Safe Haskell	None
Language	Haskell98

Math.Algebra.Field.Base

Synopsis

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 #
Methods (==) :: Q -> Q -> Bool # (/=) :: Q -> Q -> Bool #
Fractional Q Source #
Methods (/) :: Q -> Q -> Q # recip :: Q -> Q # fromRational :: Rational -> Q #
Num Q Source #
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 #
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 #
Methods showsPrec :: Int -> Q -> ShowS # show :: Q -> String # showList :: [Q] -> ShowS #
HopfAlgebra Q (SL2 ABCD) Source #
Methods antipode :: Vect Q (SL2 ABCD) -> Vect Q (SL2 ABCD) Source #
Bialgebra Q (SL2 ABCD) Source #

Coalgebra Q (SL2 ABCD) Source #
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 #
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 #
Methods pvalue :: (Q, Sqrt n) -> UPoly Q Source #
HopfAlgebra (LaurentPoly Q) (SL2q String) Source #
Methods antipode :: Vect (LaurentPoly Q) (SL2q String) -> Vect (LaurentPoly Q) (SL2q String) Source #
Bialgebra (LaurentPoly Q) (SL2q String) Source #

Bialgebra (LaurentPoly Q) (M2q String) Source #

Coalgebra (LaurentPoly Q) (SL2q String) Source #
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 #
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 #
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 #
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 #
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 #
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 #
Methods coaction :: Vect (LaurentPoly Q) (Aq20 String) -> Vect (LaurentPoly Q) (Tensor (M2q String) (Aq20 String)) Source #
Invertible (NPoly LPQ BraidGens) Source #
Methods inv :: NPoly LPQ BraidGens -> NPoly LPQ BraidGens Source #
Invertible (NPoly LPQ IwahoriHeckeGens) Source #
Methods inv :: NPoly LPQ IwahoriHeckeGens -> 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 #
Methods pvalue :: (F5, ConwayF25) -> UPoly F5 Source #
PolynomialAsType F3 ConwayF27 Source #
Methods pvalue :: (F3, ConwayF27) -> UPoly F3 Source #
PolynomialAsType F3 ConwayF9 Source #
Methods pvalue :: (F3, ConwayF9) -> UPoly F3 Source #
PolynomialAsType F2 ConwayF32 Source #
Methods pvalue :: (F2, ConwayF32) -> UPoly F2 Source #
PolynomialAsType F2 ConwayF16 Source #
Methods pvalue :: (F2, ConwayF16) -> UPoly F2 Source #
PolynomialAsType F2 ConwayF8 Source #
Methods pvalue :: (F2, ConwayF8) -> UPoly F2 Source #
PolynomialAsType F2 ConwayF4 Source #
Methods pvalue :: (F2, ConwayF4) -> UPoly F2 Source #
Eq (Fp n) Source #
Methods (==) :: Fp n -> Fp n -> Bool # (/=) :: Fp n -> Fp n -> Bool #
IntegerAsType n => Fractional (Fp n) Source #
Methods (/) :: Fp n -> Fp n -> Fp n # recip :: Fp n -> Fp n # fromRational :: Rational -> Fp n #
IntegerAsType n => Num (Fp n) Source #
Methods (+) :: Fp n -> Fp n -> Fp n # (-) :: Fp n -> Fp n -> Fp n # (*) :: Fp n -> Fp n -> Fp n # negate :: Fp n -> Fp n # abs :: Fp n -> Fp n # signum :: Fp n -> Fp n # fromInteger :: Integer -> Fp n #
Ord (Fp n) Source #
Methods compare :: Fp n -> Fp n -> Ordering # (<) :: Fp n -> Fp n -> Bool # (<=) :: Fp n -> Fp n -> Bool # (>) :: Fp n -> Fp n -> Bool # (>=) :: Fp n -> Fp n -> Bool # max :: Fp n -> Fp n -> Fp n # min :: Fp n -> Fp n -> Fp n #
Show (Fp n) Source #
Methods showsPrec :: Int -> Fp n -> ShowS # show :: Fp n -> String # showList :: [Fp n] -> ShowS #
IntegerAsType p => FinSet (Fp p) Source #
Methods elts :: [Fp p] Source #
IntegerAsType p => FiniteField (Fp p) Source #
Methods eltsFq :: Fp p -> [Fp p] Source # basisFq :: Fp p -> [Fp p] Source #

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

Minimal complete definition

eltsFq, basisFq

Methods

eltsFq :: fq -> [fq] Source #

basisFq :: fq -> [fq] Source #

Instances

FiniteField J9 Source #
Methods eltsFq :: J9 -> [J9] Source # basisFq :: J9 -> [J9] Source #
FiniteField F9 Source #
Methods eltsFq :: F9 -> [F9] Source # basisFq :: F9 -> [F9] Source #
IntegerAsType p => FiniteField (Fp p) Source #
Methods eltsFq :: Fp p -> [Fp p] Source # basisFq :: Fp p -> [Fp p] Source #
(FiniteField k, PolynomialAsType k poly) => FiniteField (ExtensionField k poly) Source #
Methods eltsFq :: ExtensionField k poly -> [ExtensionField k poly] Source # basisFq :: ExtensionField k poly -> [ExtensionField k poly] Source #