Struct QuadraticInt 

pub struct QuadraticInt<T> { /* private fields */ }

Quadratic integer a + bω, where ω is √D or (1+√D)/2, based on QuadraticIntCoeffs

The different between QuadraticInt and QuadraticSurd is that the operations for the latter will be in normal fields of real numbers or complex numbers, while the operations for the former will be in the quadratic field (specifically in the quadratic integer ring ℤ[ω]). Therefore, the arithmetic operations between QuadraticInts can only be performed with equivalent bases (e.g. √18=3√2 is compatible with √2). However for QuadraticSurd, you can mix the number with different bases if they are both pure quadratic numbers, such as √2 * √3 = √6.

Implementations

impl<T: QuadraticBase> QuadraticInt<T>

where for<'r> &'r T: RefNum<T>,

pub fn new(a: T, b: T, r: T) -> Self

Create a quadratic integer from a + b√r, where a, b, r are all integers

pub fn from_coeffs(coeffs: QuadraticIntCoeffs<T>, discr: T) -> Self

Create a quadratic integer a + bω, where ω is √D or (1+√D)/2.

Panics

• If the discriminant is negative and feature “complex” is not enabled
• The discriminant is congruent to 0 modulo 4

pub fn conj(self) -> Self

pub fn norm(self) -> T

pub fn is_rational(&self) -> bool

pub fn is_pure(&self) -> bool

Trait Implementations

impl<T: Add<Output = T>> Add<T> for QuadraticInt<T>

type Output = QuadraticInt<T>

The resulting type after applying the + operator.

fn add(self, rhs: T) -> Self::Output

Performs the + operation.

impl<T: QuadraticBase> Add for QuadraticInt<T>

where for<'r> &'r T: RefNum<T>,

type Output = QuadraticInt<T>

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self::Output

Performs the + operation.

impl<T: Clone> Clone for QuadraticInt<T>

fn clone(&self) -> QuadraticInt<T>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<T: Debug> Debug for QuadraticInt<T>

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

Formats the value using the given formatter.

impl<T: QuadraticBase> Div<T> for QuadraticInt<T>

where for<'r> &'r T: RefNum<T>,

type Output = QuadraticInt<T>

The resulting type after applying the / operator.

fn div(self, rhs: T) -> Self::Output

Performs the / operation.

impl<T: QuadraticBase> Div for QuadraticInt<T>

where for<'r> &'r T: RefNum<T>,

type Output = QuadraticInt<T>

The resulting type after applying the / operator.

fn div(self, rhs: Self) -> Self::Output

Performs the / operation.

impl<T: QuadraticBase> Mul<T> for QuadraticInt<T>

where for<'r> &'r T: RefNum<T>,

type Output = QuadraticInt<T>

The resulting type after applying the * operator.

fn mul(self, rhs: T) -> Self::Output

Performs the * operation.

impl<T: QuadraticBase> Mul for QuadraticInt<T>

where for<'r> &'r T: RefNum<T>,

type Output = QuadraticInt<T>

The resulting type after applying the * operator.

fn mul(self, rhs: Self) -> Self::Output

Performs the * operation.

impl<T: Neg<Output = T>> Neg for QuadraticInt<T>

type Output = QuadraticInt<T>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<T: QuadraticBase> One for QuadraticInt<T>

where for<'r> &'r T: RefNum<T>,

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool

where Self: PartialEq,

Returns true if self is equal to the multiplicative identity.

impl<T: QuadraticBase> PartialEq for QuadraticInt<T>

where for<'r> &'r T: RefNum<T>,

fn eq(&self, other: &Self) -> 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<T: QuadraticBase> Rem<T> for QuadraticInt<T>

where for<'r> &'r T: RefNum<T>,

type Output = QuadraticInt<T>

The resulting type after applying the % operator.

fn rem(self, rhs: T) -> Self::Output

Performs the % operation.

impl<T: QuadraticBase> Rem for QuadraticInt<T>

where for<'r> &'r T: RefNum<T>,

type Output = QuadraticInt<T>

The resulting type after applying the % operator.

fn rem(self, rhs: Self) -> Self::Output

Performs the % operation.

impl<T: Sub<Output = T>> Sub<T> for QuadraticInt<T>

type Output = QuadraticInt<T>

The resulting type after applying the - operator.

fn sub(self, rhs: T) -> Self::Output

Performs the - operation.

impl<T: QuadraticBase> Sub for QuadraticInt<T>

where for<'r> &'r T: RefNum<T>,

type Output = QuadraticInt<T>

The resulting type after applying the - operator.

fn sub(self, rhs: Self) -> Self::Output

Performs the - operation.

impl<T: QuadraticBase> Zero for QuadraticInt<T>

where for<'r> &'r T: RefNum<T>,

fn zero() -> Self

Returns the additive identity element of Self, 0.

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.

impl<T: Copy> Copy for QuadraticInt<T>

impl<T: QuadraticBase> Eq for QuadraticInt<T>

where for<'r> &'r T: RefNum<T>,