+ def entry_algebra_gens(self):
+ r"""
+ Return a tuple of the generators of (that is, a basis for) the
+ entries of this matrix algebra.
+
+ This can be overridden in subclasses to work around the
+ inconsistency in the ``gens()`` methods of the various
+ entry algebras.
+ """
+ return self.entry_algebra().gens()
+
+ def _entry_algebra_element_to_vector(self, entry):
+ r"""
+ Return a vector representation (of length equal to the cardinality
+ of :meth:`entry_algebra_gens`) of the given ``entry``.
+
+ This can be overridden in subclasses to work around the fact that
+ real numbers, complex numbers, quaternions, et cetera, all require
+ different incantations to turn them into a vector.
+
+ It only makes sense to "guess" here in the superclass when no
+ subclass that overrides :meth:`entry_algebra_gens` exists. So
+ if you have a special subclass for your annoying entry algebra,
+ override this with the correct implementation there instead of
+ adding a bunch of awkward cases to this superclass method.
+
+ SETUP::
+
+ sage: from mjo.hurwitz import Octonions
+ sage: from mjo.matrix_algebra import MatrixAlgebra
+
+ EXAMPLES:
+
+ Real numbers::
+
+ sage: A = MatrixAlgebra(1, AA, QQ)
+ sage: A._entry_algebra_element_to_vector(AA(17))
+ (17)
+
+ Octonions::
+
+ sage: A = MatrixAlgebra(1, Octonions(), QQ)
+ sage: e = A.entry_algebra_gens()
+ sage: A._entry_algebra_element_to_vector(e[0])
+ (1, 0, 0, 0, 0, 0, 0, 0)
+ sage: A._entry_algebra_element_to_vector(e[1])
+ (0, 1, 0, 0, 0, 0, 0, 0)
+ sage: A._entry_algebra_element_to_vector(e[2])
+ (0, 0, 1, 0, 0, 0, 0, 0)
+ sage: A._entry_algebra_element_to_vector(e[3])
+ (0, 0, 0, 1, 0, 0, 0, 0)
+ sage: A._entry_algebra_element_to_vector(e[4])
+ (0, 0, 0, 0, 1, 0, 0, 0)
+ sage: A._entry_algebra_element_to_vector(e[5])
+ (0, 0, 0, 0, 0, 1, 0, 0)
+ sage: A._entry_algebra_element_to_vector(e[6])
+ (0, 0, 0, 0, 0, 0, 1, 0)
+ sage: A._entry_algebra_element_to_vector(e[7])
+ (0, 0, 0, 0, 0, 0, 0, 1)
+
+ Sage matrices::
+
+ sage: MS = MatrixSpace(QQ,2)
+ sage: A = MatrixAlgebra(1, MS, QQ)
+ sage: A._entry_algebra_element_to_vector(MS([[1,2],[3,4]]))
+ (1, 2, 3, 4)
+
+ """
+ if hasattr(entry, 'to_vector'):
+ return entry.to_vector()
+
+ from sage.modules.free_module import FreeModule
+ d = len(self.entry_algebra_gens())
+ V = FreeModule(self.entry_algebra().base_ring(), d)
+
+ if hasattr(entry, 'list'):
+ # sage matrices
+ return V(entry.list())
+
+ # This works in AA, and will crash if it doesn't know what to
+ # do, and that's fine because then I don't know what to do
+ # either.
+ return V((entry,))
+
+
+