Trait libbgs::numbers::SylowDecomposable

pub trait SylowDecomposable<S>: Factor<S> + GroupElem + Eq {
    // Required method
    fn find_sylow_generator(i: usize) -> Self;

    // Provided methods
    fn is_sylow_generator(candidate: &Self, d: (u128, usize)) -> Option<Self> { ... }
    fn count_elements_of_order(ds: &[usize]) -> u128 { ... }
}

Groups that can be decomposed into a direct sum of cyclic Sylow subgroups. In particular, these groups must be finite and cyclic.

Required Methods

fn find_sylow_generator(i: usize) -> Self

Finds a Sylow generator for the Sylow subgroup of prime power index i.

Provided Methods

fn is_sylow_generator(candidate: &Self, d: (u128, usize)) -> Option<Self>

True if the given element is a generator of the Sylow subgroup of the prime power represented by d.

fn count_elements_of_order(ds: &[usize]) -> u128

Returns the number of elements of a particular order. The argument is the powers of the prime factors of the group’s order.

Implementors

impl<S, const L: usize, C: SylowDecomposable<S>> SylowDecomposable<S> for SylowElem<S, L, C>

impl<S, const P: u128> SylowDecomposable<S> for FpNum<P>where FpNum<P>: Factor<S>,

impl<S, const P: u128> SylowDecomposable<S> for QuadNum<P>where QuadNum<P>: Factor<S>,