Calculating the first m+1 partial quotients of the n-th root of a positive rational using Lagrange's method

The method of Lagrange (1797) is used to find the the first m+1 partial quotients of (b/c)1/n, b ≥ 1, c ≥ 1, b ≠ c.
We apply the algorithm for finding the continued fraction of the unique real root > 1 of a polynomial f(x) ∈ Z[x] to the case where f(x) = cxn - b if b/c > 1, f(x) = bxn - c if b/c < 1.

References

  1. Number Theory with Computer Applications, R. Kumanduri and C. Romero, Prentice Hall 1997, page 261
  2. Elements of Computer Algebra with Applications, A.G. Akritas, Wiley 1989, 333-399.
  3. Art of computer programming, volume 2, D.E. Knuth, problem 13, Ch. 4.5.3.
  4. Continued fractions for some algebraic numbers, S. Lang and H. Trotter, J. für Math. 255 (1972) 112-134; Addendum 267 (1974) ibid. 219-220.
  5. A new proof of Vincent's theorem, A. Alesina, M. Galuzzi, L'Enseignement Math 44 (1988), 219-256.
For a program that develops the continued fraction of all real roots of a suitably general polynomial, see CALC.

Enter b (≥ 1):
Enter c (≥ 1, c ≠ b):
Enter n (1 < n ≤ 100):
Enter m (0 ≤ m < 1000):

Last modified 30th June 2006
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