Struct cyclotomic::fields::sparse::Number

pub struct Number {
    order: i64,
    coeffs: FxHashMap<i64, BigRational>,
}

Represents a polynomial in the orderth root of unity.

Fields

order: i64

coeffs: FxHashMap<i64, BigRational>

Implementations

impl Number

pub fn new(order: i64, coeffs: &FxHashMap<i64, BigRational>) -> Number

pub fn increase_order_to(z: &mut Self, new_order: i64)

pub fn match_orders(z1: &mut Number, z2: &mut Number)

Trait Implementations

impl AdditiveGroup for Number

fn add(&mut self, rhs: &mut Self) -> &mut Self

Simplest possible - term wise addition using hashing.

Purposely written so it is obviously symmetric in the parameters, thus commutative by inspection. Of course, there are tests for that.

fn add_invert(&mut self) -> &mut Self

impl Clone for Number

fn clone(&self) -> Number

Returns a copy of the value.

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

Performs copy-assignment from source.

impl CyclotomicFieldElement for Number

fn e(n: i64, k: i64) -> Self

Returns $\zeta_n$^k.

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

Multiplies in-place by scalar. Recall that $\mathbb{Q}(\zeta_n)$ is a $\mathbb{Q}$-vector space.

fn zero_order(n: i64) -> Number

Gives zero expressed as an element of $\mathbb{Q}(\zeta_n)$

fn one_order(n: i64) -> Number

Gives one expressed as an element of $\mathbb{Q}(\zeta_n)$

impl Debug for Number

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

Formats the value using the given formatter.

impl FieldElement for Number

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

Equality, but can shuffle coefficients around and simplify expressions for greater efficiency.

impl MultiplicativeGroup for Number

fn mul(&mut self, rhs: &mut Self) -> &mut Self

Multiplies term by term, not bothering to do anything interesting.

fn mul_invert(&mut self) -> &mut Self

Gives the inverse of $z$ using the product of Galois conjugates.

I don't think there's a "trivial" or "stupid" way of doing this. The product of the Galois conjugates is rational, we can normalise to get the multiplicative inverse.