Calculating the first m + 1 partial quotients of the unique positive root of a trinomial axn + bxn-1 + c
We are dealing with polyomial f(x)=axn + bxn-1 + c with integer coefficients, a > 0, c < 0. This will have a unique positive root α which we will assume is greater than 1.
The method of Lagrange (1797) is used to find the the first m + 1 partial quotients of α.
For a program that develops the continued fraction of all real roots of a suitably general polynomial, see CALC.
- Number Theory with Computer Applications, R. Kumanduri and C. Romero, Prentice Hall 1997, page 261
- Elements of Computer Algebra with Applications, A.G. Akritas, Wiley 1989, 333-399.
- Art of computer programming, volume 2, D.E. Knuth, problem 13, Ch. 4.5.3.
- Continued fractions for some algebraic numbers, S. Lang and H. Trotter, J. für Math. 255 (1972) 112-134; Addendum 267 (1974) ibid. 219-220.
- A new proof of Vincent's theorem, A. Alesina, M. Galuzzi, L'Enseignement Math 44 (1988), 219-256.
- An explanation of some exotic continued fractions found by Brillart, H.M. Stark, Computers in number theory, Academic Press 1971, 21-35.
Last modified 21st July 2006
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