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

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

Instances details
Eq Q Source # 
Instance details

Defined in Math.Algebra.Field.Base

Methods

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

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

Fractional Q Source # 
Instance details

Defined in Math.Algebra.Field.Base

Methods

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

recip :: Q -> Q

fromRational :: Rational -> Q

Num Q Source # 
Instance details

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 Source # 
Instance details

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 Source # 
Instance details

Defined in Math.Algebra.Field.Base

Methods

showsPrec :: Int -> Q -> ShowS

show :: Q -> String

showList :: [Q] -> ShowS

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

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

Invertible (NPoly LPQ IwahoriHeckeGens) Source # 
Instance details

Defined in Math.Projects.KnotTheory.IwahoriHecke

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

Instances details
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

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

IntegerAsType n => Fractional (Fp n) Source # 
Instance details

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) Source # 
Instance details

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) Source # 
Instance details

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) Source # 
Instance details

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) 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

Instances details
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 #

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 #

type F13 = Fp T13 Source #

type F17 = Fp T17 Source #

type F19 = Fp T19 Source #

type F23 = Fp T23 Source #

type F29 = Fp T29 Source #

type F31 = Fp T31 Source #

type F37 = Fp T37 Source #

type F41 = Fp T41 Source #

type F43 = Fp T43 Source #

type F47 = Fp T47 Source #

type F53 = Fp T53 Source #

type F59 = Fp T59 Source #

type F61 = Fp T61 Source #

type F67 = Fp T67 Source #

type F71 = Fp T71 Source #

type F73 = Fp T73 Source #

type F79 = Fp T79 Source #

type F83 = Fp T83 Source #

type F89 = Fp T89 Source #

type F97 = Fp T97 Source #