octonions: add list() method for octonion matrices.

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

diff --git a/mjo/octonions.py b/mjo/octonions.py
index 352c4c586e7506a218bcc9e7f9cb6332c1cd72c7..c2b829f98b9b49dbe078172a3669f0cb8b6406e4 100644 (file)
--- 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"""
@@ -445,6 +467,41 @@ 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 +540,11 @@ 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.