sirlensalot / fadno-braids Goto Github PK

class (Integral b, Monoid ab) => Braid b ab | ab -> b where

    {-# MINIMAL toGens,minIndex,maxIndex,invert #-}

    -- | "Length", number of "steps"/columns/artin generators.
    stepCount :: ab -> Int
    -- | "N", braid group index, number of strands/rows/"i"s.
    strandCount :: ab -> b
    -- | Common format is a series of "steps" of absolute-indexed generators.
    toGens :: ab -> [[Gen b]]
    -- | Minimum index (i) value
    minIndex :: ab -> b
    -- | Maximum index (i) value. Note this means values of (i+1) obtain, per generators.
    maxIndex :: ab -> b
    -- | Invert indices
    invert :: ab -> ab
    -- | convert to single-gen
    toArtin :: ab -> Artin b
    -- | convert to multi-gen
    toMultiGen :: ab -> MultiGen b

    strandCount a = (maxIndex a + 2) - minIndex a

    stepCount = length . toGens -- inefficient

    toArtin = Artin . concat . toGens

    toMultiGen = MultiGen . map gensToStep . toGens