Allow several implementations in random matrix

[SimonKing]

With the optional meataxe package installed, I get

sage: K.<a>=FiniteField(3^2)
sage: MS = MatrixSpace(K, 2, 5, implementation="generic")
sage: type(MS.random_element())
<type 'sage.matrix.matrix_generic_dense.Matrix_generic_dense'>

which is good, but

sage: type(random_matrix(K, 2, 5, implementation="generic"))
<type 'sage.matrix.matrix_gfpn_dense.Matrix_gfpn_dense'>

which is bad.

So, the random_matrix constructor should take into account what was contributed in #23706.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​571c12f

Fix changed random_matrix output in tests

[vdelecroix]

Could you change the following doctest (matrix/special.py line 403)

The default implementation of :meth:`~sage.matrix.matrix2.randomize` relies
on the ``random_element()`` method for the base ring.  The ``density`` and
``sparse`` keywords behave as described above. Since we have a different
randomisation when using the optional meataxe package, we have to make sure
that we use the default implementation in this test::

    sage: K.<a>=FiniteField(3^2)
    sage: from sage.matrix.matrix_generic_dense import Matrix_generic_dense
    sage: MS = MatrixSpace(K, 2, 5)
    sage: MS._MatrixSpace__matrix_class = Matrix_generic_dense
    sage: random_matrix(K, 2, 5)
    [      1       a       1 2*a + 1       2]
    [    2*a   a + 2       0       2       1]

It could now be much simpler without any special hack.

[SimonKing]

Replying to vdelecroix:

Could you change the following doctest (matrix/special.py line 403)

The first commit does this:

@@ -407,10 +419,7 @@ def random_matrix(ring, nrows, ncols=None, algorithm='randomize', *args, **kwds)
     that we use the default implementation in this test::
 
         sage: K.<a>=FiniteField(3^2)
-        sage: from sage.matrix.matrix_generic_dense import Matrix_generic_dense
-        sage: MS = MatrixSpace(K, 2, 5)
-        sage: MS._MatrixSpace__matrix_class = Matrix_generic_dense
-        sage: random_matrix(K, 2, 5)
+        sage: random_matrix(K, 2, 5, implementation='generic')
         [      1       a       1 2*a + 1       2]
         [    2*a   a + 2       0       2       1]

So, I did change that test. Actually the whole purpose of this ticket was to fix this test (that would fail because of #23706 when meataxe is installed).

[vdelecroix]

Then I think that I should close #24449 as duplicate as Jeroen suggested.

[jdemeyer]

Doctest failure in src/sage/misc/lazy_import.pyx

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​652ca07

Fix a doctest in lazy_import

[SimonKing]

Replying to jdemeyer:

Doctest failure in src/sage/misc/lazy_import.pyx

Done

[dimpase]

It seems there should be doctests/examples showing the use of MeatAxe package as a backend.

[SimonKing]

Replying to dimpase:

It seems there should be doctests/examples showing the use of MeatAxe package as a backend.

See basically all tests in sage.matrix.matrix_gfpn_dense