-1. Add CartesianProductEJA.
+1. Add references and start citing them.
-2. Add references and start citing them.
+2. Pre-cache charpoly for some more algebras.
-3. Implement the octonion simple EJA.
+3. Profile the construction of "large" matrix algebras (like the
+ 15-dimensional QuaternionHermitianAlgebra(3)) to find out why
+ they're so slow.
-4. Override random_instance(), one(), et cetera in DirectSumEJA.
+4. What the ever-loving fuck is this shit?
-5. Switch to QQ in *all* algebras for _charpoly_coefficients().
- This only works when we know that the basis can be rationalized...
- which is the case at least for the concrete EJAs we provide,
- but not in general.
+ sage: O = Octonions(QQ)
+ sage: e0 = O.monomial(0)
+ sage: e0*[[[[]]]]
+ [[[[]]]]*e0
-6. Pass already_echelonized (default: False) and echelon_basis
- (default: None) into the subalgebra constructor. The value of
- already_echelonized can be passed to V.span_of_basis() to save
- some time, and usinf e.g. FreeModule_submodule_with_basis_field
- we may somehow be able to pass the echelon basis straight in to
- save time.
+5. Every once in a long while, the test
- This may require supporting "basis" as a list of basis vectors
- (as opposed to superalgebra elements) in the subalgebra constructor.
+ sage: set_random_seed()
+ sage: x = random_eja().random_element()
+ sage: x.is_invertible() == (x.det() != 0)
-7. The inner product should be an *argument* to the main EJA
- constructor. Afterwards, the basis normalization step should be
- optional (and enabled by default) for ALL algebras, since any
- algebra can have a nonstandard inner-product and its basis can be
- normalized with respect to that inner- product. For example, the
- HadamardEJA could be equipped with an inner- product that is twice
- the usual one. Then for the basis to be orthonormal, we would need
- to divide e.g. (1,0,0) by <(1,0,0),(1,0,0)> = 2 to normalize it.
+ in eja_element.py returns False.
projects / sage.d.git / blobdiff