It looks like your problem is with the cup_product method for cochains in 
sage/homology/chains.py. Is that right? As far as I can tell, that method 
is not used anywhere else in the Sage library. In any case, feel free to 
create a pull request to fix and improve it.

On Saturday, June 17, 2023 at 9:28:05 PM UTC-7 Ezra Akresh wrote:

> We have provided an example inside this Cocalc notebook: 
> https://cocalc.com/share/public_paths/9a10e579b445d6b489fe88dd6ad4e4375d4f5fba
>
> On Friday, June 16, 2023 at 5:50:24 PM UTC-5 John H Palmieri wrote:
>
>> Can you please provide an example where things do not work? Are you 
>> talking about manifolds or cell complexes or some other classes?
>>
>> On Friday, June 16, 2023 at 1:14:32 PM UTC-7 Ezra Akresh wrote:
>>
>>> In a recent project, my team and I developed functions for the cup 
>>> product and wedge product of cochains utilizing the functionality of 
>>> various Sage classes. We noticed that the current cup product function only 
>>> works for 0-simplices because the orientations do not match. We were 
>>> wondering if it would be helpful if we submitted our code to be added to 
>>> the library.
>>>
>>

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