Math.Algebra.NonCommutative.NCPoly

Description

Synopsis

• newtype Monomial v = M [v]
• divM :: Eq v => Monomial v -> Monomial v -> Maybe (Monomial v, Monomial v)
• newtype NPoly r v = NP [(Monomial v, r)]
• cmpTerm :: Ord a => (a, t) -> (a, t1) -> Ordering
• mergeTerms :: (Eq a1, Num a1, Ord a) => [(a, a1)] -> [(a, a1)] -> [(a, a1)]
• collect :: (Eq a1, Eq a, Num a1) => [(a, a1)] -> [(a, a1)]
• data Var
  • = X
  • | Y
  • | Z
• var :: Num k => v -> NPoly k v
• x :: NPoly Q Var
• y :: NPoly Q Var
• z :: NPoly Q Var
• lm :: NPoly t t1 -> Monomial t1
• lc :: NPoly t t1 -> t
• lt :: NPoly r v -> NPoly r v
• quotRemNP :: (Eq r, Fractional r, Ord v, Show v) => NPoly r v -> [NPoly r v] -> ([(NPoly r v, NPoly r v)], NPoly r v)
• remNP :: (Eq r, Fractional r, Ord v, Show v) => NPoly r v -> [NPoly r v] -> NPoly r v
• (%%) :: (Eq r, Fractional r, Ord v, Show v) => NPoly r v -> [NPoly r v] -> NPoly r v
• remNP2 :: (Eq r, Num r, Ord v, Show v) => NPoly r v -> [NPoly r v] -> NPoly r v
• toMonic :: (Eq r, Fractional r, Ord v, Show v) => NPoly r v -> NPoly r v
• inject :: (Eq v, Eq r, Num r, Show v) => r -> NPoly r v
• subst :: (Eq r1, Eq v, Eq r, Num r1, Num r, Ord v1, Show v1, Show r, Show v) => [(NPoly r v, NPoly r1 v1)] -> NPoly r1 v -> NPoly r1 v1
• class Invertible a where
  • inv :: a -> a
• (^-) :: (Integral b, Num a, Invertible a) => a -> b -> a

Documentation