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README
fandobraids: Braid representations in Haskell
Braids represented as Haskell types with support for generation and transformations.
Braid Typeclass
Braid b a
is a typeclass over the braid rep itself and its value type. Since a goal of this library is to use braids for nonmathematical purposes (ie music composition), a Braid can be indexed over any Integral
type, to support braids representing pitch values in a register for instance.
Generators
All braids are represented using Artin generators as Gen
, with Polarity
defining the "power" of a generator as O
ver or U
nder.
Generator indexes differ from the literature in that they are generally 0indexed whereas Artin generators are 1indexed. However, again these braids can represent other ranges of numbers as branch indexes.
Braid instances
Artin
creates canonical, "oneatatime", generator braids.
MultiGen
creates "compressed", "manyatatime" braids.
DimBraid
is for creating "padded" braids, since generators cannot express the absence of a cross.
Braid builders
bandGen
creates Birman/Ko/Leestyle band generators. In addition, stylized braid builders like buildBraid
and terraceBraid
are offered.
Transformations/Moves
In addition to operations like merge
etc, the type Move
represents Reidemeistertype isotopy moves. makeTree
unfolds a potentiallyinfinite tree representing all possible applications of a move.
Graphics
drawBraid
and drawStrands
allow drawings of braids, admitting extra functions for colorizing etc.