Struct Complex 

pub struct Complex { /* private fields */ }

An exact complex number re + im·i, each part a Rational. Because the parts are exact, i·i == −1 and (1+i)(1−i) == 2 hold with no floating error, and the Gaussian rationals are closed under + − × ÷ (every nonzero value has an exact inverse). The magnitude √(re²+im²) is irrational in general — request it as an f64 view via Complex::abs_f64 rather than forcing the exact value inexact.

Complex numbers are NOT ordered, so there is deliberately no Ord/PartialOrd.

Implementations

impl Complex

pub fn new(re: Rational, im: Rational) -> Complex

pub fn from_rational(re: Rational) -> Complex

A real number as re + 0i.

pub fn from_i64(x: i64) -> Complex

pub fn zero() -> Complex

pub fn one() -> Complex

pub fn i() -> Complex

The imaginary unit i (0 + 1i).

pub fn re(&self) -> &Rational

pub fn im(&self) -> &Rational

pub fn is_zero(&self) -> bool

pub fn is_real(&self) -> bool

True when the imaginary part is zero (the value is a plain real).

pub fn conjugate(&self) -> Complex

re − im·i.

pub fn norm_sqr(&self) -> Rational

re² + im² — the squared magnitude, exact (a nonnegative Rational).

pub fn abs_f64(&self) -> f64

The magnitude √(re²+im²) as an f64 (lossy by nature — the exact value is generally irrational). The components stay exact; this is a view.

pub fn negated(&self) -> Complex

pub fn add(&self, other: &Complex) -> Complex

pub fn sub(&self, other: &Complex) -> Complex

pub fn mul(&self, other: &Complex) -> Complex

(a+bi)(c+di) = (ac − bd) + (ad + bc)i.

pub fn recip(&self) -> Option<Complex>

1/self via the conjugate over the squared magnitude — None only for zero.

pub fn div(&self, other: &Complex) -> Option<Complex>

self / other — None when other == 0.

pub fn pow(&self, exp: i32) -> Option<Complex>

self raised to an integer power. Negative exponents take the reciprocal first; None only for zero raised to a negative power. 0^0 == 1.

pub fn parse(s: &str) -> Option<Complex>

Parse "3+4i", "3-4i", "4i", "-i", "i", or a bare real "3" /"1/2". Round-trips the Display form. None on malformed input.

Trait Implementations

impl Clone for Complex

fn clone(&self) -> Complex

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Complex

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

Formats the value using the given formatter.

impl Display for Complex

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

Formats the value using the given formatter.

impl From<Rational> for Complex

fn from(x: Rational) -> Self

Converts to this type from the input type.

impl From<i64> for Complex

fn from(x: i64) -> Self

Converts to this type from the input type.

impl Hash for Complex

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl PartialEq for Complex

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

Tests for self and other values to be equal, and is used by ==.

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

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

impl Eq for Complex

impl StructuralPartialEq for Complex