From 5264b3ce110d63d79b76ec3fa05daecd38a78e7c Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Tue, 20 Aug 2019 09:01:50 -0400
Subject: [PATCH] eja: add tests to ensure the Jordan axiom for inner products
 is satisfied.

---
 mjo/eja/eja_algebra.py | 55 ++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 55 insertions(+)

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 42b2474..9b02880 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -722,6 +722,17 @@ class RealCartesianProductEJA(FiniteDimensionalEuclideanJordanAlgebra):
         sage: RealCartesianProductEJA(3, prefix='r').gens()
         (r0, r1, r2)
 
+    Our inner product satisfies the Jordan axiom::
+
+        sage: set_random_seed()
+        sage: n = ZZ.random_element(1,5)
+        sage: J = RealCartesianProductEJA(n)
+        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)
@@ -1213,6 +1224,17 @@ class RealSymmetricEJA(FiniteDimensionalEuclideanJordanAlgebra):
         sage: RealSymmetricEJA(3, prefix='q').gens()
         (q0, q1, q2, q3, q4, q5)
 
+    Our inner product satisfies the Jordan axiom::
+
+        sage: set_random_seed()
+        sage: n = ZZ.random_element(1,5)
+        sage: J = RealSymmetricEJA(n)
+        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):
         S = _real_symmetric_basis(n, field=field)
@@ -1271,6 +1293,17 @@ class ComplexHermitianEJA(FiniteDimensionalEuclideanJordanAlgebra):
         sage: ComplexHermitianEJA(2, prefix='z').gens()
         (z0, z1, z2, z3)
 
+    Our inner product satisfies the Jordan axiom::
+
+        sage: set_random_seed()
+        sage: n = ZZ.random_element(1,5)
+        sage: J = ComplexHermitianEJA(n)
+        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):
         S = _complex_hermitian_basis(n)
@@ -1337,6 +1370,17 @@ class QuaternionHermitianEJA(FiniteDimensionalEuclideanJordanAlgebra):
         sage: QuaternionHermitianEJA(2, prefix='a').gens()
         (a0, a1, a2, a3, a4, a5)
 
+    Our inner product satisfies the Jordan axiom::
+
+        sage: set_random_seed()
+        sage: n = ZZ.random_element(1,5)
+        sage: J = QuaternionHermitianEJA(n)
+        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):
         S = _quaternion_hermitian_basis(n)
@@ -1399,6 +1443,17 @@ class JordanSpinEJA(FiniteDimensionalEuclideanJordanAlgebra):
         sage: JordanSpinEJA(2, prefix='B').gens()
         (B0, B1)
 
+    Our inner product satisfies the Jordan axiom::
+
+        sage: set_random_seed()
+        sage: n = ZZ.random_element(1,5)
+        sage: J = JordanSpinEJA(n)
+        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)
-- 
2.43.2