Math.ExpPairs.Process

Sequences of \( A \)- and \( B \)-processes of van der Corput's method of exponential sums. A good reference 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 \( B \)-process is involutive, a sequence of \( A \)- and \( B \)-processes can be rewritten as a sequence of A and BA.

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 :: Type -> Type

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-0.2.1.0-J4IGbuSTVwXCgBqjoU0P5n" False) (C1 (MetaCons "A" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons "BA" PrefixI False) (U1 :: Type -> Type))

data Path

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

Constructors

Path !ProcessMatrix ![Process]

Instances

Eq Path

Defined in Math.ExpPairs.Process

Methods

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

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

Ord Path

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

Defined in Math.ExpPairs.Process

Methods

readsPrec :: Int -> ReadS Path

readList :: ReadS [Path]

readPrec :: ReadPrec Path

readListPrec :: ReadPrec [Path]

Show Path

Defined in Math.ExpPairs.Process

Methods

showsPrec :: Int -> Path -> ShowS

show :: Path -> String

showList :: [Path] -> ShowS

Generic Path

Defined in Math.ExpPairs.Process

Associated Types

type Rep Path :: Type -> Type

Methods

from :: Path -> Rep Path x

to :: Rep Path x -> Path

Semigroup Path

Defined in Math.ExpPairs.Process

Methods

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

sconcat :: NonEmpty Path -> Path

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

Monoid Path

Defined in Math.ExpPairs.Process

Methods

mempty :: Path

mappend :: Path -> Path -> Path

mconcat :: [Path] -> Path

Pretty Path

Defined in Math.ExpPairs.Process

Methods

pretty :: Path -> Doc ann

prettyList :: [Path] -> Doc ann

type Rep Path

Defined in Math.ExpPairs.Process

type Rep Path = D1 (MetaData "Path" "Math.ExpPairs.Process" "exp-pairs-0.2.1.0-J4IGbuSTVwXCgBqjoU0P5n" 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 a single process.