recover -- recover the binary form from its apolar ideal

i1 : F = randomBinaryForm 7

        7     6       5 2     4 3     3 4     2 5       6     7
o1 = 18t  + 2t t  + 9t t  + 2t t  + 4t t  + 3t t  + 6t t  + 3t
        0     0 1     0 1     0 1     0 1     0 1     0 1     1

o1 : QQ[t ..t ]
         0   1

i2 : I = apolar F

                  4          3             2 2             3          4 
o2 = ideal (75621t  + 740842t t  - 3587636t t  - 2099787t t  + 741116t ,
                  0          0 1           0 1           0 1          1 
     ------------------------------------------------------------------------
          3 2        2 3          4        5
     1355t t  - 5785t t  - 3840t t  + 1321t )
          0 1        0 1        0 1        1

o2 : Ideal of QQ[t ..t ]
                  0   1

i3 : I5 = apolar(F,5)

                 3 2        2 3          4        5       4          2 3  
o3 = ideal (1355t t  - 5785t t  - 3840t t  + 1321t , 1355t t  - 7610t t  -
                 0 1        0 1        0 1        1       0 1        0 1  
     ------------------------------------------------------------------------
         4       5      5         2 3           4         5
     5t t  + 338t , 271t  - 47505t t  - 33770t t  + 11872t )
       0 1       1      0         0 1         0 1         1

o3 : Ideal of QQ[t ..t ]
                  0   1

i4 : recover I

        7     6       5 2     4 3     3 4     2 5       6     7
o4 = 18t  + 2t t  + 9t t  + 2t t  + 4t t  + 3t t  + 6t t  + 3t
        0     0 1     0 1     0 1     0 1     0 1     0 1     1

o4 : QQ[t ..t ]
         0   1

i5 : recover I5

        7     6       5 2     4 3     3 4     2 5       6     7
o5 = 18t  + 2t t  + 9t t  + 2t t  + 4t t  + 3t t  + 6t t  + 3t
        0     0 1     0 1     0 1     0 1     0 1     0 1     1

o5 : QQ[t ..t ]
         0   1