Very small edits to _fplll_enumerate()

[GiacomoPope]

Very small edits which were noticed while reviewing #38492 but missed before merge. Could marginally help performance for larger matrices by using fpylll class methods.

[yyyyx4]

**********************************************************************
File "src/sage/modules/free_quadratic_module_integer_symmetric.py", line 1544, in sage.modules.free_quadratic_module_integer_symmetric.FreeQuadraticModule_integer_symmetric._fplll_enumerate
Failed example:
    [next(close) for _ in range(10)]
Expected:
    [(1, 0, 6, -9), (1, -1, 5, -9), (2, 0, 6, -9), (1, 0, 5, -9), (1, -1, 5, -10),
     (2, 1, 6, -9), (1, 0, 5, -10), (2, 0, 5, -9), (1, 0, 6, -8), (1, -1, 6, -9)]
Got:
    [(-12, -3, 15, -20),
     (-12, -2, 16, -19),
     (-12, -2, 16, -20),
     (-12, -3, 16, -19),
     (-12, -3, 16, -20),
     (-13, -3, 15, -20),
     (-12, -2, 17, -19),
     (-11, -2, 16, -19),
     (-11, -2, 16, -20),
     (-13, -4, 15, -20)]
**********************************************************************
File "src/sage/modules/free_quadratic_module_integer_symmetric.py", line 1621, in sage.modules.free_quadratic_module_integer_symmetric.FreeQuadraticModule_integer_symmetric.enumerate_close_vectors
Failed example:
    [next(close) for _ in range(10)]
Expected:
    [(1, -18, 123, 148), (2, -19, 124, 148), (0, -17, 122, 148), (3, -20, 125, 148), (-1, -16, 121, 148),
     (-2, -20, 125, 152), (-2, -23, 123, 148), (4, -21, 126, 148), (-3, -22, 122, 148), (-3, -19, 124, 152)]
Got:
    [(597, 2079, 2106, 3216),
     (598, 2078, 2107, 3216),
     (598, 2081, 2109, 3220),
     (597, 2082, 2108, 3220),
     (596, 2080, 2105, 3216),
     (599, 2077, 2108, 3216),
     (599, 2080, 2110, 3220),
     (601, 2083, 2107, 3216),
     (602, 2082, 2108, 3216),
     (596, 2083, 2107, 3220)]
**********************************************************************

[GiacomoPope]

Oh I'm stupid. I shouldn't have made this change.

Only thing I'd like to try is make gso.babai(target) work, but I can only get this working with gso.babai(target, gso=True) and gso.to_canonical() errors...

Will close this unless you think making gso.babai work for the closest vector is interesting @yyyyx4

[yyyyx4]

There's already a reference to Babai in sage.modules.free_module_integer.FreeModule_submodule_with_basis_integer. I guess this one would be more general? Not sure.

[GiacomoPope]

sage: LL = IntegerLattice(gram)
sage: LL.babai(t)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In[32], line 1
----> 1 LL.babai(t)

File /private/var/tmp/sage-10.4-current/local/var/lib/sage/venv-python3.12.4/lib/python3.12/site-packages/sage/modules/free_module_integer.py:875, in FreeModule_submodule_with_basis_integer.approximate_closest_vector(self, t, delta, *args, **kwargs)
    873 b = t
    874 for i in reversed(range(G.nrows())):
--> 875     b -= B[i] * ((b * G[i]) / (G[i] * G[i])).round("even")
    876 return (t - b).change_ring(ZZ)

TypeError: round() takes exactly 0 positional arguments (1 given)

haha another error from types, I guess?

I'm sure the babai should just work but who knows if it's even any faster as we'd have to make the integer lattice here which is annoying. I was hoping to just keep everything within the MatGSO object to avoid having to call "solve" etc to get the closest vector