Copyright	(c) Masahiro Sakai 2013-2014
License	BSD-style
Maintainer	masahiro.sakai@gmail.com
Stability	provisional
Portability	non-portable (ScopedTypeVariables, MultiParamTypeClasses, DeriveDataTypeable, TemplateHaskell, BangPatterns)
Safe Haskell	None
Language	Haskell2010

Data.FiniteField.PrimeField

Contents

Template haskell utilities

Description

Finite field of prime order p, Fp = Z/pZ.

References:

http://en.wikipedia.org/wiki/Finite_field

Synopsis

Documentation

data PrimeField (p :: Nat) Source #

Finite field of prime order p, Fp = Z/pZ.

NB: Primality of p is assumed, but not checked.

Instances

Instances details

KnownNat p => Bounded (PrimeField p) Source #
Instance details Defined in Data.FiniteField.PrimeField Methods minBound :: PrimeField p # maxBound :: PrimeField p #
KnownNat p => Enum (PrimeField p) Source #
Instance details Defined in Data.FiniteField.PrimeField Methods succ :: PrimeField p -> PrimeField p # pred :: PrimeField p -> PrimeField p # toEnum :: Int -> PrimeField p # fromEnum :: PrimeField p -> Int # enumFrom :: PrimeField p -> [PrimeField p] # enumFromThen :: PrimeField p -> PrimeField p -> [PrimeField p] # enumFromTo :: PrimeField p -> PrimeField p -> [PrimeField p] # enumFromThenTo :: PrimeField p -> PrimeField p -> PrimeField p -> [PrimeField p] #
Eq (PrimeField p) Source #
Instance details Defined in Data.FiniteField.PrimeField Methods (==) :: PrimeField p -> PrimeField p -> Bool # (/=) :: PrimeField p -> PrimeField p -> Bool #
KnownNat p => Fractional (PrimeField p) Source #
Instance details Defined in Data.FiniteField.PrimeField Methods (/) :: PrimeField p -> PrimeField p -> PrimeField p # recip :: PrimeField p -> PrimeField p # fromRational :: Rational -> PrimeField p #
KnownNat p => Num (PrimeField p) Source #
Instance details Defined in Data.FiniteField.PrimeField Methods (+) :: PrimeField p -> PrimeField p -> PrimeField p # (-) :: PrimeField p -> PrimeField p -> PrimeField p # (*) :: PrimeField p -> PrimeField p -> PrimeField p # negate :: PrimeField p -> PrimeField p # abs :: PrimeField p -> PrimeField p # signum :: PrimeField p -> PrimeField p # fromInteger :: Integer -> PrimeField p #
Ord (PrimeField p) Source #
Instance details Defined in Data.FiniteField.PrimeField Methods compare :: PrimeField p -> PrimeField p -> Ordering # (<) :: PrimeField p -> PrimeField p -> Bool # (<=) :: PrimeField p -> PrimeField p -> Bool # (>) :: PrimeField p -> PrimeField p -> Bool # (>=) :: PrimeField p -> PrimeField p -> Bool # max :: PrimeField p -> PrimeField p -> PrimeField p # min :: PrimeField p -> PrimeField p -> PrimeField p #
KnownNat p => Read (PrimeField p) Source #
Instance details Defined in Data.FiniteField.PrimeField Methods readsPrec :: Int -> ReadS (PrimeField p) # readList :: ReadS [PrimeField p] # readPrec :: ReadPrec (PrimeField p) # readListPrec :: ReadPrec [PrimeField p] #
Show (PrimeField p) Source #
Instance details Defined in Data.FiniteField.PrimeField Methods showsPrec :: Int -> PrimeField p -> ShowS # show :: PrimeField p -> String # showList :: [PrimeField p] -> ShowS #
NFData (PrimeField p) Source #
Instance details Defined in Data.FiniteField.PrimeField Methods rnf :: PrimeField p -> () #
KnownNat p => Hashable (PrimeField p) Source #
Instance details Defined in Data.FiniteField.PrimeField Methods hashWithSalt :: Int -> PrimeField p -> Int # hash :: PrimeField p -> Int #
KnownNat p => FiniteField (PrimeField p) Source #
Instance details Defined in Data.FiniteField.PrimeField Methods order :: PrimeField p -> Integer Source # char :: PrimeField p -> Integer Source # pthRoot :: PrimeField p -> PrimeField p Source # allValues :: [PrimeField p] Source #

toInteger :: PrimeField p -> Integer Source #

conversion to Integer

Template haskell utilities

Here is usage example for primeField:

a :: $(primeField 15485867)
a = 1

primeField :: Integer -> TypeQ Source #

Create a PrimeField type