X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_element.py;h=0fae507b328a1c358f7c4e7f88aab30cf5406104;hb=251e308af6c3a57b418a06546a572af83eade7ec;hp=6547668965a690b883a5ac59757ef1e625016604;hpb=dfdd66902d789e47702cfd4c263bbe59dffb168c;p=sage.d.git

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index 6547668..0fae507 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,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)