matrix_algebra: add _entry_algebra_element_to_vector() method.

[sage.d.git] / mjo / matrix_algebra.py

diff --git a/mjo/matrix_algebra.py b/mjo/matrix_algebra.py
index c38e8556203243536fc0af87078840f82e2d57cb..8491f277d5cc81b955c6ddaed0298549d15aa779 100644 (file)
--- a/mjo/matrix_algebra.py
+++ b/mjo/matrix_algebra.py
@@ -198,14 +198,16 @@ class MatrixAlgebra(CombinatorialFreeModule):
         # sticking a "1" in each position doesn't give us a basis for
         # the space. We actually need to stick each of e0, e1, ...  (a
         # basis for the entry algebra itself) into each position.
-        I = range(n)
-        J = range(n)
         self._entry_algebra = entry_algebra
-        entry_basis = entry_algebra.gens()
 
-        basis_indices = [(i,j,e) for i in range(n)
-                                 for j in range(n)
-                                 for e in entry_algebra.gens()]
+        # Needs to make the (overridden) method call when, for example,
+        # the entry algebra is the complex numbers and its gens() method
+        # lies to us.
+        entry_basis = self.entry_algebra_gens()
+
+        basis_indices = [(i,j,e) for j in range(n)
+                                 for i in range(n)
+                                 for e in entry_basis]
 
         super().__init__(scalars,
                          basis_indices,
@@ -227,6 +229,92 @@ class MatrixAlgebra(CombinatorialFreeModule):
         """
         return self._entry_algebra
 
+    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 VectorSpace
+        d = len(self.entry_algebra_gens())
+        V = VectorSpace(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,))
+
+
+
     def nrows(self):
         return self._nrows
     ncols = nrows