I'm facing a similar issue. I think SymPy is not treating correctly the sum 
of (co)vectors.
In this question I exemplify my issue 
https://stackoverflow.com/questions/78226587/sympy-manipulation-of-wedge-products
Could anyone shed a light on how to properly sum differential forms?
Thanks in advance,
Tomás
On Monday, March 25, 2024 at 12:06:45 AM UTC Samith Kavishke wrote:

> I could not find the problem that you are stating in the video lecture
>
> On Thursday, March 21, 2024 at 9:21:52 PM UTC+5:30 [email protected] 
> wrote:
>
>> Can you please specify what purpose you are using it for. I do not know 
>> its use yet but would like to get back to you after researching on its 
>> usage .
>>
>> _ _ _ _ _ _ _  
>> Shishir
>>
>> On Tuesday 19 March 2024 at 22:54:42 UTC+5:30 [email protected] 
>> wrote:
>>
>>> Can anyone help me with this, please?
>>>
>>> On Mon, Mar 11, 2024, 06:06 Giovanni Sutanto <[email protected]> 
>>> wrote:
>>>
>>>> Hi SymPy Community,
>>>>
>>>> I am now trying to understand what happens when I perform WedgeProduct 
>>>> operations on SymPy.
>>>>
>>>> So, I understand how to use the SymPy's Wedge Product to some extent, 
>>>> i.e. I was the one who responded to the question on Stack Overflow: 
>>>> https://stackoverflow.com/questions/76981303/computing-the-wedge-product
>>>>
>>>> However, when I have:
>>>> '''
>>>> my_matrix = Matrix([[2, 0, 5], [0, 7, 0]])
>>>> r2_r_oneforms = R2_r.base_oneforms()
>>>> r2_r_vectors = R2_r.base_vectors()
>>>>
>>>> cols = [None] * 3
>>>> for j in range(3):
>>>>   cols[j] = 0
>>>>   for i in range(2):
>>>>     cols[j] += my_matrix[i, j] * r2_r_vectors[i]
>>>>
>>>> cols_wedge_product = WedgeProduct(*r2_r_oneforms)(*cols)
>>>> print('cols_wedge_product = ', cols_wedge_product)
>>>> '''
>>>> What I get is:
>>>> cols_wedge_product = -42
>>>>
>>>> Where does the number -42 come from?
>>>>
>>>> On the other hand, if:
>>>> my_matrix = Matrix([[1, 0, 1], [0, 1, 0]])
>>>> I get:
>>>> cols_wedge_product = 0
>>>> What computation leads to 0 here?
>>>>
>>>> Can any of you please explain it, e.g. in the terms of the example in 
>>>> the video lecture https://youtu.be/xRf9-hdxB0w?feature=shared&t=2961 ?
>>>>
>>>> Thanks so much in advance for your time!
>>>>
>>>>
>>>> Best Regards,
>>>>
>>>> Giovanni
>>>>
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>>>> .
>>>>
>>>

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