Safe Haskell	Safe-Inferred
Language	Haskell2010

FinFields

Description

This module supports finite (Galois) fields.

Function gf creates types implementing finite fields.

Synopsis

data FiniteField
- = FiniteField {
  - meta :: FiniteFieldMeta
  - value :: Integer
  }
- | Literal {
  - value :: Integer
  }
data FiniteFieldMeta = FiniteFieldMeta {
- modulus :: Integer
- byteLength :: Int
}
gf :: Integer -> FiniteField
toBytes :: Int -> [Integer] -> ByteString
fromBytes :: Int -> ByteString -> [Integer]

Documentation

data FiniteField Source #

Instantiate an object from a field and subsequently apply overloaded operators such as (+), (-), (*), (/) etc., to compute with field elements.

Constructors

FiniteField
Fields meta :: FiniteFieldMeta value :: Integer
Literal
Fields value :: Integer

Instances

Instances details

Num FiniteField Source #	Addition, Subtraction, Multiplication.
Instance details Defined in FinFields Methods (+) :: FiniteField -> FiniteField -> FiniteField # (-) :: FiniteField -> FiniteField -> FiniteField # (*) :: FiniteField -> FiniteField -> FiniteField # negate :: FiniteField -> FiniteField # abs :: FiniteField -> FiniteField # signum :: FiniteField -> FiniteField # fromInteger :: Integer -> FiniteField #
Fractional FiniteField Source #	Multiplicative inverse, Division.
Instance details Defined in FinFields Methods (/) :: FiniteField -> FiniteField -> FiniteField # recip :: FiniteField -> FiniteField # fromRational :: Rational -> FiniteField #
Show FiniteField Source #
Instance details Defined in FinFields Methods showsPrec :: Int -> FiniteField -> ShowS # show :: FiniteField -> String # showList :: [FiniteField] -> ShowS #
Eq FiniteField Source #	Equality test.
Instance details Defined in FinFields Methods (==) :: FiniteField -> FiniteField -> Bool # (/=) :: FiniteField -> FiniteField -> Bool #

data FiniteFieldMeta Source #

Constructors

FiniteFieldMeta
Fields modulus :: Integer byteLength :: Int

Instances

Instances details

Show FiniteFieldMeta Source #
Instance details Defined in FinFields Methods showsPrec :: Int -> FiniteFieldMeta -> ShowS # show :: FiniteFieldMeta -> String # showList :: [FiniteFieldMeta] -> ShowS #

gf :: Integer -> FiniteField Source #

Create a finite (Galois) field for given modulus (prime number).

toBytes :: Int -> [Integer] -> ByteString Source #

Return byte string representing the given list/ndarray of integers x.

fromBytes :: Int -> ByteString -> [Integer] Source #

Return the list of integers represented by the given byte string.