Struct libbgs::markoff::Coord

pub struct Coord<const P: u128>(pub FpNum<P>);

A coordinate for a Markoff triple. May represent any of $a$, $b$, or $c$ in a Markoff triple $(a, b, c)$. This is a single field struct containing only an FpNum<P> for prime P.

Tuple Fields

0: FpNum<P>

Implementations

impl<const P: u128> Coord<P>

pub fn to_chi(&self) -> Either<QuadNum<P>, FpNum<P>>

Returns an element $\chi$ such that, for a coordinate $a$, $a = \chi + \chi^{-1}$. If $a$ is a quadratic residue modulo P, then $\chi \in \mathbb{F}_p$, and the result will be a Right<FpNum<P>>. Otherwise, $\chi \in \mathbb{F}_{p^2}$, and the result will be a Left<QuadNum<P>>.

pub fn rot( self, b: Coord<P>, c: Coord<P> ) -> impl Iterator<Item = (Coord<P>, Coord<P>)>

Returns an iterator yielding the coordinates $(b, c)$ contained in the orbit with fixed coordinate $a$ (the coordinate on which rot is called), beginning with $(a, b, c)$.

pub fn part(self, b: Coord<P>) -> Option<Box<dyn Iterator<Item = Coord<P>>>>

Returns an iterator yielding the values $b$ such that $(a, b, c)$ is a Markoff triple for some value $c$.

pub fn rot_order<S1, S2>(&self) -> RotOrderwhere FpNum<P>: Factor<S1>, QuadNum<P>: Factor<S2>,

Returns the order of the map $\text{rot}_a$, that is, $\lvert \langle \text{rot}_a \rangle \rvert$, along with the type of RotOrder that it is.

pub fn endgame<S>() -> (u128, u128)where FpNum<P>: Factor<S>, QuadNum<P>: Factor<S>,

Returns an upper bound on the endgame breakpoint. That is, every triple with order larger than the value returned by this method is guarenteed to lie in the endgame.

Trait Implementations

impl<const P: u128> Clone for Coord<P>

fn clone(&self) -> Coord<P>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<const P: u128> From<Coord<P>> for u128

fn from(src: Coord<P>) -> u128

Converts to this type from the input type.

impl<const P: u128> From<u128> for Coord<P>

fn from(src: u128) -> Coord<P>

Converts to this type from the input type.

impl<const P: u128> PartialEq<Coord<P>> for Coord<P>

fn eq(&self, other: &Coord<P>) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<const P: u128> Copy for Coord<P>

impl<const P: u128> Eq for Coord<P>

impl<const P: u128> StructuralEq for Coord<P>

impl<const P: u128> StructuralPartialEq for Coord<P>