Struct Polynomial 

pub struct Polynomial { /* private fields */ }

Dense univariate polynomial with f64 coefficients, little-endian.

Implementations

impl Polynomial

pub fn new(coeffs: Vec<f64>) -> Self

Build from coefficients (index i = coefficient of x^i), trimming any near-zero high-order terms.

pub fn zero() -> Self

The zero polynomial.

pub fn constant(c: f64) -> Self

The constant polynomial c.

pub fn coeffs(&self) -> &[f64]

Borrow the (trimmed) coefficient slice, little-endian.

pub fn is_zero(&self) -> bool

True if this is the zero polynomial.

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

Degree of the polynomial, or None for the zero polynomial.

pub fn leading(&self) -> f64

Leading coefficient (highest-order). 0.0 for the zero polynomial.

pub fn eval(&self, x: f64) -> f64

Evaluate at x using Horner’s method.

pub fn add(&self, other: &Polynomial) -> Polynomial

Sum self + other.

pub fn sub(&self, other: &Polynomial) -> Polynomial

Difference self - other.

pub fn scale(&self, s: f64) -> Polynomial

Scale every coefficient by s.

pub fn mul(&self, other: &Polynomial) -> Polynomial

Product self * other (schoolbook convolution).

pub fn div_rem(&self, divisor: &Polynomial) -> Option<(Polynomial, Polynomial)>

Polynomial long division: returns (quotient, remainder) with self == quotient * divisor + remainder and deg(remainder) < deg(divisor). Fails closed (None) when dividing by the zero polynomial.

pub fn derivative(&self) -> Polynomial

First derivative.

pub fn monic(&self) -> Polynomial

Make the polynomial monic (leading coefficient 1). Zero polynomial maps to itself.

pub fn gcd(&self, other: &Polynomial) -> Polynomial

Greatest common divisor via the Euclidean algorithm, returned monic (so it is unique up to the normalisation gcd of the zero polynomial with p is monic(p)).

pub fn resultant(&self, other: &Polynomial) -> f64

Resultant of self and other via the Euclidean remainder sequence.

The resultant is zero iff the two polynomials share a common root (over the complex numbers / have a non-constant gcd). It is computed by running the Euclidean algorithm and accumulating the standard degree/leading-coefficient factors that relate res(a, b) to res(b, a mod b):

res(a, b) = (-1)^(deg a · deg b) · lc(b)^(deg a − deg r) · res(b, r)

with base cases res(a, const c) = c^(deg a) and a zero result whenever a remainder vanishes with positive remaining degree (a common factor).

Trait Implementations

impl Clone for Polynomial

fn clone(&self) -> Polynomial

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Polynomial

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

Formats the value using the given formatter.

impl PartialEq for Polynomial

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

Tests for self and other values to be equal, and is used by ==.

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 StructuralPartialEq for Polynomial