Copyright	(c) 2011 Daniel Fischer 2017 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.Jacobi

Description

Jacobi symbol.

Synopsis

Documentation

Type for result of jacobi.

Constructors

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