Struct Polynomial 

pub struct Polynomial { /* private fields */ }

A polynomial in variables numbered from 0, with rational coefficients. No coefficient is zero, so equal polynomials are structurally equal.

Implementations

impl Polynomial

pub fn zero() -> Polynomial

pub fn one() -> Polynomial

pub fn constant(c: Rational) -> Polynomial

pub fn var(i: usize) -> Polynomial

Variable i.

pub fn monomial(c: Rational, exponents: Vec<u32>) -> Polynomial

c · Π x_i^e_i.

pub fn from_univariate(p: &Poly, v: usize) -> Polynomial

The univariate p in variable v.

pub fn is_zero(&self) -> bool

pub fn as_constant(&self) -> Option<Rational>

The value of a polynomial with no variable; None for any other.

pub fn terms(&self) -> impl Iterator<Item = (&[u32], &Rational)>

The terms, exponents with no trailing zero, in increasing order of exponents.

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

pub fn neg(&self) -> Polynomial

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

pub fn scale(&self, k: &Rational) -> Polynomial

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

pub fn pow(&self, k: u32) -> Polynomial

pub fn degree_in(&self, v: usize) -> u32

The degree in variable v; zero for the zero polynomial.

pub fn variables(&self) -> BTreeSet<usize>

The variables that occur.

pub fn coefficient_in(&self, v: usize, k: u32) -> Polynomial

The coefficient of x_v^k, a polynomial in the other variables.

pub fn leading_in(&self, v: usize) -> Polynomial

The coefficient of the highest power of x_v.

pub fn substitute(&self, v: usize, x: &Rational) -> Polynomial

x_v set to x.

pub fn compose(&self, v: usize, p: &Polynomial) -> Polynomial

x_v replaced by the polynomial p.

pub fn derivative(&self, v: usize) -> Polynomial

∂/∂x_v.

pub fn to_univariate(&self, v: usize) -> Option<Poly>

The polynomial as one in x_v alone; None when another variable occurs.

pub fn resultant(&self, o: &Polynomial, v: usize) -> Polynomial

The resultant in x_v: lc^{deg o} · Π o(α) over the roots α in x_v of self, a polynomial in the other variables, by the univariate resultant’s convention (Poly::resultant). Zero when either is zero; self^{deg o} when self does not hold x_v.

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 Default for Polynomial

fn default() -> Polynomial

Returns the “default value” for a type.

impl Display for Polynomial

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

Terms from the highest exponents down, variable i written x{i}.

impl Hash for Polynomial

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, Self: Sized,

Feeds a slice of this type into the given Hasher.

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 Eq for Polynomial

impl StructuralPartialEq for Polynomial