Struct algebraics::polynomial::Polynomial

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

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()

Implementations

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)

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>

pub fn to_one_if_nonzero(&self) -> Option<Self>

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

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

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

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<'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<&'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<'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<&'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<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<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<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<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> AddAssign<&'a Polynomial<T>> for Polynomial<T>

fn add_assign(&mut self, rhs: &Polynomial<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> AddAssign<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<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: 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.

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: 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: 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: PolynomialCoefficient> Default for Polynomial<T>

fn default() -> Self

Returns the “default value” for a type.

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

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

fn div_assign(&mut self, rhs: &Polynomial<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> 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<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<'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<&'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<'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<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<'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<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<'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 + 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<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> From<&'_ [T]> for Polynomial<T>

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

Converts to this type from the input type.

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

fn from(coefficient: &T) -> Self

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

fn from(coefficient: T) -> Self

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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 + FromPrimitive> FromPrimitive for Polynomial<T>

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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>

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

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

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

Converts this type into the (usually inferred) input type.

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?

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

fn mul_assign(&mut self, rhs: &Polynomial<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: PolynomialCoefficient> MulAssign<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<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> 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: 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: 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: 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: 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: 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> 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<'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<&'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<'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<&'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> 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<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<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<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> SubAssign<&'a Polynomial<T>> for Polynomial<T>

fn sub_assign(&mut self, rhs: &Polynomial<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> SubAssign<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<T: PolynomialCoefficient + ToPrimitive> ToPrimitive for Polynomial<T>

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

Converts the value of self to an i8. If the value cannot be represented by an i8, then None is returned.

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

Converts the value of self to a u8. If the value cannot be represented by a u8, then None is returned.

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

Converts the value of self to an i16. If the value cannot be represented by an i16, then None is returned.

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

Converts the value of self to a u16. If the value cannot be represented by a u16, then None is returned.

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

Converts the value of self to an i32. If the value cannot be represented by an i32, then None is returned.

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

Converts the value of self to a u32. If the value cannot be represented by a u32, then None is returned.

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

Converts the value of self to an i64. If the value cannot be represented by an i64, then None is returned.

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

Converts the value of self to a u64. If the value cannot be represented by a u64, then None is returned.

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

Converts the value of self to an i128. If the value cannot be represented by an i128 (i64 under the default implementation), then None is returned.

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

Converts the value of self to a u128. If the value cannot be represented by a u128 (u64 under the default implementation), then None is returned.

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

Converts the value of self to an isize. If the value cannot be represented by an isize, then None is returned.

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

Converts the value of self to a usize. If the value cannot be represented by a usize, then None is returned.

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

Converts the value of self to an f32. Overflows may map to positive or negative inifinity, otherwise None is returned if the value cannot be represented by an f32.

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

Converts the value of self to an f64. Overflows may map to positive or negative inifinity, otherwise None is returned if the value cannot be represented by an f64.

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

fn zero() -> Self

Returns the additive identity element of Self, 0.

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

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

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