SymPy Wedge Product Question

[Giovanni Sutanto]

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

[Giovanni Sutanto]

Can anyone help me with this, please?

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[Shishir Kushwaha]

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

[Samith Kavishke]

I could not find the problem that you are stating in the video lecture

[Tomás Silva]

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

[Carsten]

HI,

 

I almost do not follow this mailing list since a while but I just stumbled on this thread.

 

Several years ago I had some trouble in learning to calculate with differential forms and and back then the sympy support was not sufficient for me (dont know about the current state). Thus I implemented my own package (on top of sympy): "pycartan" [1]. As it is typical for research code, it served its purpose (doing some calculations related to control theory), and after this it lays around without attention (and with almost no docs).

 

Maybe it is still useful for some people. Unfortunately the "best" documentation available for this package is the collection of unittests [2].

 

If there is serious interest in this package I might be motivated to put some time/effort in it. For reaching out I suggest to contact me via [3].

 

[1] https://github.com/TUD-RST/pycartan/

[2] https://github.com/TUD-RST/pycartan/blob/master/pycartan/tests/test_pycartan.py

[3] https://wwwpub.zih.tu-dresden.de/~knoll/en/

 

Best,

Carsten

 

Gesendet: Dienstag, 26. März 2024 um 19:37 Uhr
Von: "Tomás Silva" <tomass...@gmail.com>
An: "sympy" <sy...@googlegroups.com>
Betreff: Re: [sympy] SymPy Wedge Product Question

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[Oscar Benjamin]

I don't know enough about this topic bur there is also galgebra which
is a library that depends on SymPy:
https://galgebra.readthedocs.io/en/latest/tutorials/algebra.html

Does that do what is needed?

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