HaskellForMaths-0.4.9: Combinatorics, group theory, commutative algebra, non-commutative algebra

Safe Haskell | None
Language | Haskell98

Math.Core.Field

Description

A module defining the field Q of rationals and the small finite fields (Galois fields) F2, F3, F4, F5, F7, F8, F9, F11, F13, F16, F17, F19, F23, F25.

Given a prime power q, Fq is the type representing elements of the field (eg `F4`), fq is a list of the elements of the field, beginning 0,1,... (eg `f4`), and for prime power fields, aq is a primitive element, which generates the multiplicative group (eg `a4`).

The design philosophy is that fq, the list of elements, represents the field. Thus, many functions elsewhere in the library expect to take fq as an argument, telling them which field to work over.

Synopsis

- newtype Q = Q Rational
- numeratorQ :: Q -> Integer
- denominatorQ :: Q -> Integer
- newtype F2 = F2 Int
- f2 :: [F2]
- newtype F3 = F3 Int
- f3 :: [F3]
- newtype F5 = F5 Int
- f5 :: [F5]
- newtype F7 = F7 Int
- f7 :: [F7]
- newtype F11 = F11 Int
- f11 :: [F11]
- newtype F13 = F13 Int
- f13 :: [F13]
- newtype F17 = F17 Int
- f17 :: [F17]
- newtype F19 = F19 Int
- f19 :: [F19]
- newtype F23 = F23 Int
- f23 :: [F23]
- newtype F4 = F4 Int
- a4 :: F4
- f4 :: [F4]
- powers :: (Eq a, Num a) => a -> [a]
- newtype F8 = F8 Int
- a8 :: F8
- f8 :: [F8]
- newtype F9 = F9 Int
- a9 :: F9
- f9 :: [F9]
- newtype F16 = F16 Int
- a16 :: F16
- f16 :: [F16]
- newtype F25 = F25 Int
- a25 :: F25
- f25 :: [F25]

# Documentation

newtype Q Source #

Q is just the rationals, but with a better show function than the Prelude version

Constructors

Q Rational |

Instances

Eq Q Source # |
Instance details Defined in Math.Core.Field Methods (==) :: Q -> Q -> Bool Source # (/=) :: Q -> Q -> Bool Source #
Fractional Q Source # |
Instance details Defined in Math.Core.Field Methods (/) :: Q -> Q -> Q Source # recip :: Q -> Q Source # fromRational :: Rational -> Q Source #
Fractional QNF Source # |
Instance details Defined in Math.NumberTheory.QuadraticField Methods (/) :: QNF -> QNF -> QNF Source # recip :: QNF -> QNF Source # fromRational :: Rational -> QNF Source #
Num Q Source # |
Instance details Defined in Math.Core.Field Methods (+) :: Q -> Q -> Q Source # (-) :: Q -> Q -> Q Source # (*) :: Q -> Q -> Q Source # negate :: Q -> Q Source # abs :: Q -> Q Source # signum :: Q -> Q Source # fromInteger :: Integer -> Q Source #
Ord Q Source # |
Instance details Defined in Math.Core.Field Methods compare :: Q -> Q -> Ordering Source # (<) :: Q -> Q -> Bool Source # (<=) :: Q -> Q -> Bool Source # (>) :: Q -> Q -> Bool Source # (>=) :: Q -> Q -> Bool Source # max :: Q -> Q -> Q Source # min :: Q -> Q -> Q Source #
Show Q Source # |
Instance details Defined in Math.Core.Field Methods showsPrec :: Int -> Q -> ShowS Source # show :: Q -> String Source # showList :: [Q] -> ShowS Source #
HasInverses (GroupAlgebra Q) Source # | Note that the inverse of a group algebra element can only be efficiently calculated if the group generated by the non-zero terms is very small (eg <100 elements).
Instance details Defined in Math.Algebras.GroupAlgebra Methods inverse :: GroupAlgebra Q -> GroupAlgebra Q Source #

numeratorQ :: Q -> Integer Source #

denominatorQ :: Q -> Integer Source #

newtype F2 Source #

F2 is a type for the finite field with 2 elements

Constructors

F2 Int |

Instances

Eq F2 Source # |
Instance details Defined in Math.Core.Field Methods (==) :: F2 -> F2 -> Bool Source # (/=) :: F2 -> F2 -> Bool Source #
Fractional F2 Source # |
Instance details Defined in Math.Core.Field Methods (/) :: F2 -> F2 -> F2 Source # recip :: F2 -> F2 Source # fromRational :: Rational -> F2 Source #
Num F2 Source # |
Instance details Defined in Math.Core.Field Methods (+) :: F2 -> F2 -> F2 Source # (-) :: F2 -> F2 -> F2 Source # (*) :: F2 -> F2 -> F2 Source # negate :: F2 -> F2 Source # abs :: F2 -> F2 Source # signum :: F2 -> F2 Source # fromInteger :: Integer -> F2 Source #
Ord F2 Source # |
Instance details Defined in Math.Core.Field Methods compare :: F2 -> F2 -> Ordering Source # (<) :: F2 -> F2 -> Bool Source # (<=) :: F2 -> F2 -> Bool Source # (>) :: F2 -> F2 -> Bool Source # (>=) :: F2 -> F2 -> Bool Source # max :: F2 -> F2 -> F2 Source # min :: F2 -> F2 -> F2 Source #
Show F2 Source # |
Instance details Defined in Math.Core.Field Methods showsPrec :: Int -> F2 -> ShowS Source # show :: F2 -> String Source # showList :: [F2] -> ShowS Source #
FinSet F2 Source # |
Instance details Defined in Math.Core.Field Methods elts :: [F2] Source #

f2 :: [F2] Source #

f2 is a list of the elements of F2

newtype F3 Source #

F3 is a type for the finite field with 3 elements

Constructors

F3 Int |

Instances

Eq F3 Source # |
Instance details Defined in Math.Core.Field Methods (==) :: F3 -> F3 -> Bool Source # (/=) :: F3 -> F3 -> Bool Source #
Fractional F3 Source # |
Instance details Defined in Math.Core.Field Methods (/) :: F3 -> F3 -> F3 Source # recip :: F3 -> F3 Source # fromRational :: Rational -> F3 Source #
Num F3 Source # |
Instance details Defined in Math.Core.Field Methods (+) :: F3 -> F3 -> F3 Source # (-) :: F3 -> F3 -> F3 Source # (*) :: F3 -> F3 -> F3 Source # negate :: F3 -> F3 Source # abs :: F3 -> F3 Source # signum :: F3 -> F3 Source # fromInteger :: Integer -> F3 Source #
Ord F3 Source # |
Instance details Defined in Math.Core.Field Methods compare :: F3 -> F3 -> Ordering Source # (<) :: F3 -> F3 -> Bool Source # (<=) :: F3 -> F3 -> Bool Source # (>) :: F3 -> F3 -> Bool Source # (>=) :: F3 -> F3 -> Bool Source # max :: F3 -> F3 -> F3 Source # min :: F3 -> F3 -> F3 Source #
Show F3 Source # |
Instance details Defined in Math.Core.Field Methods showsPrec :: Int -> F3 -> ShowS Source # show :: F3 -> String Source # showList :: [F3] -> ShowS Source #
FinSet F3 Source # |
Instance details Defined in Math.Core.Field Methods elts :: [F3] Source #

f3 :: [F3] Source #

f3 is a list of the elements of F3

newtype F5 Source #

F5 is a type for the finite field with 5 elements

Constructors

F5 Int |

Instances

Eq F5 Source # |
Instance details Defined in Math.Core.Field Methods (==) :: F5 -> F5 -> Bool Source # (/=) :: F5 -> F5 -> Bool Source #
Fractional F5 Source # |
Instance details Defined in Math.Core.Field Methods (/) :: F5 -> F5 -> F5 Source # recip :: F5 -> F5 Source # fromRational :: Rational -> F5 Source #
Num F5 Source # |
Instance details Defined in Math.Core.Field Methods (+) :: F5 -> F5 -> F5 Source # (-) :: F5 -> F5 -> F5 Source # (*) :: F5 -> F5 -> F5 Source # negate :: F5 -> F5 Source # abs :: F5 -> F5 Source # signum :: F5 -> F5 Source # fromInteger :: Integer -> F5 Source #
Ord F5 Source # |
Instance details Defined in Math.Core.Field Methods compare :: F5 -> F5 -> Ordering Source # (<) :: F5 -> F5 -> Bool Source # (<=) :: F5 -> F5 -> Bool Source # (>) :: F5 -> F5 -> Bool Source # (>=) :: F5 -> F5 -> Bool Source # max :: F5 -> F5 -> F5 Source # min :: F5 -> F5 -> F5 Source #
Show F5 Source # |
Instance details Defined in Math.Core.Field Methods showsPrec :: Int -> F5 -> ShowS Source # show :: F5 -> String Source # showList :: [F5] -> ShowS Source #
FinSet F5 Source # |
Instance details Defined in Math.Core.Field Methods elts :: [F5] Source #

f5 :: [F5] Source #

f5 is a list of the elements of F5

newtype F7 Source #

F7 is a type for the finite field with 7 elements

Constructors

F7 Int |

Instances

Eq F7 Source # |
Instance details Defined in Math.Core.Field Methods (==) :: F7 -> F7 -> Bool Source # (/=) :: F7 -> F7 -> Bool Source #
Fractional F7 Source # |
Instance details Defined in Math.Core.Field Methods (/) :: F7 -> F7 -> F7 Source # recip :: F7 -> F7 Source # fromRational :: Rational -> F7 Source #
Num F7 Source # |
Instance details Defined in Math.Core.Field Methods (+) :: F7 -> F7 -> F7 Source # (-) :: F7 -> F7 -> F7 Source # (*) :: F7 -> F7 -> F7 Source # negate :: F7 -> F7 Source # abs :: F7 -> F7 Source # signum :: F7 -> F7 Source # fromInteger :: Integer -> F7 Source #
Ord F7 Source # |
Instance details Defined in Math.Core.Field Methods compare :: F7 -> F7 -> Ordering Source # (<) :: F7 -> F7 -> Bool Source # (<=) :: F7 -> F7 -> Bool Source # (>) :: F7 -> F7 -> Bool Source # (>=) :: F7 -> F7 -> Bool Source # max :: F7 -> F7 -> F7 Source # min :: F7 -> F7 -> F7 Source #
Show F7 Source # |
Instance details Defined in Math.Core.Field Methods showsPrec :: Int -> F7 -> ShowS Source # show :: F7 -> String Source # showList :: [F7] -> ShowS Source #
FinSet F7 Source # |
Instance details Defined in Math.Core.Field Methods elts :: [F7] Source #

f7 :: [F7] Source #

f7 is a list of the elements of F7

newtype F11 Source #

F11 is a type for the finite field with 11 elements

Constructors

F11 Int |

Instances

Eq F11 Source # |
Instance details Defined in Math.Core.Field Methods (==) :: F11 -> F11 -> Bool Source # (/=) :: F11 -> F11 -> Bool Source #
Fractional F11 Source # |
Instance details Defined in Math.Core.Field Methods (/) :: F11 -> F11 -> F11 Source # recip :: F11 -> F11 Source # fromRational :: Rational -> F11 Source #
Num F11 Source # |
Instance details Defined in Math.Core.Field Methods (+) :: F11 -> F11 -> F11 Source # (-) :: F11 -> F11 -> F11 Source # (*) :: F11 -> F11 -> F11 Source # negate :: F11 -> F11 Source # abs :: F11 -> F11 Source # signum :: F11 -> F11 Source # fromInteger :: Integer -> F11 Source #
Ord F11 Source # |
Instance details Defined in Math.Core.Field Methods compare :: F11 -> F11 -> Ordering Source # (<) :: F11 -> F11 -> Bool Source # (<=) :: F11 -> F11 -> Bool Source # (>) :: F11 -> F11 -> Bool Source # (>=) :: F11 -> F11 -> Bool Source # max :: F11 -> F11 -> F11 Source # min :: F11 -> F11 -> F11 Source #
Show F11 Source # |
Instance details Defined in Math.Core.Field Methods showsPrec :: Int -> F11 -> ShowS Source # show :: F11 -> String Source # showList :: [F11] -> ShowS Source #
FinSet F11 Source # |
Instance details Defined in Math.Core.Field Methods elts :: [F11] Source #

f11 :: [F11] Source #

f11 is a list of the elements of F11

newtype F13 Source #

F13 is a type for the finite field with 13 elements

Constructors

F13 Int |

Instances

Eq F13 Source # |
Instance details Defined in Math.Core.Field Methods (==) :: F13 -> F13 -> Bool Source # (/=) :: F13 -> F13 -> Bool Source #
Fractional F13 Source # |
Instance details Defined in Math.Core.Field Methods (/) :: F13 -> F13 -> F13 Source # recip :: F13 -> F13 Source # fromRational :: Rational -> F13 Source #
Num F13 Source # |
Instance details Defined in Math.Core.Field Methods (+) :: F13 -> F13 -> F13 Source # (-) :: F13 -> F13 -> F13 Source # (*) :: F13 -> F13 -> F13 Source # negate :: F13 -> F13 Source # abs :: F13 -> F13 Source # signum :: F13 -> F13 Source # fromInteger :: Integer -> F13 Source #
Ord F13 Source # |
Instance details Defined in Math.Core.Field Methods compare :: F13 -> F13 -> Ordering Source # (<) :: F13 -> F13 -> Bool Source # (<=) :: F13 -> F13 -> Bool Source # (>) :: F13 -> F13 -> Bool Source # (>=) :: F13 -> F13 -> Bool Source # max :: F13 -> F13 -> F13 Source # min :: F13 -> F13 -> F13 Source #
Show F13 Source # |
Instance details Defined in Math.Core.Field Methods showsPrec :: Int -> F13 -> ShowS Source # show :: F13 -> String Source # showList :: [F13] -> ShowS Source #
FinSet F13 Source # |
Instance details Defined in Math.Core.Field Methods elts :: [F13] Source #

f13 :: [F13] Source #

f13 is a list of the elements of F13

newtype F17 Source #

F17 is a type for the finite field with 17 elements

Constructors

F17 Int |

Instances

Eq F17 Source # |
Instance details Defined in Math.Core.Field Methods (==) :: F17 -> F17 -> Bool Source # (/=) :: F17 -> F17 -> Bool Source #
Fractional F17 Source # |
Instance details Defined in Math.Core.Field Methods (/) :: F17 -> F17 -> F17 Source # recip :: F17 -> F17 Source # fromRational :: Rational -> F17 Source #
Num F17 Source # |
Instance details Defined in Math.Core.Field Methods (+) :: F17 -> F17 -> F17 Source # (-) :: F17 -> F17 -> F17 Source # (*) :: F17 -> F17 -> F17 Source # negate :: F17 -> F17 Source # abs :: F17 -> F17 Source # signum :: F17 -> F17 Source # fromInteger :: Integer -> F17 Source #
Ord F17 Source # |
Instance details Defined in Math.Core.Field Methods compare :: F17 -> F17 -> Ordering Source # (<) :: F17 -> F17 -> Bool Source # (<=) :: F17 -> F17 -> Bool Source # (>) :: F17 -> F17 -> Bool Source # (>=) :: F17 -> F17 -> Bool Source # max :: F17 -> F17 -> F17 Source # min :: F17 -> F17 -> F17 Source #
Show F17 Source # |
Instance details Defined in Math.Core.Field Methods showsPrec :: Int -> F17 -> ShowS Source # show :: F17 -> String Source # showList :: [F17] -> ShowS Source #
FinSet F17 Source # |
Instance details Defined in Math.Core.Field Methods elts :: [F17] Source #

f17 :: [F17] Source #

f17 is a list of the elements of F17

newtype F19 Source #

F19 is a type for the finite field with 19 elements

Constructors

F19 Int |

Instances

Eq F19 Source # |
Instance details Defined in Math.Core.Field Methods (==) :: F19 -> F19 -> Bool Source # (/=) :: F19 -> F19 -> Bool Source #
Fractional F19 Source # |
Instance details Defined in Math.Core.Field Methods (/) :: F19 -> F19 -> F19 Source # recip :: F19 -> F19 Source # fromRational :: Rational -> F19 Source #
Num F19 Source # |
Instance details Defined in Math.Core.Field Methods (+) :: F19 -> F19 -> F19 Source # (-) :: F19 -> F19 -> F19 Source # (*) :: F19 -> F19 -> F19 Source # negate :: F19 -> F19 Source # abs :: F19 -> F19 Source # signum :: F19 -> F19 Source # fromInteger :: Integer -> F19 Source #
Ord F19 Source # |
Instance details Defined in Math.Core.Field Methods compare :: F19 -> F19 -> Ordering Source # (<) :: F19 -> F19 -> Bool Source # (<=) :: F19 -> F19 -> Bool Source # (>) :: F19 -> F19 -> Bool Source # (>=) :: F19 -> F19 -> Bool Source # max :: F19 -> F19 -> F19 Source # min :: F19 -> F19 -> F19 Source #
Show F19 Source # |
Instance details Defined in Math.Core.Field Methods showsPrec :: Int -> F19 -> ShowS Source # show :: F19 -> String Source # showList :: [F19] -> ShowS Source #
FinSet F19 Source # |
Instance details Defined in Math.Core.Field Methods elts :: [F19] Source #

f19 :: [F19] Source #

f19 is a list of the elements of F19

newtype F23 Source #

F23 is a type for the finite field with 23 elements

Constructors

F23 Int |

Instances

Eq F23 Source # |
Instance details Defined in Math.Core.Field Methods (==) :: F23 -> F23 -> Bool Source # (/=) :: F23 -> F23 -> Bool Source #
Fractional F23 Source # |
Instance details Defined in Math.Core.Field Methods (/) :: F23 -> F23 -> F23 Source # recip :: F23 -> F23 Source # fromRational :: Rational -> F23 Source #
Num F23 Source # |
Instance details Defined in Math.Core.Field Methods (+) :: F23 -> F23 -> F23 Source # (-) :: F23 -> F23 -> F23 Source # (*) :: F23 -> F23 -> F23 Source # negate :: F23 -> F23 Source # abs :: F23 -> F23 Source # signum :: F23 -> F23 Source # fromInteger :: Integer -> F23 Source #
Ord F23 Source # |
Instance details Defined in Math.Core.Field Methods compare :: F23 -> F23 -> Ordering Source # (<) :: F23 -> F23 -> Bool Source # (<=) :: F23 -> F23 -> Bool Source # (>) :: F23 -> F23 -> Bool Source # (>=) :: F23 -> F23 -> Bool Source # max :: F23 -> F23 -> F23 Source # min :: F23 -> F23 -> F23 Source #
Show F23 Source # |
Instance details Defined in Math.Core.Field Methods showsPrec :: Int -> F23 -> ShowS Source # show :: F23 -> String Source # showList :: [F23] -> ShowS Source #
FinSet F23 Source # |
Instance details Defined in Math.Core.Field Methods elts :: [F23] Source #

f23 :: [F23] Source #

f23 is a list of the elements of F23

newtype F4 Source #

F4 is a type for the finite field with 4 elements. F4 is represented as the extension of F2 by an element a4 satisfying x^2+x+1 = 0

Constructors

F4 Int |

Instances

Eq F4 Source # |
Instance details Defined in Math.Core.Field Methods (==) :: F4 -> F4 -> Bool Source # (/=) :: F4 -> F4 -> Bool Source #
Fractional F4 Source # |
Instance details Defined in Math.Core.Field Methods (/) :: F4 -> F4 -> F4 Source # recip :: F4 -> F4 Source # fromRational :: Rational -> F4 Source #
Num F4 Source # |
Instance details Defined in Math.Core.Field Methods (+) :: F4 -> F4 -> F4 Source # (-) :: F4 -> F4 -> F4 Source # (*) :: F4 -> F4 -> F4 Source # negate :: F4 -> F4 Source # abs :: F4 -> F4 Source # signum :: F4 -> F4 Source # fromInteger :: Integer -> F4 Source #
Ord F4 Source # |
Instance details Defined in Math.Core.Field Methods compare :: F4 -> F4 -> Ordering Source # (<) :: F4 -> F4 -> Bool Source # (<=) :: F4 -> F4 -> Bool Source # (>) :: F4 -> F4 -> Bool Source # (>=) :: F4 -> F4 -> Bool Source # max :: F4 -> F4 -> F4 Source # min :: F4 -> F4 -> F4 Source #
Show F4 Source # |
Instance details Defined in Math.Core.Field Methods showsPrec :: Int -> F4 -> ShowS Source # show :: F4 -> String Source # showList :: [F4] -> ShowS Source #
FinSet F4 Source # |
Instance details Defined in Math.Core.Field Methods elts :: [F4] Source #

a4 :: F4 Source #

a4 is a primitive element for F4 as an extension over F2. a4 satisfies x^2+x+1 = 0.

f4 :: [F4] Source #

f4 is a list of the elements of F4

powers :: (Eq a, Num a) => a -> [a] Source #

newtype F8 Source #

F8 is a type for the finite field with 8 elements. F8 is represented as the extension of F2 by an element a8 satisfying x^3+x+1 = 0

Constructors

F8 Int |

Instances

Eq F8 Source # |
Instance details Defined in Math.Core.Field Methods (==) :: F8 -> F8 -> Bool Source # (/=) :: F8 -> F8 -> Bool Source #
Fractional F8 Source # |
Instance details Defined in Math.Core.Field Methods (/) :: F8 -> F8 -> F8 Source # recip :: F8 -> F8 Source # fromRational :: Rational -> F8 Source #
Num F8 Source # |
Instance details Defined in Math.Core.Field Methods (+) :: F8 -> F8 -> F8 Source # (-) :: F8 -> F8 -> F8 Source # (*) :: F8 -> F8 -> F8 Source # negate :: F8 -> F8 Source # abs :: F8 -> F8 Source # signum :: F8 -> F8 Source # fromInteger :: Integer -> F8 Source #
Ord F8 Source # |
Instance details Defined in Math.Core.Field Methods compare :: F8 -> F8 -> Ordering Source # (<) :: F8 -> F8 -> Bool Source # (<=) :: F8 -> F8 -> Bool Source # (>) :: F8 -> F8 -> Bool Source # (>=) :: F8 -> F8 -> Bool Source # max :: F8 -> F8 -> F8 Source # min :: F8 -> F8 -> F8 Source #
Show F8 Source # |
Instance details Defined in Math.Core.Field Methods showsPrec :: Int -> F8 -> ShowS Source # show :: F8 -> String Source # showList :: [F8] -> ShowS Source #
FinSet F8 Source # |
Instance details Defined in Math.Core.Field Methods elts :: [F8] Source #

a8 :: F8 Source #

a8 is a primitive element for F8 as an extension over F2. a8 satisfies x^3+x+1 = 0.

f8 :: [F8] Source #

f8 is a list of the elements of F8

newtype F9 Source #

F9 is a type for the finite field with 9 elements. F9 is represented as the extension of F3 by an element a9 satisfying x^2+2x+2 = 0

Constructors

F9 Int |

Instances

Eq F9 Source # |
Instance details Defined in Math.Core.Field Methods (==) :: F9 -> F9 -> Bool Source # (/=) :: F9 -> F9 -> Bool Source #
Fractional F9 Source # |
Instance details Defined in Math.Core.Field Methods (/) :: F9 -> F9 -> F9 Source # recip :: F9 -> F9 Source # fromRational :: Rational -> F9 Source #
Num F9 Source # |
Instance details Defined in Math.Core.Field Methods (+) :: F9 -> F9 -> F9 Source # (-) :: F9 -> F9 -> F9 Source # (*) :: F9 -> F9 -> F9 Source # negate :: F9 -> F9 Source # abs :: F9 -> F9 Source # signum :: F9 -> F9 Source # fromInteger :: Integer -> F9 Source #
Ord F9 Source # |
Instance details Defined in Math.Core.Field Methods compare :: F9 -> F9 -> Ordering Source # (<) :: F9 -> F9 -> Bool Source # (<=) :: F9 -> F9 -> Bool Source # (>) :: F9 -> F9 -> Bool Source # (>=) :: F9 -> F9 -> Bool Source # max :: F9 -> F9 -> F9 Source # min :: F9 -> F9 -> F9 Source #
Show F9 Source # |
Instance details Defined in Math.Core.Field Methods showsPrec :: Int -> F9 -> ShowS Source # show :: F9 -> String Source # showList :: [F9] -> ShowS Source #
FinSet F9 Source # |
Instance details Defined in Math.Core.Field Methods elts :: [F9] Source #

a9 :: F9 Source #

a9 is a primitive element for F9 as an extension over F3. a9 satisfies x^2+2x+2 = 0.

f9 :: [F9] Source #

f9 is a list of the elements of F9

newtype F16 Source #

F16 is a type for the finite field with 16 elements. F16 is represented as the extension of F2 by an element a16 satisfying x^4+x+1 = 0

Constructors

F16 Int |

Instances

Eq F16 Source # |
Instance details Defined in Math.Core.Field Methods (==) :: F16 -> F16 -> Bool Source # (/=) :: F16 -> F16 -> Bool Source #
Fractional F16 Source # |
Instance details Defined in Math.Core.Field Methods (/) :: F16 -> F16 -> F16 Source # recip :: F16 -> F16 Source # fromRational :: Rational -> F16 Source #
Num F16 Source # |
Instance details Defined in Math.Core.Field Methods (+) :: F16 -> F16 -> F16 Source # (-) :: F16 -> F16 -> F16 Source # (*) :: F16 -> F16 -> F16 Source # negate :: F16 -> F16 Source # abs :: F16 -> F16 Source # signum :: F16 -> F16 Source # fromInteger :: Integer -> F16 Source #
Ord F16 Source # |
Instance details Defined in Math.Core.Field Methods compare :: F16 -> F16 -> Ordering Source # (<) :: F16 -> F16 -> Bool Source # (<=) :: F16 -> F16 -> Bool Source # (>) :: F16 -> F16 -> Bool Source # (>=) :: F16 -> F16 -> Bool Source # max :: F16 -> F16 -> F16 Source # min :: F16 -> F16 -> F16 Source #
Show F16 Source # |
Instance details Defined in Math.Core.Field Methods showsPrec :: Int -> F16 -> ShowS Source # show :: F16 -> String Source # showList :: [F16] -> ShowS Source #
FinSet F16 Source # |
Instance details Defined in Math.Core.Field Methods elts :: [F16] Source #

a16 :: F16 Source #

a16 is a primitive element for F16 as an extension over F2. a16 satisfies x^4+x+1 = 0.

f16 :: [F16] Source #

f16 is a list of the elements of F16

newtype F25 Source #

F25 is a type for the finite field with 25 elements. F25 is represented as the extension of F5 by an element a25 satisfying x^2+4x+2 = 0

Constructors

F25 Int |

Instances

Eq F25 Source # |
Instance details Defined in Math.Core.Field Methods (==) :: F25 -> F25 -> Bool Source # (/=) :: F25 -> F25 -> Bool Source #
Fractional F25 Source # |
Instance details Defined in Math.Core.Field Methods (/) :: F25 -> F25 -> F25 Source # recip :: F25 -> F25 Source # fromRational :: Rational -> F25 Source #
Num F25 Source # |
Instance details Defined in Math.Core.Field Methods (+) :: F25 -> F25 -> F25 Source # (-) :: F25 -> F25 -> F25 Source # (*) :: F25 -> F25 -> F25 Source # negate :: F25 -> F25 Source # abs :: F25 -> F25 Source # signum :: F25 -> F25 Source # fromInteger :: Integer -> F25 Source #
Ord F25 Source # |
Instance details Defined in Math.Core.Field Methods compare :: F25 -> F25 -> Ordering Source # (<) :: F25 -> F25 -> Bool Source # (<=) :: F25 -> F25 -> Bool Source # (>) :: F25 -> F25 -> Bool Source # (>=) :: F25 -> F25 -> Bool Source # max :: F25 -> F25 -> F25 Source # min :: F25 -> F25 -> F25 Source #
Show F25 Source # |
Instance details Defined in Math.Core.Field Methods showsPrec :: Int -> F25 -> ShowS Source # show :: F25 -> String Source # showList :: [F25] -> ShowS Source #
FinSet F25 Source # |
Instance details Defined in Math.Core.Field Methods elts :: [F25] Source #

a25 :: F25 Source #

a25 is a primitive element for F25 as an extension over F5. a25 satisfies x^2+4x+2 = 0.

f25 :: [F25] Source #

f25 is a list of the elements of F25