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 <
[email protected]> 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 <[email protected]> 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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