divisors.cpp File Reference

Primary module interface unit for module divisors. More...

#include <algorithm>
#include <cassert>
#include <vector>
import prime_decomposition;
import base;

Include dependency graph for divisors.cpp:

Functions
template<Integer T>
constexpr T	ntlib::count_divisors (const prime_factors< T > &factors) noexcept
	Counts the number of divisors of a given number n.
template<Integer T, Integer Exp>
constexpr T	ntlib::divisor_function (const prime_factors< T > &factors, Exp x) noexcept
	Computes the divisor function for a given number n.
template<Integer T>
constexpr std::vector< T >	ntlib::enumerate_divisors (const prime_factors< T > &factors)
	Enumerates all divisors of a given number n.

Detailed Description

Primary module interface unit for module divisors.

Function Documentation

count_divisors()

template<Integer T>

T ntlib::count_divisors ( const prime_factors< T > & factors )

nodiscardconstexprexportnoexcept

Counts the number of divisors of a given number n.

Template Parameters

T	An integer-like type.

Parameters

factors

The prime decomposition of n.

Returns

The number of divisors of n.

divisor_function()

template<Integer T, Integer Exp>

T ntlib::divisor_function ( const prime_factors< T > & factors, Exp x )

nodiscardconstexprexportnoexcept

Computes the divisor function for a given number n.

The divisor function for n is defined as \(\sigma_x(n) = \sum_{d \mid n} d^x\).

Template Parameters

T	An integer-like type.
Exp	An integer-like type.

Parameters

factors	The prime decomposition of n.
x	The power to which all divisors should be taken. Must be non-negative.

Returns

The value of \(\sigma_x(n)\).

enumerate_divisors()

template<Integer T>

std::vector< T > ntlib::enumerate_divisors ( const prime_factors< T > & factors )

nodiscardconstexprexport

Enumerates all divisors of a given number n.

In particular, this is equal to \(\sigma_0(n)\).

Template Parameters

T	An integer-like type.

Parameters

factors

The prime decomposition of n.

Returns

All divisors of n.