X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=427a9539bb69aa4ab25e0687f0336a09377d57e0;hb=2eb57d9d9487ef2533c177d2771a7c47b2528c4b;hp=dd671c5fd7ab847a4c635748923bf0cba12a63ad;hpb=ba5ac5253ad25bf78e7655699d6d05630d91c1a5;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index dd671c5..427a953 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,44 +1,24 @@
-Trace inner product tests:
+1. Finish DirectSumEJA: add to_matrix(), random_instance(),
+   one()... methods. Make it subclass RationalBasisEuclideanJordanAlgebra.
+   This is not a general direct sum / cartesian product implementation,
+   it's used only with the other rationalbasis algebras (to make non-
+   simple EJAs out of the simple ones).
 
-            TESTS:
+2. Add references and start citing them.
 
-            The trace inner product is commutative::
+3. Implement the octonion simple EJA.
 
-            sage: set_random_seed()
-            sage: J = random_eja()
-            sage: x = J.random_element(); y = J.random_element()
-            sage: x.trace_inner_product(y) == y.trace_inner_product(x)
-            True
+4. Pre-cache charpoly for some small algebras?
 
-            The trace inner product is bilinear::
+RealSymmetricEJA(4):
 
-            sage: set_random_seed()
-            sage: J = random_eja()
-            sage: x = J.random_element()
-            sage: y = J.random_element()
-            sage: z = J.random_element()
-            sage: a = QQ.random_element();
-            sage: actual = (a*(x+z)).trace_inner_product(y)
-            sage: expected = a*x.trace_inner_product(y) + a*z.trace_inner_product(y)
-            sage: actual == expected
-            True
-            sage: actual = x.trace_inner_product(a*(y+z))
-            sage: expected = a*x.trace_inner_product(y) +  a*x.trace_inner_product(z)
-            sage: actual == expected
-            True
+sage: F = J.base_ring()
+sage: a0 = (1/4)*X[4]**2*X[6]**2 - (1/2)*X[2]*X[5]*X[6]**2 - (1/2)*X[3]*X[4]*X[6]*X[7] + (F(2).sqrt()/2)*X[1]*X[5]*X[6]*X[7] + (1/4)*X[3]**2*X[7]**2 - (1/2)*X[0]*X[5]*X[7]**2 + (F(2).sqrt()/2)*X[2]*X[3]*X[6]*X[8] - (1/2)*X[1]*X[4]*X[6*X[8] - (1/2)*X[1]*X[3]*X[7]*X[8] + (F(2).sqrt()/2)*X[0]*X[4]*X[7]*X[8] + (1/4)*X[1]**2*X[8]**2 - (1/2)*X[0]*X[2]*X[8]**2 - (1/2)*X[2]*X[3]**2*X[9] + (F(2).sqrt()/2)*X[1]*X[3]*X[4]*X[9] - (1/2)*X[0]*X[4]**2*X[9] - (1/2)*X[1]**2*X[5]*X[9] + X[0]*X[2]*X[5]*X[9]
 
-            The trace inner product is associative::
+5. Compute the scalar in the general natural_inner_product() for
+   matrices, so no overrides are necessary. Actually, this is
+   probably better implemented as a dimension_over_reals() method
+   that returns 1, 2, or 4.
 
-            sage: pass
-
-            The trace inner product satisfies the compatibility
-            condition in the definition of a Euclidean Jordan algebra:
-
-            sage: set_random_seed()
-            sage: J = random_eja()
-            sage: x = J.random_element()
-            sage: y = J.random_element()
-            sage: z = J.random_element()
-            sage: (x*y).trace_inner_product(z) == y.trace_inner_product(x*z)
-            True
-	    
\ No newline at end of file
+6. The main EJA element constructor is happy to convert between
+   e.g. HadamardEJA(3) and JordanSpinEJA(3).