Safe Haskell	None
Language	Haskell98

Math.Algebra.Field.Base

Synopsis

newtype Q = Q Rational
numeratorQ :: Q -> Integer
denominatorQ :: Q -> Integer
extendedEuclid :: Integral b => b -> b -> (b, b, b)
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 #
Instance details Defined in Math.Algebra.Field.Base Methods (==) :: Q -> Q -> Bool Source # (/=) :: Q -> Q -> Bool Source #
Fractional Q Source #
Instance details Defined in Math.Algebra.Field.Base Methods (/) :: Q -> Q -> Q Source # recip :: Q -> Q Source # fromRational :: Rational -> Q Source #
Num Q Source #
Instance details Defined in Math.Algebra.Field.Base 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.Algebra.Field.Base 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.Algebra.Field.Base Methods showsPrec :: Int -> Q -> ShowS Source # show :: Q -> String Source # showList :: [Q] -> ShowS Source #
Invertible LPQ Source #
Instance details Defined in Math.Projects.KnotTheory.Braid Methods inv :: LPQ -> LPQ Source #
HopfAlgebra Q (SL2 ABCD) Source #
Instance details Defined in Math.Algebras.AffinePlane Methods antipode :: Vect Q (SL2 ABCD) -> Vect Q (SL2 ABCD) Source #
Bialgebra Q (SL2 ABCD) Source #
Instance details Defined in Math.Algebras.AffinePlane
Coalgebra Q (SL2 ABCD) Source #
Instance details Defined in Math.Algebras.AffinePlane Methods counit :: Vect Q (SL2 ABCD) -> Q Source # comult :: Vect Q (SL2 ABCD) -> Vect Q (Tensor (SL2 ABCD) (SL2 ABCD)) Source #
Algebra Q (SL2 ABCD) Source #
Instance details Defined in Math.Algebras.AffinePlane Methods unit :: Q -> Vect Q (SL2 ABCD) Source # mult :: Vect Q (Tensor (SL2 ABCD) (SL2 ABCD)) -> Vect Q (SL2 ABCD) Source #
IntegerAsType n => PolynomialAsType Q (Sqrt n) Source #
Instance details Defined in Math.Algebra.Field.Extension Methods pvalue :: (Q, Sqrt n) -> UPoly Q Source #
HopfAlgebra (LaurentPoly Q) (SL2q String) Source #
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods antipode :: Vect (LaurentPoly Q) (SL2q String) -> Vect (LaurentPoly Q) (SL2q String) Source #
Bialgebra (LaurentPoly Q) (SL2q String) Source #
Instance details Defined in Math.QuantumAlgebra.QuantumPlane
Bialgebra (LaurentPoly Q) (M2q String) Source #
Instance details Defined in Math.QuantumAlgebra.QuantumPlane
Coalgebra (LaurentPoly Q) (SL2q String) Source #
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods counit :: Vect (LaurentPoly Q) (SL2q String) -> LaurentPoly Q Source # comult :: Vect (LaurentPoly Q) (SL2q String) -> Vect (LaurentPoly Q) (Tensor (SL2q String) (SL2q String)) Source #
Coalgebra (LaurentPoly Q) (M2q String) Source #
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods counit :: Vect (LaurentPoly Q) (M2q String) -> LaurentPoly Q Source # comult :: Vect (LaurentPoly Q) (M2q String) -> Vect (LaurentPoly Q) (Tensor (M2q String) (M2q String)) Source #
Algebra (LaurentPoly Q) (SL2q String) Source #
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods unit :: LaurentPoly Q -> Vect (LaurentPoly Q) (SL2q String) Source # mult :: Vect (LaurentPoly Q) (Tensor (SL2q String) (SL2q String)) -> Vect (LaurentPoly Q) (SL2q String) Source #
Algebra (LaurentPoly Q) (M2q String) Source #
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods unit :: LaurentPoly Q -> Vect (LaurentPoly Q) (M2q String) Source # mult :: Vect (LaurentPoly Q) (Tensor (M2q String) (M2q String)) -> Vect (LaurentPoly Q) (M2q String) Source #
Algebra (LaurentPoly Q) (Aq02 String) Source #
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods unit :: LaurentPoly Q -> Vect (LaurentPoly Q) (Aq02 String) Source # mult :: Vect (LaurentPoly Q) (Tensor (Aq02 String) (Aq02 String)) -> Vect (LaurentPoly Q) (Aq02 String) Source #
Algebra (LaurentPoly Q) (Aq20 String) Source #
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods unit :: LaurentPoly Q -> Vect (LaurentPoly Q) (Aq20 String) Source # mult :: Vect (LaurentPoly Q) (Tensor (Aq20 String) (Aq20 String)) -> Vect (LaurentPoly Q) (Aq20 String) Source #
Comodule (LaurentPoly Q) (M2q String) (Aq20 String) Source #
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods coaction :: Vect (LaurentPoly Q) (Aq20 String) -> Vect (LaurentPoly Q) (Tensor (M2q String) (Aq20 String)) Source #
Invertible (NPoly LPQ BraidGens) Source #
Instance details Defined in Math.Projects.KnotTheory.Braid Methods inv :: NPoly LPQ BraidGens -> NPoly LPQ BraidGens Source #
Invertible (NPoly LPQ IwahoriHeckeGens) Source #
Instance details Defined in Math.Projects.KnotTheory.IwahoriHecke Methods inv :: NPoly LPQ IwahoriHeckeGens -> NPoly LPQ IwahoriHeckeGens Source #

numeratorQ :: Q -> Integer Source #

denominatorQ :: Q -> Integer Source #

extendedEuclid :: Integral b => b -> b -> (b, b, b) Source #

newtype Fp n Source #

Constructors

Fp Integer

Instances

PolynomialAsType F5 ConwayF25 Source #
Instance details Defined in Math.Algebra.Field.Extension Methods pvalue :: (F5, ConwayF25) -> UPoly F5 Source #
PolynomialAsType F3 ConwayF27 Source #
Instance details Defined in Math.Algebra.Field.Extension Methods pvalue :: (F3, ConwayF27) -> UPoly F3 Source #
PolynomialAsType F3 ConwayF9 Source #
Instance details Defined in Math.Algebra.Field.Extension Methods pvalue :: (F3, ConwayF9) -> UPoly F3 Source #
PolynomialAsType F2 ConwayF32 Source #
Instance details Defined in Math.Algebra.Field.Extension Methods pvalue :: (F2, ConwayF32) -> UPoly F2 Source #
PolynomialAsType F2 ConwayF16 Source #
Instance details Defined in Math.Algebra.Field.Extension Methods pvalue :: (F2, ConwayF16) -> UPoly F2 Source #
PolynomialAsType F2 ConwayF8 Source #
Instance details Defined in Math.Algebra.Field.Extension Methods pvalue :: (F2, ConwayF8) -> UPoly F2 Source #
PolynomialAsType F2 ConwayF4 Source #
Instance details Defined in Math.Algebra.Field.Extension Methods pvalue :: (F2, ConwayF4) -> UPoly F2 Source #
Eq (Fp n) Source #
Instance details Defined in Math.Algebra.Field.Base Methods (==) :: Fp n -> Fp n -> Bool Source # (/=) :: Fp n -> Fp n -> Bool Source #
IntegerAsType n => Fractional (Fp n) Source #
Instance details Defined in Math.Algebra.Field.Base Methods (/) :: Fp n -> Fp n -> Fp n Source # recip :: Fp n -> Fp n Source # fromRational :: Rational -> Fp n Source #
IntegerAsType n => Num (Fp n) Source #
Instance details Defined in Math.Algebra.Field.Base Methods (+) :: Fp n -> Fp n -> Fp n Source # (-) :: Fp n -> Fp n -> Fp n Source # (*) :: Fp n -> Fp n -> Fp n Source # negate :: Fp n -> Fp n Source # abs :: Fp n -> Fp n Source # signum :: Fp n -> Fp n Source # fromInteger :: Integer -> Fp n Source #
Ord (Fp n) Source #
Instance details Defined in Math.Algebra.Field.Base Methods compare :: Fp n -> Fp n -> Ordering Source # (<) :: Fp n -> Fp n -> Bool Source # (<=) :: Fp n -> Fp n -> Bool Source # (>) :: Fp n -> Fp n -> Bool Source # (>=) :: Fp n -> Fp n -> Bool Source # max :: Fp n -> Fp n -> Fp n Source # min :: Fp n -> Fp n -> Fp n Source #
Show (Fp n) Source #
Instance details Defined in Math.Algebra.Field.Base Methods showsPrec :: Int -> Fp n -> ShowS Source # show :: Fp n -> String Source # showList :: [Fp n] -> ShowS Source #
IntegerAsType p => FinSet (Fp p) Source #
Instance details Defined in Math.Algebra.Field.Base Methods elts :: [Fp p] Source #
IntegerAsType p => FiniteField (Fp p) Source #
Instance details Defined in Math.Algebra.Field.Base Methods eltsFq :: Fp p -> [Fp p] Source # basisFq :: Fp p -> [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 #
Instance details Defined in Math.Projects.MiniquaternionGeometry Methods eltsFq :: J9 -> [J9] Source # basisFq :: J9 -> [J9] Source #
FiniteField F9 Source #
Instance details Defined in Math.Projects.MiniquaternionGeometry Methods eltsFq :: F9 -> [F9] Source # basisFq :: F9 -> [F9] Source #
IntegerAsType p => FiniteField (Fp p) Source #
Instance details Defined in Math.Algebra.Field.Base Methods eltsFq :: Fp p -> [Fp p] Source # basisFq :: Fp p -> [Fp p] Source #
(FiniteField k, PolynomialAsType k poly) => FiniteField (ExtensionField k poly) Source #
Instance details Defined in Math.Algebra.Field.Extension Methods eltsFq :: ExtensionField k poly -> [ExtensionField k poly] Source # basisFq :: ExtensionField k poly -> [ExtensionField k poly] Source #