Sort #34892 doctest output vectors to fix randomness

[grhkm21]

Reported at #38492 (comment) by @jhpalmieri and @GMS103. Added an extra test because why not.

[grhkm21]

By the way, is this intended?

sage: L = IntegralLattice(Matrix(QQ, [[1000, 0], [0, 1]]))
....: L.0.norm()
1

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[yyyyx4]

By the way, is this intended?

sage: L = IntegralLattice(Matrix(QQ, [[1000, 0], [0, 1]]))
....: L.0.norm()
1

This is because the given matrix is interpreted as the Gram matrix of the lattice: The basis vectors are always (1,0) and (0,1), and their pairwise inner products are specified by the matrix entries. To compute the norm, you'd have to do L.0 * L.gram_matrix() * L.0, I suppose. Perhaps there's a shortcut.

[yyyyx4]

Indeed, presumably this is not optimal. The parent of this vector is set to the correct lattice, but the .norm() method behaves the same as for the standard Euclidean lattice regardless of the actual parent. This seems like something worth fixing.

[grhkm21]

Yeah that's what I was thinking, v.parent() gives the lattice

[yyyyx4]

Your patch (thanks!) will fix the doctest failures, but it also leaves us with tests which basically only check that the method doesn't crash. I'm not sure how to best resolve this. Practically, perhaps we can get away with a sorted() and deal with it properly if/when it breaks again on some other setup?

[jhpalmieri]

If you don't want to use sorted, you could check membership of some entries. Do you know whether (3, 2, -2, -4) will alway be among the first 20 entries, for example? I don't know the code at all. Are there any meaningful tests you can run on the output?

By the way, is this intended?

sage: L = IntegralLattice(Matrix(QQ, [[1000, 0], [0, 1]]))
....: L.0.norm()
1

This is because the given matrix is interpreted as the Gram matrix of the lattice: The basis vectors are always (1,0) and (0,1), and their pairwise inner products are specified by the matrix entries. To compute the norm, you'd have to do L.0 * L.gram_matrix() * L.0, I suppose. Perhaps there's a shortcut.

Why does the second line start with ....: instead of sage:?

[grhkm21]

By the way, is this intended?

sage: L = IntegralLattice(Matrix(QQ, [[1000, 0], [0, 1]]))
....: L.0.norm()
1

This is because the given matrix is interpreted as the Gram matrix of the lattice: The basis vectors are always (1,0) and (0,1), and their pairwise inner products are specified by the matrix entries. To compute the norm, you'd have to do L.0 * L.gram_matrix() * L.0, I suppose. Perhaps there's a shortcut.

Why does the second line start with ....: instead of sage:?

Because I copied this from my REPL and it's not a doctest.

[grhkm21]

For now, I will add change it to a sorted call, and if it breaks in any other architecture then too bad we can figure out from there, perhaps testing membership of a short vector as suggested.

[jhpalmieri]

By the way, is this intended?

sage: L = IntegralLattice(Matrix(QQ, [[1000, 0], [0, 1]]))
....: L.0.norm()
1

This is because the given matrix is interpreted as the Gram matrix of the lattice: The basis vectors are always (1,0) and (0,1), and their pairwise inner products are specified by the matrix entries. To compute the norm, you'd have to do L.0 * L.gram_matrix() * L.0, I suppose. Perhaps there's a shortcut.

Why does the second line start with ....: instead of sage:?

Because I copied this from my REPL and it's not a doctest.

Sorry, I thought you were quoting from the code.

[yyyyx4]

From CI:

sage -t --random-seed=247508190430796794056562297888034052375 src/sage/modules/free_quadratic_module_integer_symmetric.py
**********************************************************************
File "src/sage/modules/free_quadratic_module_integer_symmetric.py", line 1604, in sage.modules.free_quadratic_module_integer_symmetric.FreeQuadraticModule_integer_symmetric.enumerate_short_vectors
Failed example:
    sorted(vecs, key=lambda v: L(v).inner_product(L(v)))
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)]
**********************************************************************
1 item had failures:
   1 of  11 in sage.modules.free_quadratic_module_integer_symmetric.FreeQuadraticModule_integer_symmetric.enumerate_short_vectors
    [248 tests, 1 failure, 1.97 s]

[grhkm21]

I'll sort it by the norm and the original vector then

[yyyyx4]

Looks good, thanks!