twentyseven-0.0.0: Rubik's cube solver

Safe HaskellNone
LanguageHaskell2010

Rubik.Symmetry

Description

  • Tables of symmetry classes

Synopsis

Documentation

type SymRepr a = RawCoord a Source

Smallest representative of a symmetry class. (An element of the symClasses table)

type SymClass' = Int Source

newtype SymClass symType a Source

Symmetry class. (Index of the smallest representative in the symClasses table)

Constructors

SymClass 

Fields

unSymClass :: SymClass'
 

Instances

Eq (SymClass symType a) Source 
Ord (SymClass symType a) Source 
Show (SymClass symType a) Source 

type SymCoord sym a = (SymClass sym a, SymCode sym) Source

type SymCoord' = Int Source

An Int representing a pair (Repr, Sym).

If x = symClass * symOrder + symCode, where symClass :: SymClass is the index of the symmetry class with smallest representative r :: SymRepr (for an arbitrary order relation), symOrder is the size of the symmetry group, symCode :: Sym is the index of a symmetry s; then s^(-1) <> r <> s is the value represented by x.

type SymOrder' = Int Source

newtype Action s a Source

Constructors

Action [a -> a] 

newtype SymClassTable s a Source

Constructors

SymClassTable 

Fields

unSymClassTable :: Vector RawCoord'
 

Instances

newtype SymReprTable s a Source

Constructors

SymReprTable 

Fields

unSymReprTable :: Vector Int
 

Instances

newtype SymMove s a Source

Constructors

SymMove (Vector SymCoord') 

Instances

type Symmetries sym a = MoveTag sym (Vector (RawMove a)) Source

symClasses Source

Arguments

:: RawEncodable a 
=> Action s a

Symmetry group, including the identity, - represented by its action on a

-> SymClassTable s a

Smallest representative

Compute the table of smallest representatives for all symmetry classes. The RawCoord' coordinate of that representative is a Repr. The table is sorted in increasing order.

symClasses' :: forall a s. RawEncodable a => Action s a -> [RawCoord a] Source

symClassTable :: Int -> SymReprTable s a -> SymClassTable s a Source

symReprTable Source

Arguments

:: (RawEncodable a, Foldable t) 
=> Int

Number of symmetries nSym

-> (RawCoord a -> t (RawCoord a)) 
-> SymReprTable s a 

symReprTable' Source

Arguments

:: Foldable t 
=> Int

Number of elements n

-> Int

Number of symmetries nSym

-> (Int -> t Int)

f x, symmetrical elements to x, including itself

-> Vector Int

v, where (y, i) = (v ! x) divMod nSym gives the representative y of the symmetry class of x and the index of one symmetry mapping x to y:

f x !! i == y.

symMoveTable Source

Arguments

:: RawEncodable a 
=> Action s a

Symmetry group

-> SymClassTable s a

(Sorted) table of representatives

-> (a -> a)

Endofunction to encode

-> SymMove s a 

symMoveTable' Source

Arguments

:: RawEncodable a 
=> Int

Symmetry group order

-> SymReprTable s a 
-> SymClassTable s a 
-> (a -> a) 
-> SymMove s a 

symMove :: SymOrder' -> SymMove s a -> SymClass s a -> SymCoord s a Source

symMove' :: SymOrder' -> SymMove sym a -> (SymClass sym a, SymCode sym) -> (SymClass sym a, SymCode sym) Source

reprToClass :: SymClassTable s a -> RawCoord a -> SymClass s a Source

symCoord :: RawEncodable a => Action s a -> SymClassTable s a -> a -> SymCoord s a Source

Find the representative as the one corresponding to the smallest coordinate

symCoord' :: Int -> SymReprTable s a -> SymClassTable s a -> RawCoord a -> SymCoord s a Source

symToRaw :: SymClassTable s a -> (RawCoord a -> SymCode s -> RawCoord a) -> SymCoord s a -> RawCoord a Source

sym :: Symmetries s a -> RawCoord a -> SymCode s -> RawCoord a Source