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;
7. Finding the nearest integer continued fraction of a quadratic irrational (A. Huwitz);
8. Finding the nearest integer continued fraction of a quadratic irrational (half regular);
9. Finding the optimal continued fraction of a quadratic irrational;
10. Finding the nearest square continued fraction of a quadratic irrational;
11. Selenius' algorithm for converting the regular continued fraction to the nearest square continued fraction;
12. An algorithm for converting the regular continued fraction to the nearest integer continued fraction;
13. Finding period-length of the simple continued fraction of √d;
14. Calculating the quadratic irrationality whose simple continued fraction is given;
15. Finding the simple continued fraction of the n-th root of a positive rational;
16. Finding the simple continued fraction of the unique positive root of a trinomial axⁿ+bx+c;
17. Finding the simple continued fraction of the unique positive root of a trinomial axⁿ+bx^n-1+c;
18. Finding the continued fraction of the unique positive root > 1 of a polynomial with integer coefficients;
19. Finding a Sturm sequence for a squarefree polynomial;
20. Factorising a non-negative unimodular matrix;
21. Factorising a non-negative non-singular matrix;
22. Finding the simple continued fraction of e^p/q.

Last modified 28th April 2008
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