Struct Monomial 

pub struct Monomial<N> {
    pub coefficient: N,
    pub deg: usize,
}

A type that represents a monomial. Operations are much faster than on other types representing the same polynomial, but terms can not be added freely.

Fields

coefficient: N

deg: usize

Implementations

impl<N> Monomial<N>

pub fn new(coefficient: N, degree: usize) -> Monomial<N>

Create a Monomial with coefficient and degree.

Example

use rustnomial::{Monomial, Degree, SizedPolynomial};
let monomial = Monomial::new(3.0, 2);
assert_eq!(3.0, monomial.coefficient);
assert_eq!(Degree::Num(2), monomial.degree());

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

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

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

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

Return the root of Monomial.

Example

use rustnomial::{Monomial, Roots, SizedPolynomial};
let monomial = Monomial::new(1, 2);
assert_eq!(Roots::OneRealRoot(0), monomial.root());
let zero = Monomial::<i32>::zero();
assert_eq!(Roots::InfiniteRoots, zero.root());
let constant = Monomial::new(1, 0);
assert_eq!(Roots::NoRoots, constant.root());

impl<N: PowUsize + Copy> Monomial<N>

pub fn pow(&self, exp: usize) -> Monomial<N>

Raises the Monomial to the power of exp.

Example

use rustnomial::Monomial;
let monomial = Monomial::new(2, 1);
let monomial_sqr = monomial.pow(2);
let monomial_cub = monomial.pow(3);
assert_eq!(monomial.clone() * monomial.clone(), monomial_sqr);
assert_eq!(monomial_sqr.clone() * monomial.clone(), monomial_cub);

Trait Implementations

impl<N: Clone> Clone for Monomial<N>

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

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<N: Debug> Debug for Monomial<N>

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

Formats the value using the given formatter.

impl<N> Derivable<N> for Monomial<N>

where N: Zero + Copy + Mul<Output = N> + TryFromUsizeExact,

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

Returns the derivative of the Monomial.

Example

use rustnomial::{Monomial, Derivable};
let monomial = Monomial::new(3.0, 2);
assert_eq!(Monomial::new(6.0, 1), monomial.derivative());

Errors

Will panic if N can not losslessly represent the degree of self.

impl<N> Display for Monomial<N>

where N: Zero + One + PartialEq + Copy + IsNegativeOne + Display,

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

Formats the value using the given formatter.

impl<N: Div<Output = N>> Div<N> for Monomial<N>

type Output = Monomial<N>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<N: DivAssign> DivAssign<N> for Monomial<N>

fn div_assign(&mut self, rhs: N)

Performs the /= operation.

impl<N> Evaluable<N> for Monomial<N>

where N: PowUsize + Mul<Output = N> + Copy,

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

Returns the value of the Monomial at the given point.

Example

use rustnomial::{Monomial, Evaluable};
let monomial = Monomial::new(5, 2);
assert_eq!(125, monomial.eval(5));
assert_eq!(1, Monomial::new(1, 0).eval(0));

impl From<Monomial<f32>> for Monomial<f64>

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

Converts to this type from the input type.

impl From<Monomial<i16>> for Monomial<f32>

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

Converts to this type from the input type.

impl From<Monomial<i16>> for Monomial<f64>

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

Converts to this type from the input type.

impl From<Monomial<i16>> for Monomial<i128>

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

Converts to this type from the input type.

impl From<Monomial<i16>> for Monomial<i32>

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

Converts to this type from the input type.

impl From<Monomial<i16>> for Monomial<i64>

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

Converts to this type from the input type.

impl From<Monomial<i32>> for Monomial<f64>

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

Converts to this type from the input type.

impl From<Monomial<i32>> for Monomial<i128>

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

Converts to this type from the input type.

impl From<Monomial<i32>> for Monomial<i64>

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

Converts to this type from the input type.

impl From<Monomial<i64>> for Monomial<i128>

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

Converts to this type from the input type.

impl From<Monomial<i8>> for Monomial<f32>

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

Converts to this type from the input type.

impl From<Monomial<i8>> for Monomial<f64>

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

Converts to this type from the input type.

impl From<Monomial<i8>> for Monomial<i128>

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

Converts to this type from the input type.

impl From<Monomial<i8>> for Monomial<i16>

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

Converts to this type from the input type.

impl From<Monomial<i8>> for Monomial<i32>

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

Converts to this type from the input type.

impl From<Monomial<i8>> for Monomial<i64>

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

Converts to this type from the input type.

impl From<Monomial<u16>> for Monomial<f32>

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

Converts to this type from the input type.

impl From<Monomial<u16>> for Monomial<f64>

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

Converts to this type from the input type.

impl From<Monomial<u16>> for Monomial<i128>

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

Converts to this type from the input type.

impl From<Monomial<u16>> for Monomial<i32>

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

Converts to this type from the input type.

impl From<Monomial<u16>> for Monomial<i64>

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

Converts to this type from the input type.

impl From<Monomial<u16>> for Monomial<u128>

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

Converts to this type from the input type.

impl From<Monomial<u16>> for Monomial<u32>

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

Converts to this type from the input type.

impl From<Monomial<u16>> for Monomial<u64>

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

Converts to this type from the input type.

impl From<Monomial<u32>> for Monomial<f64>

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

Converts to this type from the input type.

impl From<Monomial<u32>> for Monomial<i128>

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

Converts to this type from the input type.

impl From<Monomial<u32>> for Monomial<i64>

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

Converts to this type from the input type.

impl From<Monomial<u32>> for Monomial<u128>

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

Converts to this type from the input type.

impl From<Monomial<u32>> for Monomial<u64>

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

Converts to this type from the input type.

impl From<Monomial<u64>> for Monomial<i128>

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

Converts to this type from the input type.

impl From<Monomial<u64>> for Monomial<u128>

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

Converts to this type from the input type.

impl From<Monomial<u8>> for Monomial<f32>

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

Converts to this type from the input type.

impl From<Monomial<u8>> for Monomial<f64>

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

Converts to this type from the input type.

impl From<Monomial<u8>> for Monomial<i128>

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

Converts to this type from the input type.

impl From<Monomial<u8>> for Monomial<i16>

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

Converts to this type from the input type.

impl From<Monomial<u8>> for Monomial<i32>

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

Converts to this type from the input type.

impl From<Monomial<u8>> for Monomial<i64>

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

Converts to this type from the input type.

impl From<Monomial<u8>> for Monomial<u128>

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

Converts to this type from the input type.

impl From<Monomial<u8>> for Monomial<u16>

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

Converts to this type from the input type.

impl From<Monomial<u8>> for Monomial<u32>

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

Converts to this type from the input type.

impl From<Monomial<u8>> for Monomial<u64>

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

Converts to this type from the input type.

impl<N> From<N> for Monomial<N>

fn from(item: N) -> Self

Converts to this type from the input type.

impl<N> FromStr for Monomial<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, SparsePolynomial<N>> for Monomial<N>

where N: Zero + Copy + Mul<Output = N> + AddAssign + PowUsize + Div<Output = N> + TryFromUsizeExact,

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

Returns the integral of the Monomial.

Example

use rustnomial::{Monomial, SparsePolynomial, Integrable, FreeSizePolynomial};
let monomial = Monomial::new(3.0, 2);
let integral = monomial.integral();
assert_eq!(&SparsePolynomial::from_terms(&[(1.0, 3)]), integral.inner());
assert_eq!(1., integral.eval(0., 1.));

impl<N: Copy + Mul<Output = N>> Mul<&Monomial<N>> for Monomial<N>

type Output = Monomial<N>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N: Mul<Output = N>> Mul<N> for Monomial<N>

type Output = Monomial<N>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Monomial<N>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N> MulAssign<&Monomial<N>> for Monomial<N>

where N: MulAssign + AddAssign + Copy,

fn mul_assign(&mut self, rhs: &Monomial<N>)

Performs the *= operation.

impl<N: MulAssign> MulAssign<N> for Monomial<N>

fn mul_assign(&mut self, rhs: N)

Performs the *= operation.

impl<N: MulAssign> MulAssign for Monomial<N>

fn mul_assign(&mut self, rhs: Monomial<N>)

Performs the *= operation.

impl<N> MutablePolynomial<N> for Monomial<N>

where N: SubAssign + AddAssign + Copy + Zero,

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 Monomial<N>

type Output = Monomial<N>

The resulting type after applying the - operator.

fn neg(self) -> Monomial<N>

Performs the unary - operation.

impl<N> PartialEq for Monomial<N>

where N: Zero + PartialEq + Copy,

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

Returns true if this Monomial is equal to other.

Example

use rustnomial::Monomial;
let a = Monomial::new(2, 2);
let b = Monomial::new(2, 2);
let c = Monomial::new(1, 2);
assert_eq!(a, b);
assert_ne!(a, c);

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

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<N: Zero + Copy> Shl<i32> for Monomial<N>

type Output = Monomial<N>

The resulting type after applying the << operator.

fn shl(self, rhs: i32) -> Monomial<N>

Performs the << operation.

impl<N: Zero + Copy> ShlAssign<i32> for Monomial<N>

fn shl_assign(&mut self, rhs: i32)

Performs the <<= operation.

impl<N: Zero + Copy> Shr<i32> for Monomial<N>

type Output = Monomial<N>

The resulting type after applying the >> operator.

fn shr(self, rhs: i32) -> Monomial<N>

Performs the >> operation.

impl<N: Zero + Copy> ShrAssign<i32> for Monomial<N>

fn shr_assign(&mut self, rhs: i32)

Performs the >>= operation.

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

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

Returns the term with the given degree of the Monomial.

Example

use rustnomial::{Monomial, SizedPolynomial, Term};
let monomial = Monomial::new(5, 2);
assert_eq!(Term::Term(5, 2), monomial.term_with_degree(2));
assert_eq!(Term::ZeroTerm, monomial.term_with_degree(1));

fn degree(&self) -> Degree

Returns the degree of the Monomial.

Example

use rustnomial::{SizedPolynomial, Monomial, Degree};
let monomial = Monomial::new(3.0, 2);
assert_eq!(Degree::Num(2), monomial.degree());
let zero_with_nonzero_deg = Monomial::new(0.0, 2);
assert_eq!(Degree::NegInf, zero_with_nonzero_deg.degree());
let nonzero_with_zero_degree = Monomial::new(1.0, 0);
assert_eq!(Degree::Num(0), nonzero_with_zero_degree.degree());

fn zero() -> Self

Return a Monomial which is equal to zero.

Example

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

fn set_to_zero(&mut self)

Sets self to zero.

Example

use rustnomial::{SizedPolynomial, Monomial};
let mut non_zero = Monomial::new(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.