numeric-prelude-0.4.3: An experimental alternative hierarchy of numeric type classes

Copyright (c) Henning Thielemann 2006 numericprelude@henning-thielemann.de provisional requires multi-parameter type classes None Haskell98

MathObj.Permutation.CycleList.Check

Description

Synopsis

Documentation

newtype Cycle i Source #

We shall make a little bit of a hack here, enabling us to use additive or multiplicative syntax for groups as we wish by simply instantiating Num with both operations corresponding to the group operation of the permutation group we're studying

There are quite a few way we could represent elements of permutation groups: the images in a row, a list of the cycles, et.c. All of these differ highly in how complex various operations end up being.

Constructors

 Cycle Fieldscycle :: [i]

Instances

 Eq i => Eq (Cycle i) Source # Methods(==) :: Cycle i -> Cycle i -> Bool #(/=) :: Cycle i -> Cycle i -> Bool # Read i => Read (Cycle i) Source # MethodsreadsPrec :: Int -> ReadS (Cycle i) #readList :: ReadS [Cycle i] # Show i => Show (Cycle i) Source # MethodsshowsPrec :: Int -> Cycle i -> ShowS #show :: Cycle i -> String #showList :: [Cycle i] -> ShowS #

data T i Source #

Constructors

 Cons Fieldsrange :: (i, i) cycles :: [Cycle i]

Instances

 Source # Methodsdomain :: Ix i => T i -> (i, i) Source #apply :: Ix i => T i -> i -> i Source #inverse :: Ix i => T i -> T i Source # Ix i => Eq (T i) Source # These instances may need more work They involve converting a permutation to a table. Methods(==) :: T i -> T i -> Bool #(/=) :: T i -> T i -> Bool # Ix i => Ord (T i) Source # Methodscompare :: T i -> T i -> Ordering #(<) :: T i -> T i -> Bool #(<=) :: T i -> T i -> Bool #(>) :: T i -> T i -> Bool #(>=) :: T i -> T i -> Bool #max :: T i -> T i -> T i #min :: T i -> T i -> T i # Show i => Show (T i) Source # MethodsshowsPrec :: Int -> T i -> ShowS #show :: T i -> String #showList :: [T i] -> ShowS # Ix i => C (T i) Source # Methodsidt :: T i Source #(<*>) :: T i -> T i -> T i Source #cumulate :: [T i] -> T i Source #

fromCycles :: (i, i) -> [[i]] -> T i Source #

Does not check whether the input values are in range.

toCycles :: T i -> [[i]] Source #

toTable :: Ix i => T i -> T i Source #

fromTable :: Ix i => T i -> T i Source #

liftCmpTable2 :: Ix i => (T i -> T i -> a) -> T i -> T i -> a Source #

liftTable2 :: Ix i => (T i -> T i -> T i) -> T i -> T i -> T i Source #

closure :: Ix i => [T i] -> [T i] Source #