From 162d7eaa821faa07e7886d8e21308b716aabd747 Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Wed, 2 Dec 2020 10:04:08 -0500 Subject: [PATCH] eja: dropp the already_echelonized TODO. We generally orthonormalize things now, but having an orthonormal basis is not the same as having a basis in RREF form. --- mjo/eja/TODO | 20 +++++--------------- 1 file changed, 5 insertions(+), 15 deletions(-) diff --git a/mjo/eja/TODO b/mjo/eja/TODO index db02b27..ccd0b5a 100644 --- a/mjo/eja/TODO +++ b/mjo/eja/TODO @@ -8,30 +8,20 @@ 3. Implement the octonion simple EJA. -4. 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 using e.g. FreeModule_submodule_with_basis_field - we may somehow be able to pass the echelon basis straight in to - save time. - - This may require supporting "basis" as a list of basis vectors - (as opposed to superalgebra elements) in the subalgebra constructor. - -5. Pre-cache charpoly for some small algebras? +4. 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] -6. Compute the scalar in the general natural_inner_product() for +5. Compute the scalar in the general natural_inner_product() for matrices, so no overrides are necessary. -7. The main EJA element constructor is happy to convert between +6. The main EJA element constructor is happy to convert between e.g. HadamardEJA(3) and JordanSpinEJA(3). -8. Figure out if CombinatorialFreeModule's use of IndexedGenerators +7. Figure out if CombinatorialFreeModule's use of IndexedGenerators can be used to replace the matrix_basis(). -9. Move the "field" argument to a keyword after basis, jp, and ip. +8. Move the "field" argument to a keyword after basis, jp, and ip. -- 2.43.2