Trait malachite_base::num::arithmetic::traits::JacobiSymbol

pub trait JacobiSymbol<RHS = Self> {
    // Required method
    fn jacobi_symbol(self, other: RHS) -> i8;
}

Calculates the Jacobi symbol of two numbers.

Required Methods

fn jacobi_symbol(self, other: RHS) -> i8

Implementations on Foreign Types

impl JacobiSymbol for i8

fn jacobi_symbol(self, n: i8) -> i8

Computes the Jacobi symbol of two numbers.

$$ f(x, y) = \left ( \frac{x}{y} \right ). $$

Worst-case complexity

$T(n) = O(n^2)$

$M(n) = O(n)$

where $T$ is time, $M$ is additional memory, and $n$ is max(self.significant_bits(), other.significant_bits()).

Panics

Panics if n is even.

Examples

See here.

impl JacobiSymbol for i16

fn jacobi_symbol(self, n: i16) -> i8

Computes the Jacobi symbol of two numbers.

$$ f(x, y) = \left ( \frac{x}{y} \right ). $$

Worst-case complexity

$T(n) = O(n^2)$

$M(n) = O(n)$

where $T$ is time, $M$ is additional memory, and $n$ is max(self.significant_bits(), other.significant_bits()).

Panics

Panics if n is even.

Examples

See here.

impl JacobiSymbol for i32

fn jacobi_symbol(self, n: i32) -> i8

Computes the Jacobi symbol of two numbers.

$$ f(x, y) = \left ( \frac{x}{y} \right ). $$

Worst-case complexity

$T(n) = O(n^2)$

$M(n) = O(n)$

where $T$ is time, $M$ is additional memory, and $n$ is max(self.significant_bits(), other.significant_bits()).

Panics

Panics if n is even.

Examples

See here.

impl JacobiSymbol for i64

fn jacobi_symbol(self, n: i64) -> i8

Computes the Jacobi symbol of two numbers.

$$ f(x, y) = \left ( \frac{x}{y} \right ). $$

Worst-case complexity

$T(n) = O(n^2)$

$M(n) = O(n)$

where $T$ is time, $M$ is additional memory, and $n$ is max(self.significant_bits(), other.significant_bits()).

Panics

Panics if n is even.

Examples

See here.

impl JacobiSymbol for i128

fn jacobi_symbol(self, n: i128) -> i8

Computes the Jacobi symbol of two numbers.

$$ f(x, y) = \left ( \frac{x}{y} \right ). $$

Worst-case complexity

$T(n) = O(n^2)$

$M(n) = O(n)$

where $T$ is time, $M$ is additional memory, and $n$ is max(self.significant_bits(), other.significant_bits()).

Panics

Panics if n is even.

Examples

See here.

impl JacobiSymbol for isize

fn jacobi_symbol(self, n: isize) -> i8

Computes the Jacobi symbol of two numbers.

$$ f(x, y) = \left ( \frac{x}{y} \right ). $$

Worst-case complexity

$T(n) = O(n^2)$

$M(n) = O(n)$

where $T$ is time, $M$ is additional memory, and $n$ is max(self.significant_bits(), other.significant_bits()).

Panics

Panics if n is even.

Examples

See here.

impl JacobiSymbol for u8

Computes the Jacobi symbol of two numbers.

$$ f(x, y) = \left ( \frac{x}{y} \right ). $$

Worst-case complexity

$T(n) = O(n^2)$

$M(n) = O(n)$

where $T$ is time, $M$ is additional memory, and $n$ is max(self.significant_bits(), other.significant_bits()).

Panics

Panics if n is even or negative.

Examples

See here.

fn jacobi_symbol(self, n: u8) -> i8

impl JacobiSymbol for u16

Computes the Jacobi symbol of two numbers.

$$ f(x, y) = \left ( \frac{x}{y} \right ). $$

Worst-case complexity

$T(n) = O(n^2)$

$M(n) = O(n)$

where $T$ is time, $M$ is additional memory, and $n$ is max(self.significant_bits(), other.significant_bits()).

Panics

Panics if n is even or negative.

Examples

See here.

fn jacobi_symbol(self, n: u16) -> i8

impl JacobiSymbol for u32

Computes the Jacobi symbol of two numbers.

$$ f(x, y) = \left ( \frac{x}{y} \right ). $$

Worst-case complexity

$T(n) = O(n^2)$

$M(n) = O(n)$

where $T$ is time, $M$ is additional memory, and $n$ is max(self.significant_bits(), other.significant_bits()).

Panics

Panics if n is even or negative.

Examples

See here.

fn jacobi_symbol(self, n: u32) -> i8

impl JacobiSymbol for u64

Computes the Jacobi symbol of two numbers.

$$ f(x, y) = \left ( \frac{x}{y} \right ). $$

Worst-case complexity

$T(n) = O(n^2)$

$M(n) = O(n)$

where $T$ is time, $M$ is additional memory, and $n$ is max(self.significant_bits(), other.significant_bits()).

Panics

Panics if n is even or negative.

Examples

See here.

fn jacobi_symbol(self, n: u64) -> i8

impl JacobiSymbol for u128

fn jacobi_symbol(self, n: u128) -> i8

Computes the Jacobi symbol of two u128s.

$$ f(x, y) = \left ( \frac{x}{y} \right ). $$

Worst-case complexity

$T(n) = O(n^2)$

$M(n) = O(n)$

where $T$ is time, $M$ is additional memory, and $n$ is max(self.significant_bits(), other.significant_bits()).

Examples

See here.

impl JacobiSymbol for usize

Computes the Jacobi symbol of two numbers.

$$ f(x, y) = \left ( \frac{x}{y} \right ). $$

Worst-case complexity

$T(n) = O(n^2)$

$M(n) = O(n)$

where $T$ is time, $M$ is additional memory, and $n$ is max(self.significant_bits(), other.significant_bits()).

Panics

Panics if n is even or negative.

Examples

See here.

fn jacobi_symbol(self, n: usize) -> i8

Implementors