X-Git-Url: https://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_element.py;h=2c425ca320a5c04e6defee044bd0deb01e76dda4;hb=99952b3ef2ad157d820f1dbd946d329987383464;hp=0fd1c5f2032151de7d752494b4117825af3109a3;hpb=928b7d49fda98ff105c92293b5797bb7a2b9873a;p=sage.d.git

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index 0fd1c5f..2c425ca 100644
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -289,30 +289,32 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         Test the second polarization identity from my notes or from
         Baes (2.4)::
 
-            sage: x,y,z = random_eja().random_elements(3)
-            sage: Lx = x.operator()
-            sage: Ly = y.operator()
-            sage: Lz = z.operator()
-            sage: Lzy = (z*y).operator()
-            sage: Lxy = (x*y).operator()
-            sage: Lxz = (x*z).operator()
-            sage: bool(Lx*Lzy + Lz*Lxy + Ly*Lxz == Lzy*Lx + Lxy*Lz + Lxz*Ly)
+            sage: x,y,z = random_eja().random_elements(3)  # long time
+            sage: Lx = x.operator()                        # long time
+            sage: Ly = y.operator()                        # long time
+            sage: Lz = z.operator()                        # long time
+            sage: Lzy = (z*y).operator()                   # long time
+            sage: Lxy = (x*y).operator()                   # long time
+            sage: Lxz = (x*z).operator()                   # long time
+            sage: lhs = Lx*Lzy + Lz*Lxy + Ly*Lxz           # long time
+            sage: rhs = Lzy*Lx + Lxy*Lz + Lxz*Ly           # long time
+            sage: bool(lhs == rhs)                         # long time
             True
 
         Test the third polarization identity from my notes or from
         Baes (2.5)::
 
-            sage: u,y,z = random_eja().random_elements(3)
-            sage: Lu = u.operator()
-            sage: Ly = y.operator()
-            sage: Lz = z.operator()
-            sage: Lzy = (z*y).operator()
-            sage: Luy = (u*y).operator()
-            sage: Luz = (u*z).operator()
-            sage: Luyz = (u*(y*z)).operator()
-            sage: lhs = Lu*Lzy + Lz*Luy + Ly*Luz
-            sage: rhs = Luyz + Ly*Lu*Lz + Lz*Lu*Ly
-            sage: bool(lhs == rhs)
+            sage: u,y,z = random_eja().random_elements(3)  # long time
+            sage: Lu = u.operator()                        # long time
+            sage: Ly = y.operator()                        # long time
+            sage: Lz = z.operator()                        # long time
+            sage: Lzy = (z*y).operator()                   # long time
+            sage: Luy = (u*y).operator()                   # long time
+            sage: Luz = (u*z).operator()                   # long time
+            sage: Luyz = (u*(y*z)).operator()              # long time
+            sage: lhs = Lu*Lzy + Lz*Luy + Ly*Luz           # long time
+            sage: rhs = Luyz + Ly*Lu*Lz + Lz*Lu*Ly         # long time
+            sage: bool(lhs == rhs)                         # long time
             True
 
         """
@@ -1512,6 +1514,12 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
             sage: (alpha*x + y).trace() == alpha*x.trace() + y.trace()
             True
 
+        The trace of a square is nonnegative::
+
+            sage: x = random_eja().random_element()
+            sage: (x*x).trace() >= 0
+            True
+
         """
         P = self.parent()
         r = P.rank()