Struct libbgs::numbers::SylowDecomp
source · pub struct SylowDecomp<S, const L: usize, C: SylowDecomposable<S>> { /* private fields */ }Expand description
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§
source§impl<S, const L: usize, C: SylowDecomposable<S>> SylowDecomp<S, L, C>
impl<S, const L: usize, C: SylowDecomposable<S>> SylowDecomp<S, L, C>
sourcepub fn new() -> 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.
sourcepub fn generator(&self, i: usize) -> &C
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 $p^t$.