Struct Polynomial 

pub struct Polynomial { /* private fields */ }

Dense polynomial representation with fixed metadata (max_degree, modulus).

Internally, coeffs always has length max_degree + 1. Coefficients beyond the true degree are stored as zeros.

Implementations

impl Polynomial

pub fn new( max_degree: usize, modulus: u64, coeffs: &[u64], ) -> Result<Self, PolynomialError>

Creates a polynomial with degree bound max_degree over modulus modulus.

Coefficients are normalized modulo modulus and then zero-padded to length max_degree + 1.

Errors

Returns:

• PolynomialError::InvalidModulus when modulus < 2,
• PolynomialError::DegreeOverflow when coeffs.len() > max_degree + 1.

pub fn zero(max_degree: usize, modulus: u64) -> Result<Self, PolynomialError>

Returns the additive identity polynomial 0.

pub fn one(max_degree: usize, modulus: u64) -> Result<Self, PolynomialError>

Returns the multiplicative identity polynomial 1.

pub fn max_degree(&self) -> usize

Returns the configured maximum degree n.

pub fn modulus(&self) -> u64

Returns the coefficient modulus q.

pub fn coefficients(&self) -> &[u64]

Returns the internal dense coefficient slice of length max_degree + 1.

pub fn trimmed_coefficients(&self) -> Vec<u64>

Returns coefficients trimmed to the actual degree.

Zero polynomial is returned as [0].

pub fn coeff(&self, degree: usize) -> Option<u64>

Returns coefficient of x^degree, or None when out of bounds.

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

Returns the true polynomial degree, or None for zero polynomial.

pub fn is_zero(&self) -> bool

Returns true when all coefficients are zero.

pub fn add(&self, rhs: &Self) -> Result<Self, PolynomialError>

Adds two polynomials coefficient-wise in Z_q[x].

Errors

Returns PolynomialError::IncompatiblePolynomials when n or q differ.

pub fn sub(&self, rhs: &Self) -> Result<Self, PolynomialError>

Subtracts rhs from self coefficient-wise in Z_q[x].

Errors

Returns PolynomialError::IncompatiblePolynomials when n or q differ.

pub fn neg(&self) -> Self

Returns additive inverse -self in Z_q[x].

pub fn scalar_mul(&self, scalar: u64) -> Self

Multiplies all coefficients by scalar in Z_q.

pub fn mul(&self, rhs: &Self) -> Result<Self, PolynomialError>

Schoolbook polynomial multiplication with strict degree bound enforcement.

Errors

Returns:

• PolynomialError::IncompatiblePolynomials when n or q differ,
• PolynomialError::ProductDegreeOverflow if exact product degree exceeds max_degree.

pub fn mul_ntt( &self, rhs: &Self, primitive_root: u64, ) -> Result<Self, PolynomialError>

NTT-based polynomial multiplication.

This computes exact convolution via NTT and then places the result in the dense output buffer (length max_degree + 1).

Errors

Returns:

• PolynomialError::IncompatiblePolynomials when n or q differ,
• PolynomialError::ProductDegreeOverflow if exact product degree exceeds max_degree,
• NTT-specific errors when modulus/root parameters are not valid.

pub fn mul_truncated(&self, rhs: &Self) -> Result<Self, PolynomialError>

Schoolbook multiplication truncated to degree max_degree.

Unlike Self::mul, this method never returns degree-overflow errors; terms above max_degree are discarded.

Errors

Returns PolynomialError::IncompatiblePolynomials when n or q differ.

pub fn rem_mod_poly(&self, modulus_poly: &Self) -> Result<Self, PolynomialError>

Reduces self modulo modulus_poly, returning self mod modulus_poly in Z_q[x].

Errors

Returns:

• PolynomialError::IncompatiblePolynomials when n or q differ,
• PolynomialError::DivisionByZeroPolynomial if modulus_poly is zero,
• PolynomialError::NonInvertibleCoefficient if leading coefficient of modulus_poly is not invertible in Z_q.

pub fn add_mod_poly( &self, rhs: &Self, modulus_poly: &Self, ) -> Result<Self, PolynomialError>

Adds two polynomials and reduces modulo modulus_poly.

pub fn sub_mod_poly( &self, rhs: &Self, modulus_poly: &Self, ) -> Result<Self, PolynomialError>

Subtracts two polynomials and reduces modulo modulus_poly.

pub fn mul_mod_poly( &self, rhs: &Self, modulus_poly: &Self, ) -> Result<Self, PolynomialError>

Multiplies two polynomials and reduces modulo modulus_poly.

This computes the exact product first (in a temporary buffer sized to exact degree), then applies polynomial reduction.

Errors

Returns compatibility and reduction-related errors as described by Self::rem_mod_poly.

pub fn evaluate(&self, x: u64) -> u64

Evaluates polynomial at x using Horner’s method in Z_q.

pub fn derivative(&self) -> Self

Returns formal derivative d/dx(self) in Z_q[x].

pub fn div_rem(&self, divisor: &Self) -> Result<(Self, Self), PolynomialError>

Polynomial long division in Z_q[x]: returns (quotient, remainder).

Errors

Returns:

• PolynomialError::IncompatiblePolynomials when n or q differ,
• PolynomialError::DivisionByZeroPolynomial if divisor is zero,
• PolynomialError::NonInvertibleCoefficient if divisor leading coefficient has no inverse in Z_q.

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 Eq for Polynomial

impl StructuralPartialEq for Polynomial