hurwitz: fix Hurwitz matrix algebra generators.

diff --git a/mjo/hurwitz.py b/mjo/hurwitz.py
index a1a6af06e944e97ea49536b8b9f76e1ecf54cde6..ccc8219b1a92036c6ac92f118339c160a885977b 100644 (file)
--- a/mjo/hurwitz.py
+++ b/mjo/hurwitz.py
@@ -440,6 +440,31 @@ class OctonionMatrixAlgebra(HurwitzMatrixAlgebra):
         +---------------------+
         | 1.00000000000000*e0 |
         +---------------------+
+        sage: A.gens()
+        (+---------------------+
+        | 1.00000000000000*e0 |
+        +---------------------+,
+        +---------------------+
+        | 1.00000000000000*e1 |
+        +---------------------+,
+        +---------------------+
+        | 1.00000000000000*e2 |
+        +---------------------+,
+        +---------------------+
+        | 1.00000000000000*e3 |
+        +---------------------+,
+        +---------------------+
+        | 1.00000000000000*e4 |
+        +---------------------+,
+        +---------------------+
+        | 1.00000000000000*e5 |
+        +---------------------+,
+        +---------------------+
+        | 1.00000000000000*e6 |
+        +---------------------+,
+        +---------------------+
+        | 1.00000000000000*e7 |
+        +---------------------+)
 
     ::
 
@@ -519,6 +544,19 @@ class QuaternionMatrixAlgebra(HurwitzMatrixAlgebra):
         +-----+
         | 1.0 |
         +-----+
+        sage: A.gens()
+        (+-----+
+        | 1.0 |
+        +-----+,
+        +---+
+        | i |
+        +---+,
+        +---+
+        | j |
+        +---+,
+        +---+
+        | k |
+        +---+)
 
     ::
 
@@ -598,6 +636,13 @@ class ComplexMatrixAlgebra(HurwitzMatrixAlgebra):
         +------------------+
         | 1.00000000000000 |
         +------------------+
+        sage: A.gens()
+        (+------------------+
+        | 1.00000000000000 |
+        +------------------+,
+        +--------------------+
+        | 1.00000000000000*I |
+        +--------------------+)
 
     ::
 

diff --git a/mjo/matrix_algebra.py b/mjo/matrix_algebra.py
index c38e8556203243536fc0af87078840f82e2d57cb..d67347b3aa1252acaf165448d1ea35ebb4a77cd7 100644 (file)
--- a/mjo/matrix_algebra.py
+++ b/mjo/matrix_algebra.py
@@ -201,11 +201,15 @@ class MatrixAlgebra(CombinatorialFreeModule):
         I = range(n)
         J = range(n)
         self._entry_algebra = entry_algebra
-        entry_basis = 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 i in range(n)
                                  for j in range(n)
-                                 for e in entry_algebra.gens()]
+                                 for e in entry_basis]
 
         super().__init__(scalars,
                          basis_indices,
@@ -227,6 +231,17 @@ 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 nrows(self):
         return self._nrows
     ncols = nrows