Math.NumberTheory.Moduli.Jacobi

Jacobi symbol.

Documentation

data JacobiSymbol

Type for result of jacobi.

Constructors

MinusOne

Zero

One

Instances

Eq JacobiSymbol

Methods

(==) :: JacobiSymbol -> JacobiSymbol -> Bool

(/=) :: JacobiSymbol -> JacobiSymbol -> Bool

Ord JacobiSymbol

Methods

compare :: JacobiSymbol -> JacobiSymbol -> Ordering

(<) :: JacobiSymbol -> JacobiSymbol -> Bool

(<=) :: JacobiSymbol -> JacobiSymbol -> Bool

(>) :: JacobiSymbol -> JacobiSymbol -> Bool

(>=) :: JacobiSymbol -> JacobiSymbol -> Bool

max :: JacobiSymbol -> JacobiSymbol -> JacobiSymbol

min :: JacobiSymbol -> JacobiSymbol -> JacobiSymbol

Show JacobiSymbol

Methods

showsPrec :: Int -> JacobiSymbol -> ShowS

show :: JacobiSymbol -> String

showList :: [JacobiSymbol] -> ShowS

Semigroup JacobiSymbol

Methods

(<>) :: JacobiSymbol -> JacobiSymbol -> JacobiSymbol

sconcat :: NonEmpty JacobiSymbol -> JacobiSymbol

stimes :: Integral b => b -> JacobiSymbol -> JacobiSymbol

Monoid JacobiSymbol

Methods

mempty :: JacobiSymbol

mappend :: JacobiSymbol -> JacobiSymbol -> JacobiSymbol

mconcat :: [JacobiSymbol] -> JacobiSymbol

jacobi :: (Integral a, Bits a) => a -> a -> JacobiSymbol

Jacobi symbol of two numbers. The "denominator" must be odd and positive, this condition is checked.

If both numbers have a common prime factor, the result is 0, otherwise it is ±1.

jacobi' :: (Integral a, Bits a) => a -> a -> JacobiSymbol

Jacobi symbol of two numbers without validity check of the "denominator".