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)

Defined in MathObj.Permutation.CycleList.Check

Methods

(==) :: Cycle i -> Cycle i -> Bool

(/=) :: Cycle i -> Cycle i -> Bool

Read i => Read (Cycle i)

Defined in MathObj.Permutation.CycleList.Check

Methods

readsPrec :: Int -> ReadS (Cycle i)

readList :: ReadS [Cycle i]

readPrec :: ReadPrec (Cycle i)

readListPrec :: ReadPrec [Cycle i]

Show i => Show (Cycle i)

Defined in MathObj.Permutation.CycleList.Check

Methods

showsPrec :: Int -> Cycle i -> ShowS

show :: Cycle i -> String

showList :: [Cycle i] -> ShowS

data T i

Constructors

Cons

Fields

• range :: (i, i)
• cycles :: [Cycle i]

Instances

C T

Defined in MathObj.Permutation.CycleList.Check

Methods

domain :: Ix i => T i -> (i, i)

apply :: Ix i => T i -> i -> i

inverse :: Ix i => T i -> T i

Ix i => Eq (T i)

These instances may need more work They involve converting a permutation to a table.

Defined in MathObj.Permutation.CycleList.Check

Methods

(==) :: T i -> T i -> Bool

(/=) :: T i -> T i -> Bool

Ix i => Ord (T i)

Defined in MathObj.Permutation.CycleList.Check

Methods

compare :: 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)

Defined in MathObj.Permutation.CycleList.Check

Methods

showsPrec :: Int -> T i -> ShowS

show :: T i -> String

showList :: [T i] -> ShowS

Ix i => C (T i)

Defined in MathObj.Permutation.CycleList.Check

Methods

idt :: T i

(<*>) :: T i -> T i -> T i

cumulate :: [T i] -> 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]