From 3734e050b5508ec030478c497ddb8a6cd8d53327 Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Fri, 5 Jul 2019 19:28:08 -0400
Subject: [PATCH] eja: add placeholder constructors for all simple EJAs.

---
 mjo/eja/euclidean_jordan_algebra.py | 58 +++++++++++++++++------------
 1 file changed, 35 insertions(+), 23 deletions(-)

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
index 8dedc4f..16ce256 100644
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -727,32 +727,44 @@ def _multiplication_table_from_matrix_basis(basis):
     return Qs
 
 
-def random_eja():
+def RealSymmetricSimpleEJA(n):
     """
-    Return a "random" finite-dimensional Euclidean Jordan Algebra.
-
-    ALGORITHM:
-
-    For now, we choose a random natural number ``n`` (greater than zero)
-    and then give you back one of the following:
-
-      * The cartesian product of the rational numbers ``n`` times; this is
-        ``QQ^n`` with the Hadamard product.
-
-      * The Jordan spin algebra on ``QQ^n``.
-
-      * The ``n``-by-``n`` rational symmetric matrices with the symmetric
-        product.
+    The rank-n simple EJA consisting of real symmetric n-by-n
+    matrices, the usual symmetric Jordan product, and the trace inner
+    product. It has dimension `(n^2 + n)/2` over the reals.
+    """
+    pass
 
-    Later this might be extended to return Cartesian products of the
-    EJAs above.
+def ComplexHermitianSimpleEJA(n):
+    """
+    The rank-n simple EJA consisting of complex Hermitian n-by-n
+    matrices over the real numbers, the usual symmetric Jordan product,
+    and the real-part-of-trace inner product. It has dimension `n^2 over
+    the reals.
+    """
+    pass
 
-    TESTS::
+def QuaternionHermitianSimpleEJA(n):
+    """
+    The rank-n simple EJA consisting of self-adjoint n-by-n quaternion
+    matrices, the usual symmetric Jordan product, and the
+    real-part-of-trace inner product. It has dimension `2n^2 - n` over
+    the reals.
+    """
+    pass
 
-        sage: random_eja()
-        Euclidean Jordan algebra of degree...
+def OctonionHermitianSimpleEJA(n):
+    """
+    This shit be crazy. It has dimension 27 over the reals.
+    """
+    n = 3
+    pass
 
+def JordanSpinSimpleEJA(n):
     """
-    n = ZZ.random_element(1,10).abs()
-    constructor = choice([eja_rn, eja_ln, eja_sn])
-    return constructor(dimension=n, field=QQ)
+    The rank-2 simple EJA consisting of real vectors ``x=(x0, x_bar)``
+    with the usual inner product and jordan product ``x*y =
+    (<x_bar,y_bar>, x0*y_bar + y0*x_bar)``. It has dimension `n` over
+    the reals.
+    """
+    pass
-- 
2.44.2