Hi Martin,
Thank you so much for your kind help. It works!
Kind regards,
Santanu
On Mon, 22 Mar 2021 at 19:49, 'Martin R. Albrecht' via sage-support <
sage-support@googlegroups.com> wrote:
> 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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> >> .
> >>
>
>
> --
>
> _pgp: https://keybase.io/martinralbrecht
> _www: https://malb.io
>
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