eja: delete redundant Jordan axiom tests.

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index a207250b4092f97e07d93a62c0ed7e23d9f9536d..29ff1da38480b3b9b07d1ff39555948e31785732 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -441,8 +441,8 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
 
         EXAMPLES:
 
 
         EXAMPLES:
 

-        The inner product must satisfy its axiom for this algebra to truly
-        be a Euclidean Jordan Algebra::
+        Our inner product satisfies the Jordan axiom, which is also
+        referred to as "associativity" for a symmetric bilinear form::

 
             sage: set_random_seed()
             sage: J = random_eja()
 
             sage: set_random_seed()
             sage: J = random_eja()


@@ -800,16 +800,6 @@ class RealCartesianProductEJA(FiniteDimensionalEuclideanJordanAlgebra):
         sage: RealCartesianProductEJA(3, prefix='r').gens()
         (r0, r1, r2)
 
         sage: RealCartesianProductEJA(3, prefix='r').gens()
         (r0, r1, r2)
 

-    Our inner product satisfies the Jordan axiom::
-
-        sage: set_random_seed()
-        sage: J = RealCartesianProductEJA.random_instance()
-        sage: x = J.random_element()
-        sage: y = J.random_element()
-        sage: z = J.random_element()
-        sage: (x*y).inner_product(z) == y.inner_product(x*z)
-        True
-

     """
     def __init__(self, n, field=QQ, **kwargs):
         V = VectorSpace(field, n)
     """
     def __init__(self, n, field=QQ, **kwargs):
         V = VectorSpace(field, n)


@@ -1058,16 +1048,6 @@ class RealSymmetricEJA(MatrixEuclideanJordanAlgebra):
         sage: RealSymmetricEJA(3, prefix='q').gens()
         (q0, q1, q2, q3, q4, q5)
 
         sage: RealSymmetricEJA(3, prefix='q').gens()
         (q0, q1, q2, q3, q4, q5)
 

-    Our inner product satisfies the Jordan axiom::
-
-        sage: set_random_seed()
-        sage: J = RealSymmetricEJA.random_instance()
-        sage: x = J.random_element()
-        sage: y = J.random_element()
-        sage: z = J.random_element()
-        sage: (x*y).inner_product(z) == y.inner_product(x*z)
-        True
-

     Our natural basis is normalized with respect to the natural inner
     product unless we specify otherwise::
 
     Our natural basis is normalized with respect to the natural inner
     product unless we specify otherwise::
 


@@ -1311,16 +1291,6 @@ class ComplexHermitianEJA(ComplexMatrixEuclideanJordanAlgebra):
         sage: ComplexHermitianEJA(2, prefix='z').gens()
         (z0, z1, z2, z3)
 
         sage: ComplexHermitianEJA(2, prefix='z').gens()
         (z0, z1, z2, z3)
 

-    Our inner product satisfies the Jordan axiom::
-
-        sage: set_random_seed()
-        sage: J = ComplexHermitianEJA.random_instance()
-        sage: x = J.random_element()
-        sage: y = J.random_element()
-        sage: z = J.random_element()
-        sage: (x*y).inner_product(z) == y.inner_product(x*z)
-        True
-

     Our natural basis is normalized with respect to the natural inner
     product unless we specify otherwise::
 
     Our natural basis is normalized with respect to the natural inner
     product unless we specify otherwise::
 


@@ -1571,16 +1541,6 @@ class QuaternionHermitianEJA(QuaternionMatrixEuclideanJordanAlgebra):
         sage: QuaternionHermitianEJA(2, prefix='a').gens()
         (a0, a1, a2, a3, a4, a5)
 
         sage: QuaternionHermitianEJA(2, prefix='a').gens()
         (a0, a1, a2, a3, a4, a5)
 

-    Our inner product satisfies the Jordan axiom::
-
-        sage: set_random_seed()
-        sage: J = QuaternionHermitianEJA.random_instance()
-        sage: x = J.random_element()
-        sage: y = J.random_element()
-        sage: z = J.random_element()
-        sage: (x*y).inner_product(z) == y.inner_product(x*z)
-        True
-

     Our natural basis is normalized with respect to the natural inner
     product unless we specify otherwise::
 
     Our natural basis is normalized with respect to the natural inner
     product unless we specify otherwise::
 


@@ -1692,16 +1652,6 @@ class JordanSpinEJA(FiniteDimensionalEuclideanJordanAlgebra):
         sage: JordanSpinEJA(2, prefix='B').gens()
         (B0, B1)
 
         sage: JordanSpinEJA(2, prefix='B').gens()
         (B0, B1)
 

-    Our inner product satisfies the Jordan axiom::
-
-        sage: set_random_seed()
-        sage: J = JordanSpinEJA.random_instance()
-        sage: x = J.random_element()
-        sage: y = J.random_element()
-        sage: z = J.random_element()
-        sage: (x*y).inner_product(z) == y.inner_product(x*z)
-        True
-

     """
     def __init__(self, n, field=QQ, **kwargs):
         V = VectorSpace(field, n)
     """
     def __init__(self, n, field=QQ, **kwargs):
         V = VectorSpace(field, n)