Copyright	(c) 2018 Andrew Lelechenko
License	MIT
Maintainer	Andrew Lelechenko <andrew.lelechenko@gmail.com>
Stability	Provisional
Portability	Non-portable (GHC extensions)
Safe Haskell	None
Language	Haskell2010

Math.NumberTheory.Moduli.Equations

Description

Polynomial modular equations.

Synopsis

solveLinear :: KnownNat m => Mod m -> Mod m -> [Mod m]
solveQuadratic :: KnownNat m => Mod m -> Mod m -> Mod m -> [Mod m]

Documentation

solveLinear #

Arguments

:: KnownNat m
=> Mod m	a
-> Mod m	b
-> [Mod m]	list of x

Find all solutions of ax + b ≡ 0 (mod m).

>>> :set -XDataKinds
>>> solveLinear (6 :: Mod 10) 4 -- solving 6x + 4 ≡ 0 (mod 10)
[(1 `modulo` 10),(6 `modulo` 10)]

solveQuadratic #

Arguments

:: KnownNat m
=> Mod m	a
-> Mod m	b
-> Mod m	c
-> [Mod m]	list of c

Find all solutions of ax² + bx + c ≡ 0 (mod m).

>>> :set -XDataKinds
>>> solveQuadratic (1 :: Mod 32) 0 (-17) -- solving x² - 17 ≡ 0 (mod 32)
[(9 `modulo` 32),(25 `modulo` 32),(7 `modulo` 32),(23 `modulo` 32)]