Copyright	(c) Andrew Lelechenko 2014-2020
License	GPL-3
Maintainer	andrew.lelechenko@gmail.com
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

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] #
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 #
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 #
Generic Process Source #
Instance details 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 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-0.2.1.0-J4IGbuSTVwXCgBqjoU0P5n" 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

Eq ProcessMatrix Source #
Instance details Defined in Math.ExpPairs.ProcessMatrix Methods (==) :: ProcessMatrix -> ProcessMatrix -> Bool # (/=) :: ProcessMatrix -> ProcessMatrix -> Bool #
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 #
Semigroup ProcessMatrix Source #
Instance details Defined in Math.ExpPairs.ProcessMatrix Methods (<>) :: ProcessMatrix -> ProcessMatrix -> ProcessMatrix # sconcat :: NonEmpty ProcessMatrix -> ProcessMatrix # stimes :: Integral b => b -> ProcessMatrix -> ProcessMatrix #
Monoid ProcessMatrix Source #
Instance details Defined in Math.ExpPairs.ProcessMatrix Methods mempty :: ProcessMatrix # mappend :: ProcessMatrix -> ProcessMatrix -> ProcessMatrix # mconcat :: [ProcessMatrix] -> ProcessMatrix #
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.