HaskellForMaths-0.4.8: Combinatorics, group theory, commutative algebra, non-commutative algebra

Safe Haskell | None
Language | Haskell98

Math.Algebra.Field.Base

Synopsis

- newtype Q = Q Rational
- numeratorQ :: Q -> Integer
- denominatorQ :: Q -> Integer
- extendedEuclid :: Integral t => t -> t -> (t, t, t)
- newtype Fp n = Fp Integer
- class (Eq fq, Fractional fq) => FiniteField fq where
  - eltsFq :: fq -> [fq]
  - basisFq :: fq -> [fq]
- primitiveElt :: (Eq a, Num a) => [a] -> a
- powers :: (Eq a, Num a) => a -> [a]
- char :: Foldable t => t a -> Int
- type F2 = Fp T2
- f2 :: [F2]
- type F3 = Fp T3
- f3 :: [F3]
- type F5 = Fp T5
- f5 :: [F5]
- type F7 = Fp T7
- f7 :: [F7]
- type F11 = Fp T11
- f11 :: [F11]
- type F13 = Fp T13
- f13 :: [F13]
- type F17 = Fp T17
- f17 :: [F17]
- type F19 = Fp T19
- f19 :: [F19]
- type F23 = Fp T23
- f23 :: [F23]
- type F29 = Fp T29
- f29 :: [F29]
- type F31 = Fp T31
- f31 :: [F31]
- type F37 = Fp T37
- f37 :: [F37]
- type F41 = Fp T41
- f41 :: [F41]
- type F43 = Fp T43
- f43 :: [F43]
- type F47 = Fp T47
- f47 :: [F47]
- type F53 = Fp T53
- f53 :: [F53]
- type F59 = Fp T59
- f59 :: [F59]
- type F61 = Fp T61
- f61 :: [F61]
- type F67 = Fp T67
- f67 :: [F67]
- type F71 = Fp T71
- f71 :: [F71]
- type F73 = Fp T73
- f73 :: [F73]
- type F79 = Fp T79
- f79 :: [F79]
- type F83 = Fp T83
- f83 :: [F83]
- type F89 = Fp T89
- f89 :: [F89]
- type F97 = Fp T97
- f97 :: [F97]

# 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 |
Fractional Q Source |
Num Q Source |
Ord Q Source |
Show Q Source |
HopfAlgebra Q (SL2 ABCD) Source |
Bialgebra Q (SL2 ABCD) Source |
Coalgebra Q (SL2 ABCD) Source |
Algebra Q (SL2 ABCD) Source |
IntegerAsType n => PolynomialAsType Q (Sqrt n) Source |
HopfAlgebra (LaurentPoly Q) (SL2q String) Source |
Bialgebra (LaurentPoly Q) (SL2q String) Source |
Bialgebra (LaurentPoly Q) (M2q String) Source |
Coalgebra (LaurentPoly Q) (SL2q String) Source |
Coalgebra (LaurentPoly Q) (M2q String) Source |
Algebra (LaurentPoly Q) (SL2q String) Source |
Algebra (LaurentPoly Q) (M2q String) Source |
Algebra (LaurentPoly Q) (Aq02 String) Source |
Algebra (LaurentPoly Q) (Aq20 String) Source |
Comodule (LaurentPoly Q) (M2q String) (Aq20 String) Source |
Invertible (NPoly LPQ BraidGens) Source |
Invertible (NPoly LPQ IwahoriHeckeGens) Source |

numeratorQ :: Q -> Integer Source

denominatorQ :: Q -> Integer Source

extendedEuclid :: Integral t => t -> t -> (t, t, t) Source

newtype Fp n Source

Constructors

Fp Integer |

Instances

PolynomialAsType F5 ConwayF25 Source |
PolynomialAsType F3 ConwayF27 Source |
PolynomialAsType F3 ConwayF9 Source |
PolynomialAsType F2 ConwayF32 Source |
PolynomialAsType F2 ConwayF16 Source |
PolynomialAsType F2 ConwayF8 Source |
PolynomialAsType F2 ConwayF4 Source |
Eq (Fp n) Source |
IntegerAsType n => Fractional (Fp n) Source |
IntegerAsType n => Num (Fp n) Source |
Ord (Fp n) Source |
Show (Fp n) Source |
IntegerAsType p => FinSet (Fp p) Source |
IntegerAsType p => FiniteField (Fp p) Source |

class (Eq fq, Fractional fq) => FiniteField fq where Source

Methods

eltsFq :: fq -> [fq] Source

basisFq :: fq -> [fq] Source

Instances

FiniteField J9 Source |
FiniteField F9 Source |
IntegerAsType p => FiniteField (Fp p) Source |
(FiniteField k, PolynomialAsType k poly) => FiniteField (ExtensionField k poly) Source |

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

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

char :: Foldable t => t a -> Int Source

type F2 = Fp T2 Source

F2 is a type for the finite field with 2 elements

f2 :: [F2] Source

f2 lists the elements of F2

type F3 = Fp T3 Source

F3 is a type for the finite field with 3 elements

f3 :: [F3] Source

f3 lists the elements of F3

type F5 = Fp T5 Source

F5 is a type for the finite field with 5 elements

f5 :: [F5] Source

f5 lists the elements of F5

type F7 = Fp T7 Source

F7 is a type for the finite field with 7 elements

f7 :: [F7] Source

f7 lists the elements of F7

type F11 = Fp T11 Source

f11 :: [F11] Source

type F13 = Fp T13 Source

f13 :: [F13] Source

type F17 = Fp T17 Source

f17 :: [F17] Source

type F19 = Fp T19 Source

f19 :: [F19] Source

type F23 = Fp T23 Source

f23 :: [F23] Source

type F29 = Fp T29 Source

f29 :: [F29] Source

type F31 = Fp T31 Source

f31 :: [F31] Source

type F37 = Fp T37 Source

f37 :: [F37] Source

type F41 = Fp T41 Source

f41 :: [F41] Source

type F43 = Fp T43 Source

f43 :: [F43] Source

type F47 = Fp T47 Source

f47 :: [F47] Source

type F53 = Fp T53 Source

f53 :: [F53] Source

type F59 = Fp T59 Source

f59 :: [F59] Source

type F61 = Fp T61 Source

f61 :: [F61] Source

type F67 = Fp T67 Source

f67 :: [F67] Source

type F71 = Fp T71 Source

f71 :: [F71] Source

type F73 = Fp T73 Source

f73 :: [F73] Source

type F79 = Fp T79 Source

f79 :: [F79] Source

type F83 = Fp T83 Source

f83 :: [F83] Source

type F89 = Fp T89 Source

f89 :: [F89] Source

type F97 = Fp T97 Source

f97 :: [F97] Source