Continued fraction BCMATH programs

1. Euclid's algorithm and the regular 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. Calculating the fraction represented by the simple continued fraction a₀+1/a₁+ ··· +1/a_n.
5. Finding the backward continued fraction of a quadratic irrational.
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 period-length of the simple continued fraction of √d using midpoint criteria.
   • Finding the positive and negative representations 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 (NICF-H) of a quadratic irrational.
8. Finding the nearest integer continued fraction (NICF-P)
   • of a quadratic irrational.
   • of √d over a range of consecutive d.
9. Finding the optimal continued fraction of a quadratic irrational.
   • Finding the optimal continued fraction of √d over a range of consecutive d.
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.
    • Testing a quadratic surd for being NSCF-reduced. This is more elegant than the previous test.
11. Solving the Pell equation x² – dy² = ±1 using midpoint criteria,
    • by the nearest integer continued fraction method (NICF-P).
    • by the nearest square continued fraction method (NSCF).
12. 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).
13. Calculating the quadratic irrationality whose periodic simple continued fraction is given.
14. Producing a quadratic surd equivalent to a given one.
15. Finding the simple continued fraction of
    • the n-th root of a positive rational.
    • the unique positive root of a trinomial axⁿ+ bx + c.
    • the unique positive root of a trinomial axⁿ+ bx^n-1+ c.
    • the unique positive root > 1 of a polynomial with integer coefficients.
16. Finding a Sturm sequence for a squarefree polynomial.
17. Factorising
    • a non-negative unimodular matrix.
    • a non-negative non-singular matrix in the style of George Raney.
    • non-negative non-singular matrix as in Perron's book, Band 1.
18. Guessing the simple continued fraction expansion of log_ba
19. Guessing the simple continued fraction expansion of log_b(a /d)
20. Finding the simple continued fraction of e^p/q.
21. Finding the simple continued fraction of (m/n)e^1/q.

Last modified 2nd January 2021
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