Struct padic::Ratio

pub struct Ratio {
    pub numer: u64,
    pub denom: u64,
    pub sign: i64,
}

Rational number struct with numerator, denominator and sign.

Fields

numer: u64

Numerator

denom: u64

Denominator

sign: i64

Sign (-1 or +1)

Implementations

impl Ratio

pub fn new(n: i64, d: i64) -> Ratio

Returns a ratio with numerator and denominator reduced to lowest terms.

Arguments

• num - A signed integer numerator.
• denom - A signed integer denominator.

Example

use padic::Ratio;
let r = Ratio::new(2, 4);
assert_eq!(r.num, 1);

pub fn add(&self, b: Ratio) -> Ratio

Returns the sum of two rational numbers

Arguments

• b - Another ratio.

Examples

use padic::Ratio;
let a = Ratio::new(-2, 5);
let b = Ratio::new(3, 5);
assert_eq!(a.add(b), Ratio::new(1, 5));

pub fn mul(&self, b: Ratio) -> Ratio

Returns the multiplication of two rational numbers

Arguments

• b - Another ratio.

Examples

use padic::Ratio;
let a = Ratio::new(-2, 5);
let b = Ratio::new(3, 5);
assert_eq!(a.mul(b), Ratio::new(-6, 25));

pub fn prime_factors(&self) -> Vec<(u64, i64)>

Returns the prime factors with multiplicity of the ratio.

Examples

use padic::Ratio;
let r = Ratio::new(2, 15);
assert_eq!(r.prime_factors(), vec![(2, 1), (3, -1), (5, -1)]);

pub fn to_float(&self) -> f64

Returns the float representation of the ratio.

Examples

use padic::Ratio;
let r = Ratio::new(2, 4);
assert_eq!(r.to_float(), 0.5);

pub fn to_string(&self) -> String

Returns the string representation of the ratio.

Examples

use padic::Ratio;
let r = Ratio::new(2, -4);
assert_eq!(r.to_string(), "-1/2");

pub fn padic_valuation(&self, prime: u64) -> i64

Returns the p-adic valuation of the ratio.

Examples

use padic::Ratio;
let r = Ratio::new(71, 9);
assert_eq!(r.padic_valuation(3), -2);

pub fn padic_absolute(&self, prime: u64) -> Ratio

Returns the p-adic absolute value of the ratio.

Examples

use padic::Ratio;
let r = Ratio::new(71, 9);
assert_eq!(r.padic_absolute(3), Ratio::new(9, 1));

pub fn to_padic(&self, prime: u64, precision: u64) -> Padic

Convert the ratio into a p-adic number.

Info: https://math.stackexchange.com/a/1187037

Arguments

• prime - A prime number.
• precision - A positive integer.

Examples

3-adic expansion of 2/5 with precision of 5 -> 1,1,2,1,0

• +2/5 = 1 - 3 * 1/5
• -1/5 = 1 - 3 * 2/5
• -2/5 = 2 - 3 * 4/5
• -4/5 = 1 - 3 * 3/5
• -3/5 = 0 - 3 * 1/5

use padic::Ratio;
let r = Ratio::new(2, 5);
let p = r.to_padic(3, 5);
assert_eq!(p.expansion, vec![1, 1, 2, 1, 0]);

pub fn next_digit(&self, prime: u64) -> (u64, Ratio)

Returns the next digit of the p-adic expansion.

Arguments

• prime - A prime number.

use padic::Ratio;
let a = Ratio::new(2, 5);
assert_eq!(a.next_digit(3), (1, Ratio::new(-1, 5)));

Trait Implementations

impl Clone for Ratio

fn clone(&self) -> Ratio

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for Ratio

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

Formats the value using the given formatter.

impl Display for Ratio

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

Formats the value using the given formatter.

impl PartialEq<Ratio> for Ratio

fn eq(&self, other: &Ratio) -> 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 StructuralPartialEq for Ratio