Struct libbgs::numbers::SylowDecomp

pub struct SylowDecomp<S, const L: usize, C: SylowDecomposable<S>> { /* private fields */ }

A decomposition of a finite cyclic group into the direct sum of its Sylow subgroups. In particular, this group represents the right hand side of the isomorphism $G \cong \bigoplus_{i = 1}^n \mathbb{Z} / p_i^{t_i} \mathbb{Z}$ where $|G| = \prod_{i = 1}^n p_i^{t_i}$ and $G$ is a finite cyclic group.

Implementations

impl<S, const L: usize, C: SylowDecomposable<S>> SylowDecomp<S, L, C>

pub fn new() -> SylowDecomp<S, L, C>

Returns a decomposition for the group. This method may be expensive because it calls find_sylow_generator for each Sylow subgroup.

pub fn generator(&self, i: usize) -> &C

Get the generators for decomposition. The index of each generator corresponds to the index of the prime power in the factorization. That is, if the prime power at index i of the factorization is $(p, t)$, then the generator at index i of the array returned by the generators method is a generator of the Sylow subgroup of order $p^t$.