X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_element.py;h=6812e2807a7ff3c3a4f7253c7af9750f5de8fbb2;hb=0ecada5937cb3c3aa7307029f165996d83a16133;hp=0fae507b328a1c358f7c4e7f88aab30cf5406104;hpb=251e308af6c3a57b418a06546a572af83eade7ec;p=sage.d.git

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index 0fae507..6812e28 100644
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -227,9 +227,9 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
 
         Ditto for the quaternions::
 
-            sage: J = QuaternionHermitianEJA(3)
+            sage: J = QuaternionHermitianEJA(2)
             sage: J.one().inner_product(J.one())
-            3
+            2
 
         TESTS:
 
@@ -396,7 +396,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: X = matrix.random(QQ,3)
             sage: X = X + X.T
             sage: J1 = RealSymmetricEJA(3)
-            sage: J2 = RealSymmetricEJA(3,QQ,orthonormalize=False)
+            sage: J2 = RealSymmetricEJA(3,field=QQ,orthonormalize=False)
             sage: expected = X.det()
             sage: actual1 = J1(X).det()
             sage: actual2 = J2(X).det()
@@ -408,9 +408,9 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         ::
 
             sage: set_random_seed()
-            sage: J1 = ComplexHermitianEJA(3)
-            sage: J2 = ComplexHermitianEJA(3,field=QQ,orthonormalize=False)
-            sage: X = matrix.random(GaussianIntegers(),3)
+            sage: J1 = ComplexHermitianEJA(2)
+            sage: J2 = ComplexHermitianEJA(2,field=QQ,orthonormalize=False)
+            sage: X = matrix.random(GaussianIntegers(), 2)
             sage: X = X + X.H
             sage: expected = AA(X.det())
             sage: actual1 = J1(J1.real_embed(X)).det()
@@ -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():
@@ -1035,22 +1049,19 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
 
         ::
 
-            sage: J = QuaternionHermitianEJA(3)
+            sage: J = QuaternionHermitianEJA(2)
             sage: J.one()
-            e0 + e5 + e14
+            e0 + e5
             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]
-            [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 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 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 0]
-            [0 0 0 0 0 0 0 0 0 0 0 1]
+            [1 0 0 0 0 0 0 0]
+            [0 1 0 0 0 0 0 0]
+            [0 0 1 0 0 0 0 0]
+            [0 0 0 1 0 0 0 0]
+            [0 0 0 0 1 0 0 0]
+            [0 0 0 0 0 1 0 0]
+            [0 0 0 0 0 0 1 0]
+            [0 0 0 0 0 0 0 1]
+
         """
         B = self.parent().matrix_basis()
         W = self.parent().matrix_space()