1 2 3 4    1 2 4
                      
                        2 4     3 2           3         2   2     2 2 2     2   3
                      2x x  - 2x x x  - 4x x x x  + 4x x x x  + 2x x x  - 2x x x ,
                        2 3     2 3 4     1 2 3 4     1 2 3 4     1 3 4     1 2 4
                      
                          3 3         4     4          2 2       2 3          3         3 2     2     2      2   2        2 2          3
                      - 3x x  + 2x x x  + 3x x x  + x x x x  - 2x x x  + x x x x  - 3x x x  + 2x x x x  - x x x x  - x x x x  + x x x x ,
                          2 3     1 2 3     2 3 4    1 2 3 4     1 3 4    0 2 3 4     1 2 4     1 2 3 4    0 2 3 4    0 1 3 4    0 1 2 4
                      
                          2 3         4       3         2   2         2 2           3       2 2 2             2
                      2x x x  - 2x x x  - 2x x x x  - 2x x x x  + 2x x x x  + 2x x x x  + 2x x x  - 2x x x x x ,
                        1 2 3     0 2 3     1 2 3 4     1 2 3 4     0 2 3 4     0 1 3 4     1 2 4     0 1 2 3 4
                      
                         2   3      2 3    2 2          3        3 2            2      3   2        2 2
                      - x x x  + x x x  + x x x x  - x x x x  + x x x  - x x x x x  - x x x  + x x x x ,
                         1 2 3    0 2 3    1 2 3 4    0 2 3 4    1 3 4    0 1 2 3 4    1 2 4    0 1 2 4
                      
                         2 4    3 2           3         2   2    2 2 2    2   3
                      - x x  + x x x  + 2x x x x  - 2x x x x  - x x x  + x x x ,
                         2 3    2 3 4     1 2 3 4     1 2 3 4    1 3 4    1 2 4
                      
                        3 3       2 2       2     2     3 3
                      2x x  - 6x x x x  + 6x x x x  - 2x x ,
                        2 3     1 2 3 4     1 2 3 4     1 4
                      
                          4 2       2 3       3         2   2        2 2       2 2 2     3   2             2      2 3
                      - 3x x  + 2x x x  + 6x x x x  - 4x x x x  + x x x x  - 3x x x  + 2x x x  - 2x x x x x  + x x x ,
                          2 3     1 2 3     1 2 3 4     1 2 3 4    0 2 3 4     1 2 4     1 3 4     0 1 2 3 4    0 1 4
                      
                          3 2       2 3     2 2               2       3   2       2   2
                      2x x x  - 2x x x  - 4x x x x  + 4x x x x x  + 2x x x  - 2x x x x ,
                        1 2 3     0 2 3     1 2 3 4     0 1 2 3 4     1 2 4     0 1 3 4
                      
                         2 2 2      3 2     3               2        4 2      2   2
                      - x x x  + x x x  + 2x x x x  - 2x x x x x  - x x  + x x x x ,
                         1 2 3    0 2 3     1 2 3 4     0 1 2 3 4    1 4    0 1 2 4
                      
                             4      2 2      2 3          3      2     2      2   2        2 2          3
                      - x x x  + x x x x  + x x x  + x x x x  - x x x x  - x x x x  - x x x x  + x x x x ,
                         1 2 3    1 2 3 4    1 3 4    0 2 3 4    1 2 3 4    0 2 3 4    0 1 3 4    0 1 2 4
                      
                          2 3     2   2         2 2       3   2             2       2 3
                      2x x x  - 4x x x x  - 2x x x x  + 2x x x  + 4x x x x x  - 2x x x ,
                        1 2 3     1 2 3 4     0 2 3 4     1 3 4     0 1 2 3 4     0 1 4
                      
                            3 2     2   3     2 2           3         3 2            2           2 2      2   2    2     2    2   3
                      - 3x x x  + 2x x x  + 3x x x x  + 3x x x x  - 2x x x  - x x x x x  - 3x x x x  + x x x x  - x x x x  + x x x ,
                          1 2 3     1 2 3     1 2 3 4     0 2 3 4     1 3 4    0 1 2 3 4     0 1 2 4    0 1 3 4    0 2 3 4    0 1 4
                      
                        2 2 2           3     3               2           2 2       2   2         2   2     2     2
                      2x x x  - 2x x x x  - 2x x x x  - 2x x x x x  + 2x x x x  + 2x x x x  + 2x x x x  - 2x x x x ,
                        1 2 3     0 1 2 3     1 2 3 4     0 1 2 3 4     0 1 3 4     0 2 3 4     0 1 2 4     0 1 3 4
                      
                         3   2        2 2    4        2 2          3 2    2     2
                      - x x x  + x x x x  + x x x  - x x x x  - x x x  + x x x x ,
                         1 2 3    0 1 2 3    1 3 4    0 2 3 4    0 1 4    0 1 2 4
                      
                         3 3    4          2 2          3        3 2      2   2        2 2          3
                      - x x  + x x x  + x x x x  + x x x x  - x x x  - x x x x  - x x x x  + x x x x ,
                         2 3    2 3 4    1 2 3 4    0 2 3 4    1 2 4    0 2 3 4    0 1 3 4    0 1 2 4
                      
                        4 2       3           2 2       2 2 2             2       2 3
                      2x x  - 4x x x x  - 2x x x x  + 2x x x  + 4x x x x x  - 2x x x ,
                        2 3     1 2 3 4     0 2 3 4     1 2 4     0 1 2 3 4     0 1 4
                      
                          5         3 2       4       2 2           3               2           2 2       2   2    2     2    2   3
                      - 3x x  + 2x x x  + 3x x x  - 2x x x x  + 4x x x x  - 2x x x x x  - 4x x x x  + 2x x x x  - x x x x  + x x x ,
                          2 3     1 2 3     1 2 4     1 2 3 4     0 2 3 4     0 1 2 3 4     0 1 2 4     0 1 3 4    0 2 3 4    0 1 4
                      
                          4         3 2     2 3       2   2         2   2     2     2
                      2x x x  - 2x x x  - 2x x x  + 2x x x x  + 2x x x x  - 2x x x x ,
                        1 2 3     0 2 3     1 2 4     0 2 3 4     0 1 2 4     0 1 3 4
                      
                         2 3        4      3 2          3        2          2 2          3 2    2     2
                      - x x x  + x x x  + x x x  - x x x x  + x x x x x  - x x x x  - x x x  + x x x x ,
                         1 2 3    0 2 3    1 2 4    0 1 2 4    0 1 2 3 4    0 2 3 4    0 1 4    0 1 2 4
                      
                           2 3        4      3        2   2        2 2          3      2 2 2            2
                      - x x x  + x x x  + x x x x  + x x x x  - x x x x  - x x x x  - x x x  + x x x x x ,
                         1 2 3    0 2 3    1 2 3 4    1 2 3 4    0 2 3 4    0 1 3 4    1 2 4    0 1 2 3 4
                      
                          3 2       2 3     2 2               2       3   2       2   2
                      2x x x  - 2x x x  - 4x x x x  + 4x x x x x  + 2x x x  - 2x x x x ,
                        1 2 3     0 2 3     1 2 3 4     0 1 2 3 4     1 2 4     0 1 3 4
                      
                            4       2 2 2       3 2           3     2 3       3               2           2 2      2   2        2   2    2     2
                      - 3x x x  + 2x x x  + 3x x x  - 2x x x x  + 3x x x  - 2x x x x  - 2x x x x x  + 2x x x x  - x x x x  - x x x x  + x x x x ,
                          1 2 3     1 2 3     0 2 3     0 1 2 3     1 2 4     1 2 3 4     0 1 2 3 4     0 1 3 4    0 2 3 4    0 1 2 4    0 1 3 4
                      
                        2 3           2 2     2   3     3 2         2           2   2
                      2x x x  - 4x x x x  + 2x x x  - 2x x x  + 4x x x x x  - 2x x x x ,
                        1 2 3     0 1 2 3     0 2 3     1 2 4     0 1 2 3 4     0 1 3 4
                      
                         3 2          3        2   2    2 2 2    4          2 2        3        2
                      - x x x  + x x x x  + x x x x  - x x x  + x x x  - x x x x  - x x x x  + x x x x x ,
                         1 2 3    0 1 2 3    0 1 2 3    0 2 3    1 2 4    0 1 2 4    0 1 3 4    0 1 2 3 4
                      
                           5         3        4        2   2         2 2      2 3
                      - x x  + 2x x x x  + x x x  - x x x x  - 2x x x x  + x x x ,
                         1 3     1 2 3 4    0 3 4    1 2 3 4     0 2 3 4    0 2 4
                      
                            4       2 2       2 3           3       2     2       2   2         2 2           3
                      2x x x  - 2x x x x  - 2x x x  - 2x x x x  + 2x x x x  + 2x x x x  + 2x x x x  - 2x x x x ,
                        1 2 3     1 2 3 4     1 3 4     0 2 3 4     1 2 3 4     0 2 3 4     0 1 3 4     0 1 2 4
                      
                            2 3     2 4       3         2   2         2 2          3         3 2            2    2 2 2    2   3
                      - 3x x x  + 2x x  + 3x x x x  - 2x x x x  + 3x x x x  - x x x x  - 3x x x  + x x x x x  - x x x  + x x x ,
                          1 2 3     1 3     1 2 3 4     1 2 3 4     0 2 3 4    0 1 3 4     0 2 4    0 1 2 3 4    0 3 4    0 2 4
                      
                        2   3         4     2 2         2 3           2 2     2     2
                      2x x x  - 2x x x  - 2x x x x  + 2x x x  + 2x x x x  - 2x x x x ,
                        1 2 3     0 1 3     1 2 3 4     0 3 4     0 1 2 4     0 2 3 4
                      
                         3 3          3    3              2          2 2      2   2        2   2    2 2 2
                      - x x  + x x x x  + x x x x  - x x x x x  + x x x x  - x x x x  - x x x x  + x x x ,
                         1 3    0 1 2 3    1 2 3 4    0 1 2 3 4    0 1 3 4    0 2 3 4    0 1 2 4    0 2 4
                      
                             4      2 2      2 3          3      2     2      2   2        2 2          3
                      - x x x  + x x x x  + x x x  + x x x x  - x x x x  - x x x x  - x x x x  + x x x x ,
                         1 2 3    1 2 3 4    1 3 4    0 2 3 4    1 2 3 4    0 2 3 4    0 1 3 4    0 1 2 4
                      
                          2 3     2   2         2 2       3   2             2       2 3
                      2x x x  - 4x x x x  - 2x x x x  + 2x x x  + 4x x x x x  - 2x x x ,
                        1 2 3     1 2 3 4     0 2 3 4     1 3 4     0 1 2 3 4     0 1 4
                      
                            3 2     2   3     2 2           3         3 2            2           2 2      2   2    2     2    2   3
                      - 3x x x  + 2x x x  + 3x x x x  + 3x x x x  - 2x x x  - x x x x x  - 3x x x x  + x x x x  - x x x x  + x x x ,
                          1 2 3     1 2 3     1 2 3 4     0 2 3 4     1 3 4    0 1 2 3 4     0 1 2 4    0 1 3 4    0 2 3 4    0 1 4
                      
                        2 2 2           3     3               2           2 2       2   2         2   2     2     2
                      2x x x  - 2x x x x  - 2x x x x  - 2x x x x x  + 2x x x x  + 2x x x x  + 2x x x x  - 2x x x x ,
                        1 2 3     0 1 2 3     1 2 3 4     0 1 2 3 4     0 1 3 4     0 2 3 4     0 1 2 4     0 1 3 4
                      
                         3   2        2 2    4        2 2          3 2    2     2
                      - x x x  + x x x x  + x x x  - x x x x  - x x x  + x x x x ,
                         1 2 3    0 1 2 3    1 3 4    0 2 3 4    0 1 4    0 1 2 4
                      
                         2 4    2   2           3               2    2 2 2    2   3
                      - x x  + x x x x  + 2x x x x  - 2x x x x x  - x x x  + x x x ,
                         1 3    1 2 3 4     0 1 3 4     0 1 2 3 4    0 3 4    0 2 4
                      
                        2   3     3 2             2         2   2     2     2     2   3
                      2x x x  - 2x x x  - 4x x x x x  + 4x x x x  + 2x x x x  - 2x x x ,
                        1 2 3     1 3 4     0 1 2 3 4     0 1 3 4     0 2 3 4     0 1 4
                      
                          2 2 2     3 3         2           2 2       2 2 2    3 3
                      - 3x x x  + 2x x  + 6x x x x x  - 3x x x x  - 3x x x  + x x ,
                          1 2 3     1 3     0 1 2 3 4     0 1 3 4     0 2 4    0 4
                      
                        3   2       2 3       2           2   2       2     2     3   2
                      2x x x  - 2x x x  - 4x x x x x  + 4x x x x  + 2x x x x  - 2x x x ,
                        1 2 3     0 1 3     0 1 2 3 4     0 1 3 4     0 1 2 4     0 3 4
                      
                         4 2      2   2       3         2            2 2 2    3   2
                      - x x  + x x x x  + 2x x x x  - 2x x x x x  - x x x  + x x x ,
                         1 3    0 1 2 3     0 1 3 4     0 1 2 3 4    0 1 4    0 2 4
                      
                           2 3      3          2 2          3        3 2            2    2 2 2    2   3
                      - x x x  + x x x x  + x x x x  + x x x x  - x x x  - x x x x x  - x x x  + x x x ,
                         1 2 3    1 2 3 4    0 2 3 4    0 1 3 4    0 2 4    0 1 2 3 4    0 3 4    0 2 4
                      
                          3 2     2 2           3               2           2 2       2   2     2     2     2   3
                      2x x x  - 2x x x x  - 2x x x x  - 2x x x x x  + 2x x x x  + 2x x x x  + 2x x x x  - 2x x x ,
                        1 2 3     1 2 3 4     0 2 3 4     0 1 2 3 4     0 1 2 4     0 1 3 4     0 2 3 4     0 1 4
                      
                            4       2 2 2       4           2           2 2       2 2 2    2     2    3 3
                      - 3x x x  + 2x x x  + 3x x x  + 2x x x x x  - 2x x x x  - 4x x x  + x x x x  + x x ,
                          1 2 3     1 2 3     0 2 4     0 1 2 3 4     0 1 3 4     0 2 4    0 1 3 4    0 4
                      
                        2 3           2 2         3         2           2 2         2   2       2     2     3   2
                      2x x x  - 2x x x x  - 2x x x x  - 2x x x x x  + 2x x x x  + 2x x x x  + 2x x x x  - 2x x x ,
                        1 2 3     0 1 2 3     0 1 2 4     0 1 2 3 4     0 2 3 4     0 1 3 4     0 1 2 4     0 3 4
                      
                         3 2          3        2 2      2 3        3        2            2 2 2    3   2
                      - x x x  + x x x x  + x x x x  - x x x  + x x x x  - x x x x x  - x x x  + x x x ,
                         1 2 3    0 1 2 3    0 1 2 4    0 2 4    0 1 3 4    0 1 2 3 4    0 1 4    0 2 4
                      
                         2   3        4    2 2        2 3          2 2    2     2
                      - x x x  + x x x  + x x x x  - x x x  - x x x x  + x x x x ,
                         1 2 3    0 1 3    1 2 3 4    0 3 4    0 1 2 4    0 2 3 4
                      
                        2 2 2           3     3               2           2 2       2   2         2   2     2     2
                      2x x x  - 2x x x x  - 2x x x x  - 2x x x x x  + 2x x x x  + 2x x x x  + 2x x x x  - 2x x x x ,
                        1 2 3     0 1 2 3     1 2 3 4     0 1 2 3 4     0 1 3 4     0 2 3 4     0 1 2 4     0 1 3 4
                      
                          2 3       3   2         2 2       2 3         3        2           2 2        2   2      2     2    3   2
                      - 3x x x  + 2x x x  + 3x x x x  - 2x x x  + 3x x x x  - x x x x x  - 3x x x x  + x x x x  - x x x x  + x x x ,
                          1 2 3     1 2 3     0 1 2 3     0 1 3     0 1 2 4    0 1 2 3 4     0 2 3 4    0 1 3 4    0 1 2 4    0 3 4
                      
                        3 2         2   2     2   3       2 2       2             3 2
                      2x x x  - 4x x x x  + 2x x x  - 2x x x x  + 4x x x x x  - 2x x x ,
                        1 2 3     0 1 2 3     0 1 3     0 1 2 4     0 1 2 3 4     0 3 4
                      
                         4          2 2        3 2    2     2      3        2   2      2 2        3
                      - x x x  + x x x x  + x x x  - x x x x  + x x x x  - x x x x  - x x x x  + x x x x ,
                         1 2 3    0 1 2 3    0 1 3    0 1 2 3    0 1 2 4    0 1 2 4    0 1 3 4    0 2 3 4
                      
                         2 4     3 2        4      4 2         2 2      2 3
                      - x x  + 2x x x  + x x x  - x x  - 2x x x x  + x x x ,
                         2 3     2 3 4    0 3 4    2 4     0 2 3 4    0 2 4
                      
                        3 3     4           2 2           3         3 2       2   2         2 2           3
                      2x x  - 2x x x  - 2x x x x  - 2x x x x  + 2x x x  + 2x x x x  + 2x x x x  - 2x x x x ,
                        2 3     2 3 4     1 2 3 4     0 2 3 4     1 2 4     0 2 3 4     0 1 3 4     0 1 2 4
                      
                          4 2       2 3     5         3           2 2           3         3 2             2    2 2 2    2   3
                      - 3x x  + 2x x x  + 3x x  - 2x x x x  + 4x x x x  - 2x x x x  - 4x x x  + 2x x x x x  - x x x  + x x x ,
                          2 3     1 2 3     2 4     1 2 3 4     0 2 3 4     0 1 3 4     0 2 4     0 1 2 3 4    0 3 4    0 2 4
                      
                          3 2       2 3       4         3               2       2 3           2 2     2     2
                      2x x x  - 2x x x  - 2x x x  + 2x x x x  - 2x x x x x  + 2x x x  + 2x x x x  - 2x x x x ,
                        1 2 3     0 2 3     1 2 4     0 2 3 4     0 1 2 3 4     0 3 4     0 1 2 4     0 2 3 4
                      
                         2 2 2      3 2    2 3        4        2 2      2   2        2   2    2 2 2
                      - x x x  + x x x  + x x x  - x x x  + x x x x  - x x x x  - x x x x  + x x x ,
                         1 2 3    0 2 3    1 2 4    0 2 4    0 1 3 4    0 2 3 4    0 1 2 4    0 2 4
                      
                         3 3    4          2 2          3        3 2      2   2        2 2          3
                      - x x  + x x x  + x x x x  + x x x x  - x x x  - x x x x  - x x x x  + x x x x ,
                         2 3    2 3 4    1 2 3 4    0 2 3 4    1 2 4    0 2 3 4    0 1 3 4    0 1 2 4
                      
                        4 2       3           2 2       2 2 2             2       2 3
                      2x x  - 4x x x x  - 2x x x x  + 2x x x  + 4x x x x x  - 2x x x ,
                        2 3     1 2 3 4     0 2 3 4     1 2 4     0 1 2 3 4     0 1 4
                      
                          5         3 2       4       2 2           3               2           2 2       2   2    2     2    2   3
                      - 3x x  + 2x x x  + 3x x x  - 2x x x x  + 4x x x x  - 2x x x x x  - 4x x x x  + 2x x x x  - x x x x  + x x x ,
                          2 3     1 2 3     1 2 4     1 2 3 4     0 2 3 4     0 1 2 3 4     0 1 2 4     0 1 3 4    0 2 3 4    0 1 4
                      
                          4         3 2     2 3       2   2         2   2     2     2
                      2x x x  - 2x x x  - 2x x x  + 2x x x x  + 2x x x x  - 2x x x x ,
                        1 2 3     0 2 3     1 2 4     0 2 3 4     0 1 2 4     0 1 3 4
                      
                         2 3        4      3 2          3        2          2 2          3 2    2     2
                      - x x x  + x x x  + x x x  - x x x x  + x x x x x  - x x x x  - x x x  + x x x x ,
                         1 2 3    0 2 3    1 2 4    0 1 2 4    0 1 2 3 4    0 2 3 4    0 1 4    0 1 2 4
                      
                           2 3      3          2 2          3        3 2            2    2 2 2    2   3
                      - x x x  + x x x x  + x x x x  + x x x x  - x x x  - x x x x x  - x x x  + x x x ,
                         1 2 3    1 2 3 4    0 2 3 4    0 1 3 4    0 2 4    0 1 2 3 4    0 3 4    0 2 4
                      
                          3 2     2 2           3               2           2 2       2   2     2     2     2   3
                      2x x x  - 2x x x x  - 2x x x x  - 2x x x x x  + 2x x x x  + 2x x x x  + 2x x x x  - 2x x x ,
                        1 2 3     1 2 3 4     0 2 3 4     0 1 2 3 4     0 1 2 4     0 1 3 4     0 2 3 4     0 1 4
                      
                            4       2 2 2       4           2           2 2       2 2 2    2     2    3 3
                      - 3x x x  + 2x x x  + 3x x x  + 2x x x x x  - 2x x x x  - 4x x x  + x x x x  + x x ,
                          1 2 3     1 2 3     0 2 4     0 1 2 3 4     0 1 3 4     0 2 4    0 1 3 4    0 4
                      
                        2 3           2 2         3         2           2 2         2   2       2     2     3   2
                      2x x x  - 2x x x x  - 2x x x x  - 2x x x x x  + 2x x x x  + 2x x x x  + 2x x x x  - 2x x x ,
                        1 2 3     0 1 2 3     0 1 2 4     0 1 2 3 4     0 2 3 4     0 1 3 4     0 1 2 4     0 3 4
                      
                         3 2          3        2 2      2 3        3        2            2 2 2    3   2
                      - x x x  + x x x x  + x x x x  - x x x  + x x x x  - x x x x x  - x x x  + x x x ,
                         1 2 3    0 1 2 3    0 1 2 4    0 2 4    0 1 3 4    0 1 2 3 4    0 1 4    0 2 4
                      
                         4 2    5         2 2         3 2    2 2 2    2   3
                      - x x  + x x  + 2x x x x  - 2x x x  - x x x  + x x x ,
                         2 3    2 4     0 2 3 4     0 2 4    0 3 4    0 2 4
                      
                        5         4         3             2 2     2     2     2   3
                      2x x  - 2x x x  - 4x x x x  + 4x x x x  + 2x x x x  - 2x x x ,
                        2 3     1 2 4     0 2 3 4     0 1 2 4     0 2 3 4     0 1 4
                      
                          6       4         4           2         2 2 2     2     2    3 3
                      - 3x  + 2x x x  + 7x x x  - 4x x x x x  - 5x x x  + 2x x x x  + x x ,
                          2     1 2 3     0 2 4     0 1 2 3 4     0 2 4     0 1 3 4    0 4
                      
                          5       4           3       2 2         2     2     3   2
                      2x x  - 2x x x  - 4x x x x  + 4x x x x  + 2x x x x  - 2x x x ,
                        1 2     0 2 3     0 1 2 4     0 2 3 4     0 1 2 4     0 3 4
                      
                         2 4      5       2 2       2 3      2 2 2    3   2
                      - x x  + x x  + 2x x x x  - 2x x x  - x x x  + x x x ,
                         1 2    0 2     0 1 2 4     0 2 4    0 1 4    0 2 4
                      
                           3 2      2 3      4        3              2      2 3          2 2    2     2
                      - x x x  + x x x  + x x x  - x x x x  + x x x x x  - x x x  - x x x x  + x x x x ,
                         1 2 3    0 2 3    1 2 4    0 2 3 4    0 1 2 3 4    0 3 4    0 1 2 4    0 2 3 4
                      
                          4         3 2     2 3       2   2         2   2     2     2
                      2x x x  - 2x x x  - 2x x x  + 2x x x x  + 2x x x x  - 2x x x x ,
                        1 2 3     0 2 3     1 2 4     0 2 3 4     0 1 2 4     0 1 3 4
                      
                            5     2 3         4           2 2         3         2           2 2         2   2      2     2    3   2
                      - 3x x  + 2x x x  + 3x x x  - 2x x x x  + 4x x x x  - 2x x x x x  - 4x x x x  + 2x x x x  - x x x x  + x x x ,
                          1 2     1 2 3     0 2 3     0 1 2 3     0 1 2 4     0 1 2 3 4     0 2 3 4     0 1 3 4    0 1 2 4    0 3 4
                      
                        2 4         3       2 2 2       2 2       2             3 2
                      2x x  - 4x x x x  + 2x x x  - 2x x x x  + 4x x x x x  - 2x x x ,
                        1 2     0 1 2 3     0 2 3     0 1 2 4     0 1 2 3 4     0 3 4
                      
                         3 3        4      2 2      2 3        3        2   2      2 2        3
                      - x x  + x x x  + x x x x  - x x x  + x x x x  - x x x x  - x x x x  + x x x x ,
                         1 2    0 1 2    0 1 2 3    0 2 3    0 1 2 4    0 1 2 4    0 1 3 4    0 2 3 4
                      
                             4      5       2 2           3        3 2      2   2
                      - x x x  + x x  + 2x x x x  - 2x x x x  - x x x  + x x x x ,
                         1 2 3    0 3     1 2 3 4     0 2 3 4    1 2 4    0 2 3 4
                      
                          2 3         4       3         2   2         2 2           3       2 2 2             2
                      2x x x  - 2x x x  - 2x x x x  - 2x x x x  + 2x x x x  + 2x x x x  + 2x x x  - 2x x x x x ,
                        1 2 3     0 2 3     1 2 3 4     1 2 3 4     0 2 3 4     0 1 3 4     1 2 4     0 1 2 3 4
                      
                            3 2     2   3       2 3         4       4       2 2           3               2      2 3          2 2    2     2
                      - 3x x x  + 2x x x  + 3x x x  - 2x x x  + 3x x x  - 2x x x x  - 3x x x x  + 3x x x x x  - x x x  - x x x x  + x x x x ,
                          1 2 3     1 2 3     0 2 3     0 1 3     1 2 4     1 2 3 4     0 2 3 4     0 1 2 3 4    0 3 4    0 1 2 4    0 2 3 4
                      
                        2 2 2           3     2 4     2 3           2         2   2
                      2x x x  - 4x x x x  + 2x x  - 2x x x  + 4x x x x x  - 2x x x x ,
                        1 2 3     0 1 2 3     0 3     1 2 4     0 1 2 3 4     0 2 3 4
                      
                         3   2        2 2      2 3    2   3    3 2          3        2          2 2
                      - x x x  + x x x x  + x x x  - x x x  + x x x  - x x x x  - x x x x x  + x x x x ,
                         1 2 3    0 1 2 3    0 1 3    0 2 3    1 2 4    0 1 2 4    0 1 2 3 4    0 2 3 4
                      
                           2 3        4      3        2   2        2 2          3      2 2 2            2
                      - x x x  + x x x  + x x x x  + x x x x  - x x x x  - x x x x  - x x x  + x x x x x ,
                         1 2 3    0 2 3    1 2 3 4    1 2 3 4    0 2 3 4    0 1 3 4    1 2 4    0 1 2 3 4
                      
                          3 2       2 3     2 2               2       3   2       2   2
                      2x x x  - 2x x x  - 4x x x x  + 4x x x x x  + 2x x x  - 2x x x x ,
                        1 2 3     0 2 3     1 2 3 4     0 1 2 3 4     1 2 4     0 1 3 4
                      
                            4       2 2 2       3 2           3     2 3       3               2           2 2      2   2        2   2    2     2
                      - 3x x x  + 2x x x  + 3x x x  - 2x x x x  + 3x x x  - 2x x x x  - 2x x x x x  + 2x x x x  - x x x x  - x x x x  + x x x x ,
                          1 2 3     1 2 3     0 2 3     0 1 2 3     1 2 4     1 2 3 4     0 1 2 3 4     0 1 3 4    0 2 3 4    0 1 2 4    0 1 3 4
                      
                        2 3           2 2     2   3     3 2         2           2   2
                      2x x x  - 4x x x x  + 2x x x  - 2x x x  + 4x x x x x  - 2x x x x ,
                        1 2 3     0 1 2 3     0 2 3     1 2 4     0 1 2 3 4     0 1 3 4
                      
                         3 2          3        2   2    2 2 2    4          2 2        3        2
                      - x x x  + x x x x  + x x x x  - x x x  + x x x  - x x x x  - x x x x  + x x x x x ,
                         1 2 3    0 1 2 3    0 1 2 3    0 2 3    1 2 4    0 1 2 4    0 1 3 4    0 1 2 3 4
                      
                         2   3        4    2 2        2 3          2 2    2     2
                      - x x x  + x x x  + x x x x  - x x x  - x x x x  + x x x x ,
                         1 2 3    0 1 3    1 2 3 4    0 3 4    0 1 2 4    0 2 3 4
                      
                        2 2 2           3     3               2           2 2       2   2         2   2     2     2
                      2x x x  - 2x x x x  - 2x x x x  - 2x x x x x  + 2x x x x  + 2x x x x  + 2x x x x  - 2x x x x ,
                        1 2 3     0 1 2 3     1 2 3 4     0 1 2 3 4     0 1 3 4     0 2 3 4     0 1 2 4     0 1 3 4
                      
                          2 3       3   2         2 2       2 3         3        2           2 2        2   2      2     2    3   2
                      - 3x x x  + 2x x x  + 3x x x x  - 2x x x  + 3x x x x  - x x x x x  - 3x x x x  + x x x x  - x x x x  + x x x ,
                          1 2 3     1 2 3     0 1 2 3     0 1 3     0 1 2 4    0 1 2 3 4     0 2 3 4    0 1 3 4    0 1 2 4    0 3 4
                      
                        3 2         2   2     2   3       2 2       2             3 2
                      2x x x  - 4x x x x  + 2x x x  - 2x x x x  + 4x x x x x  - 2x x x ,
                        1 2 3     0 1 2 3     0 1 3     0 1 2 4     0 1 2 3 4     0 3 4
                      
                         4          2 2        3 2    2     2      3        2   2      2 2        3
                      - x x x  + x x x x  + x x x  - x x x x  + x x x x  - x x x x  - x x x x  + x x x x ,
                         1 2 3    0 1 2 3    0 1 3    0 1 2 3    0 1 2 4    0 1 2 4    0 1 3 4    0 2 3 4
                      
                           3 2      2 3      4        3              2      2 3          2 2    2     2
                      - x x x  + x x x  + x x x  - x x x x  + x x x x x  - x x x  - x x x x  + x x x x ,
                         1 2 3    0 2 3    1 2 4    0 2 3 4    0 1 2 3 4    0 3 4    0 1 2 4    0 2 3 4
                      
                          4         3 2     2 3       2   2         2   2     2     2
                      2x x x  - 2x x x  - 2x x x  + 2x x x x  + 2x x x x  - 2x x x x ,
                        1 2 3     0 2 3     1 2 4     0 2 3 4     0 1 2 4     0 1 3 4
                      
                            5     2 3         4           2 2         3         2           2 2         2   2      2     2    3   2
                      - 3x x  + 2x x x  + 3x x x  - 2x x x x  + 4x x x x  - 2x x x x x  - 4x x x x  + 2x x x x  - x x x x  + x x x ,
                          1 2     1 2 3     0 2 3     0 1 2 3     0 1 2 4     0 1 2 3 4     0 2 3 4     0 1 3 4    0 1 2 4    0 3 4
                      
                        2 4         3       2 2 2       2 2       2             3 2
                      2x x  - 4x x x x  + 2x x x  - 2x x x x  + 4x x x x x  - 2x x x ,
                        1 2     0 1 2 3     0 2 3     0 1 2 4     0 1 2 3 4     0 3 4
                      
                         3 3        4      2 2      2 3        3        2   2      2 2        3
                      - x x  + x x x  + x x x x  - x x x  + x x x x  - x x x x  - x x x x  + x x x x ,
                         1 2    0 1 2    0 1 2 3    0 2 3    0 1 2 4    0 1 2 4    0 1 3 4    0 2 3 4
                      
                         2 2 2           3    2 4    2 3           2        2   2
                      - x x x  + 2x x x x  - x x  + x x x  - 2x x x x x  + x x x x ,
                         1 2 3     0 1 2 3    0 3    1 2 4     0 1 2 3 4    0 2 3 4
                      
                        2 3           2 2     2   3     3 2         2           2   2
                      2x x x  - 4x x x x  + 2x x x  - 2x x x  + 4x x x x x  - 2x x x x ,
                        1 2 3     0 1 2 3     0 2 3     1 2 4     0 1 2 3 4     0 1 3 4
                      
                          2 4     3 2           3         2   2     2 2 2     2   3      2 2       2            3 2
                      - 3x x  + 2x x x  + 6x x x x  - 4x x x x  - 3x x x  + 2x x x  + x x x x  - 2x x x x x  + x x x ,
                          1 2     1 2 3     0 1 2 3     0 1 2 3     0 2 3     0 1 3    0 1 2 4     0 1 2 3 4    0 3 4
                      
                        3 3       2 2       2     2     3 3
                      2x x  - 6x x x x  + 6x x x x  - 2x x ,
                        1 2     0 1 2 3     0 1 2 3     0 3
                      
                         4 2      2 3       3         2   2      2 2 2    3   2
                      - x x  + x x x  + 2x x x x  - 2x x x x  - x x x  + x x x ,
                         1 2    0 1 2     0 1 2 3     0 1 2 3    0 1 3    0 2 3
                      
                         2 4        4     2   2         2 2      2 2 2      3 2
                      - x x  + x x x  + 2x x x x  - 2x x x x  - x x x  + x x x ,
                         1 3    0 2 3     1 2 3 4     0 2 3 4    1 2 4    0 2 4
                      
                        2   3       2 3     2 2           3         3 2             2       3   2         2 2
                      2x x x  - 2x x x  - 2x x x x  + 2x x x x  - 2x x x  + 2x x x x x  + 2x x x  - 2x x x x ,
                        1 2 3     0 2 3     1 2 3 4     0 2 3 4     1 3 4     0 1 2 3 4     1 2 4     0 1 2 4
                      
                          2 2 2       3 2     3 3           3     2 3         4       3               2          2 2      2   2        2   2    2 2 2
                      - 3x x x  + 3x x x  + 2x x  - 2x x x x  + 3x x x  - 3x x x  - 2x x x x  + 2x x x x x  + x x x x  - x x x x  - x x x x  + x x x ,
                          1 2 3     0 2 3     1 3     0 1 2 3     1 2 4     0 2 4     1 2 3 4     0 1 2 3 4    0 1 3 4    0 2 3 4    0 1 2 4    0 2 4
                      
                        3   2         2 2       2 3     2   3     3 2           3         2           2 2
                      2x x x  - 2x x x x  - 2x x x  + 2x x x  - 2x x x  + 2x x x x  + 2x x x x x  - 2x x x x ,
                        1 2 3     0 1 2 3     0 1 3     0 2 3     1 2 4     0 1 2 4     0 1 2 3 4     0 2 3 4
                      
                         4 2       2   2    2 2 2    4           2 2      2 3
                      - x x  + 2x x x x  - x x x  + x x x  - 2x x x x  + x x x ,
                         1 3     0 1 2 3    0 2 3    1 2 4     0 1 2 4    0 2 4
                      
                         2   3      2 3    2 2          3        3 2            2      3   2        2 2
                      - x x x  + x x x  + x x x x  - x x x x  + x x x  - x x x x x  - x x x  + x x x x ,
                         1 2 3    0 2 3    1 2 3 4    0 2 3 4    1 3 4    0 1 2 3 4    1 2 4    0 1 2 4
                      
                        2 2 2       3 2     3               2         4 2       2   2
                      2x x x  - 2x x x  - 4x x x x  + 4x x x x x  + 2x x  - 2x x x x ,
                        1 2 3     0 2 3     1 2 3 4     0 1 2 3 4     1 4     0 1 2 4
                      
                          2 3         4       3   2         2 2     3 2           3       4           2          2 2          3 2    2     2
                      - 3x x x  + 3x x x  + 2x x x  - 2x x x x  + 3x x x  - 3x x x x  - 2x x x  + 3x x x x x  - x x x x  - x x x  + x x x x ,
                          1 2 3     0 2 3     1 2 3     0 1 2 3     1 2 4     0 1 2 4     1 3 4     0 1 2 3 4    0 2 3 4    0 1 4    0 1 2 4
                      
                        3 2           3         2   2     2 2 2     4           2 2         3         2
                      2x x x  - 2x x x x  - 2x x x x  + 2x x x  - 2x x x  + 2x x x x  + 2x x x x  - 2x x x x x ,
                        1 2 3     0 1 2 3     0 1 2 3     0 2 3     1 2 4     0 1 2 4     0 1 3 4     0 1 2 3 4
                      
                         4           2 2      2 3      5         3        2   2
                      - x x x  + 2x x x x  - x x x  + x x  - 2x x x x  + x x x x ,
                         1 2 3     0 1 2 3    0 2 3    1 4     0 1 2 4    0 1 2 4
                      
                         3 3          3    3              2          2 2      2   2        2   2    2 2 2
                      - x x  + x x x x  + x x x x  - x x x x x  + x x x x  - x x x x  - x x x x  + x x x ,
                         1 3    0 1 2 3    1 2 3 4    0 1 2 3 4    0 1 3 4    0 2 3 4    0 1 2 4    0 2 4
                      
                        3   2         2 2     4         2 2           3 2     2     2
                      2x x x  - 2x x x x  - 2x x x  + 2x x x x  + 2x x x  - 2x x x x ,
                        1 2 3     0 1 2 3     1 3 4     0 2 3 4     0 1 4     0 1 2 4
                      
                          3 2           3       4 2       2   2       2 2       2 3        3        2            2 2 2    3   2
                      - 3x x x  + 3x x x x  + 2x x  - 2x x x x  + 3x x x x  - 3x x x  - x x x x  + x x x x x  - x x x  + x x x ,
                          1 2 3     0 1 2 3     1 3     0 1 2 3     0 1 2 4     0 2 4    0 1 3 4    0 1 2 3 4    0 1 4    0 2 4
                      
                        4           2 2         3 2     2     2       3         2   2       2 2         3
                      2x x x  - 2x x x x  - 2x x x  + 2x x x x  - 2x x x x  + 2x x x x  + 2x x x x  - 2x x x x ,
                        1 2 3     0 1 2 3     0 1 3     0 1 2 3     0 1 2 4     0 1 2 4     0 1 3 4     0 2 3 4
                      
                         5         3        2   2        4       2 2        3 2
                      - x x  + 2x x x x  - x x x x  + x x x  - 2x x x x  + x x x ,
                         1 3     0 1 2 3    0 1 2 3    0 1 4     0 1 2 4    0 2 4
                      
                         2 2 2      3 2    2 3        4        2 2      2   2        2   2    2 2 2
                      - x x x  + x x x  + x x x  - x x x  + x x x x  - x x x x  - x x x x  + x x x ,
                         1 2 3    0 2 3    1 2 4    0 2 4    0 1 3 4    0 2 3 4    0 1 2 4    0 2 4
                      
                        2 3         4       3 2           3         2           2 2           3 2     2     2
                      2x x x  - 2x x x  - 2x x x  + 2x x x x  - 2x x x x x  + 2x x x x  + 2x x x  - 2x x x x ,
                        1 2 3     0 2 3     1 2 4     0 1 2 4     0 1 2 3 4     0 2 3 4     0 1 4     0 1 2 4
                      
                          2 4       5     3 2           3         2 2       2 3         3         2            2 2 2    3   2
                      - 3x x  + 3x x  + 2x x x  - 2x x x x  + 4x x x x  - 4x x x  - 2x x x x  + 2x x x x x  - x x x  + x x x ,
                          1 2     0 2     1 2 3     0 1 2 3     0 1 2 4     0 2 4     0 1 3 4     0 1 2 3 4    0 1 4    0 2 4
                      
                        3 3         4       2 2       2 3         3         2   2       2 2         3
                      2x x  - 2x x x  - 2x x x x  + 2x x x  - 2x x x x  + 2x x x x  + 2x x x x  - 2x x x x ,
                        1 2     0 1 2     0 1 2 3     0 2 3     0 1 2 4     0 1 2 4     0 1 3 4     0 2 3 4
                      
                         4 2       2 3    2 4      4       2 2        3 2
                      - x x  + 2x x x  - x x  + x x x  - 2x x x x  + x x x ,
                         1 2     0 1 2    0 2    0 1 4     0 1 2 4    0 2 4
                      
                         3   2        2 2      2 3    2   3    3 2          3        2          2 2
                      - x x x  + x x x x  + x x x  - x x x  + x x x  - x x x x  - x x x x x  + x x x x ,
                         1 2 3    0 1 2 3    0 1 3    0 2 3    1 2 4    0 1 2 4    0 1 2 3 4    0 2 3 4
                      
                        3 2           3         2   2     2 2 2     4           2 2         3         2
                      2x x x  - 2x x x x  - 2x x x x  + 2x x x  - 2x x x  + 2x x x x  + 2x x x x  - 2x x x x x ,
                        1 2 3     0 1 2 3     0 1 2 3     0 2 3     1 2 4     0 1 2 4     0 1 3 4     0 1 2 3 4
                      
                          3 3         4     4          2 2       2 3         3 2     2     2      3        2   2      2 2        3
                      - 3x x  + 3x x x  + 2x x x  + x x x x  - 3x x x  - 2x x x  + 2x x x x  + x x x x  - x x x x  - x x x x  + x x x x ,
                          1 2     0 1 2     1 2 3    0 1 2 3     0 2 3     0 1 3     0 1 2 3    0 1 2 4    0 1 2 4    0 1 3 4    0 2 3 4
                      
                        4 2       2 3       3         2   2       2 2 2     3   2
                      2x x  - 2x x x  - 4x x x x  + 4x x x x  + 2x x x  - 2x x x ,
                        1 2     0 1 2     0 1 2 3     0 1 2 3     0 1 3     0 2 3
                      
                         5         3 2    2   3      4       2 2        3 2
                      - x x  + 2x x x  - x x x  + x x x  - 2x x x x  + x x x
                         1 2     0 1 2    0 1 2    0 1 3     0 1 2 3    0 2 3
                     }

o6 : RationalMap (rational map from PP^4 to PP^149)
i7 : describe segre Phi

o7 = rational map defined by forms of degree 6
     source variety: PP^4
     target variety: PP^149
     coefficient ring: ZZ/65521
i8 : degreeMap segre Phi

o8 = 1
i9 : Psi = multirationalMap {h,h};

o9 : MultirationalMap (rational map from PP^4 to PP^4 x PP^4)
i10 : degreeMap segre Psi

o10 = 2
i11 : projectiveDegrees segre Psi

o11 = {1, 4, 16, 32, 32}

o11 : List

See also