Struct SparsePolynomial 

pub struct SparsePolynomial { /* private fields */ }

Available on crate feature exact only.

An exact polynomial Σ coefficient[e] * t^e with nonnegative u128 exponents.

Terms are stored in increasing exponent order. Coefficients are reduced rational numbers with positive denominators; zero coefficients are absent. Duplicate input exponents are summed exactly, including cancellation. Self::leading_term means the least exponent with a nonzero coefficient, appropriate to an infinitesimal t → 0+, rather than the highest degree.

Storage and arbitrary-precision coefficients allocate on the heap. Construction consumes owned terms; queries borrow them; cloning makes a deep copy. The determinant budget does not cover construction. Multivariate encodings, perturbation-variable assignment and interpretation of coefficient signs belong to callers, who must prove their encoding preserves the desired order and exponent addition. No multivariate ordering is inferred here.

Implementations

impl SparsePolynomial

pub const fn zero() -> Self

Construct the zero polynomial without allocating.

pub fn try_from_terms( terms: impl IntoIterator<Item = (u128, BigRational)>, ) -> Result<Self, LaError>

Consume terms, normalize rational coefficients and combine equal exponents.

Input order is immaterial to a successful result. Raw unreduced or negative-denominator rationals are accepted. Validation precedes zero removal, so even 0/0 is rejected. The iterator is consumed only up to the first invalid coefficient; this constructor has no work budget.

Errors

Returns LaError::NonFinite with input origin and a NonFiniteLocation::PolynomialTerm for a zero denominator.

pub const fn terms(&self) -> &BTreeMap<u128, BigRational>

Borrow all nonzero terms in increasing exponent order.

pub fn is_zero(&self) -> bool

Whether every coefficient is exactly zero.

pub fn leading_term(&self) -> Option<(u128, &BigRational)>

Borrow the first nonzero coefficient in increasing exponent order.

None proves this is the zero polynomial. A failed determinant evaluation never returns a polynomial, so it cannot be confused with this result.

Trait Implementations

impl Clone for SparsePolynomial

fn clone(&self) -> Self

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.

impl Default for SparsePolynomial

fn default() -> Self

Returns the “default value” for a type.

impl Eq for SparsePolynomial

impl PartialEq for SparsePolynomial

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

Equality operator ==.

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

Inequality operator !=.

impl StructuralPartialEq for SparsePolynomial