continued_fraction.cpp File Reference

Primary module interface unit for module continued_fraction. More...

#include <vector>
import rational;
import base;

Include dependency graph for continued_fraction.cpp:

Functions
template<Integer T>
std::vector< T >	ntlib::quadratic_irrational_cf (const T &n)
	Continued fraction representation for a quadratic irrational.
template<Integer T>
rational< T >	ntlib::nth_convergent_quadratic_irrational_cf (std::size_t n, const std::vector< T > &cf)

Detailed Description

Primary module interface unit for module continued_fraction.

Function Documentation

nth_convergent_quadratic_irrational_cf()

template<Integer T>

rational< T > ntlib::nth_convergent_quadratic_irrational_cf ( std::size_t n, const std::vector< T > & cf )

export

Computes the n-th convergent of the regular, periodic continued fraction for a quadratic irrational.

Algorithm from: http://mathworld.wolfram.com/PellEquation.html

Parameters

n	The n-th convergent is calculated.
cf	The continued fraction representation of the quadratic irrational.

Returns

The numerator and denominator of the n-th convergent.

quadratic_irrational_cf()

template<Integer T>

std::vector< T > ntlib::quadratic_irrational_cf ( const T & n )

export

Continued fraction representation for a quadratic irrational.

Let \(n\) be a non-square natural number. This function template computes the continued fraction representation of \(\sqrt{n}\).

For non-squares (and only these) the continued fraction is regular and periodic.

Template Parameters

T	An integer-like type.

Parameters

n	The number n. Must not be a perfect square.

Returns

The regular, periodic continued fraction representing sqrt(n). The first position gives the whole number part, the second until the last one form the period.