Effective Algebraic Topology

This is a fork of AT, a Haskell rewrite of Kenzo, a collection of algorithms for 'effective algebraic topology'. See the links for more details and great references.

Playing around with this code is the only chance I have of understanding it!

Examples

See the examples/ folder.

Plan

• Tweak stuff and see what happens (get faster?)
  • Changed the representation of degeneracies.
  • Changed the free abelian group implementation to use Data.Map.Lazy, and it did get a bit faster on my computer.
  • Faster smith normal form (I think it's already pretty fast since we want the multiplier matrices, if we don't need those we can get much faster)
• Write a series of accessible articles about it (WIP)
• Dependent types?
• Take on some unfinished plans of the original repo
• Try to modularize stuff
  • stop exposing Combination internals

References

• Discrete Vector Fields and Fundamental Algebraic Topology. Book covering a lot of effective homology stuff, in particular DVFs.
• Francis Sergeraert's Talks.
• Constructive Homological Algebra and Applications.