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fando-braids: Braid representations in Haskell
Braids represented as Haskell types with support for generation and transformations.
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 non-mathematical purposes (ie music composition), a Braid can be indexed over any
Integral type, to support braids representing pitch values in a register for instance.
All braids are represented using Artin generators as
Polarity defining the "power" of a generator as
Generator indexes differ from the literature in that they are generally 0-indexed whereas Artin generators are 1-indexed. However, again these braids can represent other ranges of numbers as branch indexes.
Artin creates canonical, "one-at-a-time", generator braids.
MultiGen creates "compressed", "many-at-a-time" braids.
DimBraid is for creating "padded" braids, since generators cannot express the absence of a cross.
bandGen creates Birman/Ko/Lee-style band generators. In addition, stylized braid builders like
terraceBraid are offered.
In addition to operations like
merge etc, the type
Move represents Reidemeister-type isotopy moves.
makeTree unfolds a potentially-infinite tree representing all possible applications of a move.
drawStrands allow drawings of braids, admitting extra functions for colorizing etc.