eja: mark some cached-value tests as "long time".

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index d99a7d873ab69e511186b7f0bc3ba3127a45c85a..6812e2807a7ff3c3a4f7253c7af9750f5de8fbb2 100644 (file)
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -444,8 +444,13 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
 
         ALGORITHM:
 
-        We appeal to the quadratic representation as in Koecher's
-        Theorem 12 in Chapter III, Section 5.
+        In general we appeal to the quadratic representation as in
+        Koecher's Theorem 12 in Chapter III, Section 5. But if the
+        parent algebra's "characteristic polynomial of" coefficients
+        happen to be cached, then we use Proposition II.2.4 in Faraut
+        and Korányi which gives a formula for the inverse based on the
+        characteristic polynomial and the Cayley-Hamilton theorem for
+        Euclidean Jordan algebras::
 
         SETUP::
 
@@ -515,22 +520,19 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             ....:    x.operator().inverse()(J.one()) == x.inverse() )
             True
 
-        Proposition II.2.4 in Faraut and Korányi gives a formula for
-        the inverse based on the characteristic polynomial and the
-        Cayley-Hamilton theorem for Euclidean Jordan algebras::
+        Check that the fast (cached) and slow algorithms give the same
+        answer::
 
-            sage: set_random_seed()
-            sage: J = ComplexHermitianEJA(3)
-            sage: x = J.random_element()
-            sage: while not x.is_invertible():
-            ....:     x = J.random_element()
-            sage: r = J.rank()
-            sage: a = x.characteristic_polynomial().coefficients(sparse=False)
-            sage: expected  = (-1)^(r+1)/x.det()
-            sage: expected *= sum( a[i+1]*x^i for i in range(r) )
-            sage: x.inverse() == expected
+            sage: set_random_seed()                              # long time
+            sage: J = random_eja(field=QQ, orthonormalize=False) # long time
+            sage: x = J.random_element()                         # long time
+            sage: while not x.is_invertible():                   # long time
+            ....:     x = J.random_element()                     # long time
+            sage: slow = x.inverse()                             # long time
+            sage: _ = J._charpoly_coefficients()                 # long time
+            sage: fast = x.inverse()                             # long time
+            sage: slow == fast                                   # long time
             True
-
         """
         if not self.is_invertible():
             raise ValueError("element is not invertible")
@@ -587,6 +589,18 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: (not J.is_trivial()) and J.zero().is_invertible()
             False
 
+        Test that the fast (cached) and slow algorithms give the same
+        answer::
+
+            sage: set_random_seed()                              # long time
+            sage: J = random_eja(field=QQ, orthonormalize=False) # long time
+            sage: x = J.random_element()                         # long time
+            sage: slow = x.is_invertible()                       # long time
+            sage: _ = J._charpoly_coefficients()                 # long time
+            sage: fast = x.is_invertible()                       # long time
+            sage: slow == fast                                   # long time
+            True
+
         """
         if self.is_zero():
             if self.parent().is_trivial():