polymerist.maths.fractions.continued

Representations and computation methods for continued fractions and ration approximations to real numbers

Attributes

`continuant_matrix`(...)	Homographic matrix for a evaluating the next continuant from a continued fraction coefficient
`continued_fraction_to_continuants`(...)	Fold a sequence of continued fraction coefficients into successive continuants (rational approximations)
`real_to_continued_fraction_coeffs`(→ Generator[int, ...)	Euclidean algorithm on a real number to produce the integral continued fraction coefficients
`extended_euclidean_algorithm`(→ tuple[int, int, int])	Compute the Extended Euclidean Algorithm between two integers "a" and "b"
`rational_approxes`(→ Generator[tuple[int, int], None, None])	Unfold a real number into its continued fraction representation, then generate successive continuants of it
`best_rational_approx`(→ tuple[int, int])	Provide a rational approximation to a value with the smallest denominator that is within some tolerance

polymerist.maths.fractions.continued.continuant_matrix(a: int, int_type: I = DEFAULT_INT_TYPE) → numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[2, 2], int][source]: Homographic matrix for a evaluating the next continuant from a continued fraction coefficient

polymerist.maths.fractions.continued.continued_fraction_to_continuants(coeffs: Iterable[int], int_type: I = DEFAULT_INT_TYPE) → Generator[tuple[int, int], None, None][source]: Fold a sequence of continued fraction coefficients into successive continuants (rational approximations)

polymerist.maths.fractions.continued.real_to_continued_fraction_coeffs(x: Real, eps: float = DEFAULT_EPS, int_type: I = DEFAULT_INT_TYPE) → Generator[int, None, None][source]: Euclidean algorithm on a real number to produce the integral continued fraction coefficients

polymerist.maths.fractions.continued.extended_euclidean_algorithm(a: int, b: int, int_type: I = DEFAULT_INT_TYPE) → tuple[int, int, int][source]: Compute the Extended Euclidean Algorithm between two integers “a” and “b” Returns the greatest common divisor of a and b, along with a pair of Bezout coefficients”x” and “y” which satisfy a*x + b*y = gcd(a, b)

polymerist.maths.fractions.continued.rational_approxes(x: Real, tol: float = DEFAULT_TOL, eps: float = DEFAULT_EPS) → Generator[tuple[int, int], None, None][source]: Unfold a real number into its continued fraction representation, then generate successive continuants of it

polymerist.maths.fractions.continued.best_rational_approx(x: Real, tol: float = DEFAULT_TOL, eps: float = DEFAULT_EPS) → tuple[int, int][source]: Provide a rational approximation to a value with the smallest denominator that is within some tolerance