Cythonize LatticePolytope.normal_form(algorithm='palp_native'), change to default, add as a Polyhedron method

[mkoeppe]

The current default algorithm, using the external, unmaintained palp package, is unreliable.

Here, as a follow-up on #35997, we make the reimplementation of the PALP algorithm in Python (palp_native) suitable as the new default by speeding it up.

We also fix a bug in introduced in #35997.

We also make it available as a method of Polyhedron (for base ring ZZ).

@xuluze

📝 Checklist

• The title is concise, informative, and self-explanatory.
• The description explains in detail what this PR is about.
• I have linked a relevant issue or discussion.
• I have created tests covering the changes.
• I have updated the documentation accordingly.

⌛ Dependencies

[dimpase]

apart from that missing trivial test, no problems

[dimpase]

LGTM, thanks

[mkoeppe]

Thanks

[mkoeppe]

Marking this as a blocker in the hope it can sneak into 10.2 with the other open blocker

[tornaria]

Marking this as a blocker in the hope it can sneak into 10.2 with the other open blocker

Why is this more worthy of "sneaking in" than e.g. #36551 ?

[vbraun]

Fails on 32-bit

**********************************************************************
File "src/sage/geometry/lattice_polytope.py", line 3141, in sage.geometry.lattice_polytope.LatticePolytopeClass.normal_form
Failed example:
    P.normal_form(algorithm="palp_modified")  # long time (22s)           # needs sage.groups
Exception raised:
    Traceback (most recent call last):
      File "sage/misc/cachefunc.pyx", line 1962, in sage.misc.cachefunc.CachedMethodCaller.__call__
        return cache[k]
    KeyError: (('palp_modified', False), ())
    During handling of the above exception, another exception occurred:
    Traceback (most recent call last):
      File "/var/lib/buildbot/slave/sage_git/build/src/sage/doctest/forker.py", line 709, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File "/var/lib/buildbot/slave/sage_git/build/src/sage/doctest/forker.py", line 1144, in compile_and_execute
        exec(compiled, globs)
      File "<doctest sage.geometry.lattice_polytope.LatticePolytopeClass.normal_form[14]>", line 1, in <module>
        P.normal_form(algorithm="palp_modified")  # long time (22s)           # needs sage.groups
        ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
      File "sage/misc/cachefunc.pyx", line 1967, in sage.misc.cachefunc.CachedMethodCaller.__call__
        w = self._instance_call(*args, **kwds)
      File "sage/misc/cachefunc.pyx", line 1842, in sage.misc.cachefunc.CachedMethodCaller._instance_call
        return self.f(self._instance, *args, **kwds)
      File "/var/lib/buildbot/slave/sage_git/build/src/sage/geometry/lattice_polytope.py", line 3204, in normal_form
        result = self._palp_modified_normal_form(permutation=permutation)
                 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
      File "/var/lib/buildbot/slave/sage_git/build/src/sage/geometry/lattice_polytope.py", line 3259, in _palp_modified_normal_form
        PM_max = PM.permutation_normal_form()
                 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
      File "sage/matrix/matrix2.pyx", line 8637, in genexpr
        if not any(aN.is_permutation_of(j) for j in aM):
      File "sage/matrix/matrix2.pyx", line 8637, in genexpr
        if not any(aN.is_permutation_of(j) for j in aM):
      File "sage/matrix/matrix2.pyx", line 8792, in sage.matrix.matrix2.Matrix.is_permutation_of
        return N_B.is_isomorphic(M_B, certificate=False, edge_labels=True)
      File "/var/lib/buildbot/slave/sage_git/build/src/sage/graphs/generic_graph.py", line 23852, in is_isomorphic
        isom = isomorphic(GC, GC2, partition, partition2, (self._directed or self.has_loops()), 1)
               ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
      File "sage/groups/perm_gps/partn_ref/refinement_graphs.pyx", line 166, in sage.groups.perm_gps.partn_ref.refinement_graphs.isomorphic
        cdef bint isomorphic = double_coset(<void *>GS1, <void *>GS2, part, ordering, n, &all_children_are_equivalent, &refine_by_degree, &compare_graphs, NULL, NULL, output)
      File "sage/groups/perm_gps/partn_ref/double_coset.pyx", line 367, in sage.groups.perm_gps.partn_ref.double_coset.double_coset
        raise MemoryError
    MemoryError
**********************************************************************
1 item had failures:
   1 of  17 in sage.geometry.lattice_polytope.LatticePolytopeClass.normal_form
    [667 tests, 1 failure, 16.73 s]
**********************************************************************

[mkoeppe]

Sorry about this; I've disabled this example now (it's also too long on 64 bit even for # long)

[github-actions]

Documentation preview for this PR (built with commit f9aeca5; changes) is ready! 🎉