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

Instances details

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

Instances details

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

Instances details

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

Instances details

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

Instances details

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

Instances details

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

Instances details

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

Instances details

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

Instances details

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

Instances details

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

Instances details

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

Instances details

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

Instances details

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

Instances details

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

Instances details

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