randomBinaryForm -- random homogeneous polynomial in two variables

i1 : F = randomBinaryForm 5

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

o1 : QQ[t ..t ]
         0   1

i2 : F = randomBinaryForm(5,4,3)

               5              4                3 2              2 3  
o2 = 209884591t  - 1249398325t t  + 2795829750t t  - 2971862250t t  +
               0              0 1              0 1              0 1  
     ------------------------------------------------------------------------
                  4             5
     1613878875t t  - 366993425t
                0 1             1

o2 : QQ[t ..t ]
         0   1

i3 : (realrank F,complexrank F)

o3 = (4, 3)

o3 : Sequence

i4 : F = randomBinaryForm(6,4,4)

                         6                       5    
o4 = 1230199624506159891t  - 5175463851202866480t t  +
                         0                       0 1  
     ------------------------------------------------------------------------
                          4 2                        3 3  
     10338793433232831000t t  - 12367324363544640000t t  +
                          0 1                        0 1  
     ------------------------------------------------------------------------
                         2 4                         5  
     9222909060317400000t t  - 4370569934562783000t t  +
                         0 1                       0 1  
     ------------------------------------------------------------------------
                         6
     1233040823578529525t
                         1

o4 : QQ[t ..t ]
         0   1

i5 : (realrank F,complexrank F)

o5 = (4, 4)

o5 : Sequence