From ea0d15a3d546c76a902a37c0db1d09ae54c5f3d9 Mon Sep 17 00:00:00 2001
From: Matthias Koeppe <mkoeppe@math.ucdavis.edu>
Date: Sat, 17 Oct 2020 10:00:46 -0700
Subject: [PATCH] sage.matrix: Resolve circular imports without using
 __init__.py

---
 src/sage/matrix/__init__.py           | 2 --
 src/sage/matrix/args.pyx              | 6 +++++-
 src/sage/matrix/matrix_mod2_dense.pyx | 8 +++++++-
 3 files changed, 12 insertions(+), 4 deletions(-)

diff --git a/src/sage/matrix/__init__.py b/src/sage/matrix/__init__.py
index 58b5ef12b66..e69de29bb2d 100644
--- a/src/sage/matrix/__init__.py
+++ b/src/sage/matrix/__init__.py
@@ -1,2 +0,0 @@
-# Resolve a cyclic import
-import sage.matrix.args
diff --git a/src/sage/matrix/args.pyx b/src/sage/matrix/args.pyx
index bf4692ad726..82e0ba58571 100644
--- a/src/sage/matrix/args.pyx
+++ b/src/sage/matrix/args.pyx
@@ -20,7 +20,8 @@ from cysignals.signals cimport sig_check
 from cypari2.gen cimport Gen
 from cypari2.types cimport typ, t_MAT, t_VEC, t_COL, t_VECSMALL, t_LIST, t_STR, t_CLOSURE
 
-from .matrix_space import MatrixSpace
+MatrixSpace = None
+
 from sage.rings.integer_ring import ZZ
 from sage.rings.real_double import RDF
 from sage.rings.complex_double import CDF
@@ -931,6 +932,9 @@ cdef class MatrixArgs:
             self.sparse = (self.typ & MA_FLAG_SPARSE) != 0
 
         if self.space is None:
+            global MatrixSpace
+            if MatrixSpace is None:
+                from .matrix_space import MatrixSpace
             self.space = MatrixSpace(self.base, self.nrows, self.ncols,
                     sparse=self.sparse, **self.kwds)
 
diff --git a/src/sage/matrix/matrix_mod2_dense.pyx b/src/sage/matrix/matrix_mod2_dense.pyx
index be2ba45a5d2..faa3860907a 100644
--- a/src/sage/matrix/matrix_mod2_dense.pyx
+++ b/src/sage/matrix/matrix_mod2_dense.pyx
@@ -118,7 +118,7 @@ from sage.libs.gmp.random cimport *
 from sage.misc.randstate cimport randstate, current_randstate
 from sage.misc.misc import cputime
 from sage.misc.verbose import verbose, get_verbose
-from sage.modules.free_module import VectorSpace
+VectorSpace = None
 from sage.modules.vector_mod2_dense cimport Vector_mod2_dense
 from sage.structure.richcmp cimport rich_to_bool
 from sage.cpython.string cimport bytes_to_str, char_to_str, str_to_bytes
@@ -507,6 +507,9 @@ cdef class Matrix_mod2_dense(matrix_dense.Matrix_dense):   # dense or sparse
             return self.rows(copy=False)[i]
         cdef Py_ssize_t j
         cdef Vector_mod2_dense z = Vector_mod2_dense.__new__(Vector_mod2_dense)
+        global VectorSpace
+        if VectorSpace is None:
+            from sage.modules.free_module import VectorSpace
         z._init(self._ncols, VectorSpace(self.base_ring(),self._ncols))
         if self._ncols:
             mzd_submatrix(z._entries, self._entries, i, 0, i+1, self._ncols)
@@ -600,6 +603,9 @@ cdef class Matrix_mod2_dense(matrix_dense.Matrix_dense):   # dense or sparse
             (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
         """
         cdef mzd_t *tmp
+        global VectorSpace
+        if VectorSpace is None:
+            from sage.modules.free_module import VectorSpace
         VS = VectorSpace(self._base_ring, self._nrows)
         if not isinstance(v, Vector_mod2_dense):
             v = VS(v)