pell_equation.cpp File Reference

Primary module interface unit for module pell_equation. More...

#include <cassert>
#include <tuple>
#include <vector>
import rational;
import continued_fraction;
import base;

Include dependency graph for pell_equation.cpp:

Functions
template<Integer T>
constexpr std::tuple< T, T >	ntlib::pell_fundamental_solution (T D) noexcept
	Compute the fundamental solution.
template<Integer T>
constexpr std::tuple< T, T >	ntlib::pell_next_solution (T D, const std::tuple< T, T > &initial, const std::tuple< T, T > &current) noexcept
	Generates the next larger solution to Pell's equation.

Detailed Description

Primary module interface unit for module pell_equation.

Function Documentation

pell_fundamental_solution()

template<Integer T>

std::tuple< T, T > ntlib::pell_fundamental_solution ( T D )

nodiscardconstexprexportnoexcept

Compute the fundamental solution.

There are infinitely many integer solutions. The fundamental solution is the one minimal in \(x\) (by absolute value) and therefore also in \(y\).

Template Parameters

T	An integer-like type.

Parameters

D	Parameter \(D \in \mathbb{N}\). Must not be a square number.

Returns

Fundamental solution \((x,y)\).

pell_next_solution()

template<Integer T>

std::tuple< T, T > ntlib::pell_next_solution ( T D, const std::tuple< T, T > & initial, const std::tuple< T, T > & current )

nodiscardconstexprexportnoexcept

Generates the next larger solution to Pell's equation.

Template Parameters

T	An integer like type.

Parameters

D	The parameter \(D\).
initial	The fundamental solution, i.e., the one minimal in x by absolute value.
current	Any solution.

Returns

The next bigger solution than current (in x, by absolute value).