MathObj.Permutation.CycleList.Check

Documentation

newtype Cycle i

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

Fields

cycle :: [i]

Instances

Eq i => Eq (Cycle i)

Read i => Read (Cycle i)

Show i => Show (Cycle i)

data T i

Constructors

Cons

Fields

range :: (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 i

Does not check whether the input values are in range.

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

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

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

errIncompat :: a

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

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

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