Math.Algebra.Polynomial.Monomial.Generic

Multivariate monomials where the set of variables is given by the inhabitants of a type

Monomials

newtype Monom v

A monomial over the set of variables represented by the inhabitants of the type v. The invariant we keep is that the exponents present in the Map are always positive.

Constructors

Monom (Map v Int)

Instances

Eq v => Eq (Monom v)

Defined in Math.Algebra.Polynomial.Monomial.Generic

Methods

(==) :: Monom v -> Monom v -> Bool

(/=) :: Monom v -> Monom v -> Bool

Ord v => Ord (Monom v)

Defined in Math.Algebra.Polynomial.Monomial.Generic

Methods

compare :: Monom v -> Monom v -> Ordering

(<) :: Monom v -> Monom v -> Bool

(<=) :: Monom v -> Monom v -> Bool

(>) :: Monom v -> Monom v -> Bool

(>=) :: Monom v -> Monom v -> Bool

max :: Monom v -> Monom v -> Monom v

min :: Monom v -> Monom v -> Monom v

Show v => Show (Monom v)

Defined in Math.Algebra.Polynomial.Monomial.Generic

Methods

showsPrec :: Int -> Monom v -> ShowS

show :: Monom v -> String

showList :: [Monom v] -> ShowS

Ord v => Semigroup (Monom v)

Defined in Math.Algebra.Polynomial.Monomial.Generic

Methods

(<>) :: Monom v -> Monom v -> Monom v

sconcat :: NonEmpty (Monom v) -> Monom v

stimes :: Integral b => b -> Monom v -> Monom v

Ord v => Monoid (Monom v)

Defined in Math.Algebra.Polynomial.Monomial.Generic

Methods

mempty :: Monom v

mappend :: Monom v -> Monom v -> Monom v

mconcat :: [Monom v] -> Monom v

Pretty v => Pretty (Monom v)

Defined in Math.Algebra.Polynomial.Monomial.Generic

Methods

pretty :: Monom v -> String

prettyInParens :: Monom v -> String

(Ord v, Pretty v) => Monomial (Monom v)

Defined in Math.Algebra.Polynomial.Monomial.Generic

Associated Types

type VarM (Monom v)

Methods

normalizeM :: Monom v -> Monom v

isNormalM :: Monom v -> Bool

fromListM :: [(VarM (Monom v), Int)] -> Monom v

toListM :: Monom v -> [(VarM (Monom v), Int)]

emptyM :: Monom v

isEmptyM :: Monom v -> Bool

variableM :: VarM (Monom v) -> Monom v

singletonM :: VarM (Monom v) -> Int -> Monom v

mulM :: Monom v -> Monom v -> Monom v

productM :: [Monom v] -> Monom v

powM :: Monom v -> Int -> Monom v

divM :: Monom v -> Monom v -> Maybe (Monom v)

diffM :: Num c => VarM (Monom v) -> Int -> Monom v -> Maybe (Monom v, c)

maxDegM :: Monom v -> Int

totalDegM :: Monom v -> Int

evalM :: Num c => (VarM (Monom v) -> c) -> Monom v -> c

varSubsM :: (VarM (Monom v) -> VarM (Monom v)) -> Monom v -> Monom v

termSubsM :: Num c => (VarM (Monom v) -> Maybe c) -> (Monom v, c) -> (Monom v, c)

type VarM (Monom v)

Defined in Math.Algebra.Polynomial.Monomial.Generic

type VarM (Monom v) = v

unMonom :: Monom v -> Map v Int

normalizeMonom :: Ord v => Monom v -> Monom v

isNormalMonom :: Monom v -> Bool

monomToList :: Ord v => Monom v -> [(v, Int)]

monomFromList :: Ord v => [(v, Int)] -> Monom v

mapMonom :: (Ord v, Ord w) => (v -> w) -> Monom v -> Monom w

Note: we can collapse variables together!

emptyMonom :: Monom v

isEmptyMonom :: Monom v -> Bool

mulMonom :: Ord v => Monom v -> Monom v -> Monom v

divMonom :: Ord v => Monom v -> Monom v -> Maybe (Monom v)

prodMonoms :: (Foldable f, Ord v) => f (Monom v) -> Monom v

powMonom :: Ord v => Monom v -> Int -> Monom v

varMonom :: Ord v => v -> Monom v

singletonMonom :: Ord v => v -> Int -> Monom v

maxDegMonom :: Monom v -> Int

totalDegMonom :: Monom v -> Int

evalMonom :: (Num c, Ord v) => (v -> c) -> Monom v -> c

termSubsMonom :: (Num c, Ord v) => (v -> Maybe c) -> (Monom v, c) -> (Monom v, c)

differentiation

diffMonom :: (Ord v, Num c) => v -> Int -> Monom v -> Maybe (Monom v, c)