X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_element.py;h=9fa8176d112668d6fed446ba5c174c7ebf618fbc;hb=9d365c6cf3b52024817cd2e97b1061216094e3df;hp=120870b7fa08b1ee0fcb936b92c62a9470a27754;hpb=1b6878559ad75aa0064503a962c8c183e13ab91a;p=sage.d.git

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index 120870b..9fa8176 100644
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -340,6 +340,8 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
 
             sage: from mjo.eja.eja_algebra import (JordanSpinEJA,
             ....:                                  TrivialEJA,
+            ....:                                  RealSymmetricEJA,
+            ....:                                  ComplexHermitianEJA,
             ....:                                  random_eja)
 
         EXAMPLES::
@@ -387,6 +389,37 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: x,y = J.random_elements(2)
             sage: (x*y).det() == x.det()*y.det()
             True
+
+        The determinant in matrix algebras is just the usual determinant::
+
+            sage: set_random_seed()
+            sage: X = matrix.random(QQ,3)
+            sage: X = X + X.T
+            sage: J1 = RealSymmetricEJA(3)
+            sage: J2 = RealSymmetricEJA(3,field=QQ,orthonormalize=False)
+            sage: expected = X.det()
+            sage: actual1 = J1(X).det()
+            sage: actual2 = J2(X).det()
+            sage: actual1 == expected
+            True
+            sage: actual2 == expected
+            True
+
+        ::
+
+            sage: set_random_seed()
+            sage: J1 = ComplexHermitianEJA(3)
+            sage: J2 = ComplexHermitianEJA(3,field=QQ,orthonormalize=False)
+            sage: X = matrix.random(GaussianIntegers(),3)
+            sage: X = X + X.H
+            sage: expected = AA(X.det())
+            sage: actual1 = J1(J1.real_embed(X)).det()
+            sage: actual2 = J2(J2.real_embed(X)).det()
+            sage: expected == actual1
+            True
+            sage: expected == actual2
+            True
+
         """
         P = self.parent()
         r = P.rank()
@@ -523,7 +556,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         zero, but we need the characteristic polynomial for the
         determinant. The minimal polynomial is a lot easier to get,
         so we use Corollary 2 in Chapter V of Koecher to check
-        whether or not the paren't algebra's zero element is a root
+        whether or not the parent algebra's zero element is a root
         of this element's minimal polynomial.
 
         That is... unless the coefficients of our algebra's
@@ -945,7 +978,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: n_max = RealSymmetricEJA._max_random_instance_size()
             sage: n = ZZ.random_element(1, n_max)
             sage: J1 = RealSymmetricEJA(n)
-            sage: J2 = RealSymmetricEJA(n,normalize_basis=False)
+            sage: J2 = RealSymmetricEJA(n,orthonormalize=False)
             sage: X = random_matrix(AA,n)
             sage: X = X*X.transpose()
             sage: x1 = J1(X)
@@ -971,15 +1004,16 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
 
 
 
-    def natural_representation(self):
+    def to_matrix(self):
         """
-        Return a more-natural representation of this element.
+        Return an (often more natural) representation of this element as a
+        matrix.
 
-        Every finite-dimensional Euclidean Jordan Algebra is a
-        direct sum of five simple algebras, four of which comprise
-        Hermitian matrices. This method returns the original
-        "natural" representation of this element as a Hermitian
-        matrix, if it has one. If not, you get the usual representation.
+        Every finite-dimensional Euclidean Jordan Algebra is a direct
+        sum of five simple algebras, four of which comprise Hermitian
+        matrices. This method returns a "natural" matrix
+        representation of this element as either a Hermitian matrix or
+        column vector.
 
         SETUP::
 
@@ -991,7 +1025,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: J = ComplexHermitianEJA(3)
             sage: J.one()
             e0 + e3 + e8
-            sage: J.one().natural_representation()
+            sage: J.one().to_matrix()
             [1 0 0 0 0 0]
             [0 1 0 0 0 0]
             [0 0 1 0 0 0]
@@ -1004,7 +1038,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: J = QuaternionHermitianEJA(3)
             sage: J.one()
             e0 + e5 + e14
-            sage: J.one().natural_representation()
+            sage: J.one().to_matrix()
             [1 0 0 0 0 0 0 0 0 0 0 0]
             [0 1 0 0 0 0 0 0 0 0 0 0]
             [0 0 1 0 0 0 0 0 0 0 0 0]
@@ -1017,15 +1051,14 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             [0 0 0 0 0 0 0 0 0 1 0 0]
             [0 0 0 0 0 0 0 0 0 0 1 0]
             [0 0 0 0 0 0 0 0 0 0 0 1]
-
         """
-        B = self.parent().natural_basis()
-        W = self.parent().natural_basis_space()
+        B = self.parent().matrix_basis()
+        W = self.parent().matrix_space()
 
         # This is just a manual "from_vector()", but of course
         # matrix spaces aren't vector spaces in sage, so they
         # don't have a from_vector() method.
-        return W.linear_combination(zip(B,self.to_vector()))
+        return W.linear_combination( zip(B, self.to_vector()) )
 
 
     def norm(self):