🧶 Braid Group: Code Resources, Visualizations & Research

📘 General background wikis on braid theory

• Braid on Wikipedia

• Braid group on Wikipedia

• https://ncatlab.org/nlab/show/braid+group

• https://www.labri.fr/perso/marckert/poulalhon.pdf

• https://homepages.math.uic.edu/~jaca2009/notes/Meneses.pdf Maybe one of the best paper which is describing some relationships between algebraic and geometric braid

• blob:https://github.com/8f3cf57d-953c-4b95-b920-e561721cbdbd

• https://github.com/louisepb/TexGen

• https://mathcenter.oxford.emory.edu/site/math108/braid_arithmetic/

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🧮 SageMath Implementation

The most comprehensive implementation is in SageMath, but due to its GPL license, it won’t be integrated here. However, having a look to the functions implemented gives a good idea of how wide this domain is.

• SageMath Braid Group Documentation

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🎨 Visualization Tools

• rexgreenway/braid-visualiser – Flat diagram visualization, available on PyPI -> used by braidpy

• (Denbox/Braid-Group-Visualization – Flat diagram but lacks good crossing visuals )

• loopspace/braids LaTeX braids package – LaTeX-based braid rendering available on github. Impressive customization, good for documentation
  (https://github.com/BnZel/poses_and_braids) (https://github.com/isaac-art/BraidLab) More of an art work

• https://github.com/rpitasky/typst-braid

• https://github.com/joeLepper/braider?tab=readme-ov-file Node. Demo https://braider.surge.sh/

• https://github.com/byorgey/braids

• https://github.com/lightningund/braid

• https://github.com/christian-oudard/logo -> interesting

• https://github.com/the-bakery/braided > protoype to edit graphically a braid diagram in web browser

• https://github.com/WhimsicalDragon/BraidMaker (weird)

• https://github.com/Sonicpineapple/Braids another online braid editor

• https://github.com/textiles-lab/show-braid

• https://github.com/mweitzel/braid html braid generator from word

• A more general way to store and visualize different textiles https://github.com/virtualtextiles/pytexlib Alternative Python library:

• braidpy (PyPI)

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🧠 Dehornoy’s Work

Author of “Le calcul des tresses”, Dehornoy contributed several algorithms like handle reduction.

• 📄 “Patrick Dehornoy: A Fast Method for Comparing Braids”

• Old Pascal Code

• Dockerized Pascal Source

• Python handle reduction

• C++ handle reduction

• gbraids – Research with n=4

  • Handle reduction

  • DynnikovCoordinates

  • Dual generator

• TU/e paper on Dehornoy

• https://github.com/jfromentin/handle

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🐍 Python Libraries (GitHub & PyPI)

• kuboon/math_braid.py is available on PyPI

  • Last updated 6 years ago

  • Scarce documentation but test in doctest

  • BSD license (usable with wrapper or code import)

  • Examples:

    # Artin generation (num = 1 to 3)
    Braid([1, 2, 3], 4)
    
    # Band generation (num = 1 to 4)
    b = Braid([[3, 1], [1, 2]], 4)
    

• rexgreenway/alexander-data – Invariant calculation (not on PyPI)

• leodana/TIPE – Dense, untested student code
  https://github.com/stla/braids

• https://github.com/MarkCBell/flipper?tab=readme-ov-file - probably very powerful, but a bit abstract

• https://github.com/mateosi98/Unknotting-Braids

• https://github.com/GriffinKowash/Cable-braids/tree/main

• https://github.com/iowyth/harmonic-braider

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📊 MATLAB / BraidLab

• Braidlab PDF Guide which was published arXiv:1410.0849 – Braidlab paper

  • Matlab code is available jeanluct/braidlab

  • Probably the best introduction to computation with braids

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Julia

https://github.com/jwvictor/Braids.jl

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https://github.com/jeanluct/cbraid?tab=readme-ov-file

🪢 Knots & Related Libraries

Braid functions are often used in knot theory.

• Algebra8/Knots

  • Project name: braidgenerator on PyPI

  • Not very useful

• Documentation Site – Well made

Knot libraries:

• pyknotid (PyPI)

• SPOCKnots/pyknotid

  • Convert braid word → knot

  • Advanced visualizations

  • Relevant code line

• xcapaldi/tbkm – Random braid visualization in terminal

• RafaelMri/Pyknots

  • Step-by-step handle reduction

  • Braid code reference

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📺 Video Resource

• YouTube: Braids Explained

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Braiding machine control

https://github.com/Brandon-Key5113/BraidyBunch https://github.com/LJYJYN/Braiding-APP https://pubs.rsc.org/en/content/articlelanding/2024/sm/d3sm01732j

Braiding machine 3d printing

https://github.com/manoharan-lab/arbitrary-topology-stl https://github.com/sapphire-arches/braiding-machine https://github.com/EricLarueMartin/FourWireBraidingMachine https://github.com/sandy9159/DIY-mini-braiding-machine https://github.com/tforgrave/braider_project