X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_element.py;h=6997766319798e5188683972c303ce450f0303e3;hb=a900f5daa84d0889ce7c1e041fb214a09e8d7bcd;hp=bef1289bbdd3820b990cf0b3ae0f4ff7334f3b01;hpb=607ba10dfea185af919a1f60b3ec7c7432d93b2b;p=sage.d.git

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index bef1289..6997766 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
 
         """
@@ -482,10 +484,12 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         of an element is the inverse of its left-multiplication operator
         applied to the algebra's identity, when that inverse exists::
 
-            sage: J = random_eja()
-            sage: x = J.random_element()
-            sage: (not x.operator().is_invertible()) or (
-            ....:    x.operator().inverse()(J.one()) == x.inverse() )
+            sage: J = random_eja()                         # long time
+            sage: x = J.random_element()                   # long time
+            sage: (not x.operator().is_invertible()) or (  # long time
+            ....:    x.operator().inverse()(J.one())       # long time
+            ....:    ==                                    # long time
+            ....:    x.inverse() )                         # long time
             True
 
         Check that the fast (cached) and slow algorithms give the same
@@ -974,9 +978,9 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
 
         The minimal polynomial should always kill its element::
 
-            sage: x = random_eja().random_element()
-            sage: p = x.minimal_polynomial()
-            sage: x.apply_univariate_polynomial(p)
+            sage: x = random_eja().random_element()  # long time
+            sage: p = x.minimal_polynomial()         # long time
+            sage: x.apply_univariate_polynomial(p)   # long time
             0
 
         The minimal polynomial is invariant under a change of basis,