X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Fmatrix_algebra.py;h=a67a9b4a1c0692d31aceffa3097343aa0df99dae;hb=23ced4147cf68d9e5d7a00be958ad3c579436f50;hp=4049ef653a8a2688c2b9d4399f2b5386212aae47;hpb=ab0536f4db17eb78f3623927653b8f7f1a7e6808;p=sage.d.git

diff --git a/mjo/matrix_algebra.py b/mjo/matrix_algebra.py
index 4049ef6..a67a9b4 100644
--- 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.
 
@@ -158,6 +158,22 @@ class MatrixAlgebra(CombinatorialFreeModule):
     the entries come from a commutative and associative ring. This
     is problematic in several interesting matrix algebras, like those
     where the entries are quaternions or octonions.
+
+    SETUP::
+
+        sage: from mjo.matrix_algebra import MatrixAlgebra
+
+    EXAMPLES::
+
+    The existence of a unit element is determined dynamically::
+
+        sage: MatrixAlgebra(ZZ,ZZ,2).one()
+        +---+---+
+        | 1 | 0 |
+        +---+---+
+        | 0 | 1 |
+        +---+---+
+
     """
     Element = MatrixAlgebraElement
 
@@ -168,6 +184,11 @@ class MatrixAlgebra(CombinatorialFreeModule):
 
         if "Unital" in entry_algebra.category().axioms():
             category = category.Unital()
+            entry_one = entry_algebra.one()
+            self.one = lambda: sum( (self.monomial((i,i,entry_one))
+                                     for i in range(self.nrows()) ),
+                                    self.zero() )
+
         if "Associative" in entry_algebra.category().axioms():
             category = category.Associative()
 
@@ -211,10 +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()
 
@@ -299,16 +348,3 @@ class HurwitzMatrixAlgebraElement(MatrixAlgebraElement):
 
 class HurwitzMatrixAlgebra(MatrixAlgebra):
     Element = HurwitzMatrixAlgebraElement
-
-    def one(self):
-        r"""
-        SETUP::
-
-            sage: from mjo.matrix_algebra import HurwitzMatrixAlgebra
-
-        """
-        return sum( (self.monomial((i,i,self.entry_algebra().one()))
-                     for i in range(self.nrows()) ),
-                    self.zero() )
-
-