HaskellForMaths-0.4.9: Combinatorics, group theory, commutative algebra, non-commutative algebra
Safe HaskellNone
LanguageHaskell98

Math.Projects.KnotTheory.LaurentMPoly

Documentation

newtype LaurentMonomial Source #

Constructors

LM (Map String Q) 

Instances

Instances details
Eq LaurentMonomial Source # 
Instance details

Defined in Math.Projects.KnotTheory.LaurentMPoly

Fractional LaurentMonomial Source # 
Instance details

Defined in Math.Projects.KnotTheory.LaurentMPoly

Num LaurentMonomial Source # 
Instance details

Defined in Math.Projects.KnotTheory.LaurentMPoly

Ord LaurentMonomial Source # 
Instance details

Defined in Math.Projects.KnotTheory.LaurentMPoly

Show LaurentMonomial Source # 
Instance details

Defined in Math.Projects.KnotTheory.LaurentMPoly

Methods

showsPrec :: Int -> LaurentMonomial -> ShowS

show :: LaurentMonomial -> String

showList :: [LaurentMonomial] -> ShowS

newtype LaurentMPoly r Source #

Constructors

LP [(LaurentMonomial, r)] 

Instances

Instances details
Invertible LPQ Source # 
Instance details

Defined in Math.Projects.KnotTheory.Braid

Methods

inv :: LPQ -> LPQ Source #

Eq r => Eq (LaurentMPoly r) Source # 
Instance details

Defined in Math.Projects.KnotTheory.LaurentMPoly

Methods

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

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

(Eq r, Fractional r) => Fractional (LaurentMPoly r) Source # 
Instance details

Defined in Math.Projects.KnotTheory.LaurentMPoly

(Eq r, Num r) => Num (LaurentMPoly r) Source # 
Instance details

Defined in Math.Projects.KnotTheory.LaurentMPoly

Ord r => Ord (LaurentMPoly r) Source # 
Instance details

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) Source # 
Instance details

Defined in Math.Projects.KnotTheory.LaurentMPoly

Methods

showsPrec :: Int -> LaurentMPoly r -> ShowS

show :: LaurentMPoly r -> String

showList :: [LaurentMPoly r] -> ShowS

Invertible (NPoly LPQ BraidGens) Source # 
Instance details

Defined in Math.Projects.KnotTheory.Braid

Invertible (NPoly LPQ IwahoriHeckeGens) Source # 
Instance details

Defined in Math.Projects.KnotTheory.IwahoriHecke

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

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

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

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

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

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

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

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

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

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