Are you confusing me with someone else? When I asked it GPT computed the homology from the CW decomposition of RP^2 with three cells. Which is a very simple exercise.
That's ok. It seems like LLMs know all about simplicial complexes and homology so I'll spend my time on more fruitful endeavors but thanks for the advice.
To be fair, it's not a simplicial complex, but simplicial and cellular homology coincide on triangulatable spaces like RP^2 so I gave it the benefit of the doubt =) algebraic topology is a pretty fun field regardless of how much a language model knows about it IMO.