{-# LANGUAGE RebindableSyntax #-} {- | Copyright : (c) Henning Thielemann 2006 Maintainer : numericprelude@henning-thielemann.de Stability : provisional Portability : requires multi-parameter type classes -} module MathObj.Permutation.CycleList.Check where import qualified MathObj.Permutation.CycleList as PermCycle import qualified MathObj.Permutation.Table as PermTable import qualified MathObj.Permutation as Perm {- import qualified Algebra.Ring as Ring import qualified Algebra.Additive as Additive import Algebra.Ring((*),one,fromInteger) import Algebra.Additive((+)) -} import Algebra.Monoid((<*>)) import qualified Algebra.Monoid as Monoid import Data.Array((!), Ix) import qualified Data.Array as Array -- import NumericPrelude.Numeric (Integer) import NumericPrelude.Base hiding (cycle) {- | 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. -} newtype Cycle i = Cycle { cycle :: [i] } deriving (Read,Eq) data T i = Cons { range :: (i, i), cycles :: [Cycle i] } {- | Does not check whether the input values are in range. -} fromCycles :: (i, i) -> [[i]] -> T i fromCycles rng = Cons rng . map Cycle toCycles :: T i -> [[i]] toCycles = map cycle . cycles toTable :: (Ix i) => T i -> PermTable.T i toTable x = PermTable.fromCycles (range x) (toCycles x) fromTable :: (Ix i) => PermTable.T i -> T i fromTable x = let rng = Array.bounds x in fromCycles rng (PermCycle.fromFunction rng (x!)) errIncompat :: a errIncompat = error "Permutation.CycleList: Incompatible domains" liftCmpTable2 :: (Ix i) => (PermTable.T i -> PermTable.T i -> a) -> T i -> T i -> a liftCmpTable2 f x y = if range x == range y then f (toTable x) (toTable y) else errIncompat liftTable2 :: (Ix i) => (PermTable.T i -> PermTable.T i -> PermTable.T i) -> T i -> T i -> T i liftTable2 f x y = fromTable (liftCmpTable2 f x y) closure :: (Ix i) => [T i] -> [T i] closure = map fromTable . PermTable.closure . map toTable instance Perm.C T where domain = range apply p = ((toCycles p) PermCycle.*>) inverse p = fromCycles (range p) (PermCycle.inverse (toCycles p)) instance Show i => Show (Cycle i) where show c = "(" ++ (unwords $ map show $ cycle c) ++ ")" instance Show i => Show (T i) where show p = case cycles p of [] -> "Id" cyc -> concatMap show cyc {- | These instances may need more work They involve converting a permutation to a table. -} instance Ix i => Eq (T i) where (==) = liftCmpTable2 (==) instance Ix i => Ord (T i) where compare = liftCmpTable2 compare {- Better: Group class and instances instance Additive.C (T i) where p + q = p * q negate = inverse zero = one instance Ring.C (T i) where (Cons op cp) * (Cons oq cq) = reduceCycles $ Cons (max op oq) (cp ++ cq) one = Cons 1 [] -} instance Ix i => Monoid.C (T i) where (<*>) = liftTable2 PermTable.compose idt = error "There is no generic unit element"