Safe Haskell	Safe-Inferred
Language	Haskell2010

ZkFold.Base.Algebra.Polynomials.Multivariate.Monomial

Synopsis

newtype M i j m = M m
type Monomial i j = (Variable i, Ord j, Semiring j)
type Monomial' = M Natural Natural (Map Natural Natural)
monomial :: Monomial i j => Map i j -> M i j (Map i j)
type Variable i = Ord i
type MonomialAny = M Integer Integer MonomialRepAny
type MonomialRepAny = Map Integer Integer
type MonomialRepBoundedDegree i d = Vector d (i, Bool)
type MonomialBoundedDegree i d = M i Bool (MonomialRepBoundedDegree i d)
evalMapM :: forall i j b. MultiplicativeMonoid b => Exponent b j => (i -> b) -> M i j (Map i j) -> b
evalVectorM :: forall i j b d. Monomial i j => MultiplicativeMonoid b => Exponent b j => (i -> b) -> M i j (Vector d (i, Bool)) -> b
mapVar :: [Natural] -> Natural -> Natural
mapVarMonomial :: [Natural] -> Monomial' -> Monomial'

Documentation

newtype M i j m Source #

Monomial type

Constructors

M m

Instances

Instances details

Arbitrary m => Arbitrary (M i j m) Source #
Instance details Defined in ZkFold.Base.Algebra.Polynomials.Multivariate.Monomial Methods arbitrary :: Gen (M i j m) # shrink :: M i j m -> [M i j m] #
FromJSON m => FromJSON (M i j m) Source #
Instance details Defined in ZkFold.Base.Algebra.Polynomials.Multivariate.Monomial Methods parseJSON :: Value -> Parser (M i j m) # parseJSONList :: Value -> Parser [M i j m] # omittedField :: Maybe (M i j m) #
ToJSON m => ToJSON (M i j m) Source #
Instance details Defined in ZkFold.Base.Algebra.Polynomials.Multivariate.Monomial Methods toJSON :: M i j m -> Value # toEncoding :: M i j m -> Encoding # toJSONList :: [M i j m] -> Value # toEncodingList :: [M i j m] -> Encoding # omitField :: M i j m -> Bool #
Generic (M i j m) Source #
Instance details Defined in ZkFold.Base.Algebra.Polynomials.Multivariate.Monomial Associated Types type Rep (M i j m) :: Type -> Type # Methods from :: M i j m -> Rep (M i j m) x # to :: Rep (M i j m) x -> M i j m #
Ord i => IsList (M i j (Map i j)) Source #
Instance details Defined in ZkFold.Base.Algebra.Polynomials.Multivariate.Monomial Associated Types type Item (M i j (Map i j)) # Methods fromList :: [Item (M i j (Map i j))] -> M i j (Map i j) # fromListN :: Int -> [Item (M i j (Map i j))] -> M i j (Map i j) # toList :: M i j (Map i j) -> [Item (M i j (Map i j))] #
(Show i, Show j, Monomial i j) => Show (M i j (Map i j)) Source #
Instance details Defined in ZkFold.Base.Algebra.Polynomials.Multivariate.Monomial Methods showsPrec :: Int -> M i j (Map i j) -> ShowS # show :: M i j (Map i j) -> String # showList :: [M i j (Map i j)] -> ShowS #
NFData m => NFData (M i j m) Source #
Instance details Defined in ZkFold.Base.Algebra.Polynomials.Multivariate.Monomial Methods rnf :: M i j m -> () #
(Eq i, Eq j) => Eq (M i j (Map i j)) Source #
Instance details Defined in ZkFold.Base.Algebra.Polynomials.Multivariate.Monomial Methods (==) :: M i j (Map i j) -> M i j (Map i j) -> Bool # (/=) :: M i j (Map i j) -> M i j (Map i j) -> Bool #
(Eq i, Ord i, Ord j) => Ord (M i j (Map i j)) Source #
Instance details Defined in ZkFold.Base.Algebra.Polynomials.Multivariate.Monomial Methods compare :: M i j (Map i j) -> M i j (Map i j) -> Ordering # (<) :: M i j (Map i j) -> M i j (Map i j) -> Bool # (<=) :: M i j (Map i j) -> M i j (Map i j) -> Bool # (>) :: M i j (Map i j) -> M i j (Map i j) -> Bool # (>=) :: M i j (Map i j) -> M i j (Map i j) -> Bool # max :: M i j (Map i j) -> M i j (Map i j) -> M i j (Map i j) # min :: M i j (Map i j) -> M i j (Map i j) -> M i j (Map i j) #
(Monomial i j, Ring j) => MultiplicativeGroup (M i j (Map i j)) Source #
Instance details Defined in ZkFold.Base.Algebra.Polynomials.Multivariate.Monomial Methods (/) :: M i j (Map i j) -> M i j (Map i j) -> M i j (Map i j) Source # invert :: M i j (Map i j) -> M i j (Map i j) Source #
Monomial i j => MultiplicativeMonoid (M i j (Map i j)) Source #
Instance details Defined in ZkFold.Base.Algebra.Polynomials.Multivariate.Monomial Methods one :: M i j (Map i j) Source #
Monomial i j => MultiplicativeSemigroup (M i j (Map i j)) Source #
Instance details Defined in ZkFold.Base.Algebra.Polynomials.Multivariate.Monomial Methods (*) :: M i j (Map i j) -> M i j (Map i j) -> M i j (Map i j) Source #
(Monomial i j, Ring j) => Exponent (M i j (Map i j)) Integer Source #
Instance details Defined in ZkFold.Base.Algebra.Polynomials.Multivariate.Monomial Methods (^) :: M i j (Map i j) -> Integer -> M i j (Map i j) Source #
Monomial i j => Exponent (M i j (Map i j)) Natural Source #
Instance details Defined in ZkFold.Base.Algebra.Polynomials.Multivariate.Monomial Methods (^) :: M i j (Map i j) -> Natural -> M i j (Map i j) Source #
type Rep (M i j m) Source #
Instance details Defined in ZkFold.Base.Algebra.Polynomials.Multivariate.Monomial type Rep (M i j m) = D1 ('MetaData "M" "ZkFold.Base.Algebra.Polynomials.Multivariate.Monomial" "zkfold-base-0.1.0.0-inplace" 'True) (C1 ('MetaCons "M" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 m)))
type Item (M i j (Map i j)) Source #
Instance details Defined in ZkFold.Base.Algebra.Polynomials.Multivariate.Monomial type Item (M i j (Map i j)) = (i, j)

type Monomial i j = (Variable i, Ord j, Semiring j) Source #

type Monomial' = M Natural Natural (Map Natural Natural) Source #

Most general type for a multivariate monomial

monomial :: Monomial i j => Map i j -> M i j (Map i j) Source #

Monomial constructor

type Variable i = Ord i Source #

type MonomialAny = M Integer Integer MonomialRepAny Source #

type MonomialRepAny = Map Integer Integer Source #

type MonomialRepBoundedDegree i d = Vector d (i, Bool) Source #

type MonomialBoundedDegree i d = M i Bool (MonomialRepBoundedDegree i d) Source #

evalMapM :: forall i j b. MultiplicativeMonoid b => Exponent b j => (i -> b) -> M i j (Map i j) -> b Source #

evalVectorM :: forall i j b d. Monomial i j => MultiplicativeMonoid b => Exponent b j => (i -> b) -> M i j (Vector d (i, Bool)) -> b Source #

mapVar :: [Natural] -> Natural -> Natural Source #

mapVarMonomial :: [Natural] -> Monomial' -> Monomial' Source #