I have been experimenting with the new .eig() binding to the Arb library in Python (Thank you for the update) and one difference compared to mpmath is that the resulting eigenvalue, eigenvector pairs are not sorted in order. Was this intended? Users wanting a drop-in replacement for mpmath eig() might come across peculiar behaviour due to no sorting.
Is there currently a way to provide Python-Flint with the guesses of eigenvalues and eigenvectors for stage 1 and let it start at stage 2? (as discussed in your blog)
I am also unsure as to the behaviour of the ball radius when using arb_mat for matrices of real numbers. When using the "approx" method for .eig() the documentation says eigenvalues and/or eigenvectors are calculated approximately without error bounds (for acb_mats) yet when using the "approx" method, a error bound is still supplied for the real part. Is this just due to the wrapping of the .eig() method for complex valued matrices?
Thank you again for all your work