HaskellForMaths-0.4.8: Combinatorics, group theory, commutative algebra, non-commutative algebra

Safe Haskell | None
Language | Haskell98

Math.Projects.KnotTheory.LaurentMPoly

# Documentation

newtype LaurentMonomial Source #

Constructors

LM (Map String Q) |

Instances

Eq LaurentMonomial Source # |
Methods (==) :: LaurentMonomial -> LaurentMonomial -> Bool # (/=) :: LaurentMonomial -> LaurentMonomial -> Bool #
Fractional LaurentMonomial Source # |
Methods (/) :: LaurentMonomial -> LaurentMonomial -> LaurentMonomial # recip :: LaurentMonomial -> LaurentMonomial # fromRational :: Rational -> LaurentMonomial #
Num LaurentMonomial Source # |
Methods (+) :: LaurentMonomial -> LaurentMonomial -> LaurentMonomial # (-) :: LaurentMonomial -> LaurentMonomial -> LaurentMonomial # (*) :: LaurentMonomial -> LaurentMonomial -> LaurentMonomial # negate :: LaurentMonomial -> LaurentMonomial # abs :: LaurentMonomial -> LaurentMonomial # signum :: LaurentMonomial -> LaurentMonomial # fromInteger :: Integer -> LaurentMonomial #
Ord LaurentMonomial Source # |

Methods

compare :: LaurentMonomial -> LaurentMonomial -> Ordering #

(<) :: LaurentMonomial -> LaurentMonomial -> Bool #

(<=) :: LaurentMonomial -> LaurentMonomial -> Bool #

(>) :: LaurentMonomial -> LaurentMonomial -> Bool #

(>=) :: LaurentMonomial -> LaurentMonomial -> Bool #

max :: LaurentMonomial -> LaurentMonomial -> LaurentMonomial #

min :: LaurentMonomial -> LaurentMonomial -> LaurentMonomial #

Show LaurentMonomial Source # |
Methods showsPrec :: Int -> LaurentMonomial -> ShowS # show :: LaurentMonomial -> String # showList :: [LaurentMonomial] -> ShowS #

degLM :: LaurentMonomial -> Q Source #

denominatorLM :: LaurentMonomial -> LaurentMonomial Source #

lcmLM :: LaurentMonomial -> LaurentMonomial -> LaurentMonomial Source #

divLM :: LaurentMonomial -> LaurentMonomial -> Maybe LaurentMonomial Source #

newtype LaurentMPoly r Source #

Constructors

LP [(LaurentMonomial, r)] |

Instances

Eq r => Eq (LaurentMPoly r) Source # |
Methods (==) :: LaurentMPoly r -> LaurentMPoly r -> Bool # (/=) :: LaurentMPoly r -> LaurentMPoly r -> Bool #
(Eq r, Fractional r) => Fractional (LaurentMPoly r) Source # |
Methods (/) :: LaurentMPoly r -> LaurentMPoly r -> LaurentMPoly r # recip :: LaurentMPoly r -> LaurentMPoly r # fromRational :: Rational -> LaurentMPoly r #
(Eq r, Num r) => Num (LaurentMPoly r) Source # |
Methods (+) :: LaurentMPoly r -> LaurentMPoly r -> LaurentMPoly r # (-) :: LaurentMPoly r -> LaurentMPoly r -> LaurentMPoly r # (*) :: LaurentMPoly r -> LaurentMPoly r -> LaurentMPoly r # negate :: LaurentMPoly r -> LaurentMPoly r # abs :: LaurentMPoly r -> LaurentMPoly r # signum :: LaurentMPoly r -> LaurentMPoly r # fromInteger :: Integer -> LaurentMPoly r #
Ord r => Ord (LaurentMPoly r) Source # |
Methods compare :: LaurentMPoly r -> LaurentMPoly r -> Ordering # (<) :: LaurentMPoly r -> LaurentMPoly r -> Bool # (<=) :: LaurentMPoly r -> LaurentMPoly r -> Bool # (>) :: LaurentMPoly r -> LaurentMPoly r -> Bool # (>=) :: LaurentMPoly r -> LaurentMPoly r -> Bool # max :: LaurentMPoly r -> LaurentMPoly r -> LaurentMPoly r # min :: LaurentMPoly r -> LaurentMPoly r -> LaurentMPoly r #
Show r => Show (LaurentMPoly r) Source # |
Methods showsPrec :: Int -> LaurentMPoly r -> ShowS # show :: LaurentMPoly r -> String # showList :: [LaurentMPoly r] -> ShowS #
Invertible (NPoly LPQ BraidGens) Source # |
Methods inv :: NPoly LPQ BraidGens -> NPoly LPQ BraidGens Source #
Invertible (NPoly LPQ IwahoriHeckeGens) Source # |
Methods inv :: NPoly LPQ IwahoriHeckeGens -> NPoly LPQ IwahoriHeckeGens Source #

cmpTerm :: Ord a => (a, t1) -> (a, t) -> Ordering Source #

mergeTerms :: (Eq t, Num t, Ord t1) => [(t1, t)] -> [(t1, t)] -> [(t1, t)] Source #

collect :: (Eq a, Eq t, Num a) => [(t, a)] -> [(t, a)] Source #

lm :: LaurentMPoly t -> LaurentMonomial Source #

lc :: LaurentMPoly t -> t Source #

lt :: LaurentMPoly r -> LaurentMPoly r Source #

quotRemLP :: (Fractional t, Eq t) => LaurentMPoly t -> LaurentMPoly t -> (LaurentMPoly t, LaurentMPoly t) Source #

reduceLP :: (Fractional t, Eq t) => LaurentMPoly t -> LaurentMPoly t -> LaurentMPoly t Source #

var :: Num r => String -> LaurentMPoly r Source #

t :: LaurentMPoly Q Source #

x :: LaurentMPoly Q Source #

y :: LaurentMPoly Q Source #

z :: LaurentMPoly Q Source #

denominatorLP :: Num r => LaurentMPoly t -> LaurentMPoly r Source #

inject :: (Num r, Eq r) => r -> LaurentMPoly r Source #

sqrtvar :: Num r => String -> LaurentMPoly r Source #

subst :: (Fractional r, Show r, Eq r) => [(LaurentMPoly r, LaurentMPoly r)] -> LaurentMPoly r -> LaurentMPoly r Source #

(^^^) :: (Show a, Fractional a, Eq a) => LaurentMPoly a -> Q -> LaurentMPoly a Source #