Safe Haskell	None
Language	Haskell2010

Math.RootLoci.Misc.Common

Contents

Pairs
Lists
Maps
Partitions
Set partitions
Signs
Numbers
Combinatorics
Utility
Mathematica-formatted output

Description

Some auxilary functions

Synopsis

data Pair a = Pair a a
sum' :: Num a => [a] -> a
unique :: Ord a => [a] -> [a]
count :: Ord b => [b] -> Map b Integer
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]
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
buildMap :: Ord k => (b -> a) -> (b -> a -> a) -> [(k, b)] -> Map k a
aut :: Partition -> Integer
exponentVector :: Partition -> [Int]
defaultSetPartition :: Partition -> SetPartition
linearIndices :: Partition -> [[Int]]
fromRat :: Rational -> Integer
safeDiv :: Integer -> Integer -> Integer
chooseN1 :: [a] -> [[a]]
symPolyNum :: Num a => Int -> [a] -> a
paren :: String -> String
expFormString :: Partition -> String
extendStringL :: Int -> String -> String
extendStringR :: Int -> String -> String
class Mathematica a where
- mathematica :: a -> String
data Indexed a = Indexed String a

Pairs

data Pair a Source #

Constructors

Pair a a

Instances

Instances details

Functor Pair Source #
Instance details Defined in Math.RootLoci.Misc.Common Methods fmap :: (a -> b) -> Pair a -> Pair b # (<$) :: a -> Pair b -> Pair a #
Eq a => Eq (Pair a) Source #
Instance details Defined in Math.RootLoci.Misc.Common Methods (==) :: Pair a -> Pair a -> Bool # (/=) :: Pair a -> Pair a -> Bool #
Ord a => Ord (Pair a) Source #
Instance details 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) Source #
Instance details 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 Source #

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

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

Synonym for histogram

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

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

evens :: [a] -> [a] Source #

odds :: [a] -> [a] Source #

interleave :: [a] -> [a] -> [a] Source #

Maps

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

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

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

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

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

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

Partitions

aut :: Partition -> Integer Source #

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] Source #

TODO: move this into combinat

Set partitions

defaultSetPartition :: Partition -> SetPartition Source #

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

linearIndices :: Partition -> [[Int]] Source #

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

Signs

Numbers

fromRat :: Rational -> Integer Source #

safeDiv :: Integer -> Integer -> Integer Source #

Combinatorics

chooseN1 :: [a] -> [[a]] Source #

Chooses (n-1) elements out of n

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

Utility

paren :: String -> String Source #

Put into parentheses

expFormString :: Partition -> String Source #

Exponential form of a partition

extendStringL :: Int -> String -> String Source #

extendStringR :: Int -> String -> String Source #

Mathematica-formatted output

class Mathematica a where Source #

Methods

mathematica :: a -> String Source #

Instances

Instances details

Mathematica Int Source #
Instance details Defined in Math.RootLoci.Misc.Common Methods mathematica :: Int -> String Source #
Mathematica Integer Source #
Instance details Defined in Math.RootLoci.Misc.Common Methods mathematica :: Integer -> String Source #
Mathematica String Source #
Instance details Defined in Math.RootLoci.Misc.Common Methods mathematica :: String -> String Source #
Mathematica Partition Source #
Instance details Defined in Math.RootLoci.Misc.Common Methods mathematica :: Partition -> String Source #
Mathematica a => Mathematica (Indexed a) Source #
Instance details Defined in Math.RootLoci.Misc.Common Methods mathematica :: Indexed a -> String Source #

data Indexed a Source #

Constructors

Indexed String a

Instances

Instances details

Mathematica a => Mathematica (Indexed a) Source #
Instance details Defined in Math.RootLoci.Misc.Common Methods mathematica :: Indexed a -> String Source #