Copyright	(c) Andrew Lelechenko 2014-2015
License	GPL-3
Maintainer	andrew.lelechenko@gmail.com
Stability	experimental
Portability	POSIX
Safe Haskell	None
Language	Haskell2010

Math.ExpPairs.Process

Description

Provides types for sequences of A- and B-processes of van der Corput. A good account on this topic can be found in Graham S. W., Kolesnik G. A. Van Der Corput's Method of Exponential Sums, Cambridge University Press, 1991, especially Ch. 5.

Synopsis

data Process
data Path = Path !ProcessMatrix ![Process]
aPath :: Path
baPath :: Path
evalPath :: Num t => Path -> (t, t, t) -> (t, t, t)
lengthPath :: Path -> Int

Documentation

data Process #

Since B^2 = id, B Corput16 = Corput16, B Hux05 = Hux05 and B HuxW87b1 = ???, the sequence of A- and B-processes, applied to initPairs can be rewritten as a sequence of A and BA.

Instances

Enum Process #
Instance details Defined in Math.ExpPairs.ProcessMatrix Methods succ :: Process -> Process # pred :: Process -> Process # toEnum :: Int -> Process # fromEnum :: Process -> Int # enumFrom :: Process -> [Process] # enumFromThen :: Process -> Process -> [Process] # enumFromTo :: Process -> Process -> [Process] # enumFromThenTo :: Process -> Process -> Process -> [Process] #
Eq Process #
Instance details Defined in Math.ExpPairs.ProcessMatrix Methods (==) :: Process -> Process -> Bool # (/=) :: Process -> Process -> Bool #
Ord Process #
Instance details Defined in Math.ExpPairs.ProcessMatrix Methods compare :: Process -> Process -> Ordering # (<) :: Process -> Process -> Bool # (<=) :: Process -> Process -> Bool # (>) :: Process -> Process -> Bool # (>=) :: Process -> Process -> Bool # max :: Process -> Process -> Process # min :: Process -> Process -> Process #
Read Process #
Instance details Defined in Math.ExpPairs.ProcessMatrix Methods readsPrec :: Int -> ReadS Process # readList :: ReadS [Process] # readPrec :: ReadPrec Process # readListPrec :: ReadPrec [Process] #
Show Process #
Instance details Defined in Math.ExpPairs.ProcessMatrix Methods showsPrec :: Int -> Process -> ShowS # show :: Process -> String # showList :: [Process] -> ShowS #
Generic Process #
Instance details Defined in Math.ExpPairs.ProcessMatrix Associated Types type Rep Process :: * -> * # Methods from :: Process -> Rep Process x # to :: Rep Process x -> Process #
Pretty Process #
Instance details Defined in Math.ExpPairs.ProcessMatrix Methods pretty :: Process -> Doc ann # prettyList :: [Process] -> Doc ann #
type Rep Process #
Instance details Defined in Math.ExpPairs.ProcessMatrix type Rep Process = D1 (MetaData "Process" "Math.ExpPairs.ProcessMatrix" "exp-pairs-0.1.6.0-A57bvNSkfW36XePlDuMIT4" False) (C1 (MetaCons "A" PrefixI False) (U1 :: * -> ) :+: C1 (MetaCons "BA" PrefixI False) (U1 :: -> *))

data Path #

Holds a list of Process and a matrix of projective transformation, which they define.

Constructors

Path !ProcessMatrix ![Process]

Instances

Eq Path #
Instance details Defined in Math.ExpPairs.Process Methods (==) :: Path -> Path -> Bool # (/=) :: Path -> Path -> Bool #
Ord Path #
Instance details Defined in Math.ExpPairs.Process Methods compare :: Path -> Path -> Ordering # (<) :: Path -> Path -> Bool # (<=) :: Path -> Path -> Bool # (>) :: Path -> Path -> Bool # (>=) :: Path -> Path -> Bool # max :: Path -> Path -> Path # min :: Path -> Path -> Path #
Read Path #
Instance details Defined in Math.ExpPairs.Process Methods readsPrec :: Int -> ReadS Path # readList :: ReadS [Path] # readPrec :: ReadPrec Path # readListPrec :: ReadPrec [Path] #
Show Path #
Instance details Defined in Math.ExpPairs.Process Methods showsPrec :: Int -> Path -> ShowS # show :: Path -> String # showList :: [Path] -> ShowS #
Generic Path #
Instance details Defined in Math.ExpPairs.Process Associated Types type Rep Path :: * -> * # Methods from :: Path -> Rep Path x # to :: Rep Path x -> Path #
Semigroup Path #
Instance details Defined in Math.ExpPairs.Process Methods (<>) :: Path -> Path -> Path # sconcat :: NonEmpty Path -> Path # stimes :: Integral b => b -> Path -> Path #
Monoid Path #
Instance details Defined in Math.ExpPairs.Process Methods mempty :: Path # mappend :: Path -> Path -> Path # mconcat :: [Path] -> Path #
Pretty Path #
Instance details Defined in Math.ExpPairs.Process Methods pretty :: Path -> Doc ann # prettyList :: [Path] -> Doc ann #
type Rep Path #
Instance details Defined in Math.ExpPairs.Process type Rep Path = D1 (MetaData "Path" "Math.ExpPairs.Process" "exp-pairs-0.1.6.0-A57bvNSkfW36XePlDuMIT4" False) (C1 (MetaCons "Path" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 ProcessMatrix) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 [Process])))

aPath :: Path #

Path consisting of a single process A.

baPath :: Path #

Path consisting of a single process BA.

evalPath :: Num t => Path -> (t, t, t) -> (t, t, t) #

Apply a projective transformation, defined by Path, to a given point in two-dimensional projective space.

lengthPath :: Path -> Int #

Count processes in the Path. Note that BA counts for one process, not two.