Math.RootLoci.Misc.Common

Some auxilary functions

Pairs

data Pair a

Constructors

Pair a a

Instances

Functor Pair

Defined in Math.RootLoci.Misc.Common

Methods

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

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

Eq a => Eq (Pair a)

Defined in Math.RootLoci.Misc.Common

Methods

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

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

Ord a => Ord (Pair a)

Defined in Math.RootLoci.Misc.Common

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)

Defined in Math.RootLoci.Misc.Common

Methods

showsPrec :: Int -> Pair a -> ShowS

show :: Pair a -> String

showList :: [Pair a] -> ShowS

Lists

sum' :: Num a => [a] -> a

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

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

Synonym for histogram

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

longZipWith :: (a -> c) -> (b -> c) -> (a -> b -> c) -> [a] -> [b] -> [c]

evens :: [a] -> [a]

odds :: [a] -> [a]

interleave :: [a] -> [a] -> [a]

Maps

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

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

insertMap :: Ord k => (b -> a) -> (b -> a -> a) -> k -> b -> Map k a -> Map k a

Example usage: insertMap (:[]) (:) ...

buildMap :: Ord k => (b -> a) -> (b -> a -> a) -> [(k, b)] -> Map k a

Example usage: buildMap (:[]) (:) ...

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)

exponentVector :: Partition -> [Int]

TODO: move this into combinat

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

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

Utility

paren :: String -> String

Put into parentheses

expFormString :: Partition -> String

Exponential form of a partition

extendStringL :: Int -> String -> String

extendStringR :: Int -> String -> String

Mathematica-formatted output

class Mathematica a where

Methods

mathematica :: a -> String

Instances

Mathematica Int

Defined in Math.RootLoci.Misc.Common

Methods

mathematica :: Int -> String

Mathematica Integer

Defined in Math.RootLoci.Misc.Common

Methods

mathematica :: Integer -> String

Mathematica String

Defined in Math.RootLoci.Misc.Common

Methods

mathematica :: String -> String

Mathematica Partition

Defined in Math.RootLoci.Misc.Common

Methods

mathematica :: Partition -> String

Mathematica a => Mathematica (Indexed a)

Defined in Math.RootLoci.Misc.Common

Methods

mathematica :: Indexed a -> String

data Indexed a

Constructors

Indexed String a

Instances

Mathematica a => Mathematica (Indexed a)

Defined in Math.RootLoci.Misc.Common

Methods

mathematica :: Indexed a -> String