Safe Haskell	Safe-Inferred
Language	Haskell2010

ZkFold.Symbolic.GroebnerBasis.Internal.Types

Documentation

data VarType Source #

Constructors

VarTypeFree
VarTypeBound
VarTypeBoolean

Instances

Instances details

Show VarType Source #
Instance details Defined in ZkFold.Symbolic.GroebnerBasis.Internal.Types Methods showsPrec :: Int -> VarType -> ShowS # show :: VarType -> String # showList :: [VarType] -> ShowS #
Eq VarType Source #
Instance details Defined in ZkFold.Symbolic.GroebnerBasis.Internal.Types Methods (==) :: VarType -> VarType -> Bool # (/=) :: VarType -> VarType -> Bool #

data Var a c Source #

Constructors

Free a
Bound a Natural
Boolean Natural

Instances

Instances details

Functor (Var a :: Type -> Type) Source #
Instance details Defined in ZkFold.Symbolic.GroebnerBasis.Internal.Types Methods fmap :: (a0 -> b) -> Var a a0 -> Var a b # (<$) :: a0 -> Var a b -> Var a a0 #
(Show a, MultiplicativeMonoid a) => Show (Var a c) Source #
Instance details Defined in ZkFold.Symbolic.GroebnerBasis.Internal.Types Methods showsPrec :: Int -> Var a c -> ShowS # show :: Var a c -> String # showList :: [Var a c] -> ShowS #
(Eq a, MultiplicativeMonoid a) => Eq (Var a c) Source #
Instance details Defined in ZkFold.Symbolic.GroebnerBasis.Internal.Types Methods (==) :: Var a c -> Var a c -> Bool # (/=) :: Var a c -> Var a c -> Bool #
(Ord a, MultiplicativeMonoid a) => Ord (Var a c) Source #
Instance details Defined in ZkFold.Symbolic.GroebnerBasis.Internal.Types Methods compare :: Var a c -> Var a c -> Ordering # (<) :: Var a c -> Var a c -> Bool # (<=) :: Var a c -> Var a c -> Bool # (>) :: Var a c -> Var a c -> Bool # (>=) :: Var a c -> Var a c -> Bool # max :: Var a c -> Var a c -> Var a c # min :: Var a c -> Var a c -> Var a c #

getVarType :: Var a c -> VarType Source #

getPower :: MultiplicativeMonoid a => Var a c -> a Source #

setPower :: a -> Var a c -> Var a c Source #

getPoly :: Var a c -> Natural Source #

data Monom a c Source #

Constructors

M c (Map Natural (Var a c))

Instances

Instances details

Functor (Monom a) Source #
Instance details Defined in ZkFold.Symbolic.GroebnerBasis.Internal.Types Methods fmap :: (a0 -> b) -> Monom a a0 -> Monom a b # (<$) :: a0 -> Monom a b -> Monom a a0 #
(Show c, Eq c, FiniteField c, Show a, Eq a, AdditiveGroup a, MultiplicativeMonoid a) => Show (Monom a c) Source #
Instance details Defined in ZkFold.Symbolic.GroebnerBasis.Internal.Types Methods showsPrec :: Int -> Monom a c -> ShowS # show :: Monom a c -> String # showList :: [Monom a c] -> ShowS #
(Eq c, Eq a, MultiplicativeMonoid a) => Eq (Monom a c) Source #
Instance details Defined in ZkFold.Symbolic.GroebnerBasis.Internal.Types Methods (==) :: Monom a c -> Monom a c -> Bool # (/=) :: Monom a c -> Monom a c -> Bool #
(AdditiveMonoid c, Eq c, Ord a, MultiplicativeMonoid a) => Ord (Monom a c) Source #
Instance details Defined in ZkFold.Symbolic.GroebnerBasis.Internal.Types Methods compare :: Monom a c -> Monom a c -> Ordering # (<) :: Monom a c -> Monom a c -> Bool # (<=) :: Monom a c -> Monom a c -> Bool # (>) :: Monom a c -> Monom a c -> Bool # (>=) :: Monom a c -> Monom a c -> Bool # max :: Monom a c -> Monom a c -> Monom a c # min :: Monom a c -> Monom a c -> Monom a c #

newtype Polynom a c Source #

Constructors

P [Monom a c]

Instances

Instances details

Functor (Polynom a) Source #
Instance details Defined in ZkFold.Symbolic.GroebnerBasis.Internal.Types Methods fmap :: (a0 -> b) -> Polynom a a0 -> Polynom a b # (<$) :: a0 -> Polynom a b -> Polynom a a0 #
(Show c, Eq c, FiniteField c, Show a, Eq a, AdditiveGroup a, MultiplicativeMonoid a) => Show (Polynom a c) Source #
Instance details Defined in ZkFold.Symbolic.GroebnerBasis.Internal.Types Methods showsPrec :: Int -> Polynom a c -> ShowS # show :: Polynom a c -> String # showList :: [Polynom a c] -> ShowS #
(Eq c, Eq a, MultiplicativeMonoid a) => Eq (Polynom a c) Source #
Instance details Defined in ZkFold.Symbolic.GroebnerBasis.Internal.Types Methods (==) :: Polynom a c -> Polynom a c -> Bool # (/=) :: Polynom a c -> Polynom a c -> Bool #
(AdditiveMonoid c, Eq c, Ord a, MultiplicativeMonoid a) => Ord (Polynom a c) Source #
Instance details Defined in ZkFold.Symbolic.GroebnerBasis.Internal.Types Methods compare :: Polynom a c -> Polynom a c -> Ordering # (<) :: Polynom a c -> Polynom a c -> Bool # (<=) :: Polynom a c -> Polynom a c -> Bool # (>) :: Polynom a c -> Polynom a c -> Bool # (>=) :: Polynom a c -> Polynom a c -> Bool # max :: Polynom a c -> Polynom a c -> Polynom a c # min :: Polynom a c -> Polynom a c -> Polynom a c #
(Eq c, FiniteField c, Ord a, MultiplicativeMonoid a) => AdditiveGroup (Polynom a c) Source #
Instance details Defined in ZkFold.Symbolic.GroebnerBasis.Internal.Types Methods (-) :: Polynom a c -> Polynom a c -> Polynom a c Source # negate :: Polynom a c -> Polynom a c Source #
(Eq c, FiniteField c, Ord a, MultiplicativeMonoid a) => AdditiveMonoid (Polynom a c) Source #
Instance details Defined in ZkFold.Symbolic.GroebnerBasis.Internal.Types Methods zero :: Polynom a c Source #
(Eq c, FiniteField c, Ord a, MultiplicativeMonoid a) => AdditiveSemigroup (Polynom a c) Source #
Instance details Defined in ZkFold.Symbolic.GroebnerBasis.Internal.Types Methods (+) :: Polynom a c -> Polynom a c -> Polynom a c Source #
(Eq c, FiniteField c, Ord a, AdditiveGroup a, MultiplicativeMonoid a) => MultiplicativeMonoid (Polynom a c) Source #
Instance details Defined in ZkFold.Symbolic.GroebnerBasis.Internal.Types Methods one :: Polynom a c Source #
(Eq c, FiniteField c, Ord a, AdditiveGroup a, MultiplicativeMonoid a) => MultiplicativeSemigroup (Polynom a c) Source #
Instance details Defined in ZkFold.Symbolic.GroebnerBasis.Internal.Types Methods (*) :: Polynom a c -> Polynom a c -> Polynom a c Source #
MultiplicativeMonoid (Polynom a c) => Exponent (Polynom a c) Natural Source #
Instance details Defined in ZkFold.Symbolic.GroebnerBasis.Internal.Types Methods (^) :: Polynom a c -> Natural -> Polynom a c Source #

lt :: Polynom c a -> Monom c a Source #

lv :: Polynom c a -> Natural Source #

oneV :: (Eq a, AdditiveMonoid a, MultiplicativeMonoid a) => Var a c -> Bool Source #

zeroM :: (Eq c, FiniteField c) => Monom a c -> Bool Source #

zeroP :: Polynom a c -> Bool Source #

addPower :: AdditiveSemigroup a => Var a c -> Var a c -> Var a c Source #

subPower :: AdditiveGroup a => Var a c -> Var a c -> Maybe (Var a c) Source #

similarM :: (Eq a, MultiplicativeMonoid a) => Monom a c -> Monom a c -> Bool Source #

addSimilar :: FiniteField c => Monom a c -> Monom a c -> Monom a c Source #

addPoly :: (Eq c, FiniteField c, Ord a, MultiplicativeMonoid a) => Polynom a c -> Polynom a c -> Polynom a c Source #

mulMono :: (FiniteField c, AdditiveMonoid a) => Monom a c -> Monom a c -> Monom a c Source #

mulPM :: (FiniteField c, AdditiveMonoid a) => Polynom a c -> Monom a c -> Polynom a c Source #

mulM :: (Eq c, FiniteField c, Ord a, AdditiveGroup a, MultiplicativeMonoid a) => Polynom a c -> Polynom a c -> Polynom a c Source #

dividable :: (Ord a, MultiplicativeMonoid a) => Monom a c -> Monom a c -> Bool Source #

divideM :: (FiniteField c, Eq a, Ring a) => Monom a c -> Monom a c -> Monom a c Source #

lcmM :: (FiniteField c, Ord a, MultiplicativeMonoid a) => Monom a c -> Monom a c -> Monom a c Source #

gcdM :: (FiniteField c, Ord a, MultiplicativeMonoid a) => Monom a c -> Monom a c -> Monom a c Source #