It would be good to have this in SymPy but unfortunately it is not
implemented yet.

It is also not available in python-flint or Flint either.

On Fri, 16 Aug 2024 at 15:38, Chris Smith <[email protected]> wrote:
>
> As far as I can tell, these matrices are not computed implicitly. You would 
> have to copy the appropriate actions onto an augmented identity matrix to see 
> what has happened (https://www.youtube.com/watch?v=UhyzLfiO4Ow).
>
> /c
>
> On Thursday, August 15, 2024 at 10:51:31 AM UTC-5 [email protected] wrote:
>>
>> Hi,
>>
>> I need to perform a Smith decomposition on (a priori not square) matrices to 
>> find a certain change of basis related to the Smith invariants.
>>
>> The Smith normal form is already implemented in SymPy in 
>> `sympy.matrices.normalforms`, but it returns only the Smith normal form, not 
>> its decomposition itself.
>>
>> In general, the Smith decomposition of a matrix A is defined in terms of 
>> three matrices V, D, W so that
>>
>> A = V * D * W
>>
>> where V,W are both square, invertible, and integer-valued matrices. Is there 
>> any way of obtaining those matrices without reimplementing the algorithm 
>> myself? I assume that these matrices are computed at least implicitely, but 
>> I could not find a way of returning them.
>>
>> thanks!
>
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