coincident-root-loci-0.2: Equivariant CSM classes of coincident root loci

Math.RootLoci.Misc.Common

Description

Some auxilary functions

Synopsis

# Pairs

data Pair a Source #

Constructors

 Pair a a

Instances

 Source # Methodsfmap :: (a -> b) -> Pair a -> Pair b #(<\$) :: a -> Pair b -> Pair a # Eq a => Eq (Pair a) Source # Methods(==) :: Pair a -> Pair a -> Bool #(/=) :: Pair a -> Pair a -> Bool # Ord a => Ord (Pair a) Source # Methodscompare :: 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 # MethodsshowsPrec :: Int -> Pair a -> ShowS #show :: Pair a -> String #showList :: [Pair a] -> ShowS #

# Lists

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 #

# 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 #

# Partitions

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

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

class IsSigned a where Source #

Minimal complete definition

signOf

Methods

signOf :: a -> Maybe Sign Source #

Instances

 Source # Methods Source # Methods Source # Methods

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

# Combinatorics

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

Chooses (n-1) elements out of n

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