Safe Haskell	Safe-Inferred
Language	Haskell2010

ZkFold.Base.Algebra.Polynomials.Multivariate.Polynomial

Synopsis

type Polynomial c i j = (Eq c, Field c, Monomial i j)
newtype Poly c i j = P [(c, Mono i j)]
polynomial :: Polynomial c i j => [(c, Mono i j)] -> Poly c i j
evalPolynomial :: forall c i j b. AdditiveMonoid b => Scale c b => ((i -> b) -> Mono i j -> b) -> (i -> b) -> Poly c i j -> b
variables :: forall c v. Ord v => Poly c v Natural -> Set v
mapVars :: Variable i2 => (i1 -> i2) -> Poly c i1 j -> Poly c i2 j
mapVarPolynomial :: Variable i => Map i i -> Poly c i j -> Poly c i j
mapCoeffs :: forall c c' i j. (c -> c') -> Poly c i j -> Poly c' i j
var :: Polynomial c i j => i -> Poly c i j
constant :: Polynomial c i j => c -> Poly c i j
lt :: Polynomial c i j => Poly c i j -> (c, Mono i j)
zeroP :: Poly c i j -> Bool
scaleM :: Polynomial c i j => (c, Mono i j) -> Poly c i j -> Poly c i j

Documentation

type Polynomial c i j = (Eq c, Field c, Monomial i j) Source #

A class for polynomials. c is the coefficient type, i is the variable type, j is the power type.

newtype Poly c i j Source #

Polynomial type

Constructors

P [(c, Mono i j)]

Instances

Instances details

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

polynomial :: Polynomial c i j => [(c, Mono i j)] -> Poly c i j Source #

Polynomial constructor

evalPolynomial :: forall c i j b. AdditiveMonoid b => Scale c b => ((i -> b) -> Mono i j -> b) -> (i -> b) -> Poly c i j -> b Source #

variables :: forall c v. Ord v => Poly c v Natural -> Set v Source #

mapVars :: Variable i2 => (i1 -> i2) -> Poly c i1 j -> Poly c i2 j Source #

mapVarPolynomial :: Variable i => Map i i -> Poly c i j -> Poly c i j Source #

mapCoeffs :: forall c c' i j. (c -> c') -> Poly c i j -> Poly c' i j Source #

var :: Polynomial c i j => i -> Poly c i j Source #

var i is a polynomial \(p(x) = x_i\)

constant :: Polynomial c i j => c -> Poly c i j Source #

constant i is a polynomial \(p(x) = const\)

lt :: Polynomial c i j => Poly c i j -> (c, Mono i j) Source #

zeroP :: Poly c i j -> Bool Source #

scaleM :: Polynomial c i j => (c, Mono i j) -> Poly c i j -> Poly c i j Source #