FareyNeighbours

Whether $p/q$ and $r/s$ are Farey neighbours — adjacent in some Farey sequence, which is the determinant test $|ps-qr|=1$.

FareyNeighbours(p, q, r, s)$|ps-qr|=1$

Typed signatures

Type	Package	Applies
(integer, integer, integer, integer) -> boolean	modular	always

Domain: The modular group

Examples

Basic #

$|1\cdot 3-2\cdot 2| = 1$

live ↗

In$\mathrm{FareyNeighbours}(1, 2, 2, 3)$Out$\mathrm{True}$

$|1\cdot 5-2\cdot 3| = 1$

live ↗

In$\mathrm{FareyNeighbours}(1, 2, 3, 5)$Out$\mathrm{True}$

Properties #

$|1\cdot 7-2\cdot 3| = 1$

live ↗

In$\mathrm{FareyNeighbours}(1, 2, 3, 7)$Out$\mathrm{True}$

About

Examples	3

See also: SternBrocotPath