Math.Projects.KnotTheory.LaurentMPoly

Documentation

newtype LaurentMonomial

Constructors

LM (Map String Q)

Instances

Eq LaurentMonomial

Defined in Math.Projects.KnotTheory.LaurentMPoly

Methods

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

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

Fractional LaurentMonomial

Defined in Math.Projects.KnotTheory.LaurentMPoly

Methods

(/) :: LaurentMonomial -> LaurentMonomial -> LaurentMonomial

recip :: LaurentMonomial -> LaurentMonomial

fromRational :: Rational -> LaurentMonomial

Num LaurentMonomial

Defined in Math.Projects.KnotTheory.LaurentMPoly

Methods

(+) :: LaurentMonomial -> LaurentMonomial -> LaurentMonomial

(-) :: LaurentMonomial -> LaurentMonomial -> LaurentMonomial

(*) :: LaurentMonomial -> LaurentMonomial -> LaurentMonomial

negate :: LaurentMonomial -> LaurentMonomial

abs :: LaurentMonomial -> LaurentMonomial

signum :: LaurentMonomial -> LaurentMonomial

fromInteger :: Integer -> LaurentMonomial

Ord LaurentMonomial

Defined in Math.Projects.KnotTheory.LaurentMPoly

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

Defined in Math.Projects.KnotTheory.LaurentMPoly

Methods

showsPrec :: Int -> LaurentMonomial -> ShowS

show :: LaurentMonomial -> String

showList :: [LaurentMonomial] -> ShowS

degLM :: LaurentMonomial -> Q

denominatorLM :: LaurentMonomial -> LaurentMonomial

lcmLM :: LaurentMonomial -> LaurentMonomial -> LaurentMonomial

divLM :: LaurentMonomial -> LaurentMonomial -> Maybe LaurentMonomial

newtype LaurentMPoly r

Constructors

LP [(LaurentMonomial, r)]

Instances

Invertible LPQ

Defined in Math.Projects.KnotTheory.Braid

Methods

inv :: LPQ -> LPQ

Eq r => Eq (LaurentMPoly r)

Defined in Math.Projects.KnotTheory.LaurentMPoly

Methods

(==) :: LaurentMPoly r -> LaurentMPoly r -> Bool

(/=) :: LaurentMPoly r -> LaurentMPoly r -> Bool

(Eq r, Fractional r) => Fractional (LaurentMPoly r)

Defined in Math.Projects.KnotTheory.LaurentMPoly

Methods

(/) :: LaurentMPoly r -> LaurentMPoly r -> LaurentMPoly r

recip :: LaurentMPoly r -> LaurentMPoly r

fromRational :: Rational -> LaurentMPoly r

(Eq r, Num r) => Num (LaurentMPoly r)

Defined in Math.Projects.KnotTheory.LaurentMPoly

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)

Defined in Math.Projects.KnotTheory.LaurentMPoly

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)

Defined in Math.Projects.KnotTheory.LaurentMPoly

Methods

showsPrec :: Int -> LaurentMPoly r -> ShowS

show :: LaurentMPoly r -> String

showList :: [LaurentMPoly r] -> ShowS

Invertible (NPoly LPQ BraidGens)

Defined in Math.Projects.KnotTheory.Braid

Methods

inv :: NPoly LPQ BraidGens -> NPoly LPQ BraidGens

Invertible (NPoly LPQ IwahoriHeckeGens)

Defined in Math.Projects.KnotTheory.IwahoriHecke

Methods

inv :: NPoly LPQ IwahoriHeckeGens -> NPoly LPQ IwahoriHeckeGens

cmpTerm :: Ord a => (a, b1) -> (a, b2) -> Ordering

mergeTerms :: (Ord a, Eq b, Num b) => [(a, b)] -> [(a, b)] -> [(a, b)]

collect :: (Num a1, Eq a2, Eq a1) => [(a2, a1)] -> [(a2, a1)]

lm :: LaurentMPoly r -> LaurentMonomial

lc :: LaurentMPoly r -> r

lt :: LaurentMPoly r -> LaurentMPoly r

quotRemLP :: (Eq r, Fractional r) => LaurentMPoly r -> LaurentMPoly r -> (LaurentMPoly r, LaurentMPoly r)

reduceLP :: (Eq r, Fractional r) => LaurentMPoly r -> LaurentMPoly r -> LaurentMPoly r

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

t :: LaurentMPoly Q

x :: LaurentMPoly Q

y :: LaurentMPoly Q

z :: LaurentMPoly Q

denominatorLP :: Num r1 => LaurentMPoly r2 -> LaurentMPoly r1

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

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

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

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