MathObj.Permutation.CycleList.Check
 Portability requires multi-parameter type classes Stability provisional Maintainer numericprelude@henning-thielemann.de
Description
Synopsis
newtype Cycle i = Cycle {
 cycle :: [i]
}
data T i = Cons {
 range :: (i, i) cycles :: [Cycle i]
}
fromCycles :: (i, i) -> [[i]] -> T i
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]
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
 cycle :: [i] Instances
 Eq i => Eq (Cycle i) Read i => Read (Cycle i) Show i => Show (Cycle i)
 data T i Source
Constructors
Cons
 range :: (i, i) cycles :: [Cycle i] Instances
 C T Ix i => Eq (T i) Ix i => Ord (T i) Show i => Show (T i) Ix i => C (T i)
 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
 errIncompat :: a 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
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