Math.ExpPairs.ProcessMatrix

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.

Constructors

A

A-process

BA

BA-process

Instances

Enum Process

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

Defined in Math.ExpPairs.ProcessMatrix

Methods

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

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

Ord Process

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

Defined in Math.ExpPairs.ProcessMatrix

Methods

readsPrec :: Int -> ReadS Process

readList :: ReadS [Process]

readPrec :: ReadPrec Process

readListPrec :: ReadPrec [Process]

Show Process

Defined in Math.ExpPairs.ProcessMatrix

Methods

showsPrec :: Int -> Process -> ShowS

show :: Process -> String

showList :: [Process] -> ShowS

Generic Process

Defined in Math.ExpPairs.ProcessMatrix

Associated Types

type Rep Process :: * -> *

Methods

from :: Process -> Rep Process x

to :: Rep Process x -> Process

Pretty Process

Defined in Math.ExpPairs.ProcessMatrix

Methods

pretty :: Process -> Doc ann

prettyList :: [Process] -> Doc ann

type Rep Process

Defined in Math.ExpPairs.ProcessMatrix

type Rep Process = D1 (MetaData "Process" "Math.ExpPairs.ProcessMatrix" "exp-pairs-0.2.0.0-KHgC3bMWFtS3BpPTx68RIa" False) (C1 (MetaCons "A" PrefixI False) (U1 :: * -> *) :+: C1 (MetaCons "BA" PrefixI False) (U1 :: * -> *))

data ProcessMatrix

Sequence of processes, represented as a matrix 3x3.

Instances

Eq ProcessMatrix

Defined in Math.ExpPairs.ProcessMatrix

Methods

(==) :: ProcessMatrix -> ProcessMatrix -> Bool

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

Num ProcessMatrix

Defined in Math.ExpPairs.ProcessMatrix

Methods

(+) :: ProcessMatrix -> ProcessMatrix -> ProcessMatrix

(-) :: ProcessMatrix -> ProcessMatrix -> ProcessMatrix

(*) :: ProcessMatrix -> ProcessMatrix -> ProcessMatrix

negate :: ProcessMatrix -> ProcessMatrix

abs :: ProcessMatrix -> ProcessMatrix

signum :: ProcessMatrix -> ProcessMatrix

fromInteger :: Integer -> ProcessMatrix

Show ProcessMatrix

Defined in Math.ExpPairs.ProcessMatrix

Methods

showsPrec :: Int -> ProcessMatrix -> ShowS

show :: ProcessMatrix -> String

showList :: [ProcessMatrix] -> ShowS

Semigroup ProcessMatrix

Defined in Math.ExpPairs.ProcessMatrix

Methods

(<>) :: ProcessMatrix -> ProcessMatrix -> ProcessMatrix

sconcat :: NonEmpty ProcessMatrix -> ProcessMatrix

stimes :: Integral b => b -> ProcessMatrix -> ProcessMatrix

Monoid ProcessMatrix

Defined in Math.ExpPairs.ProcessMatrix

Methods

mempty :: ProcessMatrix

mappend :: ProcessMatrix -> ProcessMatrix -> ProcessMatrix

mconcat :: [ProcessMatrix] -> ProcessMatrix

Pretty ProcessMatrix

Defined in Math.ExpPairs.ProcessMatrix

Methods

pretty :: ProcessMatrix -> Doc ann

prettyList :: [ProcessMatrix] -> Doc ann

aMatrix :: ProcessMatrix

Return process matrix for A-process.

baMatrix :: ProcessMatrix

Return process matrix for BA-process.

evalMatrix :: Num t => ProcessMatrix -> (t, t, t) -> (t, t, t)

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