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I hope this is the right place to ask the following question, if not please guide me towards the correct forum...

I want to show that two certain finite simplicial sets are not weakly homotopy equivalent. They are too large to prove it by hand, so I would like to write a computer program to check this for me. Problem is: I never worked with any CAS (I have a background in computer science though).

Before I write a math-engine from scratch, which existent language do you suggest to use? I will need the following features:

  • Permutation groups
  • Powers of a finite set $X^{\times n} = X \times ... \times X$
  • $d$-skeleton of a degreewise finite simplicial set
  • Unions of images of morphisms of simplicial sets
  • rational/integral homology of a simplicial set, fundamental group, rational/integral homotopy type in decreasing order of likeliness.

I just tried to do my first steps in SAGE, but already ran into syntax problems. So I really want to make sure I choose the correct language for my task, before spending much time in the rabbit hole of familiarizing myself with a new language.

Thank you for your time.

Jonas Linssen
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  • I'm pretty sure this is uncomputable in full generality (essentially because it is uncomputable whether two finitely presented groups are isomorphic, which can be the fundamental groups of your simplicial sets). – Eric Wofsey Nov 08 '23 at 16:34
  • That is correct. I don't really expect to be able to compute everything about my finite simplicial sets. For example the homotopy groups of spheres are complicated. My point is that I want to learn a language, which can do as much as possible. Maybe the fundamental groups are trivial? Maybe they are finite? The point is: I don't know. – Jonas Linssen Nov 08 '23 at 16:54

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