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.