Safe Haskell	None
Language	Haskell2010

Math.Singular.Factory.Internal.Factory

Contents

Version and configuration info
Basic operations and instances
pretty printing
Galois fields
Base domains
Monomials
coefficients
Terms
Marshalling from CF
Orphan instances

Description

Medium-level bindings to singular-factory

Synopsis

maxCharacteristic :: Int
factoryVersion :: String
packageVersion :: String
haveFLINT :: Bool
haveNTL :: Bool
haveGMP :: Bool
safeEqCF :: CF -> CF -> Bool
nativeEqCF :: CF -> CF -> Bool
isZeroCF :: CF -> Bool
isOneCF :: CF -> Bool
varCF :: Var -> CF
varPowCF :: Var -> Int -> CF
powCF :: CF -> Int -> CF
modCF :: CF -> CF -> CF
divCF :: CF -> CF -> CF
substituteCF :: Var -> CF -> CF -> CF
gcdPolyCF :: CF -> CF -> CF
reduceCF :: CF -> CF -> CF
factorizeCF :: CF -> [(CF, Int)]
showCF :: CF -> String
showCF_with :: (Int -> String) -> CF -> String
showCF_dense :: CF -> String
printCF :: CF -> IO ()
showIO :: CF -> IO String
showIO_with :: (Int -> String) -> CF -> IO String
showIO_dense :: CF -> IO String
data GFValue
- = GFZero
- | GFSubField {
  - _gfGenExpo :: !Int
  - _gfModP :: !Int
  }
- | GFGenPow {
  - _gfGenExpo :: !Int
  }
showGFValue1 :: String -> GFValue -> String
showGFValue2 :: String -> GFValue -> String
data BaseValue
- = ZZ !Integer
- | QQ !Rational
- | FF !Int
- | GF !GFValue
baseValueIsOne :: BaseValue -> Bool
prettyBaseValue :: BaseValue -> String
type Level = Int
type Expo = Int
newtype Monom = Monom [(Level, Expo)]
monomIsNull :: Monom -> Bool
prettyMonom :: Monom -> String
prettyMonomWith :: (Int -> String) -> Monom -> String
type Coeff = BaseValue
coeffIsOne :: Coeff -> Bool
prettyCoeff :: BaseValue -> String
data Term = Term !Coeff !Monom
prettyTerm :: Term -> String
prettyTermWith :: (Int -> String) -> Term -> String
getZZ :: CF -> IO (Maybe Integer)
getQQ :: CF -> IO (Maybe Rational)
getFF :: CF -> IO (Maybe Int)
getGF :: CF -> IO (Maybe GFValue)
getBaseValue :: CF -> IO (Maybe BaseValue)
getBaseValueNotGF :: CF -> IO (Maybe BaseValue)
isInBaseDomainCF :: CF -> Bool
isInCoeffDomainCF :: CF -> Bool
isInPolyDomainCF :: CF -> Bool
isInQuotDomainCF :: CF -> Bool
isInExtensionCF :: CF -> Bool
valueZZ :: CF -> Integer
valueQQ :: CF -> Rational
valueGF :: CF -> GFValue
valueFF :: CF -> Int
makeMonom :: [(Level, Expo)] -> Monom
makeTerm :: [(Level, Expo)] -> BaseValue -> Term
genericMarshalFromCF :: ([(Level, Expo)] -> BaseValue -> a) -> CF -> IO [a]
genericMarshalFromCF_dlist :: ([(Level, Expo)] -> BaseValue -> a) -> CF -> IO (DList a)
marshalUnivariateFromCF :: CF -> IO [(CF, Int)]

Documentation

maxCharacteristic :: Int Source #

The maximum prime characteristic Factory can handle (note: for prime power fields the limit is much smaller)

Version and configuration info

factoryVersion :: String Source #

packageVersion :: String Source #

haveFLINT :: Bool Source #

haveNTL :: Bool Source #

haveGMP :: Bool Source #

Basic operations and instances

safeEqCF :: CF -> CF -> Bool Source #

Because the native equality comparison seems to be unreliable, we provide an alternative implementation which subtracts the two polynomials and then tests for the result being zero...

nativeEqCF :: CF -> CF -> Bool Source #

Note: this does not seem to be reliable in practice... Better subtract them and then use isZeroCF...

isZeroCF :: CF -> Bool Source #

isOneCF :: CF -> Bool Source #

varCF :: Var -> CF Source #

varPowCF :: Var -> Int -> CF Source #

powCF :: CF -> Int -> CF Source #

modCF :: CF -> CF -> CF Source #

divCF :: CF -> CF -> CF Source #

substituteCF :: Var -> CF -> CF -> CF Source #

gcdPolyCF :: CF -> CF -> CF Source #

reduceCF :: CF -> CF -> CF Source #

factorizeCF :: CF -> [(CF, Int)] Source #

pretty printing

showCF :: CF -> String Source #

showCF_with :: (Int -> String) -> CF -> String Source #

showCF_dense :: CF -> String Source #

printCF :: CF -> IO () Source #

showIO :: CF -> IO String Source #

showIO_with :: (Int -> String) -> CF -> IO String Source #

showIO_dense :: CF -> IO String Source #

Galois fields

data GFValue Source #

Values in a Galois field.

They can either 0, or a power of the canonical generator (of the multiplicative group, which is cyclic).

Furthermore, they can be possibly also element of the prime subfield.

Constructors

GFZero
GFSubField
Fields _gfGenExpo :: !Int _gfModP :: !Int
GFGenPow
Fields _gfGenExpo :: !Int

Instances

Eq GFValue Source #
Instance details Defined in Math.Singular.Factory.Internal.Factory Methods (==) :: GFValue -> GFValue -> Bool # (/=) :: GFValue -> GFValue -> Bool #
Ord GFValue Source #
Instance details Defined in Math.Singular.Factory.Internal.Factory Methods compare :: GFValue -> GFValue -> Ordering # (<) :: GFValue -> GFValue -> Bool # (<=) :: GFValue -> GFValue -> Bool # (>) :: GFValue -> GFValue -> Bool # (>=) :: GFValue -> GFValue -> Bool # max :: GFValue -> GFValue -> GFValue # min :: GFValue -> GFValue -> GFValue #
Show GFValue Source #
Instance details Defined in Math.Singular.Factory.Internal.Factory Methods showsPrec :: Int -> GFValue -> ShowS # show :: GFValue -> String # showList :: [GFValue] -> ShowS #

showGFValue1 :: String -> GFValue -> String Source #

Elements of the prime subfield are shown as numbers, the rest as powers of the generator

showGFValue2 :: String -> GFValue -> String Source #

Elements of the prime subfield are also shown as powers of the generator

Base domains

data BaseValue Source #

Constructors

ZZ !Integer
QQ !Rational
FF !Int
GF !GFValue

Instances

Eq BaseValue Source #
Instance details Defined in Math.Singular.Factory.Internal.Factory Methods (==) :: BaseValue -> BaseValue -> Bool # (/=) :: BaseValue -> BaseValue -> Bool #
Ord BaseValue Source #
Instance details Defined in Math.Singular.Factory.Internal.Factory Methods compare :: BaseValue -> BaseValue -> Ordering # (<) :: BaseValue -> BaseValue -> Bool # (<=) :: BaseValue -> BaseValue -> Bool # (>) :: BaseValue -> BaseValue -> Bool # (>=) :: BaseValue -> BaseValue -> Bool # max :: BaseValue -> BaseValue -> BaseValue # min :: BaseValue -> BaseValue -> BaseValue #
Show BaseValue Source #
Instance details Defined in Math.Singular.Factory.Internal.Factory Methods showsPrec :: Int -> BaseValue -> ShowS # show :: BaseValue -> String # showList :: [BaseValue] -> ShowS #

baseValueIsOne :: BaseValue -> Bool Source #

prettyBaseValue :: BaseValue -> String Source #

Monomials

type Level = Int Source #

type Expo = Int Source #

newtype Monom Source #

Constructors

Monom [(Level, Expo)]

Instances

Eq Monom Source #
Instance details Defined in Math.Singular.Factory.Internal.Factory Methods (==) :: Monom -> Monom -> Bool # (/=) :: Monom -> Monom -> Bool #
Ord Monom Source #
Instance details Defined in Math.Singular.Factory.Internal.Factory Methods compare :: Monom -> Monom -> Ordering # (<) :: Monom -> Monom -> Bool # (<=) :: Monom -> Monom -> Bool # (>) :: Monom -> Monom -> Bool # (>=) :: Monom -> Monom -> Bool # max :: Monom -> Monom -> Monom # min :: Monom -> Monom -> Monom #
Show Monom Source #
Instance details Defined in Math.Singular.Factory.Internal.Factory Methods showsPrec :: Int -> Monom -> ShowS # show :: Monom -> String # showList :: [Monom] -> ShowS #

monomIsNull :: Monom -> Bool Source #

prettyMonom :: Monom -> String Source #

prettyMonomWith :: (Int -> String) -> Monom -> String Source #

coefficients

type Coeff = BaseValue Source #

coeffIsOne :: Coeff -> Bool Source #

prettyCoeff :: BaseValue -> String Source #

Terms

data Term Source #

Constructors

Term !Coeff !Monom

Instances

Eq Term Source #
Instance details Defined in Math.Singular.Factory.Internal.Factory Methods (==) :: Term -> Term -> Bool # (/=) :: Term -> Term -> Bool #
Ord Term Source #
Instance details Defined in Math.Singular.Factory.Internal.Factory Methods compare :: Term -> Term -> Ordering # (<) :: Term -> Term -> Bool # (<=) :: Term -> Term -> Bool # (>) :: Term -> Term -> Bool # (>=) :: Term -> Term -> Bool # max :: Term -> Term -> Term # min :: Term -> Term -> Term #
Show Term Source #
Instance details Defined in Math.Singular.Factory.Internal.Factory Methods showsPrec :: Int -> Term -> ShowS # show :: Term -> String # showList :: [Term] -> ShowS #

prettyTerm :: Term -> String Source #

prettyTermWith :: (Int -> String) -> Term -> String Source #

Marshalling from CF

getZZ :: CF -> IO (Maybe Integer) Source #

getQQ :: CF -> IO (Maybe Rational) Source #

getFF :: CF -> IO (Maybe Int) Source #

getGF :: CF -> IO (Maybe GFValue) Source #

getBaseValue :: CF -> IO (Maybe BaseValue) Source #

getBaseValueNotGF :: CF -> IO (Maybe BaseValue) Source #

isInBaseDomainCF :: CF -> Bool Source #

isInCoeffDomainCF :: CF -> Bool Source #

isInPolyDomainCF :: CF -> Bool Source #

isInQuotDomainCF :: CF -> Bool Source #

isInExtensionCF :: CF -> Bool Source #

valueZZ :: CF -> Integer Source #

valueQQ :: CF -> Rational Source #

valueGF :: CF -> GFValue Source #

valueFF :: CF -> Int Source #

makeMonom :: [(Level, Expo)] -> Monom Source #

makeTerm :: [(Level, Expo)] -> BaseValue -> Term Source #

genericMarshalFromCF :: ([(Level, Expo)] -> BaseValue -> a) -> CF -> IO [a] Source #

genericMarshalFromCF_dlist :: ([(Level, Expo)] -> BaseValue -> a) -> CF -> IO (DList a) Source #

marshalUnivariateFromCF :: CF -> IO [(CF, Int)] Source #

Orphan instances

Num CF Source #
Instance details Methods (+) :: CF -> CF -> CF # (-) :: CF -> CF -> CF # (*) :: CF -> CF -> CF # negate :: CF -> CF # abs :: CF -> CF # signum :: CF -> CF # fromInteger :: Integer -> CF #