Trait ComplexSubset

pub trait ComplexSubset:
    PartialEq
    + Clone
    + Semiring {
    type Real: Real + ComplexSubset<Natural = Self::Natural, Integer = Self::Integer, Real = Self::Real>;
    type Natural: Natural + IntegerSubset<Signed = Self::Integer, Unsigned = Self::Natural> + ComplexSubset<Natural = Self::Natural, Integer = Self::Integer, Real = Self::Real>;
    type Integer: Integer + IntegerSubset<Signed = Self::Integer, Unsigned = Self::Natural> + ComplexSubset<Natural = Self::Natural, Integer = Self::Integer, Real = Self::Real>;

    // Required methods
    fn as_real(self) -> Self::Real;
    fn as_natural(self) -> Self::Natural;
    fn as_integer(self) -> Self::Integer;
    fn floor(self) -> Self;
    fn ceil(self) -> Self;
    fn round(self) -> Self;
    fn trunc(self) -> Self;
    fn fract(self) -> Self;
    fn im(self) -> Self;
    fn re(self) -> Self;
    fn conj(self) -> Self;

    // Provided methods
    fn modulus_sqrd(self) -> Self { ... }
    fn modulus(self) -> Self::Real { ... }
}

An algebraic stucture that is a subset of the Complex numbers

This trait is both meant as an ensapsulation of the naturals, integers, real numbers, and complex numbers. This way, users can work with a particular set of similar-precision numeric types abstractly similarly to how they would normally.

Required Associated Types

type Real: Real + ComplexSubset<Natural = Self::Natural, Integer = Self::Integer, Real = Self::Real>

type Natural: Natural + IntegerSubset<Signed = Self::Integer, Unsigned = Self::Natural> + ComplexSubset<Natural = Self::Natural, Integer = Self::Integer, Real = Self::Real>

type Integer: Integer + IntegerSubset<Signed = Self::Integer, Unsigned = Self::Natural> + ComplexSubset<Natural = Self::Natural, Integer = Self::Integer, Real = Self::Real>

Required Methods

fn as_real(self) -> Self::Real

Converts self to a real number, discarding any imaginary component, if complex.

fn as_natural(self) -> Self::Natural

Converts self to a natural number, truncating when necessary.

fn as_integer(self) -> Self::Integer

Converts self to an integer, truncating when necessary.

fn floor(self) -> Self

Rounds the real and imaginary components of self to the closest integer downward

fn ceil(self) -> Self

Rounds the real and imaginary components of self to the closest integer upward

fn round(self) -> Self

Rounds the real and imaginary components of self to the closest integer

fn trunc(self) -> Self

Rounds the real and imaginary components of self by removing the factional parts

fn fract(self) -> Self

Removes the integral parts of the real and imaginary components of self

fn im(self) -> Self

Sets the real component of self to 0

fn re(self) -> Self

Sets the imaginary component of self to 0

fn conj(self) -> Self

The complex conjugate of self

Provided Methods

fn modulus_sqrd(self) -> Self

The square of the complex absolute value of self

This is computed as self * self.conj() by default

fn modulus(self) -> Self::Real

The complex absolute value of self

This is computed as the square root of modulus_sqrd by default

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementations on Foreign Types

impl ComplexSubset for f32

type Real = f32

type Natural = u32

type Integer = i32

fn as_real(self) -> Self::Real

fn as_natural(self) -> Self::Natural

fn as_integer(self) -> Self::Integer

fn floor(self) -> Self

fn ceil(self) -> Self

fn round(self) -> Self

fn trunc(self) -> Self

fn fract(self) -> Self

fn im(self) -> Self

fn re(self) -> Self

fn conj(self) -> Self

fn modulus_sqrd(self) -> Self

fn modulus(self) -> Self::Real

impl ComplexSubset for f64

type Real = f64

type Natural = u64

type Integer = i64

fn as_real(self) -> Self::Real

fn as_natural(self) -> Self::Natural

fn as_integer(self) -> Self::Integer

fn floor(self) -> Self

fn ceil(self) -> Self

fn round(self) -> Self

fn trunc(self) -> Self

fn fract(self) -> Self

fn im(self) -> Self

fn re(self) -> Self

fn conj(self) -> Self

fn modulus_sqrd(self) -> Self

fn modulus(self) -> Self::Real

impl ComplexSubset for i32

type Real = f32

type Natural = u32

type Integer = i32

fn as_real(self) -> Self::Real

fn as_natural(self) -> Self::Natural

fn as_integer(self) -> Self::Integer

fn floor(self) -> Self

fn ceil(self) -> Self

fn round(self) -> Self

fn trunc(self) -> Self

fn fract(self) -> Self

fn im(self) -> Self

fn re(self) -> Self

fn conj(self) -> Self

fn modulus_sqrd(self) -> Self

fn modulus(self) -> Self::Real

impl ComplexSubset for i64

type Real = f64

type Natural = u64

type Integer = i64

fn as_real(self) -> Self::Real

fn as_natural(self) -> Self::Natural

fn as_integer(self) -> Self::Integer

fn floor(self) -> Self

fn ceil(self) -> Self

fn round(self) -> Self

fn trunc(self) -> Self

fn fract(self) -> Self

fn im(self) -> Self

fn re(self) -> Self

fn conj(self) -> Self

fn modulus_sqrd(self) -> Self

fn modulus(self) -> Self::Real

impl ComplexSubset for u32

type Real = f32

type Natural = u32

type Integer = i32

fn as_real(self) -> Self::Real

fn as_natural(self) -> Self::Natural

fn as_integer(self) -> Self::Integer

fn floor(self) -> Self

fn ceil(self) -> Self

fn round(self) -> Self

fn trunc(self) -> Self

fn fract(self) -> Self

fn im(self) -> Self

fn re(self) -> Self

fn conj(self) -> Self

fn modulus_sqrd(self) -> Self

fn modulus(self) -> Self::Real

impl ComplexSubset for u64

type Real = f64

type Natural = u64

type Integer = i64

fn as_real(self) -> Self::Real

fn as_natural(self) -> Self::Natural

fn as_integer(self) -> Self::Integer

fn floor(self) -> Self

fn ceil(self) -> Self

fn round(self) -> Self

fn trunc(self) -> Self

fn fract(self) -> Self

fn im(self) -> Self

fn re(self) -> Self

fn conj(self) -> Self

fn modulus_sqrd(self) -> Self

fn modulus(self) -> Self::Real

Implementors