exp-pairs-0.1.4.0: Linear programming over exponent pairs

Copyright(c) Andrew Lelechenko, 2014-2015
LicenseGPL-3
Maintainerandrew.lelechenko@gmail.com
Stabilityexperimental
PortabilityTemplateHaskell
Safe HaskellNone
LanguageHaskell2010

Math.ExpPairs.Process

Description

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.

Synopsis

Documentation

data Process Source

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.

data Path Source

Holds a list of Process and a matrix of projective transformation, which they define. It also provides a fancy Show instance. E. g.,

show (mconcat $ replicate 10 aPath) == "A^10"

Constructors

Path !ProcessMatrix ![Process] 

aPath :: Path Source

Path consisting of a single process A.

baPath :: Path Source

Path consisting of a single process BA.

evalPath :: Num t => Path -> (t, t, t) -> (t, t, t) Source

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

lengthPath :: Path -> Int Source

Count processes in the Path. Note that BA counts for one process, not two.