Continued fraction BCMATH programs

1. Euclid's algorithm and the continued fraction expansion of a rational number.
2. The optimal continued fraction (OCF) expansion of a rational number.
3. Nearest integer version of Euclid's algorithm.
4. Guessing the simple continued fraction expansion of log_ba.
5. Calculating the fraction represented by the simple continued fraction a₀+1/a₁+ ··· +1/a_n.
6. Finding the simple continued fraction of a quadratic irrational.
   • Finding the simple continued fraction of √d over a range of consecutive d.
   • Finding the positive and negative representations of the simple continued fraction of a quadratic surd, as far as the end of the first period.
   • Testing a quadratic surd for being RCF-reduced.
7. Finding the nearest integer continued fraction of a quadratic irrational (A. Hurwitz).
8. Finding the nearest integer continued fraction of a quadratic irrational (half regular).
   • Finding the nearest integer continued fraction of √d over a range of consecutive d.
9. Finding the optimal continued fraction of a quadratic irrational.
10. Finding the nearest square continued fraction of a quadratic irrational.
    • Finding the nearest square continued fraction of √d over a range of consecutive d.
    • Testing a quadratic surd for being NSCF-reduced.
11. Finding period-length of the simple continued fraction of √d using midpoint criteria.
12. Solving the Pell equation x² - dy² = ±1 by the nearest integer continued fraction method (NICF-P), using midpoint criteria.
13. Solving the Pell equation x² - dy² = ±1 by the nearest square continued fraction method (NSCF), using midpoint criteria.
14. Solving the diophantine equation x² - xy - (D-1)y²/4 = ±1, using the nearest square continued fraction of (1+√D)/2, D ≡ 1(mod 4).
15. Calculating the quadratic irrationality whose periodic simple continued fraction is given.
16. Finding the simple continued fraction of the n-th root of a positive rational.
17. Finding the simple continued fraction of the unique positive root of a trinomial axⁿ+bx+c.
18. Finding the simple continued fraction of the unique positive root of a trinomial axⁿ+bx^n-1+c.
19. Finding the continued fraction of the unique positive root > 1 of a polynomial with integer coefficients.
20. Finding a Sturm sequence for a squarefree polynomial.
21. Factorising a non-negative unimodular matrix.
22. Factorising a non-negative non-singular matrix.
23. Finding the simple continued fraction of e^p/q.
24. Producing a quadratic surd equivalent to a given one.

Last modified 3th February 2010
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