eja: make AA the default field because everything cool requires it.

[sage.d.git] / mjo / eja / eja_element.py

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index 7c4c79ddcd7315e654620a0be8f8bccf5ab9ac11..0f6a47cd4f10efbcb0298725c4ae26537eae6372 100644 (file)
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -113,7 +113,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         We should always get back an element of the algebra::
 
             sage: set_random_seed()
-            sage: p = PolynomialRing(QQ, 't').random_element()
+            sage: p = PolynomialRing(AA, 't').random_element()
             sage: J = random_eja()
             sage: x = J.random_element()
             sage: x.apply_univariate_polynomial(p) in J
@@ -575,7 +575,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         The spectral decomposition of a non-regular element should always
         contain at least one non-minimal idempotent::
 
-            sage: J = RealSymmetricEJA(3, AA)
+            sage: J = RealSymmetricEJA(3)
             sage: x = sum(J.gens())
             sage: x.is_regular()
             False
@@ -586,7 +586,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         On the other hand, the spectral decomposition of a regular
         element should always be in terms of minimal idempotents::
 
-            sage: J = JordanSpinEJA(4, AA)
+            sage: J = JordanSpinEJA(4)
             sage: x = sum( i*J.gens()[i] for i in range(len(J.gens())) )
             sage: x.is_regular()
             True
@@ -909,9 +909,9 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: set_random_seed()
             sage: n_max = RealSymmetricEJA._max_test_case_size()
             sage: n = ZZ.random_element(1, n_max)
-            sage: J1 = RealSymmetricEJA(n,QQ)
-            sage: J2 = RealSymmetricEJA(n,QQ,normalize_basis=False)
-            sage: X = random_matrix(QQ,n)
+            sage: J1 = RealSymmetricEJA(n)
+            sage: J2 = RealSymmetricEJA(n,normalize_basis=False)
+            sage: X = random_matrix(AA,n)
             sage: X = X*X.transpose()
             sage: x1 = J1(X)
             sage: x2 = J2(X)
@@ -1003,7 +1003,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: J = HadamardEJA(2)
             sage: x = sum(J.gens())
             sage: x.norm()
-            sqrt(2)
+            1.414213562373095?
 
         ::
 
@@ -1065,10 +1065,10 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: n = x_vec.degree()
             sage: x0 = x_vec[0]
             sage: x_bar = x_vec[1:]
-            sage: A = matrix(QQ, 1, [x_vec.inner_product(x_vec)])
+            sage: A = matrix(AA, 1, [x_vec.inner_product(x_vec)])
             sage: B = 2*x0*x_bar.row()
             sage: C = 2*x0*x_bar.column()
-            sage: D = matrix.identity(QQ, n-1)
+            sage: D = matrix.identity(AA, n-1)
             sage: D = (x0^2 - x_bar.inner_product(x_bar))*D
             sage: D = D + 2*x_bar.tensor_product(x_bar)
             sage: Q = matrix.block(2,2,[A,B,C,D])
@@ -1192,7 +1192,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         The spectral decomposition of the identity is ``1`` times itself,
         and the spectral decomposition of zero is ``0`` times the identity::
 
-            sage: J = RealSymmetricEJA(3,AA)
+            sage: J = RealSymmetricEJA(3)
             sage: J.one()
             e0 + e2 + e5
             sage: J.one().spectral_decomposition()
@@ -1202,7 +1202,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
 
         TESTS::
 
-            sage: J = RealSymmetricEJA(4,AA)
+            sage: J = RealSymmetricEJA(4)
             sage: x = sum(J.gens())
             sage: sd = x.spectral_decomposition()
             sage: l0 = sd[0][0]
@@ -1453,14 +1453,14 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: J = HadamardEJA(2)
             sage: x = sum(J.gens())
             sage: x.trace_norm()
-            sqrt(2)
+            1.414213562373095?
 
         ::
 
             sage: J = JordanSpinEJA(4)
             sage: x = sum(J.gens())
             sage: x.trace_norm()
-            2*sqrt(2)
+            2.828427124746190?
 
         """
         return self.trace_inner_product(self).sqrt()