X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=f415681182dd18bf401aba539a66f916e4f0c191;hb=7f55521ab4652d3ca10cd085f8e9d41bf149e8e5;hp=dd671c5fd7ab847a4c635748923bf0cba12a63ad;hpb=ba5ac5253ad25bf78e7655699d6d05630d91c1a5;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index dd671c5..f415681 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,44 +1,38 @@
-Trace inner product tests:
-
-            TESTS:
-
-            The trace inner product is commutative::
-
-            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
-
-            The trace inner product is bilinear::
-
-            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
-
-            The trace inner product is associative::
-
-            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
+1. Add references and start citing them.
+
+2. Pre-cache charpoly for some small algebras?
+
+RealSymmetricEJA(4):
+
+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]
+
+3. Profile the construction of "large" matrix algebras (like the
+   15-dimensional QuaternionHermitianAlgebra(3)) to find out why
+   they're so slow.
+
+4. Instead of storing a basis multiplication matrix, just make
+   product_on_basis() a cached method and manually cache its
+   entries. The cython cached method lookup should be faster than a
+   python-based matrix lookup anyway. NOTE: we should still be able
+   to recompute the table somehow. Is this worth it?
+
+5. What the ever-loving fuck is this shit?
+
+       sage: O = Octonions(QQ)
+       sage: e0 = O.monomial(0)
+       sage: e0*[[[[]]]]
+       [[[[]]]]*e0
+
+6. In fact, could my octonion matrix algebra be generalized for any
+   algebra of matrices over the reals whose entries are not real? Then
+   we wouldn't need real embeddings at all. They might even be fricking
+   vector spaces if I did that...
+
+7. Every once in a long while, the test
+
+       sage: set_random_seed()
+       sage: x = random_eja().random_element()
+       sage: x.is_invertible() == (x.det() != 0)
+
+   in eja_element.py returns False.