From 4261af7feeec74eee15057c31617bb6a59313e86 Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Sun, 13 Dec 2020 18:23:54 -0500
Subject: [PATCH] eja: unbreak DirectSumEJA, poorly.

---
 mjo/eja/eja_algebra.py | 59 +++++++++++++++++++++++++++++++++---------
 1 file changed, 47 insertions(+), 12 deletions(-)

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index ae41b8c..39703dd 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -2652,7 +2652,8 @@ class TrivialEJA(ConcreteEJA):
         # inappropriate for us.
         return cls(**kwargs)
 
-class DirectSumEJA(ConcreteEJA):
+
+class DirectSumEJA(FiniteDimensionalEJA):
     r"""
     The external (orthogonal) direct sum of two other Euclidean Jordan
     algebras. Essentially the Cartesian product of its two factors.
@@ -2676,6 +2677,10 @@ class DirectSumEJA(ConcreteEJA):
         8
         sage: J.rank()
         5
+        sage: J.matrix_space()
+        The Cartesian product of (Full MatrixSpace of 2 by 1 dense matrices
+        over Algebraic Real Field, Full MatrixSpace of 3 by 3 dense matrices
+        over Algebraic Real Field)
 
     TESTS:
 
@@ -2695,21 +2700,50 @@ class DirectSumEJA(ConcreteEJA):
         if J1.base_ring() != J2.base_ring():
             raise ValueError("algebras must share the same base field")
         field = J1.base_ring()
-        self._factors = (J1, J2)
-        basis = tuple( (a,b) for a in J1.basis() for b in J2.basis() )
-
-        def jordan_product(x,y):
-            return (x[0]*y[0], x[1]*y[1])
 
-        def inner_product(x,y):
-            return x[0].inner_product(y[0]) + x[1].inner_product(y[1])
+        M = J1.matrix_space().cartesian_product(J2.matrix_space())
+        self._cartprod_algebra = J1.cartesian_product(J2)
 
-        super().__init__(basis, jordan_product, inner_product)
+        self._matrix_basis = tuple( [M((a,0)) for a in J1.matrix_basis()] +
+                                    [M((0,b)) for b in J2.matrix_basis()] )
 
+        n = len(self._matrix_basis)
+        self._sets = None
+        CombinatorialFreeModule.__init__(
+                         self,
+                         field,
+                         range(n),
+                         category=self._cartprod_algebra.category(),
+                         bracket=False,
+                         **kwargs)
         self.rank.set_cache(J1.rank() + J2.rank())
 
 
-    def factors(self):
+
+    def product(self,x,y):
+        r"""
+        SETUP::
+
+            sage: from mjo.eja.eja_algebra import (JordanSpinEJA,
+            ....:                                  ComplexHermitianEJA,
+            ....:                                  DirectSumEJA)
+
+        TESTS::
+
+            sage: set_random_seed()
+            sage: J1 = JordanSpinEJA(3, field=QQ)
+            sage: J2 = ComplexHermitianEJA(2, field=QQ, orthonormalize=False)
+            sage: J = DirectSumEJA(J1,J2)
+            sage: J.random_element()*J.random_element() in J
+            True
+
+        """
+        xv = self._cartprod_algebra.from_vector(x.to_vector())
+        yv = self._cartprod_algebra.from_vector(y.to_vector())
+        return self.from_vector((xv*yv).to_vector())
+
+
+    def cartesian_factors(self):
         r"""
         Return the pair of this algebra's factors.
 
@@ -2724,12 +2758,13 @@ class DirectSumEJA(ConcreteEJA):
             sage: J1 = HadamardEJA(2, field=QQ)
             sage: J2 = JordanSpinEJA(3, field=QQ)
             sage: J = DirectSumEJA(J1,J2)
-            sage: J.factors()
+            sage: J.cartesian_factors()
             (Euclidean Jordan algebra of dimension 2 over Rational Field,
              Euclidean Jordan algebra of dimension 3 over Rational Field)
 
         """
-        return self._factors
+        return self._cartprod_algebra.cartesian_factors()
+
 
 #     def projections(self):
 #         r"""
-- 
2.43.2