Safe Haskell	Safe-Inferred
Language	Haskell2010

ZkFold.Base.Algebra.Polynomials.Multivariate.Monomial

Synopsis

type Variable i = (Eq i, Ord i)
type Monomial i j = (Variable i, Ord j, Semiring j)
newtype Mono i j = M (Map i j)
monomial :: Monomial i j => Map i j -> Mono i j
evalMonomial :: forall i j b. MultiplicativeMonoid b => Exponent b j => (i -> b) -> Mono i j -> b
mapVar :: Variable i => Map i i -> i -> i
mapVarMonomial :: Variable i => Map i i -> Mono i j -> Mono i j
oneM :: Mono i j -> Bool
dividable :: forall i j. Monomial i j => Mono i j -> Mono i j -> Bool
lcmM :: Monomial i j => Mono i j -> Mono i j -> Mono i j
gcdM :: Monomial i j => Mono i j -> Mono i j -> Mono i j

Documentation

type Variable i = (Eq i, Ord i) Source #

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

newtype Mono i j Source #

Monomial type

Constructors

M (Map i j)

Instances

Instances details

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

monomial :: Monomial i j => Map i j -> Mono i j Source #

Monomial constructor

evalMonomial :: forall i j b. MultiplicativeMonoid b => Exponent b j => (i -> b) -> Mono i j -> b Source #

mapVar :: Variable i => Map i i -> i -> i Source #

Maps a variable index using the provided Map

mapVarMonomial :: Variable i => Map i i -> Mono i j -> Mono i j Source #

oneM :: Mono i j -> Bool Source #

dividable :: forall i j. Monomial i j => Mono i j -> Mono i j -> Bool Source #

lcmM :: Monomial i j => Mono i j -> Mono i j -> Mono i j Source #

gcdM :: Monomial i j => Mono i j -> Mono i j -> Mono i j Source #