[soist]

You made an incorrect assessment of a basic calculation in algebraic topology and claimed that it was correct. You didn't even look at what it was computing and simply looked at the final answer which lined up with the answer on Wikipedia. Simplicial calculations for projective planes are not simple. The usual calculations are done with cellular decomposition and that's why the LLM gives the wrong answer, the actual answer is not in the dataset and requires reasoning.

[bubblyworld]

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.

I recommend that you give it a try.

[soist]

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.

[bubblyworld]

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.

[soist]

Do you have a reference for this equivalency?

[bubblyworld]

It's in Hatcher iirc