Struct algebraics::polynomial::Polynomial

pub struct Polynomial<T: PolynomialCoefficient> { /* fields omitted */ }

A single-variable polynomial.

the term at index n is self.coefficients()[n] * pow(x, n)

Invariants

self.coefficients().last() is either None or Some(v) where !v.is_zero()

Methods

impl<T: PolynomialCoefficient> Polynomial<T>

pub fn checked_pseudo_div_rem(self, rhs: &Self) -> Option<PseudoDivRem<T>>

pub fn pseudo_div_rem(self, rhs: &Self) -> PseudoDivRem<T>

pub fn exact_pseudo_div(self, rhs: &Self) -> (Polynomial<T>, T)

pub fn checked_exact_pseudo_div(self, rhs: &Self) -> Option<(Polynomial<T>, T)>

impl<T: PolynomialCoefficient + for<'a> ExactDiv<&'a T, Output = T>> Polynomial<T>

pub fn checked_div_rem(self, rhs: &Self) -> Option<(Self, Self)>

pub fn div_rem(self, rhs: &Self) -> (Self, Self)

impl<T: PolynomialDivSupported> Polynomial<T>

pub fn checked_powmod<E: Clone + Integer>(
    &self,
    exponent: E,
    modulus: &Self
) -> Option<Self>

pub fn powmod<E: Clone + Integer>(&self, exponent: E, modulus: &Self) -> Self

impl Polynomial<BigInt>

pub fn factor_with_rng<R: Rng + ?Sized>(
    &self,
    rng: &mut R
) -> PolynomialFactors<BigInt>

pub fn factor(&self) -> PolynomialFactors<BigInt>

impl<T: PolynomialCoefficient + for<'a> ExactDiv<&'a T, Output = T>> Polynomial<T>

pub fn subresultant_gcd(self, rhs: Self) -> Polynomial<T>

returns the non-reduced GCD computed from the subresultant remainder sequence.

The algorithm used is derived from the one given in http://web.archive.org/web/20190221040758/https://pdfs.semanticscholar.org/2e6b/95ba84e2160748ba8fc310cdc408fc9bbade.pdf

pub fn nonzero_resultant(self, rhs: Self) -> Option<T>

pub fn resultant(self, rhs: Self) -> T where
    T: Zero, 

impl<T: PolynomialCoefficient> Polynomial<T>

pub fn is_one(&self) -> bool

impl<T: PolynomialCoefficient> Polynomial<T>

pub fn make_monomial(coefficient: T, variable_exponent: usize) -> Self

pub fn nonzero_coefficient(&self, index: usize) -> Option<T>

pub fn coefficient(&self, index: usize) -> T where
    T: Zero, 

pub fn nonzero_highest_power_coefficient(&self) -> Option<T>

pub fn highest_power_coefficient(&self) -> T where
    T: Zero, 

pub fn into_coefficients(self) -> Vec<T>

pub fn split_out_divisor(self) -> (Vec<T::Element>, T::Divisor)

Important traits for Iter<'_, T>

impl<'_, T: PolynomialCoefficient> Iterator for Iter<'_, T> type Item = T;

pub fn iter(&self) -> Iter<T>

pub fn len(&self) -> usize

pub fn is_empty(&self) -> bool

pub fn degree(&self) -> Option<usize>

pub fn negate(&mut self)

pub fn nonzero_content(&self) -> Option<T> where
    T: GCD<Output = T> + PartialOrd, 

returns greatest common divisor of all coefficients

pub fn content(&self) -> T where
    T: GCD<Output = T> + PartialOrd + Zero, 

returns greatest common divisor of all coefficients

pub fn primitive_part_assign(&mut self) where
    T: GCD<Output = T> + PartialOrd + for<'a> ExactDiv<&'a T, Output = T>, 

pub fn into_primitive_part(self) -> Self where
    T: GCD<Output = T> + PartialOrd + for<'a> ExactDiv<&'a T, Output = T>, 

pub fn primitive_part(&self) -> Self where
    T: GCD<Output = T> + PartialOrd + for<'a> ExactDiv<&'a T, Output = T>, 

pub fn monic_assign(&mut self) where
    T: for<'a> ExactDiv<&'a T, Output = T>, 

pub fn into_monic(self) -> Self where
    T: for<'a> ExactDiv<&'a T, Output = T>, 

pub fn nonzero_reducing_factor(&self) -> Option<T> where
    T: PolynomialReducingFactorSupported, 

returns the factor f of the passed in polynomial p where p / f is content-free (for integer polynomials) or monic (for polynomials over fields).

pub fn reducing_factor(&self) -> T where
    T: PolynomialReducingFactorSupported + Zero, 

returns the factor f of the passed in polynomial p where p / f is content-free (for integer polynomials) or monic (for polynomials over fields). returns zero when p is zero.

pub fn reduce_assign(&mut self) where
    T: PolynomialReducingFactorSupported + for<'a> ExactDiv<&'a T, Output = T>, 

converts self to be content-free (for integer polynomials) or monic (for polynomials over fields).

pub fn into_reduced(self) -> Self where
    T: PolynomialReducingFactorSupported + for<'a> ExactDiv<&'a T, Output = T>, 

returns self converted to be content-free (for integer polynomials) or monic (for polynomials over fields).

pub fn to_reduced(&self) -> Self where
    T: PolynomialReducingFactorSupported + for<'a> ExactDiv<&'a T, Output = T>, 

returns self converted to be content-free (for integer polynomials) or monic (for polynomials over fields).

pub fn to_sturm_sequence(&self) -> Vec<Polynomial<T>> where
    T: PolynomialDivSupported, 

pub fn into_sturm_sequence(self) -> Vec<Polynomial<T>> where
    T: PolynomialDivSupported, 

pub fn to_primitive_sturm_sequence(&self) -> Vec<Polynomial<T>> where
    T: GCD<Output = T> + PartialOrd + for<'a> ExactDiv<&'a T, Output = T>, 

pub fn into_primitive_sturm_sequence(self) -> Vec<Polynomial<T>> where
    T: GCD<Output = T> + PartialOrd + for<'a> ExactDiv<&'a T, Output = T>, 

pub fn into_derivative(self) -> Self

pub fn derivative(&self) -> Self

pub fn eval_generic<V: for<'a> Mul<&'a V, Output = V> + Add<T, Output = V>>(
    &self,
    at: &V,
    zero: V
) -> V

pub fn into_eval_generic<V: for<'a> Mul<&'a V, Output = V> + Add<T, Output = V>>(
    self,
    at: &V,
    zero: V
) -> V

pub fn eval(&self, at: &T) -> T

pub fn into_eval(self, at: &T) -> T

pub fn set_one_if_nonzero(&mut self) -> Result<(), ()>

pub fn into_one_if_nonzero(self) -> Result<Self, Self>

#[must_use] pub fn to_one_if_nonzero(&self) -> Option<Self>

#[must_use] pub fn nonzero_max_norm(&self) -> Option<T> where
    T: Ord + PolynomialCoefficientAbsSupported, 

#[must_use] pub fn max_norm(&self) -> T where
    T: Ord + PolynomialCoefficientAbsSupported + Zero, 

#[must_use] pub fn nonzero_manhattan_norm(&self) -> Option<T> where
    T: PolynomialCoefficientAbsSupported, 

#[must_use] pub fn manhattan_norm(&self) -> T where
    T: PolynomialCoefficientAbsSupported + Zero, 

impl<T> Polynomial<T> where
    T: PolynomialDivSupported + RingCharacteristic<Type = CharacteristicZero> + PolynomialReducingFactorSupported + GCD<Output = T> + PartialOrd, 

pub fn square_free_factorization_using_yuns_algorithm(
    &self
) -> SquareFreePolynomialFactors<T>

splits self into square-free factors using Yun's algorithm

Note that the returned factors are not necessarily irreducible.

impl<T: PolynomialDivSupported + PolynomialReducingFactorSupported> Polynomial<T>

pub fn is_square_free(&self) -> bool

Trait Implementations

impl<T: PolynomialCoefficient<Divisor = DivisorIsOne, Element = T> + One> PolynomialCoefficient for Polynomial<T> where
    T::Element: Zero + One, 

type Element = Polynomial<T>

type Divisor = DivisorIsOne

const NESTING_DEPTH: usize

fn is_element_zero(element: &Self::Element) -> bool

fn is_element_one(element: &Self::Element) -> bool

fn is_coefficient_zero(coefficient: &Self) -> bool

fn is_coefficient_one(coefficient: &Self) -> bool

fn set_element_zero(element: &mut Self::Element)

fn set_element_one(element: &mut Self::Element)

fn set_coefficient_zero(coefficient: &mut Self)

fn set_coefficient_one(coefficient: &mut Self)

fn make_zero_element(_element: Cow<Self::Element>) -> Self::Element

fn make_one_element(element: Cow<Self::Element>) -> Self::Element

fn make_zero_coefficient_from_element(_element: Cow<Self::Element>) -> Self

fn make_one_coefficient_from_element(element: Cow<Self::Element>) -> Self

fn make_zero_coefficient_from_coefficient(_coefficient: Cow<Self>) -> Self

fn make_one_coefficient_from_coefficient(coefficient: Cow<Self>) -> Self

fn negate_element(element: &mut Self::Element)

fn mul_element_by_usize(
    element: Cow<Self::Element>,
    multiplier: usize
) -> Self::Element

fn mul_assign_element_by_usize(element: &mut Self::Element, multiplier: usize)

fn divisor_to_element(
    _v: Cow<Self::Divisor>,
    other_element: Cow<Self::Element>
) -> Self::Element

fn coefficients_to_elements(
    coefficients: Cow<[Self]>
) -> (Vec<Self::Element>, Self::Divisor)

fn make_coefficient(
    element: Cow<Self::Element>,
    _divisor: Cow<Self::Divisor>
) -> Self

fn reduce_divisor(_elements: &mut [Self::Element], _divisor: &mut Self::Divisor)

fn get_reduced_divisor(
    elements: &[Self::Element],
    _divisor: &Self::Divisor
) -> (Vec<Self::Element>, Self::Divisor)

fn coefficient_to_element(
    coefficient: Cow<Self>
) -> (Self::Element, Self::Divisor)

fn divisor_pow_usize(_base: Self::Divisor, _exponent: usize) -> Self::Divisor

fn element_pow_usize(base: Self::Element, exponent: usize) -> Self::Element

fn coefficient_pow_usize(base: Self, exponent: usize) -> Self

fn from_iterator<I: Iterator<Item = Self>>(iter: I) -> Polynomial<Self>

impl<T> GCD<Polynomial<T>> for Polynomial<T> where
    T: PolynomialCoefficient + PolynomialDivSupported + PolynomialReducingFactorSupported, 

type Output = Self

fn gcd(&self, rhs: &Self) -> Self

fn gcd_lcm(&self, rhs: &Self) -> GCDAndLCM<Self>

#[must_use] fn lcm(&self, rhs: &Rhs) -> Self::Output

impl<T> ExtendedGCD<Polynomial<T>> for Polynomial<T> where
    T: PolynomialCoefficient + PolynomialDivSupported + PolynomialReducingFactorSupported, 

fn extended_gcd(&self, rhs: &Self) -> ExtendedGCDResult<Self>

fn extended_gcd_lcm(&self, rhs: &Self) -> ExtendedGCDAndLCM<Self>

impl<T: PolynomialCoefficient + for<'a> ExactDiv<&'a T, Output = T>> ExactDiv<Polynomial<T>> for Polynomial<T>

type Output = Polynomial<T>

fn exact_div(self, rhs: Polynomial<T>) -> Polynomial<T>

fn checked_exact_div(self, rhs: Polynomial<T>) -> Option<Polynomial<T>>

impl<'_, T: PolynomialCoefficient + for<'a> ExactDiv<&'a T, Output = T>> ExactDiv<&'_ Polynomial<T>> for Polynomial<T>

type Output = Polynomial<T>

fn exact_div(self, rhs: &Polynomial<T>) -> Polynomial<T>

fn checked_exact_div(self, rhs: &Polynomial<T>) -> Option<Polynomial<T>>

impl<'_, T: PolynomialCoefficient + for<'a> ExactDiv<&'a T, Output = T>> ExactDiv<Polynomial<T>> for &'_ Polynomial<T>

type Output = Polynomial<T>

fn exact_div(self, rhs: Polynomial<T>) -> Polynomial<T>

fn checked_exact_div(self, rhs: Polynomial<T>) -> Option<Polynomial<T>>

impl<'l, 'r, T: PolynomialCoefficient + for<'a> ExactDiv<&'a T, Output = T>> ExactDiv<&'r Polynomial<T>> for &'l Polynomial<T>

type Output = Polynomial<T>

fn exact_div(self, rhs: &Polynomial<T>) -> Polynomial<T>

fn checked_exact_div(self, rhs: &Polynomial<T>) -> Option<Polynomial<T>>

impl<'a, T: PolynomialCoefficient + for<'b> ExactDiv<&'b T, Output = T>> ExactDiv<&'a T> for &'a Polynomial<T>

type Output = Polynomial<T>

fn exact_div(self, rhs: &T) -> Polynomial<T>

fn checked_exact_div(self, rhs: &T) -> Option<Polynomial<T>>

impl<'a, T: PolynomialCoefficient + for<'b> ExactDiv<&'b T, Output = T>> ExactDiv<T> for &'a Polynomial<T>

type Output = Polynomial<T>

fn exact_div(self, rhs: T) -> Polynomial<T>

fn checked_exact_div(self, rhs: T) -> Option<Polynomial<T>>

impl<'a, T: PolynomialCoefficient + for<'b> ExactDiv<&'b T, Output = T>> ExactDiv<&'a T> for Polynomial<T>

type Output = Polynomial<T>

fn exact_div(self, rhs: &T) -> Polynomial<T>

fn checked_exact_div(self, rhs: &T) -> Option<Polynomial<T>>

impl<T: PolynomialCoefficient + for<'a> ExactDiv<&'a T, Output = T>> ExactDiv<T> for Polynomial<T>

type Output = Polynomial<T>

fn exact_div(self, rhs: T) -> Polynomial<T>

fn checked_exact_div(self, rhs: T) -> Option<Polynomial<T>>

impl<T: PolynomialCoefficient + for<'a> ExactDiv<&'a T, Output = T>> ExactDivAssign<Polynomial<T>> for Polynomial<T>

fn exact_div_assign(&mut self, rhs: Polynomial<T>)

fn checked_exact_div_assign(&mut self, rhs: Polynomial<T>) -> Result<(), ()>

impl<'_, T: PolynomialCoefficient + for<'a> ExactDiv<&'a T, Output = T>> ExactDivAssign<&'_ Polynomial<T>> for Polynomial<T>

fn exact_div_assign(&mut self, rhs: &Polynomial<T>)

fn checked_exact_div_assign(&mut self, rhs: &Polynomial<T>) -> Result<(), ()>

impl<T: PolynomialCoefficient + for<'a> ExactDiv<&'a T, Output = T>> ExactDivAssign<T> for Polynomial<T>

fn exact_div_assign(&mut self, rhs: T)

fn checked_exact_div_assign(&mut self, rhs: T) -> Result<(), ()>

impl<'a, T: PolynomialCoefficient + for<'b> ExactDiv<&'b T, Output = T>> ExactDivAssign<&'a T> for Polynomial<T>

fn exact_div_assign(&mut self, rhs: &T)

fn checked_exact_div_assign(&mut self, rhs: &T) -> Result<(), ()>

impl<T: PolynomialCoefficient> Into<(Vec<<T as PolynomialCoefficient>::Element>, <T as PolynomialCoefficient>::Divisor)> for Polynomial<T>

fn into(self) -> (Vec<T::Element>, T::Divisor)

Performs the conversion.

impl<'a, T: PolynomialCoefficient> From<Cow<'a, [T]>> for Polynomial<T>

fn from(coefficients: Cow<'a, [T]>) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<Vec<T>> for Polynomial<T>

fn from(coefficients: Vec<T>) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 0]> for Polynomial<T>

fn from(coefficients: [T; 0]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 1]> for Polynomial<T>

fn from(coefficients: [T; 1]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 2]> for Polynomial<T>

fn from(coefficients: [T; 2]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 3]> for Polynomial<T>

fn from(coefficients: [T; 3]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 4]> for Polynomial<T>

fn from(coefficients: [T; 4]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 5]> for Polynomial<T>

fn from(coefficients: [T; 5]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 6]> for Polynomial<T>

fn from(coefficients: [T; 6]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 7]> for Polynomial<T>

fn from(coefficients: [T; 7]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 8]> for Polynomial<T>

fn from(coefficients: [T; 8]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 9]> for Polynomial<T>

fn from(coefficients: [T; 9]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 10]> for Polynomial<T>

fn from(coefficients: [T; 10]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 11]> for Polynomial<T>

fn from(coefficients: [T; 11]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 12]> for Polynomial<T>

fn from(coefficients: [T; 12]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 13]> for Polynomial<T>

fn from(coefficients: [T; 13]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 14]> for Polynomial<T>

fn from(coefficients: [T; 14]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 15]> for Polynomial<T>

fn from(coefficients: [T; 15]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 16]> for Polynomial<T>

fn from(coefficients: [T; 16]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 17]> for Polynomial<T>

fn from(coefficients: [T; 17]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 18]> for Polynomial<T>

fn from(coefficients: [T; 18]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 19]> for Polynomial<T>

fn from(coefficients: [T; 19]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 20]> for Polynomial<T>

fn from(coefficients: [T; 20]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 21]> for Polynomial<T>

fn from(coefficients: [T; 21]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 22]> for Polynomial<T>

fn from(coefficients: [T; 22]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 23]> for Polynomial<T>

fn from(coefficients: [T; 23]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 24]> for Polynomial<T>

fn from(coefficients: [T; 24]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 25]> for Polynomial<T>

fn from(coefficients: [T; 25]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 26]> for Polynomial<T>

fn from(coefficients: [T; 26]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 27]> for Polynomial<T>

fn from(coefficients: [T; 27]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 28]> for Polynomial<T>

fn from(coefficients: [T; 28]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 29]> for Polynomial<T>

fn from(coefficients: [T; 29]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 30]> for Polynomial<T>

fn from(coefficients: [T; 30]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 31]> for Polynomial<T>

fn from(coefficients: [T; 31]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<[T; 32]> for Polynomial<T>

fn from(coefficients: [T; 32]) -> Self

Performs the conversion.

impl<'_, T: PolynomialCoefficient> From<&'_ [T]> for Polynomial<T>

fn from(coefficients: &[T]) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<T> for Polynomial<T>

fn from(coefficient: T) -> Self

Performs the conversion.

impl<'_, T: PolynomialCoefficient> From<&'_ T> for Polynomial<T>

fn from(coefficient: &T) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> From<(Vec<<T as PolynomialCoefficient>::Element>, <T as PolynomialCoefficient>::Divisor)> for Polynomial<T>

fn from((elements, divisor): (Vec<T::Element>, T::Divisor)) -> Self

Performs the conversion.

impl<T: PolynomialCoefficient> IntoIterator for Polynomial<T>

type Item = T

The type of the elements being iterated over.

type IntoIter = IntoIter<T>

Which kind of iterator are we turning this into?

Important traits for IntoIter<T>

impl<T: PolynomialCoefficient> Iterator for IntoIter<T> type Item = T;

fn into_iter(self) -> IntoIter<T>

Creates an iterator from a value.

impl<'a, T: PolynomialCoefficient> IntoIterator for &'a Polynomial<T>

type Item = T

The type of the elements being iterated over.

type IntoIter = Iter<'a, T>

Which kind of iterator are we turning this into?

fn into_iter(self) -> Self::IntoIter

Creates an iterator from a value.

impl<T: Clone + PolynomialCoefficient> Clone for Polynomial<T> where
    T::Element: Clone,
    T::Divisor: Clone, 

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

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<T: PolynomialCoefficient> Default for Polynomial<T>

fn default() -> Self

Returns the "default value" for a type.

impl<T: Eq + PolynomialCoefficient> Eq for Polynomial<T> where
    T::Element: Eq,
    T::Divisor: Eq, 

impl<T: PartialEq + PolynomialCoefficient> PartialEq<Polynomial<T>> for Polynomial<T> where
    T::Element: PartialEq,
    T::Divisor: PartialEq, 

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

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Polynomial<T>) -> bool

This method tests for !=.

impl<T: Display + PolynomialCoefficient> Display for Polynomial<T>

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

Formats the value using the given formatter.

impl<T: Debug + PolynomialCoefficient> Debug for Polynomial<T> where
    T::Element: Debug,
    T::Divisor: Debug, 

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

Formats the value using the given formatter.

impl<T: PolynomialDivSupported> Div<Polynomial<T>> for Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the / operator.

fn div(self, rhs: Polynomial<T>) -> Polynomial<T>

Performs the / operation.

impl<'_, T: PolynomialDivSupported> Div<&'_ Polynomial<T>> for Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the / operator.

fn div(self, rhs: &Polynomial<T>) -> Polynomial<T>

Performs the / operation.

impl<'_, T: PolynomialDivSupported> Div<Polynomial<T>> for &'_ Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the / operator.

fn div(self, rhs: Polynomial<T>) -> Polynomial<T>

Performs the / operation.

impl<'a, 'b, T: PolynomialDivSupported> Div<&'a Polynomial<T>> for &'b Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the / operator.

fn div(self, rhs: &Polynomial<T>) -> Polynomial<T>

Performs the / operation.

impl<'a, T: PolynomialCoefficient + for<'b> ExactDiv<&'b T, Output = T>> Div<&'a T> for &'a Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the / operator.

fn div(self, rhs: &T) -> Polynomial<T>

Performs the / operation.

impl<'a, T: PolynomialCoefficient + for<'b> ExactDiv<&'b T, Output = T>> Div<T> for &'a Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the / operator.

fn div(self, rhs: T) -> Polynomial<T>

Performs the / operation.

impl<'a, T: PolynomialCoefficient + for<'b> ExactDiv<&'b T, Output = T>> Div<&'a T> for Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the / operator.

fn div(self, rhs: &T) -> Polynomial<T>

Performs the / operation.

impl<T: PolynomialCoefficient + for<'a> ExactDiv<&'a T, Output = T>> Div<T> for Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the / operator.

fn div(self, rhs: T) -> Polynomial<T>

Performs the / operation.

impl<T: PolynomialDivSupported> Rem<Polynomial<T>> for Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the % operator.

fn rem(self, rhs: Polynomial<T>) -> Polynomial<T>

Performs the % operation.

impl<'_, T: PolynomialDivSupported> Rem<&'_ Polynomial<T>> for Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the % operator.

fn rem(self, rhs: &Polynomial<T>) -> Polynomial<T>

Performs the % operation.

impl<'_, T: PolynomialDivSupported> Rem<Polynomial<T>> for &'_ Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the % operator.

fn rem(self, rhs: Polynomial<T>) -> Polynomial<T>

Performs the % operation.

impl<'a, 'b, T: PolynomialDivSupported> Rem<&'a Polynomial<T>> for &'b Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the % operator.

fn rem(self, rhs: &Polynomial<T>) -> Polynomial<T>

Performs the % operation.

impl<T: PolynomialCoefficient> Sub<Polynomial<T>> for Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, T: PolynomialCoefficient> Sub<&'a Polynomial<T>> for Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, T: PolynomialCoefficient> Sub<Polynomial<T>> for &'a Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, T: PolynomialCoefficient> Sub<&'a Polynomial<T>> for &'a Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<T: PolynomialCoefficient> Sub<T> for Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, T: PolynomialCoefficient> Sub<&'a T> for Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, T: PolynomialCoefficient> Sub<T> for &'a Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, T: PolynomialCoefficient> Sub<&'a T> for &'a Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<T: PolynomialCoefficient> Add<Polynomial<T>> for Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, T: PolynomialCoefficient> Add<&'a Polynomial<T>> for Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, T: PolynomialCoefficient> Add<Polynomial<T>> for &'a Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, T: PolynomialCoefficient> Add<&'a Polynomial<T>> for &'a Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<T: PolynomialCoefficient> Add<T> for Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, T: PolynomialCoefficient> Add<&'a T> for Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, T: PolynomialCoefficient> Add<T> for &'a Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, T: PolynomialCoefficient> Add<&'a T> for &'a Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, T: PolynomialCoefficient> Mul<&'a Polynomial<T>> for &'a Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the * operator.

fn mul(self, rhs: &Polynomial<T>) -> Polynomial<T>

Performs the * operation.

impl<'a, T: PolynomialCoefficient> Mul<Polynomial<T>> for &'a Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the * operator.

fn mul(self, rhs: Polynomial<T>) -> Polynomial<T>

Performs the * operation.

impl<'a, T: PolynomialCoefficient> Mul<&'a Polynomial<T>> for Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the * operator.

fn mul(self, rhs: &Polynomial<T>) -> Polynomial<T>

Performs the * operation.

impl<T: PolynomialCoefficient> Mul<Polynomial<T>> for Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the * operator.

fn mul(self, rhs: Polynomial<T>) -> Polynomial<T>

Performs the * operation.

impl<'a, T: PolynomialCoefficient> Mul<&'a T> for &'a Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the * operator.

fn mul(self, rhs: &T) -> Polynomial<T>

Performs the * operation.

impl<'a, T: PolynomialCoefficient> Mul<T> for &'a Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the * operator.

fn mul(self, rhs: T) -> Polynomial<T>

Performs the * operation.

impl<'a, T: PolynomialCoefficient> Mul<&'a T> for Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the * operator.

fn mul(self, rhs: &T) -> Polynomial<T>

Performs the * operation.

impl<T: PolynomialCoefficient> Mul<T> for Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the * operator.

fn mul(self, rhs: T) -> Polynomial<T>

Performs the * operation.

impl<T: PolynomialCoefficient> Neg for Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the - operator.

fn neg(self) -> Polynomial<T>

Performs the unary - operation.

impl<'_, T: PolynomialCoefficient> Neg for &'_ Polynomial<T>

type Output = Polynomial<T>

The resulting type after applying the - operator.

fn neg(self) -> Polynomial<T>

Performs the unary - operation.

impl<T: PolynomialCoefficient> AddAssign<Polynomial<T>> for Polynomial<T>

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

Performs the += operation.

impl<'a, T: PolynomialCoefficient> AddAssign<&'a Polynomial<T>> for Polynomial<T>

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

Performs the += operation.

impl<T: PolynomialCoefficient> AddAssign<T> for Polynomial<T>

fn add_assign(&mut self, rhs: T)

Performs the += operation.

impl<'a, T: PolynomialCoefficient> AddAssign<&'a T> for Polynomial<T>

fn add_assign(&mut self, rhs: &T)

Performs the += operation.

impl<T: PolynomialCoefficient> SubAssign<Polynomial<T>> for Polynomial<T>

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

Performs the -= operation.

impl<'a, T: PolynomialCoefficient> SubAssign<&'a Polynomial<T>> for Polynomial<T>

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

Performs the -= operation.

impl<T: PolynomialCoefficient> SubAssign<T> for Polynomial<T>

fn sub_assign(&mut self, rhs: T)

Performs the -= operation.

impl<'a, T: PolynomialCoefficient> SubAssign<&'a T> for Polynomial<T>

fn sub_assign(&mut self, rhs: &T)

Performs the -= operation.

impl<T: PolynomialCoefficient> MulAssign<Polynomial<T>> for Polynomial<T>

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

Performs the *= operation.

impl<'a, T: PolynomialCoefficient> MulAssign<&'a Polynomial<T>> for Polynomial<T>

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

Performs the *= operation.

impl<T: PolynomialCoefficient> MulAssign<T> for Polynomial<T>

fn mul_assign(&mut self, rhs: T)

Performs the *= operation.

impl<'a, T: PolynomialCoefficient> MulAssign<&'a T> for Polynomial<T>

fn mul_assign(&mut self, rhs: &T)

Performs the *= operation.

impl<T: PolynomialDivSupported> DivAssign<Polynomial<T>> for Polynomial<T>

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

Performs the /= operation.

impl<'_, T: PolynomialDivSupported> DivAssign<&'_ Polynomial<T>> for Polynomial<T>

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

Performs the /= operation.

impl<T: PolynomialCoefficient + for<'a> ExactDiv<&'a T, Output = T>> DivAssign<T> for Polynomial<T>

fn div_assign(&mut self, rhs: T)

Performs the /= operation.

impl<'a, T: PolynomialCoefficient + for<'b> ExactDiv<&'b T, Output = T>> DivAssign<&'a T> for Polynomial<T>

fn div_assign(&mut self, rhs: &T)

Performs the /= operation.

impl<T: PolynomialDivSupported> RemAssign<Polynomial<T>> for Polynomial<T>

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

Performs the %= operation.

impl<'_, T: PolynomialDivSupported> RemAssign<&'_ Polynomial<T>> for Polynomial<T>

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

Performs the %= operation.

impl<T: Hash + PolynomialCoefficient> Hash for Polynomial<T> where
    T::Element: Hash,
    T::Divisor: Hash, 

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, 

Feeds a slice of this type into the given [Hasher].

impl<T: PolynomialCoefficient> StructuralPartialEq for Polynomial<T>

impl<T: PolynomialCoefficient> StructuralEq for Polynomial<T>

impl<T: PolynomialCoefficient> FromIterator<T> for Polynomial<T>

fn from_iter<I: IntoIterator<Item = T>>(iter: I) -> Self

Creates a value from an iterator.

impl<T: PolynomialCoefficient> CheckedAdd for Polynomial<T>

fn checked_add(&self, rhs: &Self) -> Option<Self>

Adds two numbers, checking for overflow. If overflow happens, None is returned.

impl<T: PolynomialDivSupported> CheckedDiv for Polynomial<T>

fn checked_div(&self, rhs: &Self) -> Option<Self>

Divides two numbers, checking for underflow, overflow and division by zero. If any of that happens, None is returned.

impl<T: PolynomialCoefficient> CheckedMul for Polynomial<T>

fn checked_mul(&self, rhs: &Self) -> Option<Self>

Multiplies two numbers, checking for underflow or overflow. If underflow or overflow happens, None is returned.

impl<T: PolynomialCoefficient> CheckedSub for Polynomial<T>

fn checked_sub(&self, rhs: &Self) -> Option<Self>

Subtracts two numbers, checking for underflow. If underflow happens, None is returned.

impl<T: PolynomialCoefficient + FromPrimitive> FromPrimitive for Polynomial<T>

fn from_i8(v: i8) -> Option<Self>

Convert an i8 to return an optional value of this type. If the type cannot be represented by this value, then None is returned.

fn from_u8(v: u8) -> Option<Self>

Convert an u8 to return an optional value of this type. If the type cannot be represented by this value, then None is returned.

fn from_i16(v: i16) -> Option<Self>

Convert an i16 to return an optional value of this type. If the type cannot be represented by this value, then None is returned.

fn from_u16(v: u16) -> Option<Self>

Convert an u16 to return an optional value of this type. If the type cannot be represented by this value, then None is returned.

fn from_i32(v: i32) -> Option<Self>

Convert an i32 to return an optional value of this type. If the type cannot be represented by this value, then None is returned.

fn from_u32(v: u32) -> Option<Self>

Convert an u32 to return an optional value of this type. If the type cannot be represented by this value, then None is returned.

fn from_i64(v: i64) -> Option<Self>

Convert an i64 to return an optional value of this type. If the type cannot be represented by this value, then None is returned.

fn from_u64(v: u64) -> Option<Self>

Convert an u64 to return an optional value of this type. If the type cannot be represented by this value, then None is returned.

fn from_i128(v: i128) -> Option<Self>

Convert an i128 to return an optional value of this type. If the type cannot be represented by this value, then None is returned.

fn from_u128(v: u128) -> Option<Self>

Convert an u128 to return an optional value of this type. If the type cannot be represented by this value, then None is returned.

fn from_isize(v: isize) -> Option<Self>

Convert an isize to return an optional value of this type. If the value cannot be represented by this value, then None is returned.

fn from_usize(v: usize) -> Option<Self>

Convert a usize to return an optional value of this type. If the type cannot be represented by this value, then None is returned.

fn from_f32(v: f32) -> Option<Self>

Convert a f32 to return an optional value of this type. If the type cannot be represented by this value, then None is returned.

fn from_f64(v: f64) -> Option<Self>

Convert a f64 to return an optional value of this type. If the type cannot be represented by this value, then None is returned.

impl<T: PolynomialCoefficient> One for Polynomial<T> where
    T::Element: One, 

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

Returns true if self is equal to the multiplicative identity.

impl<'_, T: PolynomialCoefficient, E: Integer + Clone> Pow<E> for &'_ Polynomial<T>

type Output = Polynomial<T>

The result after applying the operator.

fn pow(self, exponent: E) -> Polynomial<T>

Returns self to the power rhs.

impl<T: PolynomialCoefficient, E: Integer + Clone> Pow<E> for Polynomial<T>

type Output = Polynomial<T>

The result after applying the operator.

fn pow(self, exponent: E) -> Polynomial<T>

Returns self to the power rhs.

impl<T: PolynomialCoefficient + ToPrimitive> ToPrimitive for Polynomial<T>

fn to_i8(&self) -> Option<i8>

Converts the value of self to an i8.

fn to_u8(&self) -> Option<u8>

Converts the value of self to an u8.

fn to_i16(&self) -> Option<i16>

Converts the value of self to an i16.

fn to_u16(&self) -> Option<u16>

Converts the value of self to an u16.

fn to_i32(&self) -> Option<i32>

Converts the value of self to an i32.

fn to_u32(&self) -> Option<u32>

Converts the value of self to an u32.

fn to_i64(&self) -> Option<i64>

Converts the value of self to an i64.

fn to_u64(&self) -> Option<u64>

Converts the value of self to an u64.

fn to_i128(&self) -> Option<i128>

Converts the value of self to an i128.

fn to_u128(&self) -> Option<u128>

Converts the value of self to an u128.

fn to_isize(&self) -> Option<isize>

Converts the value of self to an isize.

fn to_usize(&self) -> Option<usize>

Converts the value of self to a usize.

fn to_f32(&self) -> Option<f32>

Converts the value of self to an f32.

fn to_f64(&self) -> Option<f64>

Converts the value of self to an f64.

impl<T: PolynomialCoefficient> Zero for Polynomial<T>

fn zero() -> Self

Returns the additive identity element of Self, 0. # Purity

fn set_zero(&mut self)

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

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

impl<T: PolynomialDivSupported> CheckedRem for Polynomial<T>

fn checked_rem(&self, rhs: &Self) -> Option<Self>

Finds the remainder of dividing two numbers, checking for underflow, overflow and division by zero. If any of that happens, None is returned.