Struct libbgs::numbers::Factorization

pub struct Factorization { /* private fields */ }

A prime power decomposition of a positive integer.

Implementations

impl Factorization

pub const fn new(factors: &'static [(u128, usize)]) -> Factorization

Creates a new factorization from the given prime powers.

pub fn maximal_divisors<const L: usize>( &self, l: u128 ) -> impl Iterator<Item = [usize; L]>

Returns an Iterator yielding the maximal divisors of the number represented by this Factorization below l; that is, if this Factorization represents the number $n$, then this Iterator yields vectors representing all elements $d$ satisfying these properties:

• $d | n$,
• $d \leq l$, and
• there are no elements $k | n$ such that $d | k$ and $k \leq l$.

The iterator cannot outlive the Factorization, although the vectors yielded by it may.

pub const fn is_empty(&self) -> bool

True if there the factorization represents 1. False otherwise.

pub const fn factor(&self, i: usize) -> u128

Returns the prime power factor represented by prime number i, $p_i^{t_i}$. This method will panic if i is out of bounds.

pub const fn factors(&self) -> &'static [(u128, usize)]

Gets the prime powers as an array. The first element of each entry is the prime, and the second is the power.

pub const fn value(&self) -> u128

Returns the positive integer represented by this Factorization.

pub fn from_powers(&self, ds: &[usize]) -> u128

Converts an array of powers on the prime factors into an integer.

pub fn exponents(&self) -> Box<[usize]>

Returns the exponents on the factorization.

pub const fn len(&self) -> usize

Returns the number of prime factors in the factorization.

pub const fn tau(&self) -> u128

Returns $\tau$(&self), the number of divisors of this integer. See OEIS sequence A000005.

pub const fn phi(&self) -> u128

Returns $\phi$(&self), the Euler totient function of this integer. The totient function $\phi(n)$ is the number of integers $\leq n$ and relatively prime to $n$. See OEIS sequence A000010.

Trait Implementations

impl Clone for Factorization

fn clone(&self) -> Factorization

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for Factorization

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Index<usize> for Factorization

type Output = (u128, usize)

The returned type after indexing.

fn index(&self, index: usize) -> &(u128, usize)

Performs the indexing (container[index]) operation.

impl PartialEq<Factorization> for Factorization

fn eq(&self, other: &Factorization) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Eq for Factorization

impl StructuralEq for Factorization

impl StructuralPartialEq for Factorization