Struct Ratio 

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

A fraction numer / denom over a EucRing T, kept in reduced form.

Implementations

impl<T> Ratio<T>

pub const fn numer(&self) -> &T

pub const fn denom(&self) -> &T

impl<T> Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

pub fn new(numer: T, denom: T) -> Ratio<T>

pub fn is_int(&self) -> bool

impl<T> Ratio<T>

where T: IntType, for<'x> &'x T: IntOps<T>,

pub fn abs(&self) -> Self

pub fn to_f64(&self) -> f64

Trait Implementations

impl<T> Add for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

type Output = Ratio<T>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<T> Add<&Ratio<T>> for &Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>, Ratio<T>: Clone,

type Output = Ratio<T>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<T> Add<&Ratio<T>> for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

type Output = Ratio<T>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<T> Add<Ratio<T>> for &Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>, Ratio<T>: Clone,

type Output = Ratio<T>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<T> AddAssign for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

fn add_assign(&mut self, rhs: Ratio<T>)

Performs the += operation.

impl<T> AddAssign<&Ratio<T>> for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

fn add_assign(&mut self, rhs: &Ratio<T>)

Performs the += operation.

impl<T> AddGrp for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

impl<T> AddGrpOps for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

impl<T> AddGrpOps<Ratio<T>> for &Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

impl<T> AddMon for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

fn sum<A, I>(itr: I) -> Self

where Self: AddAssign<A>, I: IntoIterator<Item = A>,

Sum an iterator into Self, folding with +=.

impl<T> AddMonOps for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

impl<T> AddMonOps<Ratio<T>> for &Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

impl<T: Clone> Clone for Ratio<T>

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

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<T: Copy> Copy for Ratio<T>

impl<T> Debug for Ratio<T>

where T: Display,

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

Formats the value using the given formatter.

impl<T> Default for Ratio<T>

where T: Default + One,

fn default() -> Self

Returns the “default value” for a type.

impl<T> Display for Ratio<T>

where T: Display,

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

Formats the value using the given formatter.

impl<T> Div for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

type Output = Ratio<T>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<T> Div<&Ratio<T>> for &Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>, Ratio<T>: Clone,

type Output = Ratio<T>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<T> Div<&Ratio<T>> for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

type Output = Ratio<T>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<T> Div<Ratio<T>> for &Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>, Ratio<T>: Clone,

type Output = Ratio<T>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<T> DivAssign for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

fn div_assign(&mut self, rhs: Ratio<T>)

Performs the /= operation.

impl<T> DivAssign<&Ratio<T>> for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

fn div_assign(&mut self, rhs: &Ratio<T>)

Performs the /= operation.

impl<T: Eq> Eq for Ratio<T>

impl<T> EucRing for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

fn divides(&self, y: &Self) -> bool

true iff self divides y (and self ≠ 0).

fn gcd(x: &Self, y: &Self) -> Self

Greatest common divisor, returned in normalized form.

fn gcdx(x: &Self, y: &Self) -> (Self, Self, Self)

Extended gcd: returns (d, s, t) such that d = gcd(x, y) = s·x + t·y, with d normalized.

fn lcm(x: &Self, y: &Self) -> Self

Least common multiple, returned in normalized form.

impl<T> EucRingOps for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

impl<T> EucRingOps<Ratio<T>> for &Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

impl<T> Field for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

impl<T> FieldOps for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

impl<T> FieldOps<Ratio<T>> for &Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

impl<T> From<(T, T)> for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

fn from(pair: (T, T)) -> Self

Converts to this type from the input type.

impl<T> From<T> for Ratio<T>

where T: One,

fn from(a: T) -> Self

Converts to this type from the input type.

impl<T> FromStr for Ratio<T>

where T: EucRing + FromStr, for<'x> &'x T: EucRingOps<T>,

type Err = ParseErr

The associated error which can be returned from parsing.

fn from_str(s: &str) -> Result<Self, Self::Err>

Parses a string s to return a value of this type.

impl<T> MathType for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

fn math_symbol() -> String

impl<T> Mon for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

fn product<A, I>(itr: I) -> Self

where Self: MulAssign<A>, I: IntoIterator<Item = A>,

Multiply an iterator of factors into Self, folding with *=.

impl<T> MonOps for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

impl<T> MonOps<Ratio<T>> for &Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

impl<T> Mul for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

type Output = Ratio<T>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T> Mul<&Ratio<T>> for &Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>, Ratio<T>: Clone,

type Output = Ratio<T>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T> Mul<&Ratio<T>> for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

type Output = Ratio<T>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T> Mul<Ratio<T>> for &Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>, Ratio<T>: Clone,

type Output = Ratio<T>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T> MulAssign for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

fn mul_assign(&mut self, rhs: Ratio<T>)

Performs the *= operation.

impl<T> MulAssign<&Ratio<T>> for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

fn mul_assign(&mut self, rhs: &Ratio<T>)

Performs the *= operation.

impl<T> Neg for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

type Output = Ratio<T>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<T> Neg for &Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

type Output = Ratio<T>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<T> One for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool

Returns true if self is equal to the multiplicative identity.

fn set_one(&mut self)

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

impl<T> Ord for Ratio<T>

where T: IntType, for<'x> &'x T: IntOps<T>,

fn cmp(&self, other: &Self) -> Ordering

This method returns an Ordering between self and other.

fn max(self, other: Self) -> Self

where Self: Sized,

Compares and returns the maximum of two values.

fn min(self, other: Self) -> Self

where Self: Sized,

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

where Self: Sized,

Restrict a value to a certain interval.

impl<T: PartialEq> PartialEq for Ratio<T>

fn eq(&self, other: &Ratio<T>) -> bool

Equality operator ==.

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

Inequality operator !=.

impl<T> PartialOrd for Ratio<T>

where T: IntType, for<'x> &'x T: IntOps<T>,

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

This method returns an ordering between self and other values if one exists.

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<T> Rem for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

type Output = Ratio<T>

The resulting type after applying the % operator.

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

Performs the % operation.

impl<T> Rem<&Ratio<T>> for &Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

type Output = Ratio<T>

The resulting type after applying the % operator.

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

Performs the % operation.

impl<T> Rem<&Ratio<T>> for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

type Output = Ratio<T>

The resulting type after applying the % operator.

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

Performs the % operation.

impl<T> Rem<Ratio<T>> for &Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

type Output = Ratio<T>

The resulting type after applying the % operator.

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

Performs the % operation.

impl<T> RemAssign for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

fn rem_assign(&mut self, rhs: Ratio<T>)

Performs the %= operation.

impl<T> RemAssign<&Ratio<T>> for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

fn rem_assign(&mut self, rhs: &Ratio<T>)

Performs the %= operation.

impl<T> Ring for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

fn inv(&self) -> Option<Self>

Multiplicative inverse, if this element is a unit; otherwise None.

fn is_unit(&self) -> bool

true iff this element is a unit (has a multiplicative inverse).

fn normalizing_unit(&self) -> Self

A unit u such that self * u is the chosen canonical associate of self.

fn c_weight(&self) -> f64

Heuristic cost of working with this element, used by chain-reduction pivot selection. Default: 0.0 for zero, 1.0 otherwise.

fn from_sign(s: Sign) -> Self

+1 if s is positive, -1 otherwise.

fn normalized(&self) -> Self

The canonical associate of self (i.e. self * self.normalizing_unit()).

fn into_normalized(self) -> Self

Like normalized, but consuming.

fn is_pm_one(&self) -> bool

true iff self is +1 or -1.

impl<T> RingOps for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

impl<T> RingOps<Ratio<T>> for &Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

impl<T: PartialEq> StructuralPartialEq for Ratio<T>

impl<T> Sub for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

type Output = Ratio<T>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<T> Sub<&Ratio<T>> for &Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>, Ratio<T>: Clone,

type Output = Ratio<T>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<T> Sub<&Ratio<T>> for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

type Output = Ratio<T>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<T> Sub<Ratio<T>> for &Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>, Ratio<T>: Clone,

type Output = Ratio<T>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<T> SubAssign for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

fn sub_assign(&mut self, rhs: Ratio<T>)

Performs the -= operation.

impl<T> SubAssign<&Ratio<T>> for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<T>,

fn sub_assign(&mut self, rhs: &Ratio<T>)

Performs the -= operation.

impl<T> TeX for Ratio<T>

where T: TeX + MathType,

fn tex_math_symbol() -> String

fn tex_string(&self) -> String

impl<T> Zero for Ratio<T>

where T: EucRing, for<'x> &'x T: EucRingOps<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.