Math.NumberTheory.Moduli.PrimitiveRoot

Deprecated: Use Math.NumberTheory.Moduli.Multiplicative instead

Description: Deprecated

Primitive roots and cyclic groups.

Primitive roots

data PrimitiveRoot m

PrimitiveRoot m is a type which is only inhabited by primitive roots of m.

Instances

Eq (PrimitiveRoot m)

Defined in Math.NumberTheory.Moduli.Multiplicative

Methods

(==) :: PrimitiveRoot m -> PrimitiveRoot m -> Bool

(/=) :: PrimitiveRoot m -> PrimitiveRoot m -> Bool

KnownNat m => Show (PrimitiveRoot m)

Defined in Math.NumberTheory.Moduli.Multiplicative

Methods

showsPrec :: Int -> PrimitiveRoot m -> ShowS

show :: PrimitiveRoot m -> String

showList :: [PrimitiveRoot m] -> ShowS

unPrimitiveRoot :: PrimitiveRoot m -> MultMod m

Extract primitive root value.

isPrimitiveRoot :: (Integral a, UniqueFactorisation a) => CyclicGroup a m -> Mod m -> Maybe (PrimitiveRoot m)

Check whether a given modular residue is a primitive root.

>>> :set -XDataKinds
>>> import Data.Maybe
>>> isPrimitiveRoot (fromJust cyclicGroup) (1 :: Mod 13)
Nothing
>>> isPrimitiveRoot (fromJust cyclicGroup) (2 :: Mod 13)
Just (PrimitiveRoot {unPrimitiveRoot = MultMod {multElement = (2 `modulo` 13)}})