X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Foctonions.py;h=c2b829f98b9b49dbe078172a3669f0cb8b6406e4;hb=ff8c9b19da5ed821366a491a95b4f6c946f315ae;hp=73acf2db2ebf76258f47ed1156113925f4f257ed;hpb=4d0aae306aa9f80009cbbea9088382e30df919af;p=sage.d.git

diff --git a/mjo/octonions.py b/mjo/octonions.py
index 73acf2d..c2b829f 100644
--- a/mjo/octonions.py
+++ b/mjo/octonions.py
@@ -345,7 +345,7 @@ class OctonionMatrix(IndexedFreeModuleElement):
     ncols = nrows
 
     @cached_method
-    def to_list(self):
+    def to_nested_list(self):
         r"""
         SETUP::
 
@@ -372,7 +372,7 @@ class OctonionMatrix(IndexedFreeModuleElement):
             +----+---+---+
             | 0  | 0 | 0 |
             +----+---+---+
-            sage: (E00e0 + 2*E00e3).to_list()
+            sage: (E00e0 + 2*E00e3).to_nested_list()
             [[e0 + 2*e3, 0, 0], [0, 0, 0], [0, 0, 0]]
 
         """
@@ -401,7 +401,29 @@ class OctonionMatrix(IndexedFreeModuleElement):
             +----+----+----+
 
         """
-        return table(self.to_list(), frame=True)._repr_()
+        return table(self.to_nested_list(), frame=True)._repr_()
+
+
+    def list(self):
+        r"""
+        Return one long list of this matrix's entries.
+
+        SETUP::
+
+            sage: from mjo.octonions import OctonionMatrixAlgebra
+
+        EXAMPLES::
+
+            sage: MS = OctonionMatrixAlgebra(3)
+            sage: E00e0 = MS.gens()[0]
+            sage: E00e3 = MS.gens()[3]
+            sage: (E00e0 + 2*E00e3).to_nested_list()
+            [[e0 + 2*e3, 0, 0], [0, 0, 0], [0, 0, 0]]
+            sage: (E00e0 + 2*E00e3).list()
+            [e0 + 2*e3, 0, 0, 0, 0, 0, 0, 0, 0]
+
+        """
+        return sum( self.to_nested_list(), [] )
 
 
     def __getitem__(self, indices):
@@ -426,7 +448,7 @@ class OctonionMatrix(IndexedFreeModuleElement):
 
         """
         i,j = indices
-        return self.to_list()[i][j]
+        return self.to_nested_list()[i][j]
 
     def trace(self):
         r"""
@@ -463,6 +485,23 @@ class OctonionMatrix(IndexedFreeModuleElement):
         """
         return self.parent()
 
+    def is_hermitian(self):
+        r"""
+
+        SETUP::
+
+            sage: from mjo.octonions import OctonionMatrixAlgebra
+
+        EXAMPLES::
+
+            sage: MS = OctonionMatrixAlgebra(3)
+            sage: MS.one().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 OctonionMatrixAlgebra(CombinatorialFreeModule):
     r"""