Hi Santanu,
With very high precision it goes through:
#+begin_src jupyter-python :kernel sagemath
A = random_matrix(ZZ, 10, 10, x=-2^500, y=2^500)
A.echelonize() # make it interesting by turning into HNF
from fpylll import FPLLL, IntegerMatrix, GSO, LLL
B = IntegerMatrix.from_matrix(A)
FPLLL.set_precision(20000) # 20000 bits of precision!
M = GSO.Mat(B, float_type="mpfr")
M.update_gso()
L = LLL.Reduction(M)
L.size_reduction()
C = B.to_matrix(matrix(ZZ, 10, 10)) # back to Sage's format
#+end_src
HNF is pretty bad for precision, so it’s an extreme example.
Cheers,
Martin
Santanu Sarkar <sarkar.santanu....@gmail.com> writes:
> Hi Martin,
> Thanks a lot. For entries upto 500 bits, it works fine.
> But for large entries, I am getting error.
> A = random_matrix(ZZ, 10, 10, x=-2^550, y=2^550)
> File "abc.sage.py", line 28, in <module>
> L.size_reduction()
> File "src/fpylll/fplll/lll.pyx", line 379, in
> fpylll.fplll.lll.LLLReduction.size_reduction
> fpylll.util.ReductionError: b'success'
>
> Kind regards,
> Santanu
>
>
> On Wed, 17 Mar 2021 at 15:47, 'Martin R. Albrecht' via sage-support <
> sage-support@googlegroups.com> wrote:
>
>> Hi there,
>>
>> You can do it by calling down to FPyLLL which (together with NTL) powers
>> lattice reduction in Sage. Here’s an example:
>>
>> #+begin_src jupyter-python :kernel sagemath
>> A = random_matrix(ZZ, 10, 10, x=-1, y=2)
>> A.echelonize() # make it interesting by turning into HNF
>> print("# Input")
>> print(A)
>> print()
>>
>> from fpylll import IntegerMatrix, GSO, LLL
>> B = IntegerMatrix.from_matrix(A)
>> M = GSO.Mat(B)
>> M.update_gso()
>> L = LLL.Reduction(M)
>> L.size_reduction()
>> C = B.to_matrix(matrix(ZZ, 10, 10)) # back to Sage's format
>>
>> print("# Output")
>> print(C)
>> print()
>> #+end_src
>>
>> #+RESULTS:
>> #+begin_example
>> # Input
>> [ 1 0 0 0 0 0 0 0 0 41]
>> [ 0 1 0 0 0 0 0 0 0 34]
>> [ 0 0 1 0 0 0 0 0 1 27]
>> [ 0 0 0 1 0 0 0 0 1 96]
>> [ 0 0 0 0 1 0 0 0 0 38]
>> [ 0 0 0 0 0 1 0 0 1 78]
>> [ 0 0 0 0 0 0 1 0 1 1]
>> [ 0 0 0 0 0 0 0 1 1 91]
>> [ 0 0 0 0 0 0 0 0 2 69]
>> [ 0 0 0 0 0 0 0 0 0 100]
>>
>> # Output
>> [ 1 0 0 0 0 0 0 0 0 41]
>> [ -1 1 0 0 0 0 0 0 0 -7]
>> [ -1 0 1 0 0 0 0 0 1 -14]
>> [ -1 -1 -1 1 0 0 0 0 0 -6]
>> [ -1 0 0 0 1 0 0 0 0 -3]
>> [ 0 0 0 -1 0 1 0 0 0 -18]
>> [ 0 0 0 0 0 0 1 0 1 1]
>> [ 0 0 0 -1 0 0 0 1 0 -5]
>> [ 1 0 0 -1 0 0 0 0 1 14]
>> [ 0 0 0 -1 0 0 0 0 -1 4]
>> #+end_example
>>
>>
>> Cheers,
>> Martin
>>
>> Santanu Sarkar <sarkar.santanu....@gmail.com> writes:
>> > Dear all,
>> > In Sagemath, is it possible to change a basis
>> > of a lattice which is size reduced? That is my interest is only on
>> > 1st condition of LLL basis.
>> >
>> >
>> > Kind regards,
>> > Santanu
>>
>>
>> --
>>
>> _pgp: https://keybase.io/martinralbrecht
>> _www: https://malb.io
>>
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>>
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