Safe Haskell	Safe-Inferred
Language	Haskell2010

ZkFold.Base.Algebra.Basic.Field

Documentation

class IrreduciblePoly f (e :: Symbol) | e -> f where Source #

Methods

irreduciblePoly :: Poly f Source #

Instances

Instances details

IrreduciblePoly Fq IP1 Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381 Methods irreduciblePoly :: Poly Fq Source #
IrreduciblePoly Fq2 IP2 Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381 Methods irreduciblePoly :: Poly Fq2 Source #
IrreduciblePoly Fq6 IP3 Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381 Methods irreduciblePoly :: Poly Fq6 Source #
IrreduciblePoly Fp "IP1" Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BN254 Methods irreduciblePoly :: Poly Fp Source #
IrreduciblePoly Fp2 "IP2" Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BN254 Methods irreduciblePoly :: Poly Fp2 Source #
IrreduciblePoly Fp6 "IP3" Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BN254 Methods irreduciblePoly :: Poly Fp6 Source #

data Zp (p :: Natural) Source #

Instances

Instances details

IrreduciblePoly Fq IP1 Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381 Methods irreduciblePoly :: Poly Fq Source #
IrreduciblePoly Fq2 IP2 Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381 Methods irreduciblePoly :: Poly Fq2 Source #
IrreduciblePoly Fq6 IP3 Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381 Methods irreduciblePoly :: Poly Fq6 Source #
IrreduciblePoly Fp "IP1" Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BN254 Methods irreduciblePoly :: Poly Fp Source #
IrreduciblePoly Fp2 "IP2" Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BN254 Methods irreduciblePoly :: Poly Fp2 Source #
IrreduciblePoly Fp6 "IP3" Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BN254 Methods irreduciblePoly :: Poly Fp6 Source #
(MultiplicativeGroup a, Order a ~ p) => Exponent a (Zp p) Source #	Exponentiation by an element of a finite field is well-defined (and lawful) if and only if the base is a finite multiplicative group of a matching order. Note that left distributivity is satisfied, meaning `a ^ (m + n) = (a ^ m) * (a ^ n)`.
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods (^) :: a -> Zp p -> a Source #
KnownNat p => FromConstant Integer (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods fromConstant :: Integer -> Zp p Source #
KnownNat p => FromConstant Natural (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods fromConstant :: Natural -> Zp p Source #
KnownNat p => Scale Integer (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods scale :: Integer -> Zp p -> Zp p Source #
KnownNat p => Scale Natural (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods scale :: Natural -> Zp p -> Zp p Source #
KnownNat p => Arbitrary (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods arbitrary :: Gen (Zp p) # shrink :: Zp p -> [Zp p] #
FromJSON (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods parseJSON :: Value -> Parser (Zp p) # parseJSONList :: Value -> Parser [Zp p] #
ToJSON (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods toJSON :: Zp p -> Value # toEncoding :: Zp p -> Encoding # toJSONList :: [Zp p] -> Value # toEncodingList :: [Zp p] -> Encoding #
Generic (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Associated Types type Rep (Zp p) :: Type -> Type # Methods from :: Zp p -> Rep (Zp p) x # to :: Rep (Zp p) x -> Zp p #
KnownNat p => Num (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods (+) :: Zp p -> Zp p -> Zp p # (-) :: Zp p -> Zp p -> Zp p # (*) :: Zp p -> Zp p -> Zp p # negate :: Zp p -> Zp p # abs :: Zp p -> Zp p # signum :: Zp p -> Zp p # fromInteger :: Integer -> Zp p #
Prime p => Fractional (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods (/) :: Zp p -> Zp p -> Zp p # recip :: Zp p -> Zp p # fromRational :: Rational -> Zp p #
Show (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods showsPrec :: Int -> Zp p -> ShowS # show :: Zp p -> String # showList :: [Zp p] -> ShowS #
KnownNat p => Binary (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods put :: Zp p -> Put # get :: Get (Zp p) # putList :: [Zp p] -> Put #
NFData (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods rnf :: Zp p -> () #
KnownNat p => Eq (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods (==) :: Zp p -> Zp p -> Bool # (/=) :: Zp p -> Zp p -> Bool #
KnownNat p => Ord (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods compare :: Zp p -> Zp p -> Ordering # (<) :: Zp p -> Zp p -> Bool # (<=) :: Zp p -> Zp p -> Bool # (>) :: Zp p -> Zp p -> Bool # (>=) :: Zp p -> Zp p -> Bool # max :: Zp p -> Zp p -> Zp p # min :: Zp p -> Zp p -> Zp p #
KnownNat p => Random (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods randomR :: RandomGen g => (Zp p, Zp p) -> g -> (Zp p, g) # random :: RandomGen g => g -> (Zp p, g) # randomRs :: RandomGen g => (Zp p, Zp p) -> g -> [Zp p] # randoms :: RandomGen g => g -> [Zp p] #
KnownNat p => AdditiveGroup (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods (-) :: Zp p -> Zp p -> Zp p Source # negate :: Zp p -> Zp p Source #
KnownNat p => AdditiveMonoid (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods zero :: Zp p Source #
KnownNat p => AdditiveSemigroup (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods (+) :: Zp p -> Zp p -> Zp p Source #
Prime p => BinaryExpansion (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Associated Types type Bits (Zp p) Source # Methods binaryExpansion :: Zp p -> Bits (Zp p) Source # fromBinary :: Bits (Zp p) -> Zp p Source #
Prime p => DiscreteField' (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods equal :: Zp p -> Zp p -> Zp p Source #
Prime p => Field (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods (//) :: Zp p -> Zp p -> Zp p Source # finv :: Zp p -> Zp p Source # rootOfUnity :: Natural -> Maybe (Zp p) Source #
(KnownNat p, KnownNat (NumberOfBits (Zp p))) => Finite (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Associated Types type Order (Zp p) :: Natural Source #
KnownNat p => MultiplicativeMonoid (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods one :: Zp p Source #
KnownNat p => MultiplicativeSemigroup (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods (*) :: Zp p -> Zp p -> Zp p Source #
KnownNat p => Ring (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field
KnownNat p => SemiEuclidean (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods divMod :: Zp p -> Zp p -> (Zp p, Zp p) Source # div :: Zp p -> Zp p -> Zp p Source # mod :: Zp p -> Zp p -> Zp p Source #
KnownNat p => Semiring (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field
ToConstant (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Associated Types type Const (Zp p) Source # Methods toConstant :: Zp p -> Const (Zp p) Source #
Prime p => TrichotomyField (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods trichotomy :: Zp p -> Zp p -> Zp p Source #
Prime p => Exponent (Zp p) Integer Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods (^) :: Zp p -> Integer -> Zp p Source #
KnownNat p => Exponent (Zp p) Natural Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods (^) :: Zp p -> Natural -> Zp p Source #
(Symbolic c, KnownNat n, KnownRegisterSize r) => StrictConv (Zp p) (UInt n r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.UInt Methods strictConv :: Zp p -> UInt n r c Source #
ToJSON (ByteString n (Interpreter (Zp p))) Source #
Instance details Defined in ZkFold.Symbolic.Data.ByteString Methods toJSON :: ByteString n (Interpreter (Zp p)) -> Value # toEncoding :: ByteString n (Interpreter (Zp p)) -> Encoding # toJSONList :: [ByteString n (Interpreter (Zp p))] -> Value # toEncodingList :: [ByteString n (Interpreter (Zp p))] -> Encoding #
ToConstant (ByteString n (Interpreter (Zp p))) Source #
Instance details Defined in ZkFold.Symbolic.Data.ByteString Associated Types type Const (ByteString n (Interpreter (Zp p))) Source # Methods toConstant :: ByteString n (Interpreter (Zp p)) -> Const (ByteString n (Interpreter (Zp p))) Source #
Substitution (Vector n b) (Zp n) b Source #
Instance details Defined in ZkFold.Base.Algebra.Polynomials.Multivariate.Substitution Methods subs :: Vector n b -> Zp n -> b Source #
(Symbolic (Interpreter (Zp p)), KnownNat n, KnownRegisterSize r) => ToJSON (UInt n r (Interpreter (Zp p))) Source #
Instance details Defined in ZkFold.Symbolic.Data.UInt Methods toJSON :: UInt n r (Interpreter (Zp p)) -> Value # toEncoding :: UInt n r (Interpreter (Zp p)) -> Encoding # toJSONList :: [UInt n r (Interpreter (Zp p))] -> Value # toEncodingList :: [UInt n r (Interpreter (Zp p))] -> Encoding #
(Symbolic (Interpreter (Zp p)), KnownNat n, KnownRegisterSize r) => ToConstant (UInt n r (Interpreter (Zp p))) Source #
Instance details Defined in ZkFold.Symbolic.Data.UInt Associated Types type Const (UInt n r (Interpreter (Zp p))) Source # Methods toConstant :: UInt n r (Interpreter (Zp p)) -> Const (UInt n r (Interpreter (Zp p))) Source #
type Rep (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field type Rep (Zp p) = D1 ('MetaData "Zp" "ZkFold.Base.Algebra.Basic.Field" "symbolic-base-0.1.0.0-inplace" 'True) (C1 ('MetaCons "Zp" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Integer)))
type Bits (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field type Bits (Zp p) = [Zp p]
type Const (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field type Const (Zp p) = Natural
type Order (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field type Order (Zp p) = p
type Const (ByteString n (Interpreter (Zp p))) Source #
Instance details Defined in ZkFold.Symbolic.Data.ByteString type Const (ByteString n (Interpreter (Zp p))) = Natural
type Const (UInt n r (Interpreter (Zp p))) Source #
Instance details Defined in ZkFold.Symbolic.Data.UInt type Const (UInt n r (Interpreter (Zp p))) = Natural

toZp :: forall p. KnownNat p => Integer -> Zp p Source #

fromZp :: Zp p -> Natural Source #

inv :: Integer -> Natural -> Natural Source #

data Ext2 f (e :: Symbol) Source #

Constructors

Ext2 f f

Instances

Instances details

IrreduciblePoly Fq2 IP2 Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381 Methods irreduciblePoly :: Poly Fq2 Source #
IrreduciblePoly Fq6 IP3 Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381 Methods irreduciblePoly :: Poly Fq6 Source #
IrreduciblePoly Fp2 "IP2" Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BN254 Methods irreduciblePoly :: Poly Fp2 Source #
IrreduciblePoly Fp6 "IP3" Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BN254 Methods irreduciblePoly :: Poly Fp6 Source #
(FromConstant f f', Field f') => FromConstant f (Ext2 f' e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods fromConstant :: f -> Ext2 f' e Source #
Scale c f => Scale c (Ext2 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods scale :: c -> Ext2 f e -> Ext2 f e Source #
(Field f, Eq f, IrreduciblePoly f e) => FromConstant (Poly f) (Ext2 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods fromConstant :: Poly f -> Ext2 f e Source #
(Field f, Eq f, IrreduciblePoly f e, Arbitrary f) => Arbitrary (Ext2 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods arbitrary :: Gen (Ext2 f e) # shrink :: Ext2 f e -> [Ext2 f e] #
Show f => Show (Ext2 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods showsPrec :: Int -> Ext2 f e -> ShowS # show :: Ext2 f e -> String # showList :: [Ext2 f e] -> ShowS #
Binary f => Binary (Ext2 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods put :: Ext2 f e -> Put # get :: Get (Ext2 f e) # putList :: [Ext2 f e] -> Put #
Eq f => Eq (Ext2 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods (==) :: Ext2 f e -> Ext2 f e -> Bool # (/=) :: Ext2 f e -> Ext2 f e -> Bool #
Ord f => Ord (Ext2 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods compare :: Ext2 f e -> Ext2 f e -> Ordering # (<) :: Ext2 f e -> Ext2 f e -> Bool # (<=) :: Ext2 f e -> Ext2 f e -> Bool # (>) :: Ext2 f e -> Ext2 f e -> Bool # (>=) :: Ext2 f e -> Ext2 f e -> Bool # max :: Ext2 f e -> Ext2 f e -> Ext2 f e # min :: Ext2 f e -> Ext2 f e -> Ext2 f e #
Field f => AdditiveGroup (Ext2 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods (-) :: Ext2 f e -> Ext2 f e -> Ext2 f e Source # negate :: Ext2 f e -> Ext2 f e Source #
Field f => AdditiveMonoid (Ext2 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods zero :: Ext2 f e Source #
Field f => AdditiveSemigroup (Ext2 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods (+) :: Ext2 f e -> Ext2 f e -> Ext2 f e Source #
(Field f, Eq f, IrreduciblePoly f e) => Field (Ext2 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods (//) :: Ext2 f e -> Ext2 f e -> Ext2 f e Source # finv :: Ext2 f e -> Ext2 f e Source # rootOfUnity :: Natural -> Maybe (Ext2 f e) Source #
(KnownNat (Order (Ext2 f e)), KnownNat (NumberOfBits (Ext2 f e))) => Finite (Ext2 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Associated Types type Order (Ext2 f e) :: Natural Source #
(Field f, Eq f, IrreduciblePoly f e) => MultiplicativeMonoid (Ext2 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods one :: Ext2 f e Source #
(Field f, Eq f, IrreduciblePoly f e) => MultiplicativeSemigroup (Ext2 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods (*) :: Ext2 f e -> Ext2 f e -> Ext2 f e Source #
(Field f, Eq f, IrreduciblePoly f e) => Ring (Ext2 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field
(Field f, Eq f, IrreduciblePoly f e) => Semiring (Ext2 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field
Field (Ext2 f e) => Exponent (Ext2 f e) Integer Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods (^) :: Ext2 f e -> Integer -> Ext2 f e Source #
MultiplicativeMonoid (Ext2 f e) => Exponent (Ext2 f e) Natural Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods (^) :: Ext2 f e -> Natural -> Ext2 f e Source #
FromConstant (Ext2 f e) (Ext2 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods fromConstant :: Ext2 f e -> Ext2 f e Source #
(Field f, Eq f, IrreduciblePoly f e) => Scale (Ext2 f e) (Ext2 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods scale :: Ext2 f e -> Ext2 f e -> Ext2 f e Source #
type Order (Ext2 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field type Order (Ext2 f e) = Order f ^ 2

data Ext3 f (e :: Symbol) Source #

Constructors

Ext3 f f f

Instances

Instances details

IrreduciblePoly Fq6 IP3 Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381 Methods irreduciblePoly :: Poly Fq6 Source #
IrreduciblePoly Fp6 "IP3" Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BN254 Methods irreduciblePoly :: Poly Fp6 Source #
(FromConstant f f', Field f') => FromConstant f (Ext3 f' ip) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods fromConstant :: f -> Ext3 f' ip Source #
Scale c f => Scale c (Ext3 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods scale :: c -> Ext3 f e -> Ext3 f e Source #
(Field f, Eq f, IrreduciblePoly f e) => FromConstant (Poly f) (Ext3 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods fromConstant :: Poly f -> Ext3 f e Source #
(Field f, Eq f, IrreduciblePoly f e, Arbitrary f) => Arbitrary (Ext3 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods arbitrary :: Gen (Ext3 f e) # shrink :: Ext3 f e -> [Ext3 f e] #
Show f => Show (Ext3 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods showsPrec :: Int -> Ext3 f e -> ShowS # show :: Ext3 f e -> String # showList :: [Ext3 f e] -> ShowS #
Binary f => Binary (Ext3 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods put :: Ext3 f e -> Put # get :: Get (Ext3 f e) # putList :: [Ext3 f e] -> Put #
Eq f => Eq (Ext3 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods (==) :: Ext3 f e -> Ext3 f e -> Bool # (/=) :: Ext3 f e -> Ext3 f e -> Bool #
Ord f => Ord (Ext3 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods compare :: Ext3 f e -> Ext3 f e -> Ordering # (<) :: Ext3 f e -> Ext3 f e -> Bool # (<=) :: Ext3 f e -> Ext3 f e -> Bool # (>) :: Ext3 f e -> Ext3 f e -> Bool # (>=) :: Ext3 f e -> Ext3 f e -> Bool # max :: Ext3 f e -> Ext3 f e -> Ext3 f e # min :: Ext3 f e -> Ext3 f e -> Ext3 f e #
Field f => AdditiveGroup (Ext3 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods (-) :: Ext3 f e -> Ext3 f e -> Ext3 f e Source # negate :: Ext3 f e -> Ext3 f e Source #
Field f => AdditiveMonoid (Ext3 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods zero :: Ext3 f e Source #
Field f => AdditiveSemigroup (Ext3 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods (+) :: Ext3 f e -> Ext3 f e -> Ext3 f e Source #
(Field f, Eq f, IrreduciblePoly f e) => Field (Ext3 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods (//) :: Ext3 f e -> Ext3 f e -> Ext3 f e Source # finv :: Ext3 f e -> Ext3 f e Source # rootOfUnity :: Natural -> Maybe (Ext3 f e) Source #
(KnownNat (Order (Ext3 f e)), KnownNat (NumberOfBits (Ext3 f e))) => Finite (Ext3 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Associated Types type Order (Ext3 f e) :: Natural Source #
(Field f, Eq f, IrreduciblePoly f e) => MultiplicativeMonoid (Ext3 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods one :: Ext3 f e Source #
(Field f, Eq f, IrreduciblePoly f e) => MultiplicativeSemigroup (Ext3 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods (*) :: Ext3 f e -> Ext3 f e -> Ext3 f e Source #
(Field f, Eq f, IrreduciblePoly f e) => Ring (Ext3 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field
(Field f, Eq f, IrreduciblePoly f e) => Semiring (Ext3 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field
Field (Ext3 f e) => Exponent (Ext3 f e) Integer Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods (^) :: Ext3 f e -> Integer -> Ext3 f e Source #
MultiplicativeMonoid (Ext3 f e) => Exponent (Ext3 f e) Natural Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods (^) :: Ext3 f e -> Natural -> Ext3 f e Source #
FromConstant (Ext3 f e) (Ext3 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods fromConstant :: Ext3 f e -> Ext3 f e Source #
(Field f, Eq f, IrreduciblePoly f e) => Scale (Ext3 f e) (Ext3 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods scale :: Ext3 f e -> Ext3 f e -> Ext3 f e Source #
type Order (Ext3 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field type Order (Ext3 f e) = Order f ^ 3