matrix_algebra: rename __repr__ to _repr_ and fix a multiplication bug.

diff --git a/mjo/matrix_algebra.py b/mjo/matrix_algebra.py
index 5b8b267f5120a4a319f77777885b19731437f518..a67a9b4a1c0692d31aceffa3097343aa0df99dae 100644 (file)
--- a/mjo/matrix_algebra.py
+++ b/mjo/matrix_algebra.py
@@ -37,7 +37,7 @@ class MatrixAlgebraElement(IndexedFreeModuleElement):
             l[i][j] += v*e
         return l
 
-    def __repr__(self):
+    def _repr_(self):
         r"""
         Display this matrix as a table.
 
@@ -232,10 +232,38 @@ class MatrixAlgebra(CombinatorialFreeModule):
     ncols = nrows
 
     def product_on_basis(self, mon1, mon2):
+        r"""
+
+        SETUP::
+
+            sage: from mjo.octonions import Octonions
+            sage: from mjo.matrix_algebra import MatrixAlgebra
+
+        TESTS::
+
+            sage: O = Octonions(QQ)
+            sage: e = O.gens()
+            sage: e[2]*e[1]
+            -e3
+            sage: A = MatrixAlgebra(O,QQ,2)
+            sage: A.product_on_basis( (0,0,e[2]), (0,0,e[1]) )
+            +-----+---+
+            | -e3 | 0 |
+            +-----+---+
+            | 0   | 0 |
+            +-----+---+
+
+        """
         (i,j,e1) = mon1
         (k,l,e2) = mon2
         if j == k:
-            return self.monomial((i,l,e1*e2))
+            # If e1*e2 has a negative sign in front of it,
+            # then (i,l,e1*e2) won't be a monomial!
+            p = e1*e2
+            if (i,l,p) in self.indices():
+                return self.monomial((i,l,p))
+            else:
+                return -self.monomial((i,l,-p))
         else:
             return self.zero()