Struct rustnomial::QuadraticTrinomial

pub struct QuadraticTrinomial<N> {
    pub coefficients: [N; 3],
}

A type that stores terms of a quadratic trinomial in a static array. Operations are much faster than on Polynomial for the same size polynomial, but terms can not be added freely.

Fields

coefficients: [N; 3]

Implementations

impl<N: Sized> QuadraticTrinomial<N>

pub fn new(coefficients: [N; 3]) -> QuadraticTrinomial<N>

Create a QuadraticTrinomial with the given coefficients.

Example

use rustnomial::{SizedPolynomial, QuadraticTrinomial, Degree};
let trinomial = QuadraticTrinomial::new([3.0, 1.0, 0.5]);
assert_eq!([3.0, 1.0, 0.5], trinomial.coefficients);
assert_eq!(Degree::Num(2), trinomial.degree());

impl<N: Zero + Copy> QuadraticTrinomial<N>

pub fn ordered_term_iter(&self) -> impl Iterator<Item = (N, usize)> + '_

impl<N> QuadraticTrinomial<N> where
    N: Copy + Zero + Mul<Output = N> + Neg<Output = N> + Sub<Output = N> + From<u8> + Div<Output = N> + AbsSqrt + IsPositive + One, 

pub fn discriminant(&self) -> N

pub fn roots(&self) -> Roots<N>

Return the roots of QuadraticTrinomial with largest first, smallest second.

pub fn complex_factors(
    &self
) -> (N, LinearBinomial<Complex<N>>, LinearBinomial<Complex<N>>)

pub fn real_factors(&self) -> Option<(N, LinearBinomial<N>, LinearBinomial<N>)>

Trait Implementations

impl<N> Add<QuadraticTrinomial<N>> for QuadraticTrinomial<N> where
    N: Add<Output = N> + Copy, 

type Output = QuadraticTrinomial<N>

The resulting type after applying the + operator.

fn add(self, rhs: QuadraticTrinomial<N>) -> QuadraticTrinomial<N>

Performs the + operation.

impl<N: Copy + AddAssign> AddAssign<QuadraticTrinomial<N>> for QuadraticTrinomial<N>

fn add_assign(&mut self, rhs: QuadraticTrinomial<N>)

Performs the += operation.

impl<N: Clone> Clone for QuadraticTrinomial<N>

fn clone(&self) -> QuadraticTrinomial<N>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<N: Debug> Debug for QuadraticTrinomial<N>

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

Formats the value using the given formatter.

impl<N> Derivable<N> for QuadraticTrinomial<N> where
    N: Zero + One + Copy + Mul<Output = N> + TryFromUsizeExact, 

fn derivative(&self) -> QuadraticTrinomial<N>

Returns the derivative of the QuadraticTrinomial.

Example

use rustnomial::{QuadraticTrinomial, Derivable};
let binomial = QuadraticTrinomial::new([3.0, 2.0, 1.0]);
assert_eq!(QuadraticTrinomial::new([0.0, 6.0, 2.0]), binomial.derivative());

impl<N> Display for QuadraticTrinomial<N> where
    N: Zero + One + IsPositive + PartialEq + Abs + Copy + IsNegativeOne + Display, 

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

Formats the value using the given formatter.

impl<N: Div<Output = N> + Copy> Div<N> for QuadraticTrinomial<N>

type Output = QuadraticTrinomial<N>

The resulting type after applying the / operator.

fn div(self, rhs: N) -> QuadraticTrinomial<N>

Performs the / operation.

impl<N: DivAssign + Copy> DivAssign<N> for QuadraticTrinomial<N>

fn div_assign(&mut self, rhs: N)

Performs the /= operation.

impl<N> Evaluable<N> for QuadraticTrinomial<N> where
    N: Add<Output = N> + Mul<Output = N> + Copy, 

fn eval(&self, point: N) -> N

Returns the value of the QuadraticTrinomial at the given point.

Example

use rustnomial::{QuadraticTrinomial, Evaluable};
let trinomial = QuadraticTrinomial::new([1, 2, 3]);
assert_eq!(6, trinomial.eval(1));
assert_eq!(3, trinomial.eval(0));

impl From<QuadraticTrinomial<f32>> for QuadraticTrinomial<f64>

fn from(item: QuadraticTrinomial<f32>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<i16>> for QuadraticTrinomial<i32>

fn from(item: QuadraticTrinomial<i16>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<i16>> for QuadraticTrinomial<i64>

fn from(item: QuadraticTrinomial<i16>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<i16>> for QuadraticTrinomial<i128>

fn from(item: QuadraticTrinomial<i16>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<i16>> for QuadraticTrinomial<f32>

fn from(item: QuadraticTrinomial<i16>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<i16>> for QuadraticTrinomial<f64>

fn from(item: QuadraticTrinomial<i16>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<i32>> for QuadraticTrinomial<i64>

fn from(item: QuadraticTrinomial<i32>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<i32>> for QuadraticTrinomial<i128>

fn from(item: QuadraticTrinomial<i32>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<i32>> for QuadraticTrinomial<f64>

fn from(item: QuadraticTrinomial<i32>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<i64>> for QuadraticTrinomial<i128>

fn from(item: QuadraticTrinomial<i64>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<i8>> for QuadraticTrinomial<i16>

fn from(item: QuadraticTrinomial<i8>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<i8>> for QuadraticTrinomial<i32>

fn from(item: QuadraticTrinomial<i8>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<i8>> for QuadraticTrinomial<i64>

fn from(item: QuadraticTrinomial<i8>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<i8>> for QuadraticTrinomial<i128>

fn from(item: QuadraticTrinomial<i8>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<i8>> for QuadraticTrinomial<f32>

fn from(item: QuadraticTrinomial<i8>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<i8>> for QuadraticTrinomial<f64>

fn from(item: QuadraticTrinomial<i8>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<u16>> for QuadraticTrinomial<u32>

fn from(item: QuadraticTrinomial<u16>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<u16>> for QuadraticTrinomial<u64>

fn from(item: QuadraticTrinomial<u16>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<u16>> for QuadraticTrinomial<u128>

fn from(item: QuadraticTrinomial<u16>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<u16>> for QuadraticTrinomial<i32>

fn from(item: QuadraticTrinomial<u16>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<u16>> for QuadraticTrinomial<i64>

fn from(item: QuadraticTrinomial<u16>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<u16>> for QuadraticTrinomial<i128>

fn from(item: QuadraticTrinomial<u16>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<u16>> for QuadraticTrinomial<f32>

fn from(item: QuadraticTrinomial<u16>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<u16>> for QuadraticTrinomial<f64>

fn from(item: QuadraticTrinomial<u16>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<u32>> for QuadraticTrinomial<u64>

fn from(item: QuadraticTrinomial<u32>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<u32>> for QuadraticTrinomial<u128>

fn from(item: QuadraticTrinomial<u32>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<u32>> for QuadraticTrinomial<i64>

fn from(item: QuadraticTrinomial<u32>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<u32>> for QuadraticTrinomial<i128>

fn from(item: QuadraticTrinomial<u32>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<u32>> for QuadraticTrinomial<f64>

fn from(item: QuadraticTrinomial<u32>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<u64>> for QuadraticTrinomial<u128>

fn from(item: QuadraticTrinomial<u64>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<u64>> for QuadraticTrinomial<i128>

fn from(item: QuadraticTrinomial<u64>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<u8>> for QuadraticTrinomial<u16>

fn from(item: QuadraticTrinomial<u8>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<u8>> for QuadraticTrinomial<u32>

fn from(item: QuadraticTrinomial<u8>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<u8>> for QuadraticTrinomial<u64>

fn from(item: QuadraticTrinomial<u8>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<u8>> for QuadraticTrinomial<u128>

fn from(item: QuadraticTrinomial<u8>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<u8>> for QuadraticTrinomial<i16>

fn from(item: QuadraticTrinomial<u8>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<u8>> for QuadraticTrinomial<i32>

fn from(item: QuadraticTrinomial<u8>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<u8>> for QuadraticTrinomial<i64>

fn from(item: QuadraticTrinomial<u8>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<u8>> for QuadraticTrinomial<i128>

fn from(item: QuadraticTrinomial<u8>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<u8>> for QuadraticTrinomial<f32>

fn from(item: QuadraticTrinomial<u8>) -> Self

Performs the conversion.

impl From<QuadraticTrinomial<u8>> for QuadraticTrinomial<f64>

fn from(item: QuadraticTrinomial<u8>) -> Self

Performs the conversion.

impl<N> FromStr for QuadraticTrinomial<N> where
    N: Zero + One + Copy + SubAssign + AddAssign + FromStr + CanNegate, 

type Err = PolynomialFromStringError

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<N> Integrable<N, Polynomial<N>> for QuadraticTrinomial<N> where
    N: Zero + TryFromUsizeExact + Copy + DivAssign + Mul<Output = N> + MulAssign + AddAssign + Div<Output = N>, 

fn integral(&self) -> Integral<N, Polynomial<N>>

Returns the integral of the Monomial.

Example

use rustnomial::{QuadraticTrinomial, Integrable, Polynomial};
let trinomial = QuadraticTrinomial::new([3.0, 0., 0.]);
let integral = trinomial.integral();
assert_eq!(&Polynomial::new(vec![1.0, 0.0, 0.0, 0.0]), integral.inner());

Errors

Will panic if N can not losslessly represent 2usize or 3usize.

impl<N: Mul<Output = N> + Copy> Mul<N> for QuadraticTrinomial<N>

type Output = QuadraticTrinomial<N>

The resulting type after applying the * operator.

fn mul(self, rhs: N) -> QuadraticTrinomial<N>

Performs the * operation.

impl<N: MulAssign + Copy> MulAssign<N> for QuadraticTrinomial<N>

fn mul_assign(&mut self, rhs: N)

Performs the *= operation.

impl<N> MutablePolynomial<N> for QuadraticTrinomial<N> where
    N: Zero + SubAssign + AddAssign + Copy, 

fn try_add_term(&mut self, coeff: N, degree: usize) -> Result<(), TryAddError>

Tries to add the term with given coefficient and degree to self, returning an error if the particular term can not be added to self without violating constraints.

fn try_sub_term(&mut self, coeff: N, degree: usize) -> Result<(), TryAddError>

Tries to subtract the term with given coefficient and degree from self, returning an error if the particular term can not be subtracted from self without violating constraints.

impl<N: Copy + Neg<Output = N>> Neg for QuadraticTrinomial<N>

type Output = QuadraticTrinomial<N>

The resulting type after applying the - operator.

fn neg(self) -> QuadraticTrinomial<N>

Performs the unary - operation.

impl<N> PartialEq<QuadraticTrinomial<N>> for QuadraticTrinomial<N> where
    N: Zero + PartialEq + Copy, 

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

Returns true if this QuadraticTrinomial is equal to other.

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

This method tests for !=.

impl<N: Zero + Copy> Shr<u32> for QuadraticTrinomial<N>

type Output = QuadraticTrinomial<N>

The resulting type after applying the >> operator.

fn shr(self, rhs: u32) -> QuadraticTrinomial<N>

Performs the >> operation.

impl<N: Zero + Copy> ShrAssign<u32> for QuadraticTrinomial<N>

fn shr_assign(&mut self, rhs: u32)

Performs the >>= operation.

impl<N: Copy + Zero> SizedPolynomial<N> for QuadraticTrinomial<N>

fn term_with_degree(&self, degree: usize) -> Term<N>

Returns the term with the given degree of the QuadraticTrinomial.

Example

use rustnomial::{QuadraticTrinomial, SizedPolynomial, Term};
let trinomial = QuadraticTrinomial::new([1, 0, 3]);
assert_eq!(Term::Term(1, 2), trinomial.term_with_degree(2));
assert_eq!(Term::ZeroTerm, trinomial.term_with_degree(1));
assert_eq!(Term::Term(3, 0), trinomial.term_with_degree(0));

fn degree(&self) -> Degree

Returns the degree of the QuadraticTrinomial.

Example

use rustnomial::{SizedPolynomial, QuadraticTrinomial, Degree};
let trinomial = QuadraticTrinomial::new([1, 2, 3]);
assert_eq!(Degree::Num(2), trinomial.degree());
let binomial = QuadraticTrinomial::new([0, 2, 3]);
assert_eq!(Degree::Num(1), binomial.degree());
let monomial = QuadraticTrinomial::new([0, 0, 3]);
assert_eq!(Degree::Num(0), monomial.degree());
let zero = QuadraticTrinomial::new([0, 0, 0]);
assert_eq!(Degree::NegInf, zero.degree());

fn zero() -> Self

Return a QuadraticTrinomial which is equal to zero.

Example

use rustnomial::{QuadraticTrinomial, SizedPolynomial};
assert!(QuadraticTrinomial::<i32>::zero().is_zero());

fn set_to_zero(&mut self)

Sets self to zero.

Example

use rustnomial::{QuadraticTrinomial, SizedPolynomial};
let mut non_zero = QuadraticTrinomial::new([1, 1, 1]);
assert!(!non_zero.is_zero());
non_zero.set_to_zero();
assert!(non_zero.is_zero());

fn terms_as_vec(&self) -> Vec<(N, usize)>

Returns a Vec containing all of the terms of self, where each item is the coefficient and degree of each non-zero term, in order of descending degree.

fn is_zero(&self) -> bool

Returns true if all terms of self are zero, and false if a non-zero term exists.

impl<N> Sub<QuadraticTrinomial<N>> for QuadraticTrinomial<N> where
    N: Copy + Sub<Output = N>, 

type Output = QuadraticTrinomial<N>

The resulting type after applying the - operator.

fn sub(self, rhs: QuadraticTrinomial<N>) -> QuadraticTrinomial<N>

Performs the - operation.

impl<N> SubAssign<QuadraticTrinomial<N>> for QuadraticTrinomial<N> where
    N: SubAssign + Copy, 

fn sub_assign(&mut self, rhs: QuadraticTrinomial<N>)

Performs the -= operation.