From link, (,) with degree d can be factorized as (++)(,) only if line ax+by+c=0 and curve f(x,y) share more than d common points. This applies to the general two-var poloynomail f(x,y).
But what if the y's degree in f(x,y) (such as x^2+xy+1) is restricted to at most 1? My intuition is that only 2 common points is enough for factorization. Can any one give me a proof? Or my intuition is wrong?
For y's degree is at most 0, it degenerates to single-variable polynomial. And it can be easily proved. So I hypotheize it can be generalized to any k smaller than d, where k the y's degree and d is the function degree.
I am asking this as I am dealing with Circle FFT, which results into F(x,y) where y's degree is at most 1.
Much thanks!
