tentative of random subset for random matrix

[fchapoton]

trying to do something for #35664 ; not yet good

📝 Checklist

• The title is concise, informative, and self-explanatory.
• I have linked a relevant issue or discussion.
• I have created tests covering the changes.
• I have updated the documentation accordingly.

[dcoudert]

It should be better to shuffle the list available and then to return the first k items (or complement n - k items).

Alternatively, if you prefer successive calls to randint, then instead of calling available.pop(index), you can simply do available[index] = available[-1].

[fchapoton]

bonne idée, merci. Mais je soupconne qu'il reste un probleme ailleurs, dans la procedure qui utilise la nouvelle fonction

[dcoudert]

Here you use uniform distribution but the original method used a beta distribution with parameters [1.6, 4.3]. ..

[fchapoton]

y a un bug avec l'usage de "enumerate"

[dcoudert]

Je ne vois vraiment pas pourquoi. C'est vraiment lié à ça ?

[github-actions]

Documentation preview for this PR (built with commit 1d36521; changes) is ready! 🎉

[fchapoton]

faut encore attendre la fin des tests

[dcoudert]

Something goes wrong

sage -t --long --random-seed=286735480429121101562228604801325644303 sage/modular/local_comp/liftings.py
**********************************************************************
File "sage/modular/local_comp/liftings.py", line 244, in sage.modular.local_comp.liftings.lift_for_SL
Failed example:
    for _ in range(100):
        d = randint(0, 10)
        p = choice([2,3,5,7,11])
        M = random_matrix(Zmod(p), d, algorithm='unimodular')
        assert lift_for_SL(M).det() == 1
Exception raised:
    Traceback (most recent call last):
      File "/sage/src/sage/doctest/forker.py", line 709, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File "/sage/src/sage/doctest/forker.py", line 1144, in compile_and_execute
        exec(compiled, globs)
      File "<doctest sage.modular.local_comp.liftings.lift_for_SL[19]>", line 4, in <module>
        M = random_matrix(Zmod(p), d, algorithm='unimodular')
            ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
      File "/sage/src/sage/matrix/special.py", line 666, in random_matrix
        return random_unimodular_matrix(parent, *args, **kwds)
               ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
      File "/sage/src/sage/matrix/special.py", line 3037, in random_unimodular_matrix
        return random_matrix(ring, size, algorithm='echelonizable', rank=size)
               ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
      File "/sage/src/sage/matrix/special.py", line 660, in random_matrix
        return random_echelonizable_matrix(parent, *args, **kwds)
               ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
      File "/sage/src/sage/matrix/special.py", line 2713, in random_echelonizable_matrix
        matrix = random_rref_matrix(parent, rank)
                 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
      File "/sage/src/sage/matrix/special.py", line 2569, in random_rref_matrix
        for rest_non_pivot_column in range(pivots[num_pivots-1]+1,num_col):
                                           ~~~~~~^^^^^^^^^^^^^^
    IndexError: list index out of range

[fchapoton]

this is a problem in size 0 x 0

[fchapoton]

Ca devrait etre ok maintenant.

[dcoudert]

to be on the safe side, you may add a test for num_col > 1 ?

[fchapoton]

bah, ca me parait pas indispensable

[dcoudert]

Parfait.

LGTM.