Struct RationalPolynomial 

pub struct RationalPolynomial<D: Domain, O: MonomialOrder = Grevlex> {
    pub numerator: SparseMultivariatePolynomial<D, O>,
    pub denominator: SparseMultivariatePolynomial<D, O>,
}

A rational polynomial $\frac{\text{num}}{\text{den}}$ over a domain D.

After construction via from_num_den, the fraction is always in canonical form:

• numerator and denominator are coprime,
• the denominator’s leading coefficient is positive (for ordered domains) or equal to 1 (for finite fields).

Fields

numerator: SparseMultivariatePolynomial<D, O>

The numerator polynomial.

denominator: SparseMultivariatePolynomial<D, O>

The denominator polynomial (always non-zero).

Implementations

impl<D: Domain, O: MonomialOrder> RationalPolynomial<D, O>

pub fn new( numerator: SparseMultivariatePolynomial<D, O>, denominator: SparseMultivariatePolynomial<D, O>, ) -> Self

Create a rational polynomial without reduction.

The caller must ensure denominator is non-zero. For a canonicalized version use from_num_den.

pub fn from_polynomial(poly: SparseMultivariatePolynomial<D, O>) -> Self

Create a rational polynomial from a polynomial (denominator = 1).

pub fn zero(domain: &D, n_vars: usize) -> Self

Return the zero rational polynomial in n_vars variables.

pub fn one(domain: &D, n_vars: usize) -> Self

Return the unit rational polynomial (1/1) in n_vars variables.

pub fn is_zero(&self) -> bool

Return whether this is the zero rational polynomial.

pub fn is_one(&self) -> bool

Return whether this is the unit rational polynomial (1/1).

pub fn n_vars(&self) -> usize

Return the number of variables.

pub fn domain(&self) -> &D

Return a reference to the coefficient domain.

pub fn neg(&self) -> Self

Return the negation: $-\frac{n}{d}$.

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

Return the multiplicative inverse: $\frac{d}{n}$.

Returns None if the numerator is zero.

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

Return the power $\left(\frac{n}{d}\right)^k$.

impl<D: EuclideanDomain, O: MonomialOrder> RationalPolynomial<D, O>

pub fn from_num_den( numerator: SparseMultivariatePolynomial<D, O>, denominator: SparseMultivariatePolynomial<D, O>, ) -> Self

Create a canonicalized rational polynomial from numerator and denominator.

The result has coprime numerator and denominator, with the denominator’s leading coefficient normalized.

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

Add two rational polynomials: $\frac{a}{b} + \frac{c}{d}$.

Uses the denominator-GCD strategy to minimize intermediate growth.

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

Subtract two rational polynomials.

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

Multiply two rational polynomials with cross-cancellation.

Computes $\gcd(a, d)$ and $\gcd(b, c)$ before multiplying to reduce intermediate coefficient growth.

pub fn div(&self, other: &Self) -> Option<Self>

Divide two rational polynomials: $\frac{a/b}{c/d} = \frac{ad}{bc}$.

Trait Implementations

impl<D: Clone + Domain, O: Clone + MonomialOrder> Clone for RationalPolynomial<D, O>

fn clone(&self) -> RationalPolynomial<D, O>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<D: Debug + Domain, O: Debug + MonomialOrder> Debug for RationalPolynomial<D, O>

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

Formats the value using the given formatter.

impl<D: Domain, O: MonomialOrder> Display for RationalPolynomial<D, O>

where D::Element: Display,

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

Formats the value using the given formatter.

impl<D: Eq + Domain, O: Eq + MonomialOrder> Eq for RationalPolynomial<D, O>

impl<D: PartialEq + Domain, O: PartialEq + MonomialOrder> PartialEq for RationalPolynomial<D, O>

fn eq(&self, other: &RationalPolynomial<D, O>) -> 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<D: PartialEq + Domain, O: PartialEq + MonomialOrder> StructuralPartialEq for RationalPolynomial<D, O>