In article <email@example.com>, firstname.lastname@example.org wrote:
> Suppose two unknown polynomials B and A can be written as > > B/A =N where N is a convergent power series which we know. > > and we also know that > > B/A = k/D where D is another polynomial and k is a constant (k and D are also > known). > > Can we then find B and A??
Have you mis-typed something? Your conditions mean that N = k/D where k and D are already polynomials. You could choose B = k and A = D, or multiply both k and D by any polynomial you liked.
For example, if k = 1 and D = x + 1 so N = 1 - x + x^2 - x^3 + .... then you could have B = 1, A = x + 1, or B = x^2 - 7, A = (x + 1)(x^2 - 7), etc. etc.