numeric-prelude-0.4.0.2: An experimental alternative hierarchy of numeric type classes

Portability requires multi-parameter type classes provisional numericprelude@henning-thielemann.de None

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) Read i => Read (Cycle i) Show i => Show (Cycle i)

data T i Source

Constructors

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

Instances

 C T Ix i => Eq (T i) These instances may need more work They involve converting a permutation to a table. Ix i => Ord (T i) Show i => Show (T i) Ix i => C (T i)

fromCycles :: (i, i) -> [[i]] -> T iSource

Does not check whether the input values are in range.

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

toTable :: Ix i => T i -> T iSource

fromTable :: Ix i => T i -> T iSource

liftCmpTable2 :: Ix i => (T i -> T i -> a) -> T i -> T i -> aSource

liftTable2 :: Ix i => (T i -> T i -> T i) -> T i -> T i -> T iSource

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