HaskellForMaths-0.4.9: Combinatorics, group theory, commutative algebra, non-commutative algebra
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LanguageHaskell98

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

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

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