Math.ExpPairs.Process

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.

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

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

Methods

(==) :: Process -> Process -> Bool

(/=) :: Process -> Process -> Bool

Ord Process

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

Methods

readsPrec :: Int -> ReadS Process

readList :: ReadS [Process]

readPrec :: ReadPrec Process

readListPrec :: ReadPrec [Process]

Show Process

Methods

showsPrec :: Int -> Process -> ShowS

show :: Process -> String

showList :: [Process] -> ShowS

Generic Process

Associated Types

type Rep Process :: * -> *

Methods

from :: Process -> Rep Process x

to :: Rep Process x -> Process

Pretty Process

Methods

pretty :: Process -> Doc ann

prettyList :: [Process] -> Doc ann

type Rep Process

type Rep Process = D1 * (MetaData "Process" "Math.ExpPairs.ProcessMatrix" "exp-pairs-0.1.6.0-Gtd6e9LEtfhDqv5Iz3ymUo" 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

Methods

(==) :: Path -> Path -> Bool

(/=) :: Path -> Path -> Bool

Ord Path

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

Methods

readsPrec :: Int -> ReadS Path

readList :: ReadS [Path]

readPrec :: ReadPrec Path

readListPrec :: ReadPrec [Path]

Show Path

Methods

showsPrec :: Int -> Path -> ShowS

show :: Path -> String

showList :: [Path] -> ShowS

Generic Path

Associated Types

type Rep Path :: * -> *

Methods

from :: Path -> Rep Path x

to :: Rep Path x -> Path

Semigroup Path

Methods

(<>) :: Path -> Path -> Path

sconcat :: NonEmpty Path -> Path

stimes :: Integral b => b -> Path -> Path

Monoid Path

Methods

mempty :: Path

mappend :: Path -> Path -> Path

mconcat :: [Path] -> Path

Pretty Path

Methods

pretty :: Path -> Doc ann

prettyList :: [Path] -> Doc ann

type Rep Path

type Rep Path = D1 * (MetaData "Path" "Math.ExpPairs.Process" "exp-pairs-0.1.6.0-Gtd6e9LEtfhDqv5Iz3ymUo" False) (C1 * (MetaCons "Path" PrefixI False) ((:*:) * (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 * ProcessMatrix)) (S1 * (MetaSel (Nothing 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.