Math.Algebra.Field.Base

Documentation

newtype Q

Q is just the rationals, but with a better show function than the Prelude version

Constructors

Q Rational

Instances

Eq Q

Defined in Math.Algebra.Field.Base

Methods

(==) :: Q -> Q -> Bool

(/=) :: Q -> Q -> Bool

Fractional Q

Defined in Math.Algebra.Field.Base

Methods

(/) :: Q -> Q -> Q

recip :: Q -> Q

fromRational :: Rational -> Q

Num Q

Defined in Math.Algebra.Field.Base

Methods

(+) :: Q -> Q -> Q

(-) :: Q -> Q -> Q

(*) :: Q -> Q -> Q

negate :: Q -> Q

abs :: Q -> Q

signum :: Q -> Q

fromInteger :: Integer -> Q

Ord Q

Defined in Math.Algebra.Field.Base

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

Defined in Math.Algebra.Field.Base

Methods

showsPrec :: Int -> Q -> ShowS

show :: Q -> String

showList :: [Q] -> ShowS

Invertible LPQ

Defined in Math.Projects.KnotTheory.Braid

Methods

inv :: LPQ -> LPQ

HopfAlgebra Q (SL2 ABCD)

Defined in Math.Algebras.AffinePlane

Methods

antipode :: Vect Q (SL2 ABCD) -> Vect Q (SL2 ABCD)

Bialgebra Q (SL2 ABCD)

Defined in Math.Algebras.AffinePlane

Coalgebra Q (SL2 ABCD)

Defined in Math.Algebras.AffinePlane

Methods

counit :: Vect Q (SL2 ABCD) -> Q

comult :: Vect Q (SL2 ABCD) -> Vect Q (Tensor (SL2 ABCD) (SL2 ABCD))

Algebra Q (SL2 ABCD)

Defined in Math.Algebras.AffinePlane

Methods

unit :: Q -> Vect Q (SL2 ABCD)

mult :: Vect Q (Tensor (SL2 ABCD) (SL2 ABCD)) -> Vect Q (SL2 ABCD)

IntegerAsType n => PolynomialAsType Q (Sqrt n)

Defined in Math.Algebra.Field.Extension

Methods

pvalue :: (Q, Sqrt n) -> UPoly Q

HopfAlgebra (LaurentPoly Q) (SL2q String)

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

antipode :: Vect (LaurentPoly Q) (SL2q String) -> Vect (LaurentPoly Q) (SL2q String)

Bialgebra (LaurentPoly Q) (SL2q String)

Defined in Math.QuantumAlgebra.QuantumPlane

Bialgebra (LaurentPoly Q) (M2q String)

Defined in Math.QuantumAlgebra.QuantumPlane

Coalgebra (LaurentPoly Q) (SL2q String)

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

counit :: Vect (LaurentPoly Q) (SL2q String) -> LaurentPoly Q

comult :: Vect (LaurentPoly Q) (SL2q String) -> Vect (LaurentPoly Q) (Tensor (SL2q String) (SL2q String))

Coalgebra (LaurentPoly Q) (M2q String)

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

counit :: Vect (LaurentPoly Q) (M2q String) -> LaurentPoly Q

comult :: Vect (LaurentPoly Q) (M2q String) -> Vect (LaurentPoly Q) (Tensor (M2q String) (M2q String))

Algebra (LaurentPoly Q) (SL2q String)

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

unit :: LaurentPoly Q -> Vect (LaurentPoly Q) (SL2q String)

mult :: Vect (LaurentPoly Q) (Tensor (SL2q String) (SL2q String)) -> Vect (LaurentPoly Q) (SL2q String)

Algebra (LaurentPoly Q) (M2q String)

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

unit :: LaurentPoly Q -> Vect (LaurentPoly Q) (M2q String)

mult :: Vect (LaurentPoly Q) (Tensor (M2q String) (M2q String)) -> Vect (LaurentPoly Q) (M2q String)

Algebra (LaurentPoly Q) (Aq02 String)

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

unit :: LaurentPoly Q -> Vect (LaurentPoly Q) (Aq02 String)

mult :: Vect (LaurentPoly Q) (Tensor (Aq02 String) (Aq02 String)) -> Vect (LaurentPoly Q) (Aq02 String)

Algebra (LaurentPoly Q) (Aq20 String)

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

unit :: LaurentPoly Q -> Vect (LaurentPoly Q) (Aq20 String)

mult :: Vect (LaurentPoly Q) (Tensor (Aq20 String) (Aq20 String)) -> Vect (LaurentPoly Q) (Aq20 String)

Comodule (LaurentPoly Q) (M2q String) (Aq20 String)

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

coaction :: Vect (LaurentPoly Q) (Aq20 String) -> Vect (LaurentPoly Q) (Tensor (M2q String) (Aq20 String))

Invertible (NPoly LPQ BraidGens)

Defined in Math.Projects.KnotTheory.Braid

Methods

inv :: NPoly LPQ BraidGens -> NPoly LPQ BraidGens

Invertible (NPoly LPQ IwahoriHeckeGens)

Defined in Math.Projects.KnotTheory.IwahoriHecke

Methods

inv :: NPoly LPQ IwahoriHeckeGens -> NPoly LPQ IwahoriHeckeGens

numeratorQ :: Q -> Integer

denominatorQ :: Q -> Integer

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

newtype Fp n

Constructors

Fp Integer

Instances

PolynomialAsType F5 ConwayF25

Defined in Math.Algebra.Field.Extension

Methods

pvalue :: (F5, ConwayF25) -> UPoly F5

PolynomialAsType F3 ConwayF27

Defined in Math.Algebra.Field.Extension

Methods

pvalue :: (F3, ConwayF27) -> UPoly F3

PolynomialAsType F3 ConwayF9

Defined in Math.Algebra.Field.Extension

Methods

pvalue :: (F3, ConwayF9) -> UPoly F3

PolynomialAsType F2 ConwayF32

Defined in Math.Algebra.Field.Extension

Methods

pvalue :: (F2, ConwayF32) -> UPoly F2

PolynomialAsType F2 ConwayF16

Defined in Math.Algebra.Field.Extension

Methods

pvalue :: (F2, ConwayF16) -> UPoly F2

PolynomialAsType F2 ConwayF8

Defined in Math.Algebra.Field.Extension

Methods

pvalue :: (F2, ConwayF8) -> UPoly F2

PolynomialAsType F2 ConwayF4

Defined in Math.Algebra.Field.Extension

Methods

pvalue :: (F2, ConwayF4) -> UPoly F2

Eq (Fp n)

Defined in Math.Algebra.Field.Base

Methods

(==) :: Fp n -> Fp n -> Bool

(/=) :: Fp n -> Fp n -> Bool

IntegerAsType n => Fractional (Fp n)

Defined in Math.Algebra.Field.Base

Methods

(/) :: Fp n -> Fp n -> Fp n

recip :: Fp n -> Fp n

fromRational :: Rational -> Fp n

IntegerAsType n => Num (Fp n)

Defined in Math.Algebra.Field.Base

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)

Defined in Math.Algebra.Field.Base

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)

Defined in Math.Algebra.Field.Base

Methods

showsPrec :: Int -> Fp n -> ShowS

show :: Fp n -> String

showList :: [Fp n] -> ShowS

IntegerAsType p => FinSet (Fp p)

Defined in Math.Algebra.Field.Base

Methods

elts :: [Fp p]

IntegerAsType p => FiniteField (Fp p)

Defined in Math.Algebra.Field.Base

Methods

eltsFq :: Fp p -> [Fp p]

basisFq :: Fp p -> [Fp p]

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

Methods

eltsFq :: fq -> [fq]

basisFq :: fq -> [fq]

Instances

FiniteField J9

Defined in Math.Projects.MiniquaternionGeometry

Methods

eltsFq :: J9 -> [J9]

basisFq :: J9 -> [J9]

FiniteField F9

Defined in Math.Projects.MiniquaternionGeometry

Methods

eltsFq :: F9 -> [F9]

basisFq :: F9 -> [F9]

IntegerAsType p => FiniteField (Fp p)

Defined in Math.Algebra.Field.Base

Methods

eltsFq :: Fp p -> [Fp p]

basisFq :: Fp p -> [Fp p]

(FiniteField k, PolynomialAsType k poly) => FiniteField (ExtensionField k poly)

Defined in Math.Algebra.Field.Extension

Methods

eltsFq :: ExtensionField k poly -> [ExtensionField k poly]

basisFq :: ExtensionField k poly -> [ExtensionField k poly]

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 is a type for the finite field with 2 elements

f2 :: [F2]

f2 lists the elements of F2

type F3 = Fp T3

F3 is a type for the finite field with 3 elements

f3 :: [F3]

f3 lists the elements of F3

type F5 = Fp T5

F5 is a type for the finite field with 5 elements

f5 :: [F5]

f5 lists the elements of F5

type F7 = Fp T7

F7 is a type for the finite field with 7 elements

f7 :: [F7]

f7 lists the elements of 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]