Safe Haskell	None
Language	Haskell2010

Algebra.Bridge.Singular.Syntax

Synopsis

class IsMonomialOrder n ord => SingularOrder n ord where
- singularOrder :: q n -> p ord -> Text
class (PrettyCoeff r, CoeffRing r) => SingularCoeff r where
- parseSingularCoeff :: Parser r
- prettySingularCoeff :: Int -> r -> ShowSCoeff
- coeffType :: proxy r -> RingCoeffSpec
type IsSingularPolynomial poly = (IsOrderedPolynomial poly, SingularCoeff (Coefficient poly), SingularOrder (Arity poly) (MOrder poly))
data SingularExpr poly where
- SingVar :: Text -> SingularExpr poly
- SingFunction :: Text -> [SingularExpr poly] -> SingularExpr poly
- SingInfix :: SingularExpr poly -> Text -> SingularExpr poly -> SingularExpr poly
- SingList :: [SingularExpr poly] -> SingularExpr poly
- SingIdeal :: [SingularExpr poly] -> SingularExpr poly
- SingPolynomial :: poly -> SingularExpr poly
- SingCoeff :: Coefficient poly -> SingularExpr poly
- SingVerbatim :: Text -> SingularExpr poly
- SingRing :: RingSpec -> SingularExpr poly
data RingSpec where
- RingSpec :: SingularOrder n ord => RingCoeffSpec -> SNat n -> proxy ord -> RingSpec
type SingularLibrary = Text
type SingularOption = Text
data RingCoeffSpec
- = RealCoeff
- | ComplexCoeff
- | IntegerCoeff
- | Char Natural
toRingSpec :: IsSingularPolynomial poly => proxy poly -> RingSpec
class PrettySingular a where
- prettySingular :: a -> Text
prettySingularPolynomial :: IsSingularPolynomial poly => poly -> Text
funE :: Text -> [SingularExpr poly] -> SingularExpr poly
coeffE :: Coefficient poly -> SingularExpr poly
polyE :: poly -> SingularExpr poly
binE :: Text -> SingularExpr poly -> SingularExpr poly -> SingularExpr poly
listE :: [SingularExpr poly] -> SingularExpr poly
idealE :: [SingularExpr poly] -> SingularExpr poly
idealE' :: Ideal poly -> SingularExpr poly
verbE :: Text -> SingularExpr poly
varE :: Text -> SingularExpr poly
data SingularCommand where
- SingExpr :: IsSingularPolynomial poly => SingularExpr poly -> SingularCommand
- SingDeclOnly :: SingularType -> Text -> SingularCommand
- SingDeclAssign :: IsSingularPolynomial poly => SingularType -> Text -> SingularExpr poly -> SingularCommand
- SingAssign :: IsSingularPolynomial poly => Text -> SingularExpr poly -> SingularCommand
- SingLibrary :: Text -> SingularCommand
- SingVerbD :: Text -> SingularCommand
- Directive :: Text -> SingularCommand
data SingularType
- = IdealT
- | IntT
- | RingT
- | PolyT
- | OtherT Text
newtype SingularProgramM a = SingularProgramM (Writer [SingularCommand] a)
type SingularProgram = SingularProgramM ()
exprC :: IsSingularPolynomial poly => SingularExpr poly -> SingularProgram
declOnlyC :: SingularType -> Text -> SingularProgram
declC :: IsSingularPolynomial poly => SingularType -> Text -> SingularExpr poly -> SingularProgramM (SingularExpr poly)
letC :: IsSingularPolynomial poly => Text -> SingularExpr poly -> SingularProgram
idealC' :: IsSingularPolynomial poly => Text -> Ideal poly -> SingularProgramM (SingularExpr poly)
idealC :: IsSingularPolynomial poly => Text -> [SingularExpr poly] -> SingularProgramM (SingularExpr poly)
ringC :: IsSingularPolynomial poly => Text -> proxy poly -> SingularProgramM (SingularExpr poly)
polyC :: IsSingularPolynomial poly => Text -> poly -> SingularProgramM (SingularExpr poly)
libC :: Text -> SingularProgram
optionC :: SingularOption -> SingularProgram
printC :: IsSingularPolynomial poly => SingularExpr poly -> SingularProgram
directC :: Text -> SingularProgram

Documentation

class IsMonomialOrder n ord => SingularOrder n ord where Source #

Methods

singularOrder :: q n -> p ord -> Text Source #

Instances

Instances details

KnownNat n => SingularOrder n Grevlex Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods singularOrder :: q n -> p Grevlex -> Text Source #
KnownNat n => SingularOrder n Lex Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods singularOrder :: q n -> p Lex -> Text Source #
(SingularOrder n o1, SingularOrder m o2, KnownNat m, KnownNat n, (n + m) ~ k) => SingularOrder k (ProductOrder n m o1 o2) Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods singularOrder :: q k -> p (ProductOrder n m o1 o2) -> Text Source #

class (PrettyCoeff r, CoeffRing r) => SingularCoeff r where Source #

Minimal complete definition

parseSingularCoeff, coeffType

Methods

parseSingularCoeff :: Parser r Source #

prettySingularCoeff :: Int -> r -> ShowSCoeff Source #

coeffType :: proxy r -> RingCoeffSpec Source #

Instances

Instances details

SingularCoeff Integer Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods parseSingularCoeff :: Parser Integer Source # prettySingularCoeff :: Int -> Integer -> ShowSCoeff Source # coeffType :: proxy Integer -> RingCoeffSpec Source #
SingularCoeff Rational Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods parseSingularCoeff :: Parser Rational Source # prettySingularCoeff :: Int -> Rational -> ShowSCoeff Source # coeffType :: proxy Rational -> RingCoeffSpec Source #
KnownNat p => SingularCoeff (F p) Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods parseSingularCoeff :: Parser (F p) Source # prettySingularCoeff :: Int -> F p -> ShowSCoeff Source # coeffType :: proxy (F p) -> RingCoeffSpec Source #

type IsSingularPolynomial poly = (IsOrderedPolynomial poly, SingularCoeff (Coefficient poly), SingularOrder (Arity poly) (MOrder poly)) Source #

Polynomial type which can be encoded to/decoded from singular polynomials.

data SingularExpr poly where Source #

Constructors

SingVar :: Text -> SingularExpr poly
SingFunction :: Text -> [SingularExpr poly] -> SingularExpr poly
SingInfix :: SingularExpr poly -> Text -> SingularExpr poly -> SingularExpr poly
SingList :: [SingularExpr poly] -> SingularExpr poly
SingIdeal :: [SingularExpr poly] -> SingularExpr poly
SingPolynomial :: poly -> SingularExpr poly
SingCoeff :: Coefficient poly -> SingularExpr poly
SingVerbatim :: Text -> SingularExpr poly
SingRing :: RingSpec -> SingularExpr poly

Instances

Instances details

Num (Coefficient poly) => Num (SingularExpr poly) Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods (+) :: SingularExpr poly -> SingularExpr poly -> SingularExpr poly # (-) :: SingularExpr poly -> SingularExpr poly -> SingularExpr poly # (*) :: SingularExpr poly -> SingularExpr poly -> SingularExpr poly # negate :: SingularExpr poly -> SingularExpr poly # abs :: SingularExpr poly -> SingularExpr poly # signum :: SingularExpr poly -> SingularExpr poly # fromInteger :: Integer -> SingularExpr poly #
Unital (Coefficient poly) => Unital (SingularExpr poly) Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods one :: SingularExpr poly # pow :: SingularExpr poly -> Natural -> SingularExpr poly # productWith :: Foldable f => (a -> SingularExpr poly) -> f a -> SingularExpr poly #
Multiplicative (SingularExpr poly) Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods (*) :: SingularExpr poly -> SingularExpr poly -> SingularExpr poly # pow1p :: SingularExpr poly -> Natural -> SingularExpr poly # productWith1 :: Foldable1 f => (a -> SingularExpr poly) -> f a -> SingularExpr poly #
Additive (SingularExpr poly) Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods (+) :: SingularExpr poly -> SingularExpr poly -> SingularExpr poly # sinnum1p :: Natural -> SingularExpr poly -> SingularExpr poly # sumWith1 :: Foldable1 f => (a -> SingularExpr poly) -> f a -> SingularExpr poly #
IsSingularPolynomial poly => PrettySingular (SingularExpr poly) Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods prettySingular :: SingularExpr poly -> Text Source #

data RingSpec where Source #

Constructors

RingSpec :: SingularOrder n ord => RingCoeffSpec -> SNat n -> proxy ord -> RingSpec

Instances

Instances details

PrettySingular RingSpec Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods prettySingular :: RingSpec -> Text Source #

type SingularLibrary = Text Source #

type SingularOption = Text Source #

data RingCoeffSpec Source #

Constructors

RealCoeff
ComplexCoeff
IntegerCoeff
Char Natural

Instances

Instances details

Eq RingCoeffSpec Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods (==) :: RingCoeffSpec -> RingCoeffSpec -> Bool # (/=) :: RingCoeffSpec -> RingCoeffSpec -> Bool #
Ord RingCoeffSpec Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods compare :: RingCoeffSpec -> RingCoeffSpec -> Ordering # (<) :: RingCoeffSpec -> RingCoeffSpec -> Bool # (<=) :: RingCoeffSpec -> RingCoeffSpec -> Bool # (>) :: RingCoeffSpec -> RingCoeffSpec -> Bool # (>=) :: RingCoeffSpec -> RingCoeffSpec -> Bool # max :: RingCoeffSpec -> RingCoeffSpec -> RingCoeffSpec # min :: RingCoeffSpec -> RingCoeffSpec -> RingCoeffSpec #
Read RingCoeffSpec Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods readsPrec :: Int -> ReadS RingCoeffSpec # readList :: ReadS [RingCoeffSpec] # readPrec :: ReadPrec RingCoeffSpec # readListPrec :: ReadPrec [RingCoeffSpec] #
Show RingCoeffSpec Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods showsPrec :: Int -> RingCoeffSpec -> ShowS # show :: RingCoeffSpec -> String # showList :: [RingCoeffSpec] -> ShowS #
PrettySingular RingCoeffSpec Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods prettySingular :: RingCoeffSpec -> Text Source #

toRingSpec :: IsSingularPolynomial poly => proxy poly -> RingSpec Source #

class PrettySingular a where Source #

Methods

prettySingular :: a -> Text Source #

Instances

Instances details

PrettySingular SingularCommand Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods prettySingular :: SingularCommand -> Text Source #
PrettySingular SingularType Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods prettySingular :: SingularType -> Text Source #
PrettySingular RingSpec Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods prettySingular :: RingSpec -> Text Source #
PrettySingular RingCoeffSpec Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods prettySingular :: RingCoeffSpec -> Text Source #
a ~ () => PrettySingular (SingularProgramM a) Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods prettySingular :: SingularProgramM a -> Text Source #
IsSingularPolynomial poly => PrettySingular (SingularExpr poly) Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods prettySingular :: SingularExpr poly -> Text Source #

prettySingularPolynomial :: IsSingularPolynomial poly => poly -> Text Source #

funE :: Text -> [SingularExpr poly] -> SingularExpr poly Source #

coeffE :: Coefficient poly -> SingularExpr poly Source #

polyE :: poly -> SingularExpr poly Source #

binE :: Text -> SingularExpr poly -> SingularExpr poly -> SingularExpr poly Source #

listE :: [SingularExpr poly] -> SingularExpr poly Source #

idealE :: [SingularExpr poly] -> SingularExpr poly Source #

idealE' :: Ideal poly -> SingularExpr poly Source #

verbE :: Text -> SingularExpr poly Source #

varE :: Text -> SingularExpr poly Source #

data SingularCommand where Source #

Constructors

SingExpr :: IsSingularPolynomial poly => SingularExpr poly -> SingularCommand
SingDeclOnly :: SingularType -> Text -> SingularCommand
SingDeclAssign :: IsSingularPolynomial poly => SingularType -> Text -> SingularExpr poly -> SingularCommand
SingAssign :: IsSingularPolynomial poly => Text -> SingularExpr poly -> SingularCommand
SingLibrary :: Text -> SingularCommand
SingVerbD :: Text -> SingularCommand
Directive :: Text -> SingularCommand

Instances

Instances details

PrettySingular SingularCommand Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods prettySingular :: SingularCommand -> Text Source #

data SingularType Source #

Constructors

IdealT
IntT
RingT
PolyT
OtherT Text

Instances

Instances details

Eq SingularType Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods (==) :: SingularType -> SingularType -> Bool # (/=) :: SingularType -> SingularType -> Bool #
Ord SingularType Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods compare :: SingularType -> SingularType -> Ordering # (<) :: SingularType -> SingularType -> Bool # (<=) :: SingularType -> SingularType -> Bool # (>) :: SingularType -> SingularType -> Bool # (>=) :: SingularType -> SingularType -> Bool # max :: SingularType -> SingularType -> SingularType # min :: SingularType -> SingularType -> SingularType #
Read SingularType Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods readsPrec :: Int -> ReadS SingularType # readList :: ReadS [SingularType] # readPrec :: ReadPrec SingularType # readListPrec :: ReadPrec [SingularType] #
Show SingularType Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods showsPrec :: Int -> SingularType -> ShowS # show :: SingularType -> String # showList :: [SingularType] -> ShowS #
PrettySingular SingularType Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods prettySingular :: SingularType -> Text Source #

newtype SingularProgramM a Source #

Constructors

SingularProgramM (Writer [SingularCommand] a)

Instances

Instances details

Monad SingularProgramM Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods (>>=) :: SingularProgramM a -> (a -> SingularProgramM b) -> SingularProgramM b # (>>) :: SingularProgramM a -> SingularProgramM b -> SingularProgramM b # return :: a -> SingularProgramM a #
Functor SingularProgramM Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods fmap :: (a -> b) -> SingularProgramM a -> SingularProgramM b # (<$) :: a -> SingularProgramM b -> SingularProgramM a #
Applicative SingularProgramM Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods pure :: a -> SingularProgramM a # (<>) :: SingularProgramM (a -> b) -> SingularProgramM a -> SingularProgramM b # liftA2 :: (a -> b -> c) -> SingularProgramM a -> SingularProgramM b -> SingularProgramM c # (>) :: SingularProgramM a -> SingularProgramM b -> SingularProgramM b # (<*) :: SingularProgramM a -> SingularProgramM b -> SingularProgramM a #
Semigroup (SingularProgramM a) Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods (<>) :: SingularProgramM a -> SingularProgramM a -> SingularProgramM a # sconcat :: NonEmpty (SingularProgramM a) -> SingularProgramM a # stimes :: Integral b => b -> SingularProgramM a -> SingularProgramM a #
a ~ () => Monoid (SingularProgramM a) Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods mempty :: SingularProgramM a # mappend :: SingularProgramM a -> SingularProgramM a -> SingularProgramM a # mconcat :: [SingularProgramM a] -> SingularProgramM a #
a ~ () => PrettySingular (SingularProgramM a) Source #
Instance details Defined in Algebra.Bridge.Singular.Syntax Methods prettySingular :: SingularProgramM a -> Text Source #

type SingularProgram = SingularProgramM () Source #

exprC :: IsSingularPolynomial poly => SingularExpr poly -> SingularProgram Source #

declOnlyC :: SingularType -> Text -> SingularProgram Source #

declC :: IsSingularPolynomial poly => SingularType -> Text -> SingularExpr poly -> SingularProgramM (SingularExpr poly) Source #

letC :: IsSingularPolynomial poly => Text -> SingularExpr poly -> SingularProgram Source #

idealC' :: IsSingularPolynomial poly => Text -> Ideal poly -> SingularProgramM (SingularExpr poly) Source #

idealC :: IsSingularPolynomial poly => Text -> [SingularExpr poly] -> SingularProgramM (SingularExpr poly) Source #

ringC :: IsSingularPolynomial poly => Text -> proxy poly -> SingularProgramM (SingularExpr poly) Source #

polyC :: IsSingularPolynomial poly => Text -> poly -> SingularProgramM (SingularExpr poly) Source #

libC :: Text -> SingularProgram Source #

optionC :: SingularOption -> SingularProgram Source #

printC :: IsSingularPolynomial poly => SingularExpr poly -> SingularProgram Source #

directC :: Text -> SingularProgram Source #