Trait PermutationMonomial 

pub trait PermutationMonomial<const N: u64>: InjectiveMonomial<N> {
    // Required method
    fn injective_exp_root_n(&self) -> Self;
}

A ring implements PermutationMonomial<N> if the algebraic function f(x) = x^N is invertible and thus acts as a permutation on elements of the ring.

In all cases we care about, this means that we can find another integer K such that x = x^{NK} for all elements of our ring.

Required Methods

fn injective_exp_root_n(&self) -> Self

Compute x -> x^K for a given K > 1 such that x^{NK} = x for all elements x.

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementations on Foreign Types

impl PermutationMonomial<7> for Goldilocks

fn injective_exp_root_n(&self) -> Goldilocks

In the field Goldilocks, a^{1/7} is equal to a^{10540996611094048183}.

This follows from the calculation 7*10540996611094048183 = 4*(2^64 - 2**32) + 1 = 1 mod (p - 1).

impl<FP, const D: u64> PermutationMonomial<D> for MontyField31<FP>

where FP: FieldParameters + RelativelyPrimePower<D>,

fn injective_exp_root_n(&self) -> MontyField31<FP>

Implementors

impl PermutationMonomial<7> for Felt