Copyright | (c) 2011 Daniel Fischer 2017-2018 Andrew Lelechenko |
---|---|
License | MIT |
Maintainer | Andrew Lelechenko <andrew.lelechenko@gmail.com> |
Safe Haskell | None |
Language | Haskell2010 |
Math.NumberTheory.Moduli.Jacobi
Description
Deprecated: Use Math.NumberTheory.Moduli.Sqrt instead
Description: Deprecated
Jacobi symbol is a generalization of the Legendre symbol, useful for primality testing and integer factorization.
Synopsis
- data JacobiSymbol
- jacobi :: (Integral a, Bits a) => a -> a -> JacobiSymbol
- symbolToNum :: Num a => JacobiSymbol -> a
Documentation
data JacobiSymbol Source #
Represents three possible values of Jacobi symbol.
Instances
Eq JacobiSymbol Source # | |
Defined in Math.NumberTheory.Moduli.JacobiSymbol | |
Ord JacobiSymbol Source # | |
Defined in Math.NumberTheory.Moduli.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 Source # | |
Defined in Math.NumberTheory.Moduli.JacobiSymbol Methods showsPrec :: Int -> JacobiSymbol -> ShowS # show :: JacobiSymbol -> String # showList :: [JacobiSymbol] -> ShowS # | |
Semigroup JacobiSymbol Source # | |
Defined in Math.NumberTheory.Moduli.JacobiSymbol Methods (<>) :: JacobiSymbol -> JacobiSymbol -> JacobiSymbol # sconcat :: NonEmpty JacobiSymbol -> JacobiSymbol # stimes :: Integral b => b -> JacobiSymbol -> JacobiSymbol # |
jacobi :: (Integral a, Bits a) => a -> a -> JacobiSymbol Source #
Jacobi symbol of two arguments. The lower argument ("denominator") must be odd and positive, this condition is checked.
If arguments have a common factor, the result
is Zero
, otherwise it is MinusOne
or One
.
>>>
jacobi 1001 9911
Zero -- arguments have a common factor 11>>>
jacobi 1001 9907
MinusOne
symbolToNum :: Num a => JacobiSymbol -> a Source #
Convenience function to convert out of a Jacobi symbol