From fac7c7f89eb71a0af23af6aeb5e822032ebf8e27 Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Fri, 26 Jul 2019 13:41:38 -0400
Subject: [PATCH] eja: rework the quadratic representation tests in terms of
 morphisms.

Just saving this WIP, because I'm starting to suspect that my
implementation of morphisms might be stupid.
---
 mjo/eja/euclidean_jordan_algebra.py | 29 ++++++++++++++---------------
 1 file changed, 14 insertions(+), 15 deletions(-)

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
index 5f01556..2b00302 100644
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -1368,7 +1368,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
                 sage: D = (x0^2 - x_bar.inner_product(x_bar))*D
                 sage: D = D + 2*x_bar.tensor_product(x_bar)
                 sage: Q = block_matrix(2,2,[A,B,C,D])
-                sage: Q == x.quadratic_representation()
+                sage: Q == x.quadratic_representation().operator_matrix()
                 True
 
             Test all of the properties from Theorem 11.2 in Alizadeh::
@@ -1377,8 +1377,8 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
                 sage: J = random_eja()
                 sage: x = J.random_element()
                 sage: y = J.random_element()
-                sage: Lx = x.operator_matrix()
-                sage: Lxx = (x*x).operator_matrix()
+                sage: Lx = x.operator()
+                sage: Lxx = (x*x).operator()
                 sage: Qx = x.quadratic_representation()
                 sage: Qy = y.quadratic_representation()
                 sage: Qxy = x.quadratic_representation(y)
@@ -1399,17 +1399,16 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
 
             Property 3:
 
-                sage: not x.is_invertible() or (
-                ....:     Qx*x.inverse().vector() == x.vector() )
+                sage: not x.is_invertible() or ( Qx(x.inverse()) == x )
                 True
 
                 sage: not x.is_invertible() or (
-                ....:   Qx.inverse()
+                ....:   ~Qx
                 ....:   ==
                 ....:   x.inverse().quadratic_representation() )
                 True
 
-                sage: Qxy*(J.one().vector()) == (x*y).vector()
+                sage: Qxy(J.one()) == x*y
                 True
 
             Property 4:
@@ -1422,15 +1421,15 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
                 sage: not x.is_invertible() or (
                 ....:   x.quadratic_representation(x.inverse())*Qx
                 ....:   ==
-                ....:   2*x.operator_matrix()*Qex - Qx )
+                ....:   2*x.operator()*Qex - Qx )
                 True
 
-                sage: 2*x.operator_matrix()*Qex - Qx == Lxx
+                sage: 2*x.operator()*Qex - Qx == Lxx
                 True
 
             Property 5:
 
-                sage: J(Qy*x.vector()).quadratic_representation() == Qy*Qx*Qy
+                sage: Qy(x).quadratic_representation() == Qy*Qx*Qy
                 True
 
             Property 6:
@@ -1441,13 +1440,13 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             Property 7:
 
                 sage: not x.is_invertible() or (
-                ....:   Qx*x.inverse().operator_matrix() == Lx )
+                ....:   Qx*x.inverse().operator() == Lx )
                 True
 
             Property 8:
 
                 sage: not x.operator_commutes_with(y) or (
-                ....:   J(Qx*y.vector())^n == J(Qxn*(y^n).vector()) )
+                ....:   Qx(y)^n == Qxn(y^n) )
                 True
 
             """
@@ -1456,9 +1455,9 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             elif not other in self.parent():
                 raise TypeError("'other' must live in the same algebra")
 
-            L = self.operator_matrix()
-            M = other.operator_matrix()
-            return ( L*M + M*L - (self*other).operator_matrix() )
+            L = self.operator()
+            M = other.operator()
+            return ( L*M + M*L - (self*other).operator() )
 
 
         def span_of_powers(self):
-- 
2.44.2