Struct SparsePolynomial 

pub struct SparsePolynomial {
    pub terms: HashMap<Monomial, BigRational>,
    pub num_vars: usize,
}

Sparse polynomial: HashMap<Monomial, Coefficient>

Efficient representation for polynomial computation:

• Addition: O(n) - merge hashmaps
• Multiplication: O(n²) - compute all monomial products
• No expression tree growth - coefficients are BigRational

Fields

terms: HashMap<Monomial, BigRational>

Terms: monomial → coefficient Only non-zero coefficients are stored

num_vars: usize

Number of variables

Implementations

impl SparsePolynomial

pub fn zero(num_vars: usize) -> Self

Create zero polynomial

pub fn from_term( monomial: Monomial, coeff: BigRational, num_vars: usize, ) -> Self

Create polynomial from single term

pub fn constant(value: BigRational, num_vars: usize) -> Self

Create constant polynomial

pub fn is_zero(&self) -> bool

Check if polynomial is zero

pub fn leading_monomial(&self, order: &MonomialOrder) -> Option<&Monomial>

Get leading monomial (w.r.t. given ordering)

pub fn leading_coefficient(&self, order: &MonomialOrder) -> Option<&BigRational>

Get leading coefficient

pub fn leading_term( &self, order: &MonomialOrder, ) -> Option<(Monomial, BigRational)>

Get leading term (monomial + coefficient)

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

Add two polynomials (O(n) operation)

pub fn neg(&self) -> Self

Negate polynomial

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

Subtract two polynomials

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

Multiply two polynomials (O(n²) operation)

pub fn scalar_mul(&self, scalar: &BigRational) -> Self

Multiply by scalar

pub fn mul_monomial(&self, monomial: &Monomial) -> Self

Multiply polynomial by a monomial

Trait Implementations

impl Clone for SparsePolynomial

fn clone(&self) -> SparsePolynomial

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for SparsePolynomial

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

Formats the value using the given formatter.