Math.NumberTheory.Moduli.Equations

Polynomial modular equations.

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

:: SFactors Integer m

-> Mod m

a

-> Mod m

b

-> Mod m

c

-> [Mod m]

list of x

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

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