Re: [sage-support] Re: Lattice reduction over polynomial lattice

[Santanu Sarkar]

Dear all,
   Thanks a lot for your kind help.

On 22 February 2017 at 13:49, Johan S. R. Nielsen 
wrote:

> Indeed, Sage has row_reduced_form for a polynomial matrix. The row reduced
> form is sufficient to find a vector in the row space which has minimal
> degree.
>
> The method used to be called weak_popov_form, but that form is slightly
> stronger and the algorithm does not compute it. Hence the warning.
>
> The current implementation is very slow. The next beta release of Sage
> should feature #21024 which introduces an implementation of the
> Mulders-Storjohann algorithm, which computes the weak Popov form, and does
> so much faster than the current row_reduced_form (hence, row_reduced_form
> will, in the future, actually call weak_popov_form). If you are impatient,
> you can checkout that ticket and recompile Sage to get the new
> implementation right away.
>
> Best,
> Johan
>
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Re: [sage-support] Re: Lattice reduction over polynomial lattice

[Johan S. R. Nielsen]

Indeed, Sage has row_reduced_form for a polynomial matrix. The row reduced 
form is sufficient to find a vector in the row space which has minimal 
degree.

The method used to be called weak_popov_form, but that form is slightly 
stronger and the algorithm does not compute it. Hence the warning.

The current implementation is very slow. The next beta release of Sage 
should feature #21024 which introduces an implementation of the 
Mulders-Storjohann algorithm, which computes the weak Popov form, and does 
so much faster than the current row_reduced_form (hence, row_reduced_form 
will, in the future, actually call weak_popov_form). If you are impatient, 
you can checkout that ticket and recompile Sage to get the new 
implementation right away.

Best,
Johan

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Re: [sage-support] Re: Lattice reduction over polynomial lattice

[John Cremona]

On 21 February 2017 at 08:38, 'Martin R. Albrecht' via sage-support
 wrote:
> Hi,
>
> I don’t think this is implemented in Sage.

I think it is: searching for weak_popov_form finds results in
matrix/matrix2.pyx with a method M.weak_popov_form(), though
admittedly the docstring for that says

".. WARNING:: This function currently does **not** compute the weak
Popov form of a matrix, but rather a row reduced form (which is a
slightly weaker requirement). See :meth:`row_reduced_form`."

John

>
> Cheers,
> Martin
>
> Santanu Sarkar writes:
>>
>> Dear all,
>>   I am searching lattice reduction for polynomial matrices in   Sage.
>> Kindly help me.
>>
>> T. Mulders and A. Storjohann. On lattice reduction for polynomial
>> matrices.
>> Journal of Symbolic Computation, 35(4):377 – 401, 2003
>>
>>
>>
>> On 20 February 2017 at 21:19, Santanu Sarkar
>> 
>> wrote:
>>
>>> Dear all,
>>>I have polynomial lattice over a finite field. So eachcomponent of
>>> the
>>> vectors v_1, v_2, v_3 are polynomials over a finite field say F_11. Hence
>>> v_1=(f_1(x), f_2(x), f_3(x)),  v_2=(g_1(x), g_2(x), g_3(x)) and
>>> v_3=(h_1(x), h_2(x), h_3(x)). Here norm is the maximum degree of each
>>>  component. Does there exist LLL algorithm for this lattice in  Sage?
>>>
>>>
>>>
>
>
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>
>
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Re: [sage-support] Re: Lattice reduction over polynomial lattice

['Martin R. Albrecht' via sage-support]

Hi,

I don’t think this is implemented in Sage.

Cheers,
Martin

Santanu Sarkar writes:

Dear all,
  I am searching lattice reduction for polynomial matrices in 
  Sage.

Kindly help me.

T. Mulders and A. Storjohann. On lattice reduction for 
polynomial matrices.

Journal of Symbolic Computation, 35(4):377 – 401, 2003



On 20 February 2017 at 21:19, Santanu Sarkar 


wrote:


Dear all,
   I have polynomial lattice over a finite field. So each 
   component of the
vectors v_1, v_2, v_3 are polynomials over a finite field say 
F_11. Hence

v_1=(f_1(x), f_2(x), f_3(x)),  v_2=(g_1(x), g_2(x), g_3(x)) and
v_3=(h_1(x), h_2(x), h_3(x)). Here norm is the maximum degree 
of each
 component. Does there exist LLL algorithm for this lattice in 
 Sage?







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[sage-support] Re: Lattice reduction over polynomial lattice

[Santanu Sarkar]

Dear all,
  I am searching lattice reduction for polynomial matrices in Sage.
Kindly help me.

T. Mulders and A. Storjohann. On lattice reduction for polynomial matrices.
Journal of Symbolic Computation, 35(4):377 – 401, 2003



On 20 February 2017 at 21:19, Santanu Sarkar 
wrote:

> Dear all,
>I have polynomial lattice over a finite field. So each component of the
> vectors v_1, v_2, v_3 are polynomials over a finite field say F_11. Hence
> v_1=(f_1(x), f_2(x), f_3(x)),  v_2=(g_1(x), g_2(x), g_3(x)) and
> v_3=(h_1(x), h_2(x), h_3(x)). Here norm is the maximum degree of each
>  component. Does there exist LLL algorithm for this lattice in Sage?
>
>
>

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