Math.ExpPairs.Process

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.

Instances

Enum Process

Eq Process

Ord Process

Read Process

Show Process

Generic Process

Memoizable Process

Pretty Process

type Rep Process

data Path

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]

Instances

Eq Path

Ord Path

Read Path

Show Path

Generic Path

Monoid Path

Pretty Path

type Rep Path

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 one process, not two.