apolar(RingElement,ZZ) -- homogeneous components of the apolar ideal

i1 : F = randomBinaryForm 7

         7       6         5 2       4 3       3 4       2 5         6  
o1 = 810t  + 405t t  + 135t t  + 315t t  + 140t t  + 126t t  + 126t t  +
         0       0 1       0 1       0 1       0 1       0 1       0 1  
     ------------------------------------------------------------------------
         7
     420t
         1

o1 : QQ[t ..t ]
         0   1

i2 : apolar(F,4)

                     4              3                2 2                3  
o2 = ideal(201527032t  - 3753654030t t  - 1695069684t t  + 7318635282t t  -
                     0              0 1              0 1              0 1  
     ------------------------------------------------------------------------
               4
     258009867t )
               1

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

i3 : apolar(F,5)

                  3 2       2 3           4        5        4            2 3
o3 = ideal (47922t t  - 396t t  - 80634t t  + 3005t , 15974t t  - 136818t t 
                  0 1       0 1         0 1        1        0 1          0 1
     ------------------------------------------------------------------------
               4        5       5          2 3            4        5
     + 79479t t  - 1794t , 2282t  - 281340t t  + 176265t t  - 3570t )
             0 1        1       0          0 1          0 1        1

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