X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Foctonions.py;h=87bf5ff1ed06b1a77b5815df8dd2248fda4b7edb;hb=9ffb2ed473d62df9f6b6db9636b0bf8fa8f3be25;hp=352c4c586e7506a218bcc9e7f9cb6332c1cd72c7;hpb=ee21aa47a00c19068c21d631fda6598a6e0648e9;p=sage.d.git

diff --git a/mjo/octonions.py b/mjo/octonions.py
index 352c4c5..87bf5ff 100644
--- a/mjo/octonions.py
+++ b/mjo/octonions.py
@@ -445,6 +445,41 @@ class OctonionMatrix(IndexedFreeModuleElement):
         zero = self.parent().octonions().zero()
         return sum( (self[i,i] for i in range(self.nrows())), zero )
 
+    def matrix_space(self):
+        r"""
+
+        SETUP::
+
+            sage: from mjo.octonions import OctonionMatrixAlgebra
+
+        TESTS::
+
+            sage: set_random_seed()
+            sage: MS = OctonionMatrixAlgebra(2)
+            sage: MS.random_element().matrix_space()
+            Module of 2 by 2 matrices with octonion entries over the
+            scalar ring Algebraic Real Field
+
+        """
+        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"""
@@ -483,6 +518,11 @@ class OctonionMatrixAlgebra(CombinatorialFreeModule):
                          prefix=prefix,
                          bracket='(')
 
+    def _repr_(self):
+        return ("Module of %d by %d matrices with octonion entries"
+                " over the scalar ring %s" %
+                (self.nrows(), self.ncols(), self.base_ring()) )
+
     def octonions(self):
         r"""
         Return the Octonion algebra that our elements' entries come from.