Math.Combinatorics.Species.Types

Some common types used by the species library, along with some utility functions.

Miscellaneous

type CycleType = [(Integer, Integer)]

A representation of the cycle type of a permutation. If c :: CycleType and (k,n) `elem` c, then the permutation has n cycles of size k.

Series types

newtype EGF

Exponential generating functions, for counting labeled species.

Constructors

EGF

Fields

• unEGF :: T Rational

Instances

Show EGF

Methods

showsPrec :: Int -> EGF -> ShowS

show :: EGF -> String

showList :: [EGF] -> ShowS

C EGF

Methods

differentiate :: EGF -> EGF

C EGF

Methods

(*) :: EGF -> EGF -> EGF

one :: EGF

fromInteger :: Integer -> EGF

(^) :: EGF -> Integer -> EGF

C EGF

Methods

zero :: EGF

(+) :: EGF -> EGF -> EGF

(-) :: EGF -> EGF -> EGF

negate :: EGF -> EGF

egfFromCoeffs :: [Rational] -> EGF

liftEGF :: (T Rational -> T Rational) -> EGF -> EGF

liftEGF2 :: (T Rational -> T Rational -> T Rational) -> EGF -> EGF -> EGF

newtype GF

Ordinary generating functions, for counting unlabeled species.

Constructors

GF (T Integer)

Instances

Show GF

Methods

showsPrec :: Int -> GF -> ShowS

show :: GF -> String

showList :: [GF] -> ShowS

C GF

Methods

(*) :: GF -> GF -> GF

one :: GF

fromInteger :: Integer -> GF

(^) :: GF -> Integer -> GF

C GF

Methods

zero :: GF

(+) :: GF -> GF -> GF

(-) :: GF -> GF -> GF

negate :: GF -> GF

gfFromCoeffs :: [Integer] -> GF

liftGF :: (T Integer -> T Integer) -> GF -> GF

liftGF2 :: (T Integer -> T Integer -> T Integer) -> GF -> GF -> GF

newtype CycleIndex

Cycle index series.

Constructors

CI (T Rational)

Instances

Show CycleIndex

Methods

showsPrec :: Int -> CycleIndex -> ShowS

show :: CycleIndex -> String

showList :: [CycleIndex] -> ShowS

C CycleIndex

Methods

differentiate :: CycleIndex -> CycleIndex

C CycleIndex

Methods

(*) :: CycleIndex -> CycleIndex -> CycleIndex

one :: CycleIndex

fromInteger :: Integer -> CycleIndex

(^) :: CycleIndex -> Integer -> CycleIndex

C CycleIndex

Methods

zero :: CycleIndex

(+) :: CycleIndex -> CycleIndex -> CycleIndex

(-) :: CycleIndex -> CycleIndex -> CycleIndex

negate :: CycleIndex -> CycleIndex

ciFromMonomials :: [T Rational] -> CycleIndex

liftCI :: (T Rational -> T Rational) -> CycleIndex -> CycleIndex

liftCI2 :: (T Rational -> T Rational -> T Rational) -> CycleIndex -> CycleIndex -> CycleIndex

Series utility functions

filterCoeffs :: C a => (Integer -> Bool) -> [a] -> [a]

Filter the coefficients of a series according to a predicate.

selectIndex :: (C a, Eq a) => Integer -> [a] -> [a]

Set every coefficient of a series to 0 except the selected index. Truncate any trailing zeroes.