X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_algebra.py;h=204a537df12d2ab4d3d27764c20c830ec324a68a;hb=fe7ba85535340f4506513cb3c73b483693526023;hp=42b2474d6971d81c8a1fcda67b079892a3e8af25;hpb=723fd0f50c7997768c3d098c707df30197b88afd;p=sage.d.git

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 42b2474..204a537 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)
@@ -786,9 +797,22 @@ def random_eja():
 
 
 
-def _real_symmetric_basis(n, field=QQ):
+def _real_symmetric_basis(n, field):
     """
     Return a basis for the space of real symmetric n-by-n matrices.
+
+    SETUP::
+
+        sage: from mjo.eja.eja_algebra import _real_symmetric_basis
+
+    TESTS::
+
+        sage: set_random_seed()
+        sage: n = ZZ.random_element(1,5)
+        sage: B = _real_symmetric_basis(n, QQbar)
+        sage: all( M.is_symmetric() for M in  B)
+        True
+
     """
     # The basis of symmetric matrices, as matrices, in their R^(n-by-n)
     # coordinates.
@@ -805,7 +829,7 @@ def _real_symmetric_basis(n, field=QQ):
     return tuple(S)
 
 
-def _complex_hermitian_basis(n, field=QQ):
+def _complex_hermitian_basis(n, field):
     """
     Returns a basis for the space of complex Hermitian n-by-n matrices.
 
@@ -846,7 +870,7 @@ def _complex_hermitian_basis(n, field=QQ):
     return tuple(S)
 
 
-def _quaternion_hermitian_basis(n, field=QQ):
+def _quaternion_hermitian_basis(n, field):
     """
     Returns a basis for the space of quaternion Hermitian n-by-n matrices.
 
@@ -1213,9 +1237,20 @@ 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)
+        S = _real_symmetric_basis(n, field)
         Qs = _multiplication_table_from_matrix_basis(S)
 
         fdeja = super(RealSymmetricEJA, self)
@@ -1271,9 +1306,20 @@ 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)
+        S = _complex_hermitian_basis(n, field)
         Qs = _multiplication_table_from_matrix_basis(S)
 
         fdeja = super(ComplexHermitianEJA, self)
@@ -1337,9 +1383,20 @@ 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)
+        S = _quaternion_hermitian_basis(n, field)
         Qs = _multiplication_table_from_matrix_basis(S)
 
         fdeja = super(QuaternionHermitianEJA, self)
@@ -1399,6 +1456,17 @@ 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)