general.hpp File Reference

Plans on linear algebra in Maxima. More...

Go to the source code of this file.

Detailed Description

Plans on linear algebra in Maxima.

Create milestones
Write tests
Write docus
  • Also hermitian_rank_eig and hermitian_rank_charpoly should be changed to compute the indices as pnn_indices.
  • So that we get pnn_indices_eig and pnn_indices_charpoly.
  • Perhaps then we create a generic function for computing the hermitian rank from a version of pnn_indices.
  • We should write a general function for counting the number of sign changes in a polynomial; function hermitian_rank_charpoly then should use this function.
  • The sign-test in hermitian_rank_eig w.r.t. bfloat-values should be extracted, and moved to module Numerical.
Algorithms for the hermitian rank
  • Currently hermitian_rank_charpoly seems fastest.
  • I (OK) would guess that the algorithm for hermitian_rank (the variation of Gaussian elimination) should be nevertheless the fastest:
    1. Since at this level we don't want to go into implementation details, I (OK) don't see how to improve the implementation of "pnn_indices".
    2. Study the literature on computing the pnn-indices.
    3. And then there are the sparsity-considerations.

Definition in file general.hpp.