expose fplll enumeration routines in IntegralLattice

[yyyyx4]

This is useful for situations where we'd like to iterate over short-ish or close-ish vectors without necessarily requiring the shortest/closest solution, and without knowing a priori how many vectors we need to try. Among other things, it shows up in some algorithms for solving (quaternion) norm equations.

[yyyyx4]

(Cc: @GiacomoPope)

[GiacomoPope]

There's the IntegerMatrix.from_matrix() method, could you not do

gmat = fpyll.IntegerMatrix.from_matrix(gram)
gso = fpylll.GSO.Mat(gmat, gram=True)

[GiacomoPope]

Some very small comments which could be ignored. Thank you for adding this to Sage, I should have done it ages ago.

[GiacomoPope]

There's also a to_matrix() method, so something like:

Mu = 1 + matrix(gso.to_matrix())

might work

[grhkm21]

This doesn't work for me https://sagecell.sagemath.org/?q=yduvls (10.3)

[GiacomoPope]

oh for the MatGSO type it's the property .gso.G

Mu = 1 + matrix(gso.G)

https://sagecell.sagemath.org/?q=qifgtc

[grhkm21]

Ahha yes. I think this should be added before it's merged, seems quicker :-)

[GiacomoPope]

Suggested change

	for length,comb in combs:
	for length, comb in combs:

[github-actions]

Documentation preview for this PR (built with commit f2c4e22; changes) is ready! 🎉
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[yyyyx4]

Thanks for the reviews! I think this is now already in the process of getting merged. Perhaps your suggested changes would best be done as a (small) follow-up?

[GiacomoPope]

Sure I'll make a PR for those two. It's essentially meaningless tho!

[jhpalmieri]

This seems to be causing doctest failures for me on OS X 14.6:

sage -t --random-seed=64986521010388899927548704615315435332 src/sage/modules/free_quadratic_module_integer_symmetric.py
**********************************************************************
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:
    [(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),
     (1, 0, 6, -8),
     (2, 0, 5, -9),
     (1, -1, 6, -9)]
**********************************************************************
File "src/sage/modules/free_quadratic_module_integer_symmetric.py", line 1601, in sage.modules.free_quadratic_module_integer_symmetric.FreeQuadraticModule_integer_symmetric.enumerate_short_vectors
Failed example:
    [next(short) for _ in range(20)]
Expected:
    [(1, -1, 1, 0), (2, -2, 2, 0), (3, -3, 3, 0), (0, 3, 2, 4), (1, 2, 3, 4),
     (4, 4, 1, 0), (3, 2, -2, -4), (3, 5, 0, 0), (4, 1, -1, -4), (-1, 4, 1, 4),
     (2, 1, 4, 4), (5, 3, 2, 0), (2, 3, -3, -4), (2, 6, -1, 0), (5, 0, 0, -4),
     (-2, 5, 0, 4), (4, -4, 4, 0), (6, 2, 3, 0), (1, 4, -4, -4), (3, 0, 5, 4)]
Got:
    [(1, -1, 1, 0),
     (2, -2, 2, 0),
     (3, -3, 3, 0),
     (0, 3, 2, 4),
     (1, 2, 3, 4),
     (4, 4, 1, 0),
     (3, 2, -2, -4),
     (3, 5, 0, 0),
     (4, 1, -1, -4),
     (-1, 4, 1, 4),
     (2, 1, 4, 4),
     (5, 3, 2, 0),
     (2, 3, -3, -4),
     (5, 0, 0, -4),
     (2, 6, -1, 0),
     (-2, 5, 0, 4),
     (4, -4, 4, 0),
     (6, 2, 3, 0),
     (1, 4, -4, -4),
     (3, 0, 5, 4)]
**********************************************************************
2 items had failures:
   1 of   7 in sage.modules.free_quadratic_module_integer_symmetric.FreeQuadraticModule_integer_symmetric._fplll_enumerate
   1 of   4 in sage.modules.free_quadratic_module_integer_symmetric.FreeQuadraticModule_integer_symmetric.enumerate_short_vectors
    [238 tests, 2 failures, 3.93 s]

Can you please open up a follow-up to fix this?

[GMS103]

FWIW, here is what I get on Apple Silicon for make ptestlong (SageMath 10.5.beta2).

macOS 12.7.6: All tests passed!
macOS 13.6.9: This failure (among others).
macOS 14.6.1: This failure (among others).

[videlec]

Is the enumeration order relevant? The only difference in the output is the transposition of the two vectors (5, 0, 0, -4) and (2, 6, -1, 0).

[grhkm21]

Yeah I don't think the output order is/should be deterministic for any reason. I can make a PR and add a sorted.

[grhkm21]

Actually, since the norm of the vectors aren't necessarily non-decreasing, the first n outputs of the iterator might not be the same. So I think it's best to mark it #random.