Math.RootLoci.Misc.Common

Some auxilary functions

Pairs

data Pair a

Constructors

Pair a a

Instances

Functor Pair

Methods

fmap :: (a -> b) -> Pair a -> Pair b

(<$) :: a -> Pair b -> Pair a

Eq a => Eq (Pair a)

Methods

(==) :: Pair a -> Pair a -> Bool

(/=) :: Pair a -> Pair a -> Bool

Ord a => Ord (Pair a)

Methods

compare :: Pair a -> Pair a -> Ordering

(<) :: Pair a -> Pair a -> Bool

(<=) :: Pair a -> Pair a -> Bool

(>) :: Pair a -> Pair a -> Bool

(>=) :: Pair a -> Pair a -> Bool

max :: Pair a -> Pair a -> Pair a

min :: Pair a -> Pair a -> Pair a

Show a => Show (Pair a)

Methods

showsPrec :: Int -> Pair a -> ShowS

show :: Pair a -> String

showList :: [Pair a] -> ShowS

Lists

unique :: Ord a => [a] -> [a]

count :: Ord b => [b] -> Map b Integer

Synonym for histogram

histogram :: Ord b => [b] -> Map b Integer

Maps

deleteLookup :: Ord a => a -> Map a b -> (Maybe b, Map a b)

unsafeDeleteLookup :: Ord a => a -> Map a b -> (b, Map a b)

Partitions

aut :: Partition -> Integer

aut(mu) is the number of symmetries of the partition mu:

aut(mu) = prod_r (e_r)!

where mu = (1^e1 2^e2 .. k^ek)

Set partitions

defaultSetPartition :: Partition -> SetPartition

Makes set partition from a partition (simply filling up from left to right) with the shape giving back the input partition

linearIndices :: Partition -> [[Int]]

Produce linear indices from a partition nu (to encode the diagonal map Delta_nu).

Signs

class IsSigned a where

Minimal complete definition

signOf

Methods

signOf :: a -> Maybe Sign

Instances

IsSigned Int

Methods

signOf :: Int -> Maybe Sign

IsSigned Integer

Methods

signOf :: Integer -> Maybe Sign

IsSigned Rational

Methods

signOf :: Rational -> Maybe Sign

signOfNum :: (Ord a, Num a) => a -> Maybe Sign

Numbers

fromRat :: Rational -> Integer

safeDiv :: Integer -> Integer -> Integer

Combinatorics

chooseN1 :: [a] -> [[a]]

Chooses (n-1) elements out of n

symPolyNum :: Num a => Int -> [a] -> a