sage.matrix: Resolve circular imports without using __init__.py

[mkoeppe]

This is preparation for making sage.matrix a namespace package in #28925.

CC: @simon-king-jena @tscrim @tobiasdiez @videlec @kiwifb

Component: refactoring

Author: Matthias Koeppe

Branch/Commit: ea0d15a

Reviewer: François Bissey

Issue created by migration from https://trac.sagemath.org/ticket/30784

[mkoeppe]

Branch: u/mkoeppe/sage_matrix__resolve_circular_imports_without_using___init___py

[mkoeppe]

Description changed:

--- 
+++ 
@@ -1 +1,2 @@
-This is preparation for making sage.matrix a namespace package in #28925.
+This is preparation for making `sage.matrix` a namespace package in #28925.
+

[mkoeppe]

Author: Matthias Koeppe

[mkoeppe]

New commits:

ea0d15a

sage.matrix: Resolve circular imports without using __init__.py

[mkoeppe]

Commit: ea0d15a

[tobiasdiez]

comment:3

What's the advantage of using global variables? I think python is also caching the imported module under the hood (https://docs.python.org/3/reference/import.html#the-module-cache).

[mkoeppe]

comment:4

I'm imitating existing code in Cython modules here, for example in src/sage/matrix/matrix_double_dense.pyx or src/sage/rings/complex_mpc.pyx. I have not timed it, but I would guess it has smaller overhead than the import mechanism.

[mkoeppe]

comment:6

Green patchbot, needs review. (One other patchbot fails with an unrelated error.)

[kiwifb]

comment:7

LGTM

[kiwifb]

Reviewer: François Bissey

[mkoeppe]

comment:8

Thanks!

[tobiasdiez]

comment:9

Without double-checking I would guess that the python import cache is heavily optimized. But even given the minimal performance penalty, I would suggest to using a simple import in favor of the global variable. The latter is a possible source of bugs (devs forgetting to use import before using it) and heavily complicates the work of static type checking tools. But maybe I'm also missing some other advantages of this approach (@francois).

[vbraun]

Changed branch from u/mkoeppe/sage_matrix__resolve_circular_imports_without_using___init___py to ea0d15a