On Sun, Nov 5, 2023 at 8:22 PM T-Rex <[email protected]> wrote:
>
> Thanks @oscar!  I didn't think I would get a reply from the blog's owner :-)
>
> Re setting of the environment variable SYMPY_GROUND_TYPES=flint:   (1) Would 
> that be in conflict with other parts of sympy/numpy/scipy?  (2) After it is 
> set to flint, is there a way to turn it back to the default?  I can see 
> scenarios where I need to bench mark various options, and it would be really 
> nice to be able to change the flag as I go along in my jupyter notebook, as 
> oppsed to restarting the program from scratch.

NumPy, SciPy, and other libraries do not use flint, only SymPy. Other
parts of SymPy do use flint, but it's all completely transparent. The
only difference is the output.

Right now, there's no way to change the option after SymPy is
imported, which is why it is set as an environment variable. So if you
want to test different things, you'll have to restart the notebook.

>
> Taboo question:  When might Sympy 1.13 be coming out?  I am know that such 
> questions are taboo, but my project has various stages/steps, and depending 
> on the availability of 1.1.3 I might want to work on the LLL-parts first 
> while waiting for 1.1.3 to become available.

There's no reason to not ask this question. And
anyways, Oscar mentioned to me that he wants to make a release soon so
(hopefully) it should be out before the end of the year, if not month.


Aaron Meurer

>
> MANY THANKS for your help and advice.
>
> On Sunday, November 5, 2023 at 10:23:54 AM UTC-5 Oscar wrote:
>>
>> On Sun, 5 Nov 2023 at 15:04, T-Rex <[email protected]> wrote:
>> >
>> > According to https://oscarbenjamin.github.io/blog/czi/post2.html sympy now 
>> > has LLL, but when I consulted the sympy documentation I could not find 
>> > actual commands that produces an LLL-reduced basis.
>>
>> SymPy has a new matrix type called DomainMatrix for which the
>> LLL-algorithm is implemented. Ideally the LLL-algorithm would be
>> exposed through the ordinary Matrix type but it is not. The
>> DomainMatrix.lll method is documented here:
>> https://docs.sympy.org/latest/modules/polys/domainmatrix.html#sympy.polys.matrices.domainmatrix.DomainMatrix.lll
>>
>> Starting with an ordinary Matrix M the command to get an LLL-reduced
>> basis in SymPy 1.12 is:
>>
>> In [1]: from sympy.polys.matrices import DomainMatrix
>>
>> In [2]: M = randMatrix(5) # make a random 5x5 Matrix
>>
>> In [3]: M
>> Out[3]:
>> ⎡74 3 71 3 27⎤
>> ⎢ ⎥
>> ⎢86 74 14 89 26⎥
>> ⎢ ⎥
>> ⎢58 2 14 54 17⎥
>> ⎢ ⎥
>> ⎢35 53 17 58 31⎥
>> ⎢ ⎥
>> ⎣72 83 33 61 85⎦
>>
>> In [4]: dM = DomainMatrix.from_Matrix(M) # Convert to DomainMatrix
>>
>> In [5]: dM.lll().to_Matrix() # Compute LLL-basis and convert back to Matrix
>> Out[5]:
>> ⎡ 7 -19 17 23 22⎤
>> ⎢ ⎥
>> ⎢51 21 -3 31 -5⎥
>> ⎢ ⎥
>> ⎢-23 51 3 4 14⎥
>> ⎢ ⎥
>> ⎢53 -2 -4 -24 18⎥
>> ⎢ ⎥
>> ⎣-14 -24 -58 -4 13⎦
>>
>> In SymPy 1.13 there will be a to_DM() method to make this a bit easier
>> so it is just:
>>
>> M.to_DM().lll().to_Matrix()
>>
>> Ideally we should add an .lll() method directly to Matrix to do this
>> without users needing to perform the conversion explicitly.
>>
>> Also SymPy 1.13 will be able to use python-flint for this. If you have
>> python-flint installed (pip install python-flint) and then set the
>> environment variable SYMPY_GROUND_TYPES=flint then the
>> DomainMatrix.lll method will automatically use Flint which is a lot
>> faster for this operation.
>>
>> --
>> Oscar
>
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