X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Fhurwitz.py;h=1f7c9dc3781a844d6d77a1e63168c52340bf6770;hb=fc29add6cf1d9ff4e8a240b0f8f2ca6672d4ea57;hp=a1a6af06e944e97ea49536b8b9f76e1ecf54cde6;hpb=37ab2f97b6f8b64360045a1db4c74b6c38651317;p=sage.d.git

diff --git a/mjo/hurwitz.py b/mjo/hurwitz.py
index a1a6af0..1f7c9dc 100644
--- a/mjo/hurwitz.py
+++ b/mjo/hurwitz.py
@@ -306,6 +306,31 @@ class Octonions(CombinatorialFreeModule):
 
 
 class HurwitzMatrixAlgebraElement(MatrixAlgebraElement):
+    def conjugate_transpose(self):
+        r"""
+        Return the conjugate-transpose of this matrix.
+
+        SETUP::
+
+            sage: from mjo.hurwitz import HurwitzMatrixAlgebra
+
+        EXAMPLES::
+
+            sage: A = HurwitzMatrixAlgebra(2, QQbar, ZZ)
+            sage: M = A([ [ I,   2*I],
+            ....:         [ 3*I, 4*I] ])
+            +------+------+
+            | -1*I | -3*I |
+            +------+------+
+            | -2*I | -4*I |
+            +------+------+
+
+        """
+        entries = [ [ self[j,i].conjugate()
+                      for j in range(self.ncols())]
+                    for i in range(self.nrows()) ]
+        return self.parent()._element_constructor_(entries)
+
     def is_hermitian(self):
         r"""
 
@@ -322,6 +347,8 @@ class HurwitzMatrixAlgebraElement(MatrixAlgebraElement):
             True
 
         """
+        # A tiny bit faster than checking equality with the conjugate
+        # transpose.
         return all( self[i,j] == self[j,i].conjugate()
                     for i in range(self.nrows())
                     for j in range(self.ncols()) )
@@ -440,6 +467,31 @@ class OctonionMatrixAlgebra(HurwitzMatrixAlgebra):
         +---------------------+
         | 1.00000000000000*e0 |
         +---------------------+
+        sage: A.gens()
+        (+---------------------+
+        | 1.00000000000000*e0 |
+        +---------------------+,
+        +---------------------+
+        | 1.00000000000000*e1 |
+        +---------------------+,
+        +---------------------+
+        | 1.00000000000000*e2 |
+        +---------------------+,
+        +---------------------+
+        | 1.00000000000000*e3 |
+        +---------------------+,
+        +---------------------+
+        | 1.00000000000000*e4 |
+        +---------------------+,
+        +---------------------+
+        | 1.00000000000000*e5 |
+        +---------------------+,
+        +---------------------+
+        | 1.00000000000000*e6 |
+        +---------------------+,
+        +---------------------+
+        | 1.00000000000000*e7 |
+        +---------------------+)
 
     ::
 
@@ -519,6 +571,19 @@ class QuaternionMatrixAlgebra(HurwitzMatrixAlgebra):
         +-----+
         | 1.0 |
         +-----+
+        sage: A.gens()
+        (+-----+
+        | 1.0 |
+        +-----+,
+        +---+
+        | i |
+        +---+,
+        +---+
+        | j |
+        +---+,
+        +---+
+        | k |
+        +---+)
 
     ::
 
@@ -598,6 +663,13 @@ class ComplexMatrixAlgebra(HurwitzMatrixAlgebra):
         +------------------+
         | 1.00000000000000 |
         +------------------+
+        sage: A.gens()
+        (+------------------+
+        | 1.00000000000000 |
+        +------------------+,
+        +--------------------+
+        | 1.00000000000000*I |
+        +--------------------+)
 
     ::