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 #

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 #
(KnownNat p, 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 #
Finite (Zp p) => EllipticCurve (Ed25519 (Zp p) :: Type) Source #	Ed25519 with `UInt 256 (Zp p)` as computational backend
Instance details Defined in ZkFold.Symbolic.Data.Ed25519 Associated Types type BaseField (Ed25519 (Zp p)) Source # type ScalarField (Ed25519 (Zp p)) Source # Methods inf :: Point (Ed25519 (Zp p)) Source # gen :: Point (Ed25519 (Zp p)) Source # add :: Point (Ed25519 (Zp p)) -> Point (Ed25519 (Zp p)) -> Point (Ed25519 (Zp p)) Source # mul :: ScalarField (Ed25519 (Zp p)) -> Point (Ed25519 (Zp p)) -> Point (Ed25519 (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] # omittedField :: Maybe (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 # omitField :: Zp p -> Bool #
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 Methods binaryExpansion :: Zp p -> [Zp p] Source # fromBinary :: [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 #
KnownNat p => EuclideanDomain (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 #
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 => Semiring (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field
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 #
ToConstant (Zp p) Natural Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field Methods toConstant :: Zp p -> Natural Source #
(Prime p, Field x, Eq x) => DiscreteField (Bool (Zp p)) x Source #
Instance details Defined in ZkFold.Symbolic.Data.DiscreteField Methods isZero :: x -> Bool (Zp p) Source #
(Prime p, Ord x) => Ord (Bool (Zp p)) x Source #
Instance details Defined in ZkFold.Symbolic.Data.Ord Methods (<=) :: x -> x -> Bool (Zp p) Source # (<) :: x -> x -> Bool (Zp p) Source # (>=) :: x -> x -> Bool (Zp p) Source # (>) :: x -> x -> Bool (Zp p) Source # max :: x -> x -> x Source # min :: x -> x -> x Source #
(Finite (Zp p), KnownNat n) => Eq (Bool (Zp p)) (UInt n (Zp p)) Source #
Instance details Defined in ZkFold.Symbolic.Data.UInt Methods (==) :: UInt n (Zp p) -> UInt n (Zp p) -> Bool (Zp p) Source # (/=) :: UInt n (Zp p) -> UInt n (Zp p) -> Bool (Zp p) Source #
(Finite (Zp p), KnownNat n) => Ord (Bool (Zp p)) (UInt n (Zp p)) Source #
Instance details Defined in ZkFold.Symbolic.Data.UInt Methods (<=) :: UInt n (Zp p) -> UInt n (Zp p) -> Bool (Zp p) Source # (<) :: UInt n (Zp p) -> UInt n (Zp p) -> Bool (Zp p) Source # (>=) :: UInt n (Zp p) -> UInt n (Zp p) -> Bool (Zp p) Source # (>) :: UInt n (Zp p) -> UInt n (Zp p) -> Bool (Zp p) Source # max :: UInt n (Zp p) -> UInt n (Zp p) -> UInt n (Zp p) Source # min :: UInt n (Zp p) -> UInt n (Zp p) -> UInt n (Zp p) Source #
(Finite (Zp p), KnownNat n) => StrictConv (Zp p) (UInt n (Zp p)) Source #
Instance details Defined in ZkFold.Symbolic.Data.UInt Methods strictConv :: Zp p -> UInt n (Zp p) Source #
(Finite (Zp p), KnownNat n) => Arbitrary (ByteString n (Zp p)) Source #
Instance details Defined in ZkFold.Symbolic.Data.ByteString Methods arbitrary :: Gen (ByteString n (Zp p)) # shrink :: ByteString n (Zp p) -> [ByteString n (Zp p)] #
(Finite (Zp p), KnownNat n) => Arbitrary (UInt n (Zp p)) Source #
Instance details Defined in ZkFold.Symbolic.Data.UInt Methods arbitrary :: Gen (UInt n (Zp p)) # shrink :: UInt n (Zp p) -> [UInt n (Zp p)] #
(Finite (Zp p), KnownNat n) => AdditiveGroup (UInt n (Zp p)) Source #
Instance details Defined in ZkFold.Symbolic.Data.UInt Methods (-) :: UInt n (Zp p) -> UInt n (Zp p) -> UInt n (Zp p) Source # negate :: UInt n (Zp p) -> UInt n (Zp p) Source #
(Finite (Zp p), KnownNat n) => AdditiveMonoid (UInt n (Zp p)) Source #
Instance details Defined in ZkFold.Symbolic.Data.UInt Methods zero :: UInt n (Zp p) Source #
(Finite (Zp p), KnownNat n) => AdditiveSemigroup (UInt n (Zp p)) Source #
Instance details Defined in ZkFold.Symbolic.Data.UInt Methods (+) :: UInt n (Zp p) -> UInt n (Zp p) -> UInt n (Zp p) Source #
(Finite (Zp p), KnownNat n) => EuclideanDomain (UInt n (Zp p)) Source #
Instance details Defined in ZkFold.Symbolic.Data.UInt Methods divMod :: UInt n (Zp p) -> UInt n (Zp p) -> (UInt n (Zp p), UInt n (Zp p)) Source # div :: UInt n (Zp p) -> UInt n (Zp p) -> UInt n (Zp p) Source # mod :: UInt n (Zp p) -> UInt n (Zp p) -> UInt n (Zp p) Source #
(Finite (Zp p), KnownNat n) => MultiplicativeMonoid (UInt n (Zp p)) Source #
Instance details Defined in ZkFold.Symbolic.Data.UInt Methods one :: UInt n (Zp p) Source #
(Finite (Zp p), KnownNat n) => MultiplicativeSemigroup (UInt n (Zp p)) Source #
Instance details Defined in ZkFold.Symbolic.Data.UInt Methods (*) :: UInt n (Zp p) -> UInt n (Zp p) -> UInt n (Zp p) Source #
(Finite (Zp p), KnownNat n) => Ring (UInt n (Zp p)) Source #
Instance details Defined in ZkFold.Symbolic.Data.UInt
(Finite (Zp p), KnownNat n) => Semiring (UInt n (Zp p)) Source #
Instance details Defined in ZkFold.Symbolic.Data.UInt
(Finite (Zp p), KnownNat n) => BoolType (ByteString n (Zp p)) Source #
Instance details Defined in ZkFold.Symbolic.Data.ByteString Methods true :: ByteString n (Zp p) Source # false :: ByteString n (Zp p) Source # not :: ByteString n (Zp p) -> ByteString n (Zp p) Source # (&&) :: ByteString n (Zp p) -> ByteString n (Zp p) -> ByteString n (Zp p) Source # (\|\|) :: ByteString n (Zp p) -> ByteString n (Zp p) -> ByteString n (Zp p) Source # xor :: ByteString n (Zp p) -> ByteString n (Zp p) -> ByteString n (Zp p) Source #
(Finite (Zp p), KnownNat n) => ShiftBits (ByteString n (Zp p)) Source #
Instance details Defined in ZkFold.Symbolic.Data.ByteString Methods shiftBits :: ByteString n (Zp p) -> Integer -> ByteString n (Zp p) Source # shiftBitsL :: ByteString n (Zp p) -> Natural -> ByteString n (Zp p) Source # shiftBitsR :: ByteString n (Zp p) -> Natural -> ByteString n (Zp p) Source # rotateBits :: ByteString n (Zp p) -> Integer -> ByteString n (Zp p) Source # rotateBitsL :: ByteString n (Zp p) -> Natural -> ByteString n (Zp p) Source # rotateBitsR :: ByteString n (Zp p) -> Natural -> ByteString n (Zp p) Source #
(Finite (Zp p), KnownNat n) => StrictNum (UInt n (Zp p)) Source #
Instance details Defined in ZkFold.Symbolic.Data.UInt Methods strictAdd :: UInt n (Zp p) -> UInt n (Zp p) -> UInt n (Zp p) Source # strictSub :: UInt n (Zp p) -> UInt n (Zp p) -> UInt n (Zp p) Source # strictMul :: UInt n (Zp p) -> UInt n (Zp p) -> UInt n (Zp p) Source #
(Finite (Zp p), KnownNat n) => ToConstant (UInt n (Zp p)) Integer Source #
Instance details Defined in ZkFold.Symbolic.Data.UInt Methods toConstant :: UInt n (Zp p) -> Integer Source #
(Finite (Zp p), KnownNat n) => ToConstant (UInt n (Zp p)) Natural Source #
Instance details Defined in ZkFold.Symbolic.Data.UInt Methods toConstant :: UInt n (Zp p) -> Natural 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 #
(KnownNat n, KnownNat m, m <= n, Mod n m ~ 0, Finite (Zp p)) => Concat (ByteString m (Zp p)) (ByteString n (Zp p)) Source #	Unfortunately, Haskell does not support dependent types yet, so we have no possibility to infer the exact type of the result (the list can contain an arbitrary number of words). We can only impose some restrictions on `n` and `m`.
Instance details Defined in ZkFold.Symbolic.Data.ByteString Methods concat :: [ByteString m (Zp p)] -> ByteString n (Zp p) Source #
(KnownNat wordSize, KnownNat n, Finite (Zp p), wordSize <= n, 1 <= wordSize, 1 <= n, Mod n wordSize ~ 0) => ToWords (ByteString n (Zp p)) (ByteString wordSize (Zp p)) Source #	A ByteString of length `n` can only be split into words of length `wordSize` if all of the following conditions are met: 1. `wordSize` is not greater than `n`; 2. `wordSize` is not zero; 3. The bytestring is not empty; 4. `wordSize` divides `n`.
Instance details Defined in ZkFold.Symbolic.Data.ByteString Methods toWords :: ByteString n (Zp p) -> [ByteString wordSize (Zp p)] Source #
(KnownNat m, KnownNat n, n <= m, Finite (Zp p)) => Truncate (ByteString m (Zp p)) (ByteString n (Zp p)) Source #	Only a bigger ByteString can be truncated into a smaller one.
Instance details Defined in ZkFold.Symbolic.Data.ByteString Methods truncate :: ByteString m (Zp p) -> ByteString n (Zp p) Source #
(KnownNat n, m <= n, Finite (Zp p)) => Extend (ByteString m (Zp p)) (ByteString n (Zp p)) Source #	Only a smaller ByteString can be extended into a bigger one.
Instance details Defined in ZkFold.Symbolic.Data.ByteString Methods extend :: ByteString m (Zp p) -> ByteString n (Zp p) Source #
(Finite (Zp p), KnownNat n, KnownNat m, n <= m) => Extend (UInt n (Zp p)) (UInt m (Zp p)) Source #
Instance details Defined in ZkFold.Symbolic.Data.UInt Methods extend :: UInt n (Zp p) -> UInt m (Zp p) Source #
(Finite (Zp p), KnownNat n) => Iso (ByteString n (Zp p)) (UInt n (Zp p)) Source #
Instance details Defined in ZkFold.Symbolic.Data.ByteString Methods from :: ByteString n (Zp p) -> UInt n (Zp p) Source #
(Finite (Zp p), KnownNat n) => Iso (UInt n (Zp p)) (ByteString n (Zp p)) Source #
Instance details Defined in ZkFold.Symbolic.Data.ByteString Methods from :: UInt n (Zp p) -> ByteString n (Zp p) Source #
(Finite (Zp p), KnownNat n, KnownNat m, m <= n) => Shrink (UInt n (Zp p)) (UInt m (Zp p)) Source #
Instance details Defined in ZkFold.Symbolic.Data.UInt Methods shrink :: UInt n (Zp p) -> UInt m (Zp p) Source #
type BaseField (Ed25519 (Zp p) :: Type) Source #
Instance details Defined in ZkFold.Symbolic.Data.Ed25519 type BaseField (Ed25519 (Zp p) :: Type) = UInt 256 (Zp p)
type ScalarField (Ed25519 (Zp p) :: Type) Source #
Instance details Defined in ZkFold.Symbolic.Data.Ed25519 type ScalarField (Ed25519 (Zp p) :: Type) = UInt 256 (Zp p)
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" "zkfold-base-0.1.0.0-inplace" 'True) (C1 ('MetaCons "Zp" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Integer)))
type Order (Zp p) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field type Order (Zp p) = p

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

fromZp :: Zp p -> 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 #
(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, 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 #
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 #
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 #
(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, 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 #
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 #
type Order (Ext3 f e) Source #
Instance details Defined in ZkFold.Base.Algebra.Basic.Field type Order (Ext3 f e) = Order f ^ 3