gh-38235: Fix diagonal matrix construction from base ring elements that have `_matrix_` methods
    
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The matrix constructors are designed to accept a scalar as the `entries`
and then construct a diagonal matrix; special case: constructing the
zero matrix from 0.

However, when the scalar is a base ring element that happens to have a
`_matrix_` method, that is tried first, leading to the errors reported
in #38221.
Here we change it so that if the base ring (or matrix space) has been
specified already and a scalar from that base ring is passed, that takes
precedence over using a `_matrix_` method. (Coercion is not attempted.)

For the special case of `zero_matrix` and `MatrixSpace.zero_matrix`, we
now use `entries=None`, which is the fastest and most robust path in
`MatrixArgs.entries_type` to designate a zero matrix.

Fixes #38221

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preview.

### ⌛ Dependencies

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URL: #38235
Reported by: Matthias Köppe
Reviewer(s): Matthias Köppe, Travis Scrimshaw

Author: Release Manager

src/sage/matrix/args.pyx

@@ -1500,6 +1500,21 @@ cdef class MatrixArgs:
             Traceback (most recent call last):
             ...
             NameError: name 'a' is not defined
+
+        Check that :issue:`38221` is fixed::
+
+            sage: # needs sage.groups
+            sage: G = CyclicPermutationGroup(7)
+            sage: R = GF(2)
+            sage: A = G.algebra(R)
+            sage: matrix(A, 3, 3, A.zero())
+            [0 0 0]
+            [0 0 0]
+            [0 0 0]
+            sage: matrix(A, 3, 3, A.one())
+            [()  0  0]
+            [ 0 ()  0]
+            [ 0  0 ()]
         """
         # Check basic Python types. This is very fast, so it doesn't
         # hurt to do these first.
@@ -1524,6 +1539,8 @@ cdef class MatrixArgs:
         cdef bint is_elt = isinstance(self.entries, Element)
         if is_elt and isinstance(self.entries, Matrix):
             return MA_ENTRIES_MATRIX
+        if is_elt and self.base is not None and self.entries.parent() == self.base:
+            return MA_ENTRIES_SCALAR
         t = type(self.entries)
         try:
             f = t._matrix_

src/sage/matrix/matrix_space.py

@@ -2170,9 +2170,20 @@ def zero_matrix(self):
             False
             sage: MM.zero().is_mutable()
             False
+
+        Check that :issue:`38221` is fixed::
+
+            sage: # needs sage.groups
+            sage: G = CyclicPermutationGroup(7)
+            sage: R = GF(2)
+            sage: A = G.algebra(R)
+            sage: S = MatrixSpace(A, 3, 3)
+            sage: S.zero_matrix()
+            [0 0 0]
+            [0 0 0]
+            [0 0 0]
         """
-        zero = self.base_ring().zero()
-        res = self.element_class(self, zero, False, False)
+        res = self.element_class(self, None, False, False)
         res.set_immutable()
         return res
 

src/sage/matrix/special.py

@@ -1000,11 +1000,23 @@ def zero_matrix(ring, nrows=None, ncols=None, sparse=False):
         [0 0 0 0 0]
         [0 0 0 0 0]
 
+    TESTS:
+
+    Check that :issue:`38221` is fixed::
+
+        sage: # needs sage.groups
+        sage: G = CyclicPermutationGroup(7)
+        sage: R = GF(2)
+        sage: A = G.algebra(R)
+        sage: zero_matrix(A, 3, 3)
+        [0 0 0]
+        [0 0 0]
+        [0 0 0]
     """
     if isinstance(ring, (Integer, int)):
         nrows, ncols = (ring, nrows)
         ring = ZZ
-    return matrix_space.MatrixSpace(ring, nrows, ncols, sparse)(0)
+    return matrix_space.MatrixSpace(ring, nrows, ncols, sparse).matrix(None)
 
 
 @matrix_method