Reorganize the Hurwitz (matrix) algebra stuff.

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

diff --git a/mjo/matrix_algebra.py b/mjo/matrix_algebra.py
index 5b8b267f5120a4a319f77777885b19731437f518..94a8410f9929986a8737f9bbb846c04490751fe5 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.hurwitz 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()
 
@@ -294,29 +322,3 @@ class MatrixAlgebra(CombinatorialFreeModule):
             return self
         else:
             return self.from_list(elt)
-
-
-class HurwitzMatrixAlgebraElement(MatrixAlgebraElement):
-    def is_hermitian(self):
-        r"""
-
-        SETUP::
-
-            sage: from mjo.matrix_algebra import HurwitzMatrixAlgebra
-
-        EXAMPLES::
-
-            sage: A = HurwitzMatrixAlgebra(QQbar, ZZ, 2)
-            sage: M = A([ [ 0,I],
-            ....:         [-I,0] ])
-            sage: M.is_hermitian()
-            True
-
-        """
-        return all( self[i,j] == self[j,i].conjugate()
-                    for i in range(self.nrows())
-                    for j in range(self.ncols()) )
-
-
-class HurwitzMatrixAlgebra(MatrixAlgebra):
-    Element = HurwitzMatrixAlgebraElement