Struct Character 

pub struct Character { /* private fields */ }

Structure to represent algebraic group characters.

Partial orders between characters are based on their complex moduli and phases in the interval $[0, 2\pi)$ with $0$ being the smallest.

Implementations

impl Character

pub fn builder() -> CharacterBuilder

Returns a builder to construct a new character.

Returns

A builder to construct a new character.

pub fn new(ts: &[(UnityRoot, usize)]) -> Self

Constructs a character from an array of unity roots and multiplicities.

Returns

A character.

pub fn threshold(&self) -> f64

Returns the threshold for approximate partial ordering comparisons.

pub fn complex_value(&self) -> Complex<f64>

The complex representation of this character.

Returns

The complex value corresponding to this character.

Panics

Panics when encountering any multiplicity that cannot be converted to f64.

pub fn get_numerical(&self, real_only: bool, precision: usize) -> String

Gets a numerical form for this character, nicely formatted up to a required precision.

Arguments

• precision - The number of decimal places.

Returns

The formatted numerical form.

pub fn simplify(&self) -> Self

Gets the simplified form for this character.

The simplified form gathers terms whose unity roots differ from each other by a factor of $-1$.

Returns

The simplified form of the character.

Panics

Panics when the multiplicity of any unitary root cannot be retrieved.

pub fn complex_conjugate(&self) -> Self

The complex conjugate of this character.

Returns

The complex conjugate of this character.

Panics

Panics when the complex conjugate cannot be found.

Trait Implementations

impl Add for Character

type Output = Character

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add<&Character> for &Character

type Output = Character

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add<&Character> for Character

type Output = Character

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add<Character> for &Character

type Output = Character

The resulting type after applying the + operator.

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

Performs the + operation.

impl Clone for Character

fn clone(&self) -> Character

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Character

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

Prints the full form for this character showing all contributing unity roots and their multiplicities.

impl<'de> Deserialize<'de> for Character

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Display for Character

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

Prints the short form for this character that shows either an integer or an imaginary integer or a compact complex number at 3 d.p.

impl Eq for Character

impl Hash for Character

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 Mul<usize> for &Character

type Output = Character

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<usize> for Character

type Output = Character

The resulting type after applying the * operator.

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

Performs the * operation.

impl MulAssign<usize> for Character

fn mul_assign(&mut self, rhs: usize)

Performs the *= operation.

impl Neg for &Character

type Output = Character

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl Neg for Character

type Output = Character

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl PartialEq for Character

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

Equality operator ==.

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

Inequality operator !=.

impl PartialOrd for Character

fn partial_cmp(&self, other: &Self) -> Option<Ordering>

Two characters are compared based on their constituent unity roots.

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

Tests less than (for self and other) and is used by the < operator.

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

Tests less than or equal to (for self and other) and is used by the <= operator.

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

Tests greater than (for self and other) and is used by the > operator.

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

Tests greater than or equal to (for self and other) and is used by the >= operator.

impl Serialize for Character

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl Sub for Character

type Output = Character

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub<&Character> for &Character

type Output = Character

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub<&Character> for Character

type Output = Character

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub<Character> for &Character

type Output = Character

The resulting type after applying the - operator.

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

Performs the - operation.

impl Zero for Character

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.