Copyright	(c) Andrew Lelechenko 2014-2020
License	GPL-3
Maintainer	[email protected]
Safe Haskell	None
Language	Haskell2010

Math.ExpPairs.ProcessMatrix

Description

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.

Synopsis

data Process
- = A
- | BA
data ProcessMatrix
aMatrix :: ProcessMatrix
baMatrix :: ProcessMatrix
evalMatrix :: Num t => ProcessMatrix -> (t, t, t) -> (t, t, t)

Documentation

data Process Source #

Since \( B \)-process is involutive, a sequence of \( A \)- and \( B \)-processes can be rewritten as a sequence of A and BA.

Constructors

A	\( A \)-process
BA	\( BA \)-process

Instances

Instances details

Enum Process Source #

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] #

Generic Process Source #

Instance details

Defined in Math.ExpPairs.ProcessMatrix

Associated Types

type Rep Process
Instance details Defined in Math.ExpPairs.ProcessMatrix type Rep Process = D1 ('MetaData "Process" "Math.ExpPairs.ProcessMatrix" "exp-pairs-0.2.1.1-8itfA9RAbYGDVV8JvWzVP7" 'False) (C1 ('MetaCons "A" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "BA" 'PrefixI 'False) (U1 :: Type -> Type))

Methods

from :: Process -> Rep Process x #

to :: Rep Process x -> Process #

Read Process Source #

Instance details

Defined in Math.ExpPairs.ProcessMatrix

Methods

readsPrec :: Int -> ReadS Process #

readList :: ReadS [Process] #

readPrec :: ReadPrec Process #

readListPrec :: ReadPrec [Process] #

Show Process Source #

Instance details

Defined in Math.ExpPairs.ProcessMatrix

Methods

showsPrec :: Int -> Process -> ShowS #

show :: Process -> String #

showList :: [Process] -> ShowS #

Eq Process Source #

Instance details

Defined in Math.ExpPairs.ProcessMatrix

Methods

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

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

Ord Process Source #

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 #

Pretty Process Source #

Instance details

Defined in Math.ExpPairs.ProcessMatrix

Methods

pretty :: Process -> Doc ann #

prettyList :: [Process] -> Doc ann #

type Rep Process Source #

Instance details

Defined in Math.ExpPairs.ProcessMatrix

type Rep Process = D1 ('MetaData "Process" "Math.ExpPairs.ProcessMatrix" "exp-pairs-0.2.1.1-8itfA9RAbYGDVV8JvWzVP7" 'False) (C1 ('MetaCons "A" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "BA" 'PrefixI 'False) (U1 :: Type -> Type))

data ProcessMatrix Source #

Sequence of processes, represented as a matrix \( 3 \times 3 \).

Instances

Instances details

Monoid ProcessMatrix Source #
Instance details Defined in Math.ExpPairs.ProcessMatrix Methods mempty :: ProcessMatrix # mappend :: ProcessMatrix -> ProcessMatrix -> ProcessMatrix # mconcat :: [ProcessMatrix] -> ProcessMatrix #
Semigroup ProcessMatrix Source #
Instance details Defined in Math.ExpPairs.ProcessMatrix Methods (<>) :: ProcessMatrix -> ProcessMatrix -> ProcessMatrix # sconcat :: NonEmpty ProcessMatrix -> ProcessMatrix # stimes :: Integral b => b -> ProcessMatrix -> ProcessMatrix #
Num ProcessMatrix Source #
Instance details 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 Source #
Instance details Defined in Math.ExpPairs.ProcessMatrix Methods showsPrec :: Int -> ProcessMatrix -> ShowS # show :: ProcessMatrix -> String # showList :: [ProcessMatrix] -> ShowS #
Eq ProcessMatrix Source #
Instance details Defined in Math.ExpPairs.ProcessMatrix Methods (==) :: ProcessMatrix -> ProcessMatrix -> Bool # (/=) :: ProcessMatrix -> ProcessMatrix -> Bool #
Pretty ProcessMatrix Source #
Instance details Defined in Math.ExpPairs.ProcessMatrix Methods pretty :: ProcessMatrix -> Doc ann # prettyList :: [ProcessMatrix] -> Doc ann #

aMatrix :: ProcessMatrix Source #

Return process matrix for \( A \)-process.

baMatrix :: ProcessMatrix Source #

Return process matrix for \( BA \)-process.

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

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